DEVELOPMENT OF SENSING FRAMEWORK FOR THE
SOIL-PLANT-ATMOSPHERE CONTINUUM
A Dissertation
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
by
Siyu Zhu
December 2020
© 2020 Siyu Zhu
ALL RIGHTS RESERVED
DEVELOPMENT OF SENSING FRAMEWORK FOR THE SOIL-PLANT-ATMOSPHERE
CONTINUUM
Siyu Zhu, Ph.D.
Cornell University 2020
Many studies have elucidated the importance of water stress on plant growth, yield, quality
and susceptibility to disease. Via the vascular network of xylem, a water conductive tissue, plant
water stress responds dynamically to variations in evaporative demand defined by micrometeoro-
logical conditions over minutes to hours, and soil water availability over hours to months.
Stem water potential is believed to be an integrator of water stress across the soil-plant-
atmosphere-continuum (SPAC), and is difficult to measure. Despite its destructive nature, 50 years
after its invention, the manually operated Schölander pressure chamber (SPC) is still the most
widely accepted tool for stem water potential measurements. Limitations in available techniques
have hindered the study of dynamic water stress in plants.
In this dissertation, we introduce a micro-tensiometer (µTM) as a new technique, for probing
the dynamic water stress of plants in an accurate and continuous manner. We examine the relia-
bility of µTM against SPC, on apple (2 months), grapevine (12 months), and almond (4 months),
to represent woody species in wet, semi-arid, and arid environments respectively. We observe:
1) nighttime disequilibrium in stem water potential that is challenging to acquire with the labor-
intensive SPC; 2) rapid response of stem water potential to evaporative demand in wet environ-
ment; and 3) slow dynamics and persistent disequilibrium of the water-stressed almond in dry
environment.
With the advantage of continuous measurements and inspired by van den Honert, we use
circuit models to interpret the observed dynamics. In a wet environment, a simple circuit with a
single hydraulic resistance and a single hydraulic capacitance, is sufficient for elucidating the rapid
response of plants to the high frequent variations in environmental demand. In a dry environment,
an additional soil compartment defined by the soil retention properties, is used to address the long
transient of soil dehydration. We now have models as new tools to resolve the complex dynamics
of water stress.
We also measure the dynamic water stress in maize, the first examination on herbaceous crops
with this tool. The measured stress is less coupled to the rapid variations in evaporative demand,
but more to the soil water potential around the roots. In fact, we extract an empirical water retention
curve for the soil that coincides with the theoretical prediction. The µTM, therefore, opens up an
opportunity to monitor the root-zone soil stress, a challenging property to access.
Finally, we explore the response of plants to fine control of irrigation events, and discover
that the transient of root response to irrigation events is shorter when less stressed (nighttime) and
longer when more stressed (daytime). This phenomenon suggests more effective irrigation events
when plants are less stressed with reduced water loss.
The micro-tensiometer and the developed circuit models, together, provide opportunities to
unveil the full dynamics of plant water stress, address the transient factor in plant physiological
responses to both short and long-term dehydration processes, and guide more efficient management
of agricultural water use.
BIOGRAPHICAL SKETCH
Siyu Zhu was born on Feb. 11, 1992 in Luoyang, China. Edified by her parents, who are
travel enthusiasts, Siyu grew up with a strong desire to explore the unknowns of the world, and
developed a variety of interests on traveling, painting, and instrumental performance. She started
her journey to the United States in 2011 at the University of Minnesota-Twin Cities, where she got
her bachelor’s degree in Chemical Engineering, and developed expertise on mathematics, physics,
and chemistry. To fulfill her curiosity about the world, she travelled to Israel, Jordan, Italy, Austria,
France, Germany, and Spain while studying in Minnesota. She started her scientific adventure by
working as an undergraduate research assistant on biomedical studies with Dr. Wei-Shou Hu, who
inspired her to continue her scientific exploration at graduate school. In 2014, she started to work
as a Ph.D. student at Cornell with Dr. Abraham Stroock, who later on gave her an eye-opening
experience of discovering the unknowns of plant hydraulics from the perspectives of an engineer.
While at graduate school, she won an opportunity to work with the Dow Chemical Company as
a Ph.D. intern, to navigate the industrial approaches to research. She defended her Ph.D. in May
2020 during the global pandemic of COVID-19. Siyu is now ready to start a new adventure in the
field of materials engineering by working at Applied Materials.
iii
To my parents Hongkai Zhu and Qiujuan Wang;
and to a happy life!
iv
ACKNOWLEDGEMENTS
I would like to express my appreciation to all who supported me throughout the six years of
inspiring experience as a graduate student at Cornell.
First, I would like to acknowledge my advisor, Professor Abe Stroock, who has always been
there to support me, guide me, and challenge me to develop into a confident researcher, engineer,
and scientist. Having Abe as my advisor is one of the best things that ever happened to me. He
is an energetic, enthusiastic, and intelligent researcher who motivates and inspires people around
him with his passion about science and nature. He is also the most patient mentor who believes in
his students, and is willing to devote his time and effort to guide them into their better self. Thanks
to Abe, I thrived into a much more confident professional than before.
Second, I would like to express my gratitude to my committee members: Professors Lailiang
Cheng and Donald Koch, who make every endeavour to help me when I meet challenges and
obstacles with my research. I would also like to thank our collaborators, Professors Alan Lakso,
Ken Shackel, Taryn Bauerle, and Fengqi You for their suggestions and communication on my
projects.
I would then like to acknowledge my colleagues: Michael Santiago, Winston Black, Erik
Huber, Annika Huber, Olivier Vincent, I-Tzu Chen, Eugene Choi, Piyush Jain, Hanwen Lu, Siyu
Bu, Rui Gao, Kathryn Haldeman, Corentin Bisot, Bill Bedell, Mengrou Shan, and John Morgan. I
am grateful for the opportunity to learn from them, and work side-by-side with them every day in
the past six years.
Last, I would like to thank my family and friends, who believed in me and supported me
through this interesting, exciting, and challenging life as a graduate student.
v
Table of Contents
Biographical Sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Metastable-Vapor-Liquid-Equilibrium (MVLE) . . . . . . . . . . . . . . . 4
1.2.2 Soil-Plant-Atmosphere Continuum (SPAC) . . . . . . . . . . . . . . . . . 6
2 Development of the Micro-Tensiometer 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Commercially Available Water Potential Sensors . . . . . . . . . . . . . . . . . . 17
2.3 Design of Micro-Tensiometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 MEMS (Micro-Electric-Mechanical-Systems) . . . . . . . . . . . . . . . . 21
2.3.2 Mesoporous Silicon Membrane (poSi) . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.5 Response Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.6 Vapor and Tissue Psychrometric Effect during Measurements . . . . . . . . 32
2.4 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.1 Micro-Tensiometer Preparation . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 Greenhouse Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5.1 GH2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.5.2 GH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3 Continuous Stem Water Potential in Apple, Grapevine, and Almond with Micro-
tensiometers 76
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2 Probing the soil-plant-atmosphere continuum with a micro-tensiometer . . . . . . . 80
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3.1 Dynamic water stress in apple, grapevine and almond. . . . . . . . . . . . 84
3.3.2 Detailed dynamics in apple and almond . . . . . . . . . . . . . . . . . . . 87
vi
3.3.3 Analysis of SPAC hydraulics in apple and almond. . . . . . . . . . . . . . 91
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5 Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.2 Packaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.5.3 Osmotic Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.5.4 Temperature Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.5.5 Embedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.6 Plant Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
3.5.7 Scholander Pressure Chamber and Micro-climatic Sensors . . . . . . . . . 114
3.5.8 Nighttime Rehydration Curve Fitting . . . . . . . . . . . . . . . . . . . . . 125
3.5.9 Resistance and Capacitance Analysis . . . . . . . . . . . . . . . . . . . . . 127
4 Modeling the Water Dynamics in Apple Trees under Well-Watered and Water-
Stressed Conditions 133
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.2 Formulation of Circuit Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.2.1 One-compartment circuit model for well-watered conditions . . . . . . . . 136
4.2.2 Two-Compartment Circuit Model for Drought Stressed Conditions . . . . . 138
4.2.3 Transpiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.2.4 Stomatal Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
4.2.5 Boundary Layer Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.2.6 Soil Water Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.3.1 Evaluation of Circuit Model for Well-Watered Apple Tree . . . . . . . . . 145
4.3.2 Nighttime Stomatal Opening and Boundary Layer Resistance . . . . . . . . 150
4.3.3 Evaluation of Circuit Model for Water-Stressed Apple Tree . . . . . . . . 153
4.3.4 A New Stomatal Conductance Model under Drought . . . . . . . . . . . . 163
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.5 Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
4.5.1 2017 and 2018 Experimental Materials and Methods . . . . . . . . . . . . 168
4.5.2 Soil Compartment Formulation . . . . . . . . . . . . . . . . . . . . . . . . 170
5 Response of Water Stress in Apple Tree to Intermittent Irrigation Events 173
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.2 Experiment Setup of Controlled Irrigation . . . . . . . . . . . . . . . . . . . . . . 175
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.5 Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6 Measurement of Water Dynamics in Maize (Zea mays L.) 193
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.2 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2.1 Embedding of the micro-tensiometer into the maize stem . . . . . . . . . . 195
6.2.2 Measured dynamics of the dry-down cycle . . . . . . . . . . . . . . . . . . 195
vii
6.2.3 Water Retention Curve of the Rhizosphere . . . . . . . . . . . . . . . . . . 202
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
6.4 Supporting Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7 Summary and Conclusion 209
A Micro-tensiometer Mask Design with L-Edit CAD 214
B CRBasicEditor Programs for Data Collection 222
B.1 Data Acquisition of the Micro-tensiometers and Micro-climatic Weather Station,
and Transmission to the IoT platform Ubidots . . . . . . . . . . . . . . . . . . . . 222
B.2 CRBasicEditor Program for Data Acquisition of Digital Scale . . . . . . . . . . . . 232
B.3 CRBasicEditor Program for Soil Water Potential Monitoring . . . . . . . . . . . . 233
C Python Programs for Irrigation Control 239
C.1 Program for launching irrigation events . . . . . . . . . . . . . . . . . . . . . . . 239
C.2 Supportive Python Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
D MATLAB Programs for Simulation and Data Transmission 271
D.1 One Compartment RC Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . 271
D.2 Two Compartment RC Circuit Model . . . . . . . . . . . . . . . . . . . . . . . . . 300
D.3 Data Submission to the IoT platform . . . . . . . . . . . . . . . . . . . . . . . . . 323
D.4 Data Acquisition from the IoT platform . . . . . . . . . . . . . . . . . . . . . . . 333
D.5 Heat Transfer Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
viii
List of Figures
1.1 Importance of Water on Agriculture. . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Water under Metastable State. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Water Movement through a Plant. . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Soil-Root-Leaf Water Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Stem Water Potential is Important for the Reproduction and Vegetative
Growth of Plants As Reported by Lakso et al30. . . . . . . . . . . . . . . . . . . 15
2.1 The Working Mechanism of the Micro-tensiometer (µTM). . . . . . . . . . . . 24
2.2 The Hydraulic Resistivity of the Synthetic Xylem on Membrane. . . . . . . . . 33
2.3 Illustration of Vapor Psychrometric Effect. . . . . . . . . . . . . . . . . . . . . 34
2.4 Preparation of a Micro-tensiometer. . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Sensor Filling, Bridge and PRT Calibrations Illustrations. . . . . . . . . . . . . 47
2.6 Measurements in Osmotic Solutions: µTM Response Time Scale and Accuracy. 50
2.7 Set-up Illustration for Greenhouse Experiments. . . . . . . . . . . . . . . . . . 53
2.8 Photos Showing Micro-Tensiometer Installation and Insulation Steps of GH4. . 55
2.9 GH2–Comparison between the Schölander pressure chamber and the µTM. . . 60
2.10 GH4 Chronological Record of the Entire Experiment Period. . . . . . . . . . . 62
2.11 The Pictures of the Apple Tree Before and After Re-watering. . . . . . . . . . . 63
2.12 Comparison between Schölander Chamber and the Micro-Tensiometer. . . . . 65
2.13 Comparison of the µTMs with ∆T−15min, Solar Radiation and Vapor Pressure
Deficit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.14 Linear comparison between the Schölander data and the sensors. . . . . . . . . 70
2.15 GH4-Second Drought Period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.16 Soil Water Dynamics by Micro-Tensiometer in Soil. . . . . . . . . . . . . . . . 73
3.1 Probing the soil-plant-atmosphere continuum with a micro-tensiometer(µTM). 83
3.2 Full Dynamics of ΨµT M and Regression Analysis against SPC across Three
Species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3 Dynamics of Stem Water Potential with the Meteorological Variables and
Transpiration on Selected Days for Apple and Almond. . . . . . . . . . . . . . 89
3.4 Hydraulic Resistance and Response Times of Plants under Wet and Arid En-
vironments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3S.1 Packaged Micro-Tensiometer with Exposed Electronics. . . . . . . . . . . . . . 100
3S.2 Osmotic Calibration of Micro-Tensiometer. . . . . . . . . . . . . . . . . . . . . 103
3S.3 Temperature Calibration of Micro-Tensiometers. . . . . . . . . . . . . . . . . . 105
3S.4 Embedding Procedure of the Micro-Tensiometer to an Apple Tree. . . . . . . . 108
3S.5 Multiple Micro-Tensiometer at Different Embedding Depth. . . . . . . . . . . 109
ix
3S.6 Stem Water Potential Changes with Deeper Embedding Depth. . . . . . . . . . 112
3S.7 Comparison of Apple Stress Dynamics with Micro-climatic Variables on Se-
lected Days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3S.8 Comparison Almond ΨµT M ΨS PC, and the Ψbase on Selected Days. . . . . . . . . 116
3S.9 Apple: Meteorological Variables, µTM, and Schölander pressure chamber. . . 119
3S.10Grapevine: Meteorological Variables, µTM, and SPC. . . . . . . . . . . . . . . 120
3S.11Almond: Meteorological Variables, Micro-Tensiometer and Schölander Pres-
sure Chamber, and Baseline Prediction. . . . . . . . . . . . . . . . . . . . . . . 121
3S.12Almond: Soil Water Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
3S.13Apple and Almond: Nighttime Rehydration Curve Fitting. . . . . . . . . . . . 126
3S.14Resistance Capacitance Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3S.15Apple: Simulated Stem Water Potential vs. Micro-Tensiometer Measurements. 130
4.1 Schematic Diagram of Plant Water Relations. . . . . . . . . . . . . . . . . . . . 135
4.2 One Compartment and Two Compartment Circuit Models. . . . . . . . . . . . 137
4.3 Example of Well-Watered Dynamics from the 2017 Field Apple Experiment. . 147
4.4 Overview of 60-day Simulation of Well-Watered Dynamics from 2017 Field
Apple. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.5 Modelled Stem Water Potential, and transpiration with Different Degree of
Stomatal Opening. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
4.6 One Compartment Model for Simulating the Drought Stress in 2018 Potted
Apple Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.7 Example of Drought-stressed Dynamics from the 2018 Potted Apple Experiment.156
4.8 Dynamic Hydraulic Resistances for Dry-down Simulation. . . . . . . . . . . . 158
4.9 Comparison of Measured and Modelled transpiration. . . . . . . . . . . . . . . 162
4.10 Comparison of Stomatal Conductance Models. . . . . . . . . . . . . . . . . . . 165
4.11 Simulation of Drought Stress with the Modified Model of Stomatal Conductance.166
5.1 Schematic Diagram of Irrigation. . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.2 Irrigation of Apple Tree from Midnight to 6am. . . . . . . . . . . . . . . . . . . 176
5.3 Overview of Stem Water Potential, Evapo-transpiration, and Soil Water Po-
tential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.4 Dynamics of Stem Water Potential with Irrigation under On-Off Control. . . . 179
5.5 Comparing the Digital Scale Measured Evapo-transpiration and Penman-
Monteith Predicted Evapo-transpiration. . . . . . . . . . . . . . . . . . . . . . 180
5.6 Apple Tree under Water Stress Shows No Response to Small Irrigation Events
during Daytime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.7 Comparison between Stem Water Potential Measured by Micro-tensiometer
and Schölander Pressure Chamber. . . . . . . . . . . . . . . . . . . . . . . . . 183
5.8 Apple Tree under Water Stress Responds to Small Irrigation Events during
Nighttime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.9 Apple Tree under Water Stress Shows Two-Step Response to Large Irrigation
Events during Midday. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.10 Apple Tree Responds to Predawn Irrigation with Replacement Cumulative ET. 188
x
6.1 Measurements of Maize Water Stress Dynamics Using A Micro-tensiometer. . 196
6.2 Dry-Down Cycle of Corn Stem Water Potential. . . . . . . . . . . . . . . . . . 197
6.3 Weight Measurements from a Digital Scale. . . . . . . . . . . . . . . . . . . . . 199
6.4 Well-watered Dynamics of Maize Water Potential from Days 3 to 7. . . . . . . 201
6.5 Modeled and Empirical Water Retention Curve. . . . . . . . . . . . . . . . . . 203
A.1 Layers of Micro-fabrication for Micro-tensiometers. . . . . . . . . . . . . . . . . . 215
A.2 Design of Piezo-resistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
A.3 Micro-Tensiometer 1x2 Cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A.4 Micro-Tensiometer 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
A.5 Micro-Tensiometer 2x3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
A.6 Micro-Tensiometer 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
A.7 Micro-tensiometer Double Wheatstone Bridge. . . . . . . . . . . . . . . . . . . . 221
xi
CHAPTER 1
INTRODUCTION
1.1 Introduction
Climate change has induced a rise in global temperatures, carbon dioxide concentration,
and variability in precipitation.1 Warmer temperatures can increase the water withdrawal from the
earth through evaporation and transpiration and reduce the water supply recharge at the same time.2
Therefore, water supply sustainability is at risk for natural ecosystems and crop agriculture (Figure
1.1a).
Water is important for agriculture. Irrigated agriculture occupies up to 80 to 90% of total
water consumption of the United States.3 The extremes in temperature and the frequency in pre-
cipitation challenge the adaptability of crops to water stress and have stimulated studies to quantify
the stress responses of trees and crops for increased water use efficiency (WUE); this index mea-
sures the grain yield per unit amount of water supplied.1,4
Studies have been done to understand the water stress responses of plants and to develop
gene modified crops with drought tolerance.5,6 Nevertheless, most of the plant drought response
processes are understood incompletely, due in part to the lack of a tool that can monitor plant
water stress accurately in real time and with minimal destruction of the plant. A recent study
has shown that destructive sampling methods disturb the original water status within the trees
and crops, and result in unreliable measurements.7 Scientists have been trying to understand the
water stress distribution inside plants, more specifically, the radial distribution of water stress in
plants. Without an appropriate tool, they need to combine the radial sap flow measured in situ, with
hydraulic resistances of cut wood measured in lab, to predict the radial distribution of water stress.8
Additionally, the mechanisms of the stomatal regulation of plant water stress, a crucial topic for
plant drought studies, have been under debate for decades. Stomatal conductance regulates the
rate of transpiration and photosynthesis, and therefore, directly affects the vegetative growth and
1
reproduction of plants.9,10 Without a reliable tool that can measure in-situ soil and plant water stress
with high-resolution and fast response, after sixty years of debate, scientists still hold different
opinions on whether the soil water stress induces chemical signaling, or the leaf water stress is the
key parameter for stomatal regulation.10
In summary, the lack of an in-situ tool with high temporal resolution, high-accuracy, and
minimal plant disturbance has been holding back our understanding on plant water stress for
decades. To resolve this technological gap, we developed a new in-situ hygrometer, called a
micro-tensiometer (µTM), based on the theory of metastable vapor liquid equilibrium (MVLE).
This new technology measures two orders of magnitude larger range than a traditional tensiome-
ter. To develop this micro-scale water sensor, we coupled the idea of a traditional tensiometer
with a micro-electro-mechanical system (MEMS) approach, while adopting the mesoporous sili-
con membrane to allow for large stresses and MEMS integration. Further, we validated the µTM
for in-situ real-time stress monitoring in living trees and crops in indoor and outdoor scenarios.
We then developed circuit models to interpret the observed stress dynamics and to enhance our
understanding on plant drought responses and mechanisms.
With the ability to measure and model real-time water stress, we aim to use the µTM to con-
duct further studies on metastable liquids and eco-physiology, to screen plants with new drought
tolerance genotypes, and to discover new phenomena that cannot be observed with the old tech-
nology. In the future, we hope to utilize both the µTM, and the circuit models together to build a
predictive control system that monitors the real-time drought stress of tree and crops, and predicts
precisely when and how much to irrigate (Figure 1.1c).
2
Figure 1.1: Importance of Water on Agriculture. a. Water Supply Sustainability Risk Index Map.2
b. Schematic diagram elucidating the application of the micro-tensiometer (µTM) for the studies on plant
drought responses by monitoring the plant water stress at five different locations on one tree: soil, root,
stem, branch and leaf. c. Schematic diagram showing expected application of the µTM for precise irrigation
scheduling, with the sensor providing real-time water stress as feedback to the control system. The corre-
lation between the crop productivity and the water stress level could be applied as a reference for accurate
water level control.12
3
1.2 Background
1.2.1 Metastable-Vapor-Liquid-Equilibrium (MVLE)
All liquids can sustain reduced pressure or even some tension due to their molecular interac-
tions. This phenomenon is called cohesion. Water is more stable under tension than most liquids
due to the strong hydrogen bonding between water molecules (Figure 1.2a). At this condition,
liquid water is in a superheated metastable phase. Cavitation occurs when the tension reaches the
stability limit of liquid water, and is able to create a vapor bubble via nucleation or the entry of
air. After cavitation, the liquid and vapor phase of water will reach a saturated liquid-vapor phase
equilibrium.11
There are a variety of methods to stretch liquid water and make it metastable.13 In tensiome-
try, tension occurs due to metastable-vapor-liquid-equilibrium (MVLE), where a volume of liquid
water is in metastable equilibrium with the outside sub-saturated vapor through a thin layer of
nanoscale porous silicon.11,14 As Figure 1.2b&c illustrate, when changing the vapor phase from
saturated to sub-saturated state, water evaporates from the air-liquid interface inside the pores and
forms a curved meniscus. The capillary pressure of the meniscus balances the pressure difference
between the liquid and the outside environment. Based on Young-Laplace eq.1.1, the capillary
force is proportional to the surface tension ( σ [mN m−1] ) and the cosine of the contact angle (
θc [◦] ) between the silicon and liquid water surface, and is inversely proportional to the radius of
the pore size (rp [nm]). By using nanoscale pores, we are able to generate a large tension inside the
bulk liquid ( ≥ -20 MPa).11
2σcos(θ )
∆P ccap = (1.1)rp
The liquid pressure in the metastable state can be derived by assuming isothermal conditions and
at the condition for phase equilibrium: the chemical potential of liquid water ( µ −1w,liq [J mol ] ) and
vapor ( µ −1w,vap [J mol ] ) are the same.
µ 0 0w,vap − µw = µw,liq − µw (1.2)
4
where µ0w is the chemical potential of pure liquid water and vapor at standard temperature (T [
◦C])
and pressure ( P0 [Pa] ).
If we assume the vapor is ideal, we can use ideal gas law to generate the sub-saturated
chemical potential of water vapor: ∫ P ∫vap Pvap
− 0 RTµw,vap µw = vw,vapdP = = RT ln aP w,vap (1.3)Psat Psat
Where Psat [kPa] is the saturated vapor pressure at standard temperature and pressure; Pvap [kPa] is
the sub-saturated vapor pressure; vw,vap is the molar volume of the water vapor, which we replaced
by ideal gas law in this eq.1.3; R = 8.314[JK−1mol−1] is the ideal gas constant; and a Pvapw,vap = P [−]sat
is the activitiy of the water vapor.
For liquid chemical potential, if we assume the density of water does not change, we can
approximate the chemical potential of the m∫etastable liquid water:Pl
µ − µ0w,liq w = vwdP = vw(Pl − P0) (1.4)
P0
Where P [Pa] is the hydrostatic pressure in liquid water; v = 18.02 × 10−6 [m3 mol−1l w ] is the
molar volume of liquid water, and is assumed to have minimal variations in the µTM working
temperature range.
Combining eq.1.3 and 1.4, the sub-saturated liquid pressure is expressed below:
− RTPl P0 = ln av w,vap = −∆Pcap (1.5)w
In eq.1.5, we indicate that the pressure difference required by phase equilibrium must be
equal to that due to capillarity.
Once the tension is large enough to reach ∆Pcap = ∆Pcap,max the contact angle reaches the
receding contact angle ( θr [◦] ) between silicon and water. Once the tension is larger than the
5
maximum capillary pressure, the meniscus will no longer hold, and the air-liquid interface will
recede through the porous membrane into the bulk liquid. This mechanism of cavitation is called
air-invasion.15
1.2.2 Soil-Plant-Atmosphere Continuum (SPAC)
Water is important for plants and soils to maintain hydration, and as a reagent in the pho-
tosynthetic reaction and as a nutrient transporter. The soil-plant-atmosphere continuum describes
the water movement from the soil, through the plant, to the atmosphere.15 This movement is driven
by the gradient in the energy state of water from high to low. The soil is the source of water for
the continuum, and has higher chemical potential. The atmosphere is the sink of the water flow,
and has lower chemical potential. Water evaporates from the leaves to the atmosphere through
evaporation. The evaporation creates a negative pressure on the water inside the plant and pulls
water from the soil to the atmosphere (Figure 1.3). The SPAC can be treated as a MVLE system
with soil as a large reservoir of liquid water, plant as the porous membrane, and the atmosphere as
the sub-saturated vapor.
Energy State of Water
Water potential ( Ψ [MPa] ) is commonly used in plant science to describe the energy state
of water. It is defined as the chemical potential of water ( µw ) relative to pure water ( µ0w) divided
by the molar volume of pure water ( vw ) at that temperature and pressure:15
µ − µ0w w
Ψ = (1.6)
vw
Therefore, water potential is the chemical potential of water in pressure units. It represents
the free energy of water per unit volume relative to pure water. Water movement in SPAC happens
spontaneously along a gradient in water potential. Based on eq.1.3, the water potential of vapor
6
Figure 1.2: Water under Metastable State. a. The schematic representation of the P-T phase diagram of
water. Water can be stretched from pure saturated liquid water to metastable liquid water by isothermally
pulling on the water along the blue arrow. The liquid water can stay in a metastable state at negative pressure
due to the strong attractive interactions between liquid water molecules. b. A schematic diagram of MVLE
in true equilibrium. Water in a reservoir is connected to the outside vapor through a porous membrane
with an average pore diameter of rp. At saturated state, the hydrostatic pressure of liquid water equals
atmospheric pressure, and the vapor is in saturated vapor state. The liquid and vapor are at equilibrium. c.
A schematic diagram of MVLE in metastable equilibrium. The same vapor-membrane-liquid system under
sub-saturated state. The vapor pressure is lower than the saturated vapor pressure. The water evaporates
from liquid state to vapor state until a stable curved meniscus forms. The surface tension of the meniscus
pulls liquid water inside the reservoir and caused a lowered hydrostatic pressure that equals the capillary
pressure.
7
Figure 1.3: Water Movement through a Plant. a. A schematic diagram of transpiration. A water potential
gradient in the direction from soil to the atmosphere drives the transpiration. b. A diagram of the site of
evaporation in leaf. Water evaporates from the water covered sites in the leaves to the atmosphere through
stomata. c. A diagram of water transport in stem xylem elements. Water can bypass the cavitated elements
through pit membranes. The nano-scale pores on porous pit membrane prevented air invasion from cavitated
xylem elements to functioning xylem elements through capillarity. d. A diagram of water adsorption onto
soil particles. The plot on the right shows the water retention curve of different soil types (reproduced from
Buckingham 190716). (Figures Modified from Stroock 201417)
8
phase can be expressed as
RT
Ψv = ln(aw,vap) (1.7)vw
Similarly, the liquid water potential can be expressed as:
Ψl = Pl − P0 (1.8)
At equilibrium (true or metastable), the liquid water potential equals the vapor water potential.
This liquid-vapor relationship is the well-known Kelvin equation, as shown below:
RT
Ψl = ln(aw,vap) (1.9)vw
Taken together, equations.1.8 and 1.9 give us the relationship to pressure in eq.1.5. Water po-
tential has been an important indicator for both plant and soil drought status.18 For example, soil
water potential has been used to schedule irrigation for agriculture.19 Plant scientists divided water
potential into four terms based on its four major contributors. The four major components are
osmotic potential ( Ψs [MPa] ), pressure potential ( Ψp [MPa] ), matric potential ( Ψm [MPa] ),
and gravity potential ( Ψg [MPa] ):
Ψ = Ψs + Ψp + Ψm + Ψg (1.10)
The osmotic potential is the reduction of the water potential due to the dissolved solutes, such
as sugars and mineral nutrients. Pressure potential represents the hydrostatic pressure of water. It
can be positive, as turgor pressure in cells, or negative, as water under tension in xylem. Matric
potential represents the capillary and adsorption effect from solid phases, such as soil particles and
mesophyll cells in leaves (Figure 1.3 b&d). Water adsorbs onto the wettable surface of the solid
particles, and forms menisci in the small pores between them through capillarity. These menisci
generate reduced pressure in the liquid phase due to surface tension, as explained in eq.1.1. The
9
smaller the radius of curvature of the meniscus, the more negative the matric potential will be.
The plant tissue can also be treated as a polymer gel. Based on Flory-Huggins theory, the matric
potential of a wet tissue can be treated approximately as the osmotic potential of a solid polymer
solution.20 Hence, the matric potential of a sample depends on the inherent surface characteristics
of a sample, its moisture fraction, particle size, and particle distribution. We use water content to
describe the moisture fraction of a material. It is defined as the volumetric fraction of water in a
wet matrix, Θ = VwV V [−] , where Vw [m3] is the volume of water in the matrix, and Vm [m3] is thew+ m
volume of the dry matrix. Every material has a typical water retention curve Θ (Ψ ,T), which shows
the relationship between the water potential and the water content. Some hygrometers measure
water potential by measuring the water content of a material (e.g., concrete) with a calibrated
water retention curve. The last potential component is gravity potential, Ψg = −ρgh , where
ρ = 997 [kg m−3] is liquid water density; g = 9.81 [m s−2] is the gravitational constant; h [m]
is the height relative to the reference state. Gravity potential pulls water towards soil through
gravitational force, and reduces plant water potential to a more negative value. Its value depends
on the reference level, and plays a key role in soil drainage.
Water Movement Through SPAC
Soil is the water source for the SPAC. Different soil types have different water holding ca-
pacity. Here, we use holding capacity to mean the threshold in water potential beyond which the
soil is saturated with water won’t have significant water content change. This capacity depends
on the matric characteristics discussed in the previous section. For example, clay has higher water
holding capacity than sand because clay has smaller particles (2 µm < 1 mm). Smaller particle size
means larger surface area for water adsorption per unit volume, and smaller pores between par-
ticles for meniscus formation. The small pores trap water through capillarity and prevents water
from drainage due to gravity. As shown in Figure 1.3d, at high water potential, both clay and sand
have high water content. However, for a water potential decrease from -10 to -1 hPa, sand has a
sharp reduction in water content, while clay has moderate decrease in water content. Therefore,
10
clay has a higher water holding capacity than the other two soil types, and sand has the lowest
water holding capacity. Water moves through the soil, for example, around the roots, down the
gradient of water potential.18
At the site of the root-soil interface, the ability of roots to absorb water depends on the water
potential difference across the root cell membrane. This driving force is mainly contributed by
pressure potential and osmotic potential.21 As soil dries out, the water uptake from the soil to the
root will decrease, due to the large hydraulic resistance between the soil and the root when the soil
and root water potential are lowered to a critical value at which connectivity of the liquid paths in
the soil is lost.15
The water movement mechanism in stems from root to leaf was first proposed as Cohesion
Adhesion theory by Dixon and Joly in 1894.22 Water is able to remain in liquid phase under neg-
ative pressure. Due to the strong intermolecular interactions between the water molecules and the
hydrophilic surface of the xylem wall, which is called adhesion, water can be pulled from the root
to the leaf through capillarity under negative pressure. This negative pressure is created at the
evaporation site from leaves, through liquid-vapor equilibrium and capillarity as described by the
Kelvin-Laplace equation (eq.1.5). Water transport in the stem happens mainly through the xylem
(Figure 1.3c). Xylem conduits are composed of small xylem elements interconnected with each
other through pit membranes. These xylem elements are elongated, hollow, dead cells with thick
highly lignified secondary walls. They form longitudinal stacks to effectively transport water.15
Compared to living cells with their intact plasma membrane, xylem allows water to be transported
from root to leaf with minimum hydraulic resistance. The walls of xylem conduits prevent them
from collapsing when the water in the xylem is experiencing large tension (∼ -10 MPa). The pit
membranes originate from primary walls of the dead cells. They are nano-scale to micro-scale
porous membranes composed of cellulose microfibriller matrix. Cavitation happens when the ten-
sion is larger than the stability limit of the water in a xylem element23 , or when there is air-invasion
from a neighboring non-functioning gas-filled xylem elements.17 If one xylem element cavitates
11
due to the negative pressure or air-seeding, the air-water interface will be trapped inside the pores
of the pit membranes. This capillary force prevents air from entering the neighboring function-
ing xylem elements. Water can still bypass the cavitated xylem elements by going through the
surrounding non-cavitated xylem elements through the pit membrane (Figure 1.3b). Although
pit membranes increase the resistance of water transport in xylem, they also protect against the
spreading of the cavitated (embolized) zone from spreading.18
The evaporation sites in the leaves could be the mesophyll cell walls, the leaf xylem conduits,
or the tissue around the stomata.24 We could assume these wetted surfaces are hydrophilic porous
matrices.17 The menisci formed in these wettable porous membranes create a large tension and pull
water from the root to the leaf.
Evaporation from a leaf’s interior is significantly inhibited by the cuticle.25 Water can mostly
diffuse to the atmosphere through stomata. Stomata are pores on the epidermis of leaves, and
regulate the gas exchange between inside the plant and the atmosphere. Stomata open during the
day in response to sunlight to start the photosynthesis. Photosynthesis produces the carbohydrates
for the growth and reproduction of the plants. Stomata opening allows carbon dioxide, the carbon
source of photosynthesis, to enter the plant, the oxygen produced by photosynthesis to be released
into the environment, and the water vapor to diffuse out of plants. The evaporation is driven by
the vapor pressure deficit ( VPD = 100−RH%100% Psat [kPa] ).
26 For one carbon dioxide to enter stomata,
approximately 400 water molecules are lost to the atmosphere under typical conditions.18 This gas
exchange ratio shows that plants need to transpire a lot of water to sustain the normal operation of
photosynthesis. Under severe water stress, plants close their stomata through physiological regu-
lation, and slow down the rate of transpiration. The water stress affects the rate of photosynthesis
at the same time.27
12
Figure 1.4: Soil-Root-Leaf Water Relations. a. Hypothetical Sketch for the Diurnal Variations of Soil-
Plant Water Relations by Slatyer.15 Solid bars indicate twelve-hour dark periods. During the day, the leaf
water potential decreases to a more negative value than the root water potential due to transpiration. The
dashed line at -1.5 MPa represents the wilting point of the plant. As the soil gets drier, the soil water potential
decreases (to more negative values), the predawn plant water potential (leaf and root) always returns to the
soil water potential, until the wilting point is reached. b. Experimental Results for the Diurnal Variations of
Soil-Plant Water Relations reported by Gardner et al.28 (Note that the y-axis is in negative bars) The diurnal
variations of a pepper leaf water potential was compared with the soil water potential around the root. The
leaf water potential was obtained by measuring the water content of a leaf through β-ray transmission. The
leaf water potential can be found through a known water retention curve. The soil water potential was
measured through a traditional tensiometer. At the beginning, the predawn leaf water potential does not
return to the soil water potential. As the soil gets drier, the predawn leaf water potential reached soil water
potential until the wilting point.
13
Soil-Root-Leaf Water Relations
The diurnal variations of soil-plant water relations are shown in Figure 1.4. Figure 1.4a is
a hypothetical sketch based on theory. Figure 1.4b is an unusual set of experimental data that
coincided with the theoretical hypothesis; reproduction of results such as these has been hindered
by the lack of appropriate tools. The rate of transpiration is not only related to plant and soil
responses, but is also influenced by VPD and solar intensity. The solar energy heats up the leaves
and drives their water evaporation. VPD drives the diffusion of water vapor from inside the leaves
to the outside environment, as explained in the previous section. During the day, the solar intensity
regulates the opening of stomata to start the gas exchange of water and carbon dioxide between the
plant and the atmosphere. Water evaporation from the leaf generates a gradient of water potential
from the root (less negative water potential) to the leaf (more negative water potential) in the plant
(Figure 1.4a). The maximum water potential measured during the day is the midday water potential
(Ψmidday). At night, no sun light is sensed by the leaves, so the stomata are believed to be closed,
meaning the transpiration and photosynthesis are stopped. The plant water potential progressively
relaxes (less negative) to the same level as the soil water potential.15 The least negative diurnal leaf
water potential is called the predawn water potential (Ψpredawn).
Stem Water Potential Indicates Whole Tree Water Stress
Both leaf water potential and stem water potential are good indicators for plant water stress
level. The predawn leaf water potential indicates the effective soil water potential, which integrates
the complete root-soil system. However, during the day, the leaf water potential is easily affected by
the variations of the transpiration rate, and shows large variations in measurements. Furthermore,
single leaf water potential measurements cannot represent the stress level of the entire tree, because
different leaves experience different micro-environments. This micro-environment is affected by
the shading from other leaves, wind speed around the leaves, and physiological effects from nearby
tissues and organs. Different from the leaf water potential, stem water potential integrates the
effects from all the leaves and organs on a tree, and is the best plant water stress indicator, as
14
Figure 1.5: Stem Water Potential is Important for the Reproduction and Vegetative Growth of Plants
As Reported by Lakso et al30. a. The vegetative growth of an apple shoot under stress conditions and
controlled well-watered conditions are compared. As stem water potential becomes more negative, the
shoot growth rate is reduced. b. The fruit growth rate of apple under stress and well-watered conditions
(control) are compared. Similar to the shoot growth, when stressed, the fruit growth rate decreases with
increasing stem water potential.
15
recommended by Naor 2000.29 The stem water potential is closely correlated with the vegetative
growth and the reproduction of plants (Figure 1.5). The vegetative growth rate and the fruit growth
rate decrease with the decreasing stem water potential (more negative). Therefore, monitoring the
stem water potential is crucial for both plant physiology studies and for agriculture.
16
CHAPTER 2
DEVELOPMENT OF THE MICRO-TENSIOMETER
2.1 Introduction
A first generation micro-tensiometer was reported by the Stroock Group in 2014.14 It
combined the technologies of micro-electro-mechanical systems technique (MEMS) and micro-
fluidics, adopted the theory of metastable vapor liquid equilibrium (MVLE) mentioned in Chapter
1,31 and demonstrated that a micro-tensiometer can measure water potentials as low as -10 MPa
before cavitation. This range of stability is required to measure the stem water potential of plants
with a typical range of (≥ -3 MPa).17
In this chapter, we first review the commercially available hygrometers, to demonstrate the
necessity of an accurate plant-based hygrometer for in situ Ψstem monitoring. We then discuss:
1) the design of micro-tensiometer as a MEMS device; 2) the methodology of micro-fabrication,
calibration, packaging, and embedding to an apple tree; 3) the theory behind the important char-
acteristics of the micro-tensiometer such as sensitivity, stability, and the response timescale; and
4) the results from the first trials of stem water potential measurements and factors that could
influence the accuracy of in situ measurements.
2.2 Commercially Available Water Potential Sensors
Water potential in plants and soils has a general range from 0 to -3 MPa, with a high re-
quirement of near-saturation accuracy because most irrigated soils have a water potential range of
0 to - 0.15 MPa.32 The stem and leaf water potential are typically > -10 MPa.33,34 There are four
major types of commercially available hydrometers: the leaf Schölander pressure chamber, the
thermocouple psychrometer, the electro-magnetic based sensors, and the tensiometer. Their accu-
racy, measurement range, response time, form factor, and ease of operation have been compared
17
in Table.2.1.17
The Schölander pressure chamber is the most widely used ex situ hygrometer.35 It measures
the leaf water potential by cutting the leaf off from the tree, sealing the entire leaf inside the pres-
sure chamber with the cut end of the stem protruding out of the chamber, and slowly pressurizing
the leaf with gas until water starts to come out from the cut end. The gas pressure inside the cham-
ber at this point is equal and opposite to the leaf water potential. The water potential measured
through this method are mainly pressure potential in the extra-cellular (apoplastic) volumes in the
leaf.33 This method is easy to operate, but requires labor to do measurements manually. Random
error happens due to individual operation and subjective end point judgement. In addition, the
high pressure gas used by the pressure chamber is hazardous. The thick-wall of pressure chamber
makes it heavy and cumbersome.
The thermocouple psychrometer has been the most accurate in situ plant hygrometer.36 It
uses the dry bulb and wet bulb temperature difference to measure the relative vapor pressure the gas
in equilibrium with the sample. Different from the pressure chamber, psychrometers can operate
automatically on intact tissue. Nevertheless, the operation of most psychrometers is an intrinsic
non-equilibrium process. The thermocouple junction is cooled to allow for vapor condensation on
it for web bulb dew point temperature measurement. The vapor condensation process is never in
equilibrium due to the varying tissue temperature.37 This temperature gradient from the tissue to the
condensation point is hard to interpret and could cause significant error in measurements. Besides,
the calibration and insulation required for accurate measurements are complicated. Therefore, the
use of this equipment has been mostly limited to research purposes.
The electro-magnetic based sensors are mostly used for in situ soil water potential measure-
ments for the prediction of irrigation scheduling.38 They measure the water content related elec-
tric resistance, capacitance, or heat dissipation of the material with known water retention curve
Θ(Ψ,T ). The Decagon MPS-6 (3.2 cm dimater; -0.001 – -100 MPa range; -0.001 – -0.1 MPa with
10% of reading accuracy) is an example of this class of sensor.39 It measures the change of the
18
dielectric permittivity of a porous ceramic disk due to the change of water content in the disk. The
disk water status changes and equilibrates with the moisture level of the surrounding soils. The
electronic response of the disk needs to be calibrated against its water content before application.
The water potential of the sample can then be found from the water retention curve of the ceramic
disk. These sensors have short response time, small form factor, but low accuracy.40
Chilled mirror hydrometers are accurate ex situ water potential sensors. They measure the
water potential of a sample with a high accuracy of ± 0.05 MPa from 0 to -5 MPa, and 1% from
-5 MPa to -300 MPa.39 After a measurement starts, the mirror temperature is lowered through a
thermo-electric cooler until water vapor starts to condense on the mirror. The condensation will be
detected by the photo detector due to the change in the mirror reflectance. The platinum resistor
thermocouple (PRT) on the mirror will record the dew point temperature, which can be translated
into water activity. Despite its accuracy, this hygrometer cannot be used for in situ continuous
measurements. For soil measurements, the destructive sampling will break the integrity of the soil
sample.41 We have been using this method in laboratory to measure the water potential of osmotic
solutions. We use the measured osmotic solution for micro-tensiometer calibration.
Tensiometers translate the chemical potential into measurable mechanical tension through
the MVLE theory discussed in Chapter 1. Conventional tensiometers are the most accurate in situ
soil water potential sensors. The reduction in liquid pressure can be sensed through the mechan-
ical deflection of the pressure transducer directly attached to the liquid. Commercially available
tensiometers have a high accuracy of ±5× 10−4MPa , but a short measurement range of 0 to -0.085
MPa42 (Table.2.1). The small measurement range is due to the air invasion through the micropores
of the ceramic membrane, and defects and impurities that facilitate nucleation in the macroscopic
internal reservoir in which the liquid is held. The limited range only allows the sensor to measure
well-watered soils for moisture sensitive crops, but not for drier conditions.43 Its relatively large
form factor also affects the integrity of the sample.
The high accuracy of tensiometers motivates researchers to extend the measurement range
19
Range Accuracy Response Form
Method
Ψ (MPa) ±Ψ(MPa) Time Factor Limitations
Temperature
Psychrometry37 -0.01 to -10.00 ±0.10 1 min < 5 cm2 sensitive;
expertise required
Low accuracy;
Electro- 44
magnetic -0.01 to -0.50 ±0.13 10 – 60 min > 30 cm
2 long
response time
Tensiometry42 2.100 to -0.085 ±5.0x10-4 30 min > 10 cm2
Limited
Schölander measurement
Pressure 33 0 to -4 n/a n/a n/a range;
Chamber Destructive
Sampling
(high accuracy) 0 to -5:
Chilled Mirror39 0 to -5 ± 0.05 Destructive
Hygrometer (low accuracy) -5 to -480: < 5 min na Sampling
-5 to -480 ± 1%
Table 2.1: Commercially Available Hygrometers.
with different approaches. Peck and Rabbidge45 introduced an osmotic tensiometer in 1966, and
extended the operating range to -1.5 MPa. They filled the tensiometers with PEG 2000 solution,
and use the osmotic potential of the solution to shift the reference potential of the tensiometer to a
more negative value. This method has been developed further to reach a limit of -1.6 MPa.46 An-
other approach was to reduce the pore size of the ceramic membrane from microscale to nanoscale;
this method extended the limit to -1.5 MPa.47 The study from our group has shown that using the
MVLE method to connect a small volume of liquid (about 0.1 nL ) to the outside sub-saturated
vapor through nanoscale porous membrane can reach a liquid pressure of Ψl ≤ −20MPa .48 This
discovery initiated the idea to build a micro-scale tensiometer. The MEMS approach significantly
reduced the sensing area of the tensiometer. An improved version of the micro-tensiometer is pre-
sented in this chapter regarding the design and application for the in situ testing in apple trees.
When compared with the previous version, the form factor of the micro-tensiometer was reduced
from 12x10 (mm × mm) to 5x5 (mm × mm) to reduce the damage on trees during embedding. Mi-
crofluidic vein structures with pattered mesoporous silicon membrane (poSi) were introduced to
20
reduce the sensor’s response time to capture the fast dynamics of the stem water potential (Ψstem).
We refer to this membrane design as "synthetic xylem". The electronic elements were changed
from aluminum to platinum for improved resistance to corrosion. A platinum resistance ther-
mometer (PRT) was designed and fabricated on the topside (silicon) side of the micro-tensiometer
for in situ temperature sensing. With the first generation micro-tensiometer, our group has success-
fully extended the measurement range to -10 MPa, and significantly reduced the sensing area from
>10 cm2 to 1.2 cm2 .14 The second-generation micro-tensiometer discussed below has a further
reduced form factor to 0.25 cm2.
A micro-tensiometer combines tensiometry, piezo-resistive MEMS pressure sensing tech-
nique, and mesoporous silicon membrane (poSi). The poSi increased the capillary pressure the
membrane can hold; the small internal volumes (10 nL) lowers chance of impurities that can cat-
alyze nucleation. In addition, the clean-room based micro-fabrication process reduced the im-
purities inside the liquid reservoir, minimizing the possible vapor nucleation sites, and helped
extending the measurement range of the sensor.23
2.3 Design of Micro-Tensiometers
2.3.1 MEMS (Micro-Electric-Mechanical-Systems)
The micro-scale pressure sensing system of the micro-tensiometer is based on the well-
developed piezoresistive-MEMS-diaphragm pressure sensing technique.49 MEMS is a technol-
ogy that builds micro-scale devices with a system of electrical and mechanical components. The
MEMS devices are manufactured based on the micro-fabrication technologies. A piezoresistive
pressure sensor translates the mechanical stress to electrical signal through a diaphragm with
piezoresistors attached. The mechanical stress on a diaphragm is measured through the resistance
change of the resistors in response to the stress. The piezoresistive technique has been developed
for macro-scale pressure sensing since the 1950’s.50 Combined with MEMS technology, piezore-
21
sistive pressures sensors can be manufactured and applied in micro-scale.51
Figure 2.1 shows the working mechanism of the µTM. Figure 2.1a is the most recent version
of µTM. The cavity in Figure 2.1a is first filled with water under high pressure. The internal water
connects to the outside through poSi with nano-scale pores (Figure 2.1b). When measuring the
sample water potential, the internal liquid pressure is reduced. The reduced pressure is measured
through diaphragm deflection (Figure 2.1c). The deflection will be sensed through the electronics
on top of the diaphragm (Figure 2.1d). In a µTM, four piezoresistors were integrated into a Wheat-
stone bridge (BR) to eliminate the offset and to minimize the temperature effects of the resistors.52
Two resistors are placed at the top and bottom of the diaphragm to sense the maximum compres-
sive stress (σmax) of the diaphragm. Two resistors are placed at the center of the diaphragm to
sense the maximum tensile stress due to the maximum deflection. The signal from piezoresistors
are maximized by using heavily boron-doped polycrystalline silicon (6 × 1019cm−3), and by using
a high resistance of 2000 Ω.53
2.3.2 Mesoporous Silicon Membrane (poSi)
The poSi was etched through anodization: silicon is an anode in the electrochemical etching
set-up, and is etched by running current through an electrolyte made of hydrofluoric acid (HF),
ethanol and water.54 The anodization usually has platinum (Pt) as cathode. The etched pore size
and structure depends on the crystal orientation of the silicon (<111> in this case), the doping type
of the silicon wafer (p-type), silicon resistivity (1-10 Ω − cm), electrolyte concentration, current
density, and etching duration. The details of anodization are presented in the Section 2.4.
2.3.3 Sensitivity
The sensitivity (S) of the sensor depends on the size of the diaphragm, the mechanical prop-
erties of the diaphragm material, and the piezo-resistive coefficients of the polysilicon (i.e. the
fractional change in resistance per unit stress).
22
23
Figure 2.1: The Working Mechanism of the Micro-tensiometer (µTM). a. Top and bottom side of the
micro-tensiometer. To get a functioning µTM, the cavity needs to be filled with water using a high pressure
( ∼ 3.45 MPa) cylinder. The liquid inside the cavity connects to the outside through mesoporous silicon
membrane. An expanded view of the mesoporous silicon membrane with synthetic xylem veins etched was
also shown. The synthetic xylem shortens the response time of the sensor. The veins are designed as a
balance of immediate response and minimization of the chance of air-invasion due to random defects in
the silicon membrane. b. An enlarged view of liquid water in a nano-scale pore connect to the outside
through a curved meniscus. The tension held by the nano-scale pores is determined by the pore size (rp) and
the contact angle between the liquid water and silicon. The liquid water in the cavity reached metastable
equilibrium state with outside sub-saturated water vapor through the capillarity of the nano-scale porous
silicon membrane. c. The cross-sectional view of the cavity and the diaphragm on top of it. The reduced
pressure is sensed through the deflection of the diaphragm. The response time constant, τ, represents the
characteristic time the sensor takes to respond to a step change of the outside vapor water potential. d. An
enlarged view of the Wheatstone Bridge (BR) and a PRT. The mechanical deflection of the diaphragm is
transduced into electronic signal through the piezoresistors in the Wheatstone Bridge. The red resistors on
the blue cavity are piezoresistors. A PRT (platinum resistor thermocouple) is placed on top of the porous
silicon membrane to measure the accurate sample temperature. The electronic signals are transferred to the
outside by wiring the six pads to the outside datalogging system.
24
The change in resistance ( ∆R ) of one polysilicon resistor can be expressed as
∆R
= πlσl + πtσt (2.1)R0
where R0 is the reference resistance of the resistor, πl is the longitudinal piezoresistive coefficient
of the polysilicon; σl is the longtitudinal stress experienced by the resistor; πt is the transverse
piezoresistive coefficient; σt is the transverse stress.52
The resistors are designed and placed on the diaphragm such that their transverse stress is
negligible, and longitudinal stress dominates. Therefore, for resistors at the edges of the diaphragm
and experiencing the maximum compressive stress, their resistance change ( ∆Redge ) is:
∆Redge
 πlσR max
(2.2)
0
Similarly, for the resistors at the center of the diaphragm and experience maximum tensile
stress, their resistance change ( ∆Rcenter ) is:
∆Rcenter
 πlσcenter (2.3)R0
The output voltage from the full Wheatstone bridge is:
V
V in
V
out = (∆Redge − ∆R incenter) = (πlσ2R 2 max − πlσcenter) (2.4)0
The maximum tensile stress and the maximum compressive stress of a rectangular diaphragm
have been well studied and their values depends on the diaphragm structure and mechanical prop-
erties, proportional to the applied pressure on the diaphragm ( ∆Pd ) for small deflections. For a
25
rectangle with half-width ”a” and half-length ”b” (b ≥ a). The internal geometry coefficients are
α, β1 and β2 , which are function of some geoparameters that can be found from literatures.54
β ∆P b21 d
σmax = 2 (2.5)h
β2∆Pdb2
σcenter = h2
(2.6)
Where h is the diaphragm thickness ( ≈ 300µm ).
The differential output signal ( VoutV ) and the theoretical sensitivity of the sensor are then:in
πlb2S = 2 (β1 − β2) (2.7)2h
Vout Vout
= S ∆Pd + ( )V V os
(2.8)
in in
Where (VoutV )os is the offset of the bridge, which is un-avoidable because the micro-fabricationin
processes are not ideal.
For accurate measurements, each micro-tensiometer needs to be calibrated to get its experi-
mental sensitivity and offset.
2.3.4 Stability
The stability of the micro-tensiometer were determined by the maximum capillary force the
mesoporous silicon can hold, or by homogeneous nucleation or heterogeneous nucleation due to
impurities inside the liquid.
26
Bridge
Response time S Stability
Diaphragm Size Temperature
τ Sensitivity (P )
Sensitivity cav
mm x mm seconds mV/V/bar bar/C bar
na predicted measured predicted measured measured measured
1x2 0.37 40 0.08 0.033 0.7 162
1.5x3 1.14 150 0.19 0.085 0.26 130
2x3.5 2.74 250 to 600 0.32 0.143 0.15 90
Table 2.2: Transient, Sensitivity and Temperature Sensitivity of the Micro-tensiometers.
The maximum capillary pressure depends on the pore size of the porous silicon membrane,
based on eq.2.1. The pores range from 2 nm to 4 nm in radius. The typical contact angle between
the liquid water surface and the oxidized hydrophilic silicon surface is about 25 degrees.55 The
surface tension of water is about 72.4 mN/m at standard temperature and pressure.56 Theoretically,
this pore size range allows a meniscus to hold pressures of -70 MPa to -130 MPa; this threshold
is much less negative than the theoretical prediction of the tension (-140 MPa) to create a vapor
bubble nucleation in pure liquid water.57 For individual sensors, the stability limit may be less
negative than the prediction due to the impurities in the liquid water or to random defects in the
porous silicon.31
2.3.5 Response Time
The response time represents the time scale for the sensor to respond to a step change in the
outside water potential; this response is similar to the charging and discharging time constant of
a RC circuit. If we treat the internal liquid and diaphragm together as the controlled system, and
assume that the water transport inside the porous silicon membrane has reached steady state much
faster than the internal liquid, we can get the following governing equation for the mass balance of
the liquid:
dV
= −UD (2.9)dt
27
3
Where V [ m3 ] is the total liquid volume; UD[ms ] is the volumetric flow rate of water through
the porous membrane based on Darcy’s law:
UD = κe f f (Ψl − Ψv) (2.10)
Where κ 3 −1 −1e f f [m Pa s ] is the effective hydraulic conductance of the porous silicon mem-
brane.
The effective bulk modulus ( Be f f [Pa] ) of the diaphragm-liquid system is:
dΨ
B V le f f = vo (2.11)dV
Where Vvo is the initial volume of the liquid reservoir.
The governing equation (eq.2.9) can be translated into a pressure diffusion equation:
Vv0 dΨl
= −κ (Ψ − Ψ
B dt e f f l v
) (2.12)
e f f
The hydraulic capacitance of the sensor ( Ce f f [m3Pa−1] ) is
V
C voe f f = (2.13)Be f f
The hydraulic resistance of the sensor is:
1
Re f f = (2.14)
κe f f
28
Using eqs.2.13 and 2.14 in eq.2.12, we find the response of the sensor is
− t
Ψl = Ψv + (Ψl,0 − Ψv)e Re f f Ce f f (2.15)
Where Ψl,0 is the initial liquid water potential.
The response of the sensor can be treated as a RC circuit with a time constant ( τ[s] ) of
τ = Re f f Ce f f (2.16)
Hydraulic Capacitance of the Rectangular Diaphragm
If we treat the effective bulk modulus of the diaphragm-liquid system as capacitors-in-
series,11 we have:
1 1 1
= + (2.17)
Be f f Bd Bw
Where Bd is the bulk modulus of the diaphragm; Bw = 2.2× 103 MPa is the bulk modulus of
liquid water.
The bulk modulus of the rectangular diaphragm is calculated from the energy of deflection (
Ede f ):
(∆P )2a4
E C ab dde f = de f (2.18)D
Eh3
D =
12(1 − 2 (2.19)ν )
29
Where D [ N · m ] is the stiffness of the diaphragm; E [ Pa ] is the Young’s modulus of the
diaphragm; ν = 0.27 is the Poisson’s ratio for the silicon diaphragm used in the micro-tensiometer.
Cde f is the coefficient associated with the energy of deflection for different diaphragm shapes.
Its values can be estimated by simulation through numerical methods.58
By definition, the bulk modulus of the diaphragm:
dP
Bd = Vvo (2.20)dV
We can get the capacity (K) of the diaphragm:
dP B
K d= = (2.21)
dVd Vvo
∆Pd = KVd (2.22)
Where ∆Pd is the pressure on the diaphragm; Vd is the deflected volume due to the pressure
Based on the fundamental definition of work done by an external force on a system in ther-
modynamics, the amount of work (energy) required from no deflection to a deflected volume of Vd
can be expressed as:
∫ Vd, f
E = ∆PddVd (2.23)
0
Where Vd, f is the final deflected volume due to ∆Pd .
Combining eq.(32) and (33), we have:
1
E = ∆PdVd, f (2.24)2
30
The volumetric deflection of the diaphragm ( Vd ) can be obtained by modifying eq.2.24:
E a5b
Vd = 2
de f
= 2Cde f ∆P (2.25)
∆Pd D
d
Therefore, based on equation eq.2.21 and eq.2.26 :
V
B vo
D
d = 5 (2.26)2Cde f a b
Combining equations eq.2.27 and eq.2.18 :
1
Be f f = (2.27)2Cde f a5b 1
DV +vo Bw
Hydraulic resistance of the Synthetic Xylem
The hydraulic resistance of the sensor has been significantly reduced by introducing the
synthetic xylem veins structure. The design of the synthetic xylem veins was based on the idea of
the how the cavitation was prevented from spreading in the xylem tissue of woody plants which is
under negative pressure (Figure 2.2).
The hydraulic path defined by this structured membrane can be represented by the circuit
diagram in Figure 2.2b. The hydraulic resistance of each element in the circuit can be calculated
using the following equation:
1
Rx = HxW (2.28)x · κLx φµ
31
Where x represents 1 to 3; Hx = 5µm is the thickness of the porous silicon membrane; Wx[m]
is the width of the cross-sectional area for the water transport; Lx[m] is the active length of the
porous silicon membrane separating adjacent veins; κ[m2] is the permeability of the porous silicon
membrane; µ[Pa · s] is the viscosity of water; φ = 0.45 is the porosity of the porous membrane.
Since R1 and R2 have the same values, R2 is replaced by R1 in the following calculations.
The hydraulic resistance of the synthetic xylem membrane system is:
1 1 1 3
Re f f = RAD = × ( 2 2 + R3) = × ( Rn 1 + R3) (2.29)
R +1 1
n 10
2 R1+R2
Where n is the number of the repeated of the motif of veins. The theoretical and experimental
comparison of the response time and sensitivity are shown in Table.2.2.
2.3.6 Vapor and Tissue Psychrometric Effect during Measurements
The water potential of a sample depends on its temperature. The temperature difference
between the sensor and the sample creates an error in measured water potential due to the difference
in their reference state of zero water potential. As discussed in Chapter 1, the water potential
measures the energy deviation of a sample from that of pure liquid water at the temperature and
pressure of the sample of interest. We call this error as psychrometric effect.
We assume isothermal conditions most of the time. However, in situ applications are always
non-isothermal. When measuring a plant tissue, for example, a vapor gap exists between the sensor
and the tissue due to the non-uniform contact surface as illustrated in Figure 2.3. The temperature,
vapor pressure and water potential of the sensor are Ts , Ps and Ψs , while those for the tissue are
Tt , Pt and Ψt . The vapor gap in between has a vapor pressure of Pvap . We assume
Ts = δT + Tt (2.30)
pvap = pt = ps (2.31)
32
Figure 2.2: The Hydraulic Resistivity of the Synthetic Xylem on Membrane. a. The hydraulic resistivity
diagram of the repeated paths connecting the internal cavity to the evaporative surface. The water flow from
point A to point B through a porous silicon membrane with a depth of 5 µm, a width of W1,and a length of
L1. The water flow from B to C through a membrane with a 5 µm thickness, W2 width and L2 in length. The
water flow from C to D through a membrane with a 5 µm thickness, W3 width and L3 in length b. Simplified
diagram for the study of hydraulic resistivity.
33
Figure 2.3: Illustration of Vapor Psychrometric Effect.
34
Where δT is the small temperature difference between the tissue and the sensor.
Based on MVLE, ( )
RTs pln vapΨs = (2.32)vw psat(Ts)
Where:
pvap pvap
=
psat(Ts) psat(δT + Tt)
pvap

p (T ) δT dpsat(Tt)sat t + dT
p (2.33)vap
= · 1
psat(Tt) 1 + δT dpsat(Tt) 1dT psat(Tt)
pvap
= [1 − dpsat(Tt) 1δT ]
psat(Tt) dT psat(Tt)
Therefore, ( )
RTs pln vapΨs = vw ( psat(Ts)) ( )
RTs pln vap
RTs dp (T ) 1
= ( + ln 1 −
sat t
δT (2.34)
vw psat(Tt)) vw dT psat(Tt)
RTs p
= ln vap + e
vw p
p
sat(Tt)
( )
RT
e sp = ln 1 −
dpsat(Tt) 1
δT (2.35)
vw dT psat(Tt)
Where ep is the error due to psychrometric effect. This error is about 7.77 MPa/◦ C around 25
◦ C.22 When the tissue has lower temperature than the sensor, the sensor will read a more negative
water potential than the real value. When the tissue has higher temperature, the vapor will condense
on the poSi and make the sensor read zero. Managing the source of error represents an important
challenge for the application of the micro-tensiometer, as discussed further in Chapter III.B.
35
2.4 Materials and Methods
2.4.1 Micro-Tensiometer Preparation
Substrates
Silicon wafers were p-type double side polished wafers with 100 mm diameter and 350 ±
25µm thickness (Addison addisonengineering.com). They had <111> crystal orientation and 1 −
10Ω · cm resistivity; and were selected for porous silicon membrane etching with desired pore size
and structure (interconnected structure with pore radius range from 2 nm to 4 nm). Double-side
polished Borofloat 33 glass wafer with 100 mm diameter and 500µm thickness, were used to bond
with the backside silicon wafer through anodic bonding (University Wafer universitywafer.com)
The bonding in the CNF (Cornell NanoScale Science and Technology Facility) clean room created
an enclosed reservoir for liquid water with reduced impurities; after bonding, the internal cavity
was only connected to the outside through the porous silicon membrane.
Fabrication
A micro-tensiometer requires double side fabrication on a silicon wafer. The backside has
etched cavities for the water reservoir and etched mesoporous silicon membrane, and is bonded
with a glass wafer. The frontside has a platinum resistance thermometer (PRT) and a Wheatstone
bridge (BR). A BR is composed of polysilicon resistors, platinum wires and pads. The whole
bonded wafer needs to be diced into 5 mm x 5 mm chips accurately at designated positions to get
micro-tensiometers. The fabrication processes below were presented in a chronological order. The
steps presented below are labeled in Figure 2.4a.
Steps i and ii: Growth of SiO2 Insulation Layer
After MOS clean for the silicon wafers, the 800 nm SiO2 insulation layer was grown into
silicon wafer by using the MRL Thermal Oxide Furnace through oxidation. The SiO2 insulation
36
Figure 2.4: Preparation of a Micro-tensiometer. a. An Illustration Micro-Fabrication Processes. (Cour-
tesy of Michael Santiago) b. A Diagram of The nano-scale porous silicon membrane etching bath.61 c. A
Diagram showing A µTM mounted to the PCB board with external wires for datalogging. The pads are
connected to the PCB board through wirebonds. The internal cavity connects to the outside vapor through
mesoporous silicon.
37
is important because the silicon wafer is conductive to electronics, and would disturb the operation
of the polysilicon resistors. The oxidation was a batch process, and 25 to 50 wafers were able to be
processed at the same time. The resistivity of the silicon wafers was checked before the oxidation
process using CDE ResMap 4-pt Probe. The wafers were first MOS cleaned and then oxidized in
the furnace using wet oxygen and nitrogen flow mixed with hydrogen chloric acid at 1000 ◦ C for
200 min. To ensure the uniformity of the grown SiO2, baffle wafers were used at the first and the
last position of the series of wafers, hydrogen chloric acid was added to the oxygen flow to ensure
good oxide quality at a high growth rate, and to help prevent defects in the oxidation layer.
Step iii: Deposition of Polysilicon Layer Deposition
A 800 nm thick polycrystalline silicon layer with a boron doping level of 6 × 1019/cm3
was deposited on top of the SiO2 insulation layer in MRL LPCVD Polysilicon furnace. This
high doping level was chosen to optimize the signal and minimize the temperature effects. The
deposition was done with a feeding rate of 270 sccm of 1.5% B2H6 and 90 sccm of 30% SiH4 at
620 ◦ C for 130 minutes. The polysilicon layer was then annealed in MRL MOS Clean Anneal
with Inert gas (Ar) at 900 ◦ C for 30 min. The polysilicon-SiO2 layer were checked in Filmmetrics
for their thickness, and in CDE ResMap 4-pt Probe for their resistivity.
Step iv: Patterning of Polysilicon Resistors
The polysilicon resistors were fabricated using photolithography with S1827 photoresist and
dry etching. The pattern of the resistors was generated using the general photolithography process
with the mask for resistors. The patterned wafers were etched using Oxford 81 Plasma Etcher
with SiF6/O2 (125 mTorr, 45 SCCM SF6, 15 SCCM O2, 100W). The RF plasma dissociated SiF6
into fluorine (F2 ) and other fragments. F2 and Si reacted to form SiF4 or SiF2 products because
Si-F has stronger bond than Si-Si. Oxygen kept fluorine concentration high, prevented them from
recombination their dissociated fragments, and led to stable end products of plasma etching. The
etching depth was checked using P10 Profilometer (P10). The etching was stopped when the color
38
of SiO2 layer appeared blue/purple/green, because SiO2 with different thickness shows different
color.
Step v: Patterning of SiO2
The SiO2 insulation layer was fabricated using photolithography (S1827) and dry etching.
After the wafers were patterned with the mask for SiO2 patterning, the patterned wafer was dry
etched in Oxford 81 using CHF3/O2 (50 mTorr, 50 SCCM CHF3, 2 SCCM O2, 200W) for 20 min,
which depends on the etch rate measured by P10. CHF3/O2 has higher selectivity against silicon,
which is favored in this case. The end products were SiF4 and CO2, which had stronger bonds than
Si-O bond. The etching was stopped when the color of the Silicon wafer appeared. The fabricated
resistors had a typical resistance of 2000 Ω .
Steps vi and vii: Patterning of Backside Cavity
The backside cavity was created by dry etching 3 µ m into the silicon wafer. The SiO2
and polysilicon layers on the backside were removed using the same dry etching method for their
fabrication. The residues were removed using a dip in BOE 6:1 (butter HF etch). The backside
cavity was patterned using the designated mask with S1827. The etching was done in Oxford 81
using SF6/O2 mentioned above. The etching rate was controlled using P10.
Steps viii to xi: Backside Patterning and Etching of Porous Silicon
The porous silicon membrane was patterned through general photolithography using the AZ
P4903 thick photoresist (6 µ m). This photoresist protected the un-exposed area from etching in
electrochemical bath during Anodization. The porous silicon etching was done in an electrochem-
ical etching bath shown in Figure 2.4b. The electrolyte was a mixture of concentrated HF (49%
HF Aqueous solution, Sigma Aldrich). and Non-Denatured Ethanol (Sigma Aldrich). (Safety
Warning: HF is corrosive and contact poisonous; Working with HF requires personal protection
equipment) The cathode was a platinum pad. The aluminum was deposited conformally on the
39
frontside of the silicon wafer to make electrical contact with the aluminum anode by using the CHA
Mark50 Evaporator of NBTC (Cornell Nanobiotechnology Center) in the clean room. To prevent
electrolyte corrosion of the aluminum, a cylindrical PTFE (poly-tetra-fluoro-ethylene) Chamber
with 76 mm diameter was used on top of the wafer for the electrolyte. The leakage was prevented
by using a Viton O-ring between the chamber and the wafer, and by enhancing the contact using
screws. The current density was set to 20 mA/cm2 with Hewlett Packard DC power supply (Model
6634B). The etching duration was 5 min at 1 µ m/min, which resulted in an expected membrane
thickness of 5 µ m. After etching, the wafers were washed using deionized water (DI) and dried
in a desiccator to allow the evaporation of HF from the porous silicon, and prevent corrosion.
The aluminum on the frontside was removed using AZ 300 MIF developer to prepare for further
fabrication of electronics.
The pores of the etched membrane were then oxidized using Rapid Thermal Anneal (RTA,
AG Associates Model 610) at 700 ◦ C in pure oxygen for 30 s with 10 ◦ C/s ramping. The oxi-
dation of the porous silicon creates Si-O bonds on the silicon surface, and made the pores more
hydrophilic, which resulted in higher sensor stability.
Step xii: Backside Silicon Wafer Anodic Bonding with Glass Wafer
The bonding was done in vacuum at 400 ◦ C using 1500 V DC in SUSS SB8e Substrate
Bonder (SUSS). Both glass wafers and silicon wafers were thoroughly cleaned before bonding to
minimize the organic residues on wafers, which is crucial for sensor stability. The glass wafers
were cleaned in nanostrip (90% sulfuric acid, 5% peroxymonosulfuric acid and <1% hydrogen
peroxide). The silicon wafers were cleaned using organic solvents acetone and IPA, followed by DI
water rinse and drying. The silicon wafers were not washed using nanostrip because the nanostrip
could damage the etched poSi. The wafers were then descumed in Anatech using oxygen plasma
before bonding. The vacuum environment in the bonder prevented wafer contamination. The 400
◦C bonding temperature softened the glass, and made it conform on the silicon for irregularities,
which improved contact. The high temperature also dissociates the sodium oxide (Na2O) in glass
40
into sodium ions (Na2+) and oxygen ions (O2−). The positive voltage on the silicon drove the (O2−)
migration towards the bonding surface and created Si-O bonds at the surface, which enhanced the
bonding strength.54
Step xiii: Fabrication of Frontside Electronics
The wafers were deposited with Ti (15 nm)/Pt (200 nm) /Ti (15 nm) metal layers through
lift-off in CVC E-gun Evaporation System (CVC, model SC4500). The electronics were patterned
using the mask for electronics with LOR 5A and S1827 photoresists. The exposed area on the wafer
(SiO2 insulation layer) were descumed using Anatech to ensure better contact with the metal. The
Titanium layers at the bottom and the top of Pt enhanced the adhesion of metal with the SiO2
insulation layer at the bottom, and with the passivation layer at the top (discussed below). The rate
and thickness of deposition were monitored through CVC directly.
The lift-off was done using the LOR remover, 1-methyl-2-pyrrolidinone (1165, provided by
CNF), in 60 ◦ C while sonicating for 30 min. Another 30 min of sonication was done to ensure
clean removal of all photoresists. The wafers were then rinsed using DI water and dried.
The resistances of the Wheatstone bridge and the PRT were checked using the IV probe
station in the CNF clean room, with expected values to be 2000 Ω and 1500 Ω respectively. The
contact resistance and linearity between the electronic wires and the polysilicon resistors were
checked as well.
Steps xiv and xv: Deposition of Frontside Passivation Layer
The passivation layer was deposited to protect the electronic on the wafer. The wafers were
cleaned in organic solvents acetone and IPA and descumed in Anatech to better adhesion. The
passivation layer was composed of 400 nm SiO2, 300 nm silicon nitride (SiNx), 200 nm of oxyni-
tride (SiON), and 100 nm of SiO2 in order at 200 ◦ C in Oxford PECVD. The duration for each
component was calculated based on the deposition rate set in the PECVD.
41
The contact pads for external wiring were opened through photolithography (S1827) using
the mask for contact pads opening, and dry etching using CHF3/O2 in Oxford 81. The possible
residues of SiO2 and Ti on the opened pads were cleaned using brief dip in BOE 30:1.
The resistances and linearity of the electronics were checked again in the IV probe station.
The photoresists were cleaned using organic solvents followed with DI rinse and drying.
Step xvi: Dicing and Labeling of Sensor
The wafers were diced using DISCO Dicing Saw with an all-purpose blade that cuts the
glass-silicon bonded wafer. The dicing was done accurately based on the dimensions of the sensors
(5 mm x 5 mm) and the position of the porous silicon membrane. The sensors were labeled from
1 to 230 on a single wafer. The wafers were labeled alphabetically based on the order they were
fabricated. For example, the P187 device used below was the number 187 device from P wafer.
Steps xvii to xix: External Wiring and Packaging
The sensor chips need to be wired up to send signals outside. The external wiring for the
sensor is composed of the wirebonding between the chips and the printed circuit board (PCB,
oshpark.com), and the wires soldered to the PCB for external data acquisition (Figure 2.4c).
Since the wirebonds were the weakest part of a packaged µTM, the copper contact pads on
the PCB board were designed so that minimum number of wirebonds were needed and the shortest
wirebond length was needed between the pads on µTM and the copper pads on the PCB. The
copper pads were connected to the outside by soldering external wires to the holes designed on the
PCB board, as illustrated in Figure 2.4c.
To add external wires, the chips were first glued onto the PCB boards using the 5min set
epoxy (LOCTITE). The Wirebonding connected 32 µm-thick aluminum wires between the contact
pads and the PCB board, and was done using the WESTBOND 7400A ultrasonic wire bonder
from the CNF. The PCB board were soldered with external wires, which could be connected to an
42
external datalogger (CR6 from Campbell Scientific).
The packaging is important to protect the sensors from external corrosion and possible dam-
age during use. The wirebonds, which were the most fragile part due to the thin wires and delicate
bonding to pads, were potted with a material designed for wirebonding (9001-E-v3.1, DYMAX).
This material had features of fast curing and small stress on wirebonds. After applying the mate-
rial on the wirebonds, the 9001 was cured for 35 min using 365 nm wavelength and 3000 µW/cm2
intensity UV light (SPECTROLINE, Model BIB-150P), followed by 15 min heat cure in 150 ◦ C.
The whole sensor-PCB system were packaged using polyurethane resin UR5041 (ELECTROL-
UBE) with high tear resistance and osmotic solution resistance to protect the sensors from external
stress during applications and the electronics from external corrosion by osmotic solution. The
resin and the hardener of UR 5041 were mixed in a weight ratio of 3.64:1 before use. The curing
was 24 hours at room temperature. To facilitate handling and insertion, the encapsulation was done
by potting the sensor-PCB in a proper size garolite tube (McMaster-Carr). This tube material has
as high of a tensile strength as metal tubes, but much lighter. The encapsulation strategy may vary
due to the experiment purposes, as shown in Section 2.4.
Bridge Calibration and Stability
The electronic signal needs to be translated into mechanical signal through calibration. Each
sensor needs to be calibrated before being put into use. The calibration was done against a precise
pressure gauge (Honeywell, TJE model, 34 MPa). The sensors were first filled with water using
a high pressure chamber (HIP High Pressure Equipment Company, Model 37-6-30) at about 3.45
MPa for 6 hours (Figure 2.5a.). Once filled, the sensors were connected to the CR6 datalogger,
while letting the sensor cavitate. The maximum output from the sensor before cavitation was taken
to be the stability limit of the sensor, and could be translated into pressure data after calibration.
After cavitation, with the cavity empty but the poSi was still wet, the µTM was put into a high-
pressure chamber immediately. This chamber was connected to a compressed pure nitrogen gas
cylinder (Airgas) through a regulator valve. After the compressed nitrogen gas was fed into the
43
cylinder, the cylinder gas pressure was sensed by the Honeywell pressure gauge (Figure 2.5bd).
The poSi was kept wet during the entire calibration process because the menisci block entry of gas
into the cavity; the capillary pressure of the menisci held the pressure difference between inside
cavity and outside as the outside gas was pressurized. This pressure difference was sensed by the
µTM through the deflection of the diaphragm, as presented in Section.2.3. The sensor reading
was then calibrated against Honeywell output for each step-change of gas pressure. Since gas
temperature went up every time more gas was filled into the pressure chamber, and relaxed back to
room temperature after about several minutes, both PRT and bridge output were recorded during
the bridge calibration, and the duration for each pressure step was long enough for temperature
relaxation.
The pressure bomb calibration data analysis was done using the following equation
Vout(P,T ) = mP+T · Phw + bP+T (2.36)
Where Vout(P,T ) was the bridge output from sensor, and was a function of both temperature
and pressure inside the chamber; Phw was the honeywelll reading; mP+T was the experimental
calibration coefficient, which, in general, was a function of temperature; bP+T was the offset of the
bridge, which was also a function of temperature. These two parameters could be obtained from
fits as in Figure 2.5d.
Based on the discussion above, we had a theoretical calibration for the sensor output
Vout(P,T ) = Vout(P) + Vout,0(T ) (2.37)
Vout(P) = BBP · Phw + bBP (2.38)
Vout,0(T ) = BBT · T + bBT (2.39)
Where mBP and bBP are calibration coefficients only for the pressure-dependent term ( Vout(P) ),
and mBT and bBT are calibration coefficients only for the temperature dependent term ( Vout(T ) ).
44
To correct for the temperature effect on the bridge output, the bridge offset was calibrated against
temperature for mBT and bBT . The calculation of mBP and bBP is presented in the following section.
The Bridge and PRT temperature calibration
Since material properties change with temperature, the bridge offset and PRT response were
calibrated against temperature using a temperature-controlled water bath (Fisher Scientific). The
calibration set-up was shown in Figure 2.5c.
Based on the temperature calibration data, we got the PRT calibration curve ( PRT (T ) ), as
well as the bridge offset dependence on temperature ( Vout,0(T ) eq.2.39:
PRT (T ) = mT · T + bT (2.40)
Where mT and bT were PRT calibration coefficients. The calibration parameters for eq.2.39 and
eq.2.40 could be obtained from Figure 2.5-e and f.
The Vout(P) term can be calculated as below:
PRT (T ) − b
Vout(P) = V
T
out(P,T ) − Vout,0(T ) = Vout(P,T ) − (mBT · + bBT ) (2.41)mT
The experimental mBP and bBP could now be obtained by plotting Vout(P) against Phw where the
temperature dependence of the Honeywell was ignored ( 5×10−4 MPa/◦ C). In other words, the mBP
and bBP may have some dependence on temperature, but this effect has been neglected in current
studies.
During the use of the sensor, we measured the Vout(P,T ) and PRT (T ) output directly from
the sensor. The temperature and pressure can be easily calculated from the two equations below:
PRT b
T (PRT ) = − T (2.42)
mT mT
V
P out
(P) − bBP
measured = (2.43)mBP
45
46
Figure 2.5: Sensor Filling, Bridge and PRT Calibrations Illustrations. a. Sensor filling system. Sen-
sors are filled using high pressure water ( ∼ 3.45 MPa) for > 6 hours.14 b. Sensor calibration set-up. The
sensors are calibrated using step-change of gas pressure from a compressed nitrogen cylinder monitored us-
ing a Honeywell pressure gauge (PH). The response of the Wheatstone Bridge (BR) and PRT is monitored
through CR6 datalogger. (Modified from Pagay 201414) c. Temperature control water bath for BR offset and
PRT calibration: The sensor response is calibrated against a step-change of the water bath temperature. d.
Pressure calibration curves for two sensors labeled with difference colors. The slope of the line regression
is the sensitivity of the sensor. The intercept with the y-axis was the offset e. BR offset calibration curve for
three sensors labeled with three different colors. The slope of a curve was the BR temperature sensitivity.
The intercept was the offset of the BR at 15◦C. f. PRT calibration curve for three sensors labeled by three
different colors. The slope and intercept were calibration parameters for a PRT. Different calibration coeffi-
cients specified for each diaphragm size is shown in Table 2.2. g. Temperature Corrected Sensor Response.
The temperature corrected response from the µTM due to a 15◦C temperature change was -0.35 bar. The
peak at the beginning proved a functioning µTM by responding to air water potential.
47
Combining with 2.43:
Vout(P,T ) − (mBT · T + bP BT ) + bBPmeasured = (2.44)mBP mBP
The output from the CR6 could be converted directly to pressure reading corrected for temperature
effects by using 1/(mBP) as the input multiplier, and − (mBT ·T+bBT )+bBPm as the input offset. An exampleBP
of a temperature corrected sensor was shown in Figure 2.5-g. A 0.35 –bar difference in offset was
observed while the temperature was changing from 15 ◦ C to 32 ◦ C.
Response Time Testing Through Osmotic Potential Measurement
As discussed before, the response time is the time constant for a sensor to respond to a step
change in the sample water potential (eq.2.16 and eq.2.17). To test the response time, a µTM was
calibrated using the positive pressure gas cylinder method shown in Figure 2.5a. The measuring
tip of the µTM was protected using an expanded PTFE membrane (ePTFE, Porex, PMV10). The
PTFE membrane only allowed vapor, not liquid water, to diffuse through. Figure 2.6b showed the
plot of the sensor response to a -19.1 osmotic solution through the ePTFE membrane. The µTM
was kept in pure water initially, and was then removed from the pure water, briefly held in the air,
and submerged in the sucrose solution (Sigma-Aldrich). The activity of the solution was checked
using a Chilled-Mirror hygrometer (Decagon WP4C). The tensiometric measurement was done in
an isothermal water bath to prevent psychrometric effect in the ePTFE membrane, as discussed in
Section.2.3.
In Figure 2.6b, after removing the offset, the µTM showed a 0.2 MPa lower water potential
than the WP4C. This difference was larger than the error range of WP4C (± 0.05 MPa for 0 to -5
MPa range). The possible reasons are: 1) the error comes from the Honeywell Pressure sensor,
against which the BR was calibrated; 2) the water adsorbed onto the sensor was brought into the
48
solution and diluted the osmotic solution. Further testing needs to be done to clarify the reason for
the difference.
Table.2.2 shows typical response times, pressure sensitivities, and temperature sensitivities,
and stability for different diaphragm sizes measured experimentally, and predicted based on the
theory discussed in Section.2.3. The measured transient time if about two orders of magnitude
larger than the predicted transient time. Since the transient time was measured experimentally
using an osmotic solution with known water potential, the solutes might have accumulated in the
poSi and increased the hydraulic resistance of the porous silicon layer. Another possibility is that a
boundary layer exists due to the loss of water from the porous silicon membrane to the neighboring
solution and diluted the solution locally. The characteristics of the porous silicon membrane might
also be changed due to the storage environment or the solution and resulted in change in its hy-
draulic resistance. Among the three major diaphragm sizes, the 1x2 device has the fastest response
time, but smallest sensitivity and the largest temperature sensitivity, while the 2x3.5 device has
the slowest response but the best sensitivity and minimum temperature sensitivity. The properties
of the 1.5x3 devices lie in between those of the 1x2 and 2x3.5 devices. Although, 1x2 devices
typically had the highest stability, and 2x3.5 devices had the lowest stability, the stability limits
varied significantly from device to device and should be confirmed before application.
2.4.2 Greenhouse Experiments
Apple Trees Growth Information
The apple trees (Malus Domestica) were grown in the Yellow Greenhouses on Cornell Cam-
pus. They were 2.5 to 3.0 m in height, with trunks 3 cm to 4 cm in diameter. They were moved
from the Cornell Orchard in pots on Feb. 10th, 2016. There were three trees in a row, separated
by about 1 m from each other. The distance between rows were about 3 m, and we had three rows
in total. Experiments were done from the beginning of April 2016 to the end of June 2016. Green-
house experiments GH1 and GH3 were trial experiments, whose data are not presented in this
49
Figure 2.6: Measurements in Osmotic Solutions: µTM Response Time Scale and Accuracy. a. Dia-
gram of the packaged sensor tested for the osmotic response. b. Plot of the sensor response to a step change
from pure liquid water to a -19.1 bar sucrose solution in isothermal water bath (25 ◦ C). The dashed red line
represents the offset of the sensor reading was -0.7 bar. The solid red line represents the final reading by
the µTM. The dashed black line represents the osmotic potential (-19.1 bar) measured by the chilled mirror
hygrometer. The time constant (τ) for this response was about 2 min.
50
thesis. The second greenhouse experiment (GH2) was from April 8th, 2016 to May 6th, 2016. The
fourth greenhouse experiment (GH4) was from May 26th, 2016 to June 26th, 2016. The trees were
well-watered before experiments. They had apples growing during the two experiment periods.
(We acknowledge Dr. Lailiang Cheng for the apple trees)
Greenhouse Experiment 2 (GH2)
Devices and Data Acquisition
One µTM (M45) was used in GH2. A Schölander pressure chamber (SOILMOISTURE
Equipment Co.) was used to measure the stem water potential as a benchmark for the sensors.
(We acknowledge Dr. Alan Lakso for the pressure chamber.) The packaging strategies of the
µTM are shown in Figure 2.7. The GH2 data were logged with a CR6 powered by a sealed
rechargeable battery BP7 (12 V, 7 Ah) from Campbell Scientific. A program was written using
CRBasic (datalogging programmer by Campbell Scentific) to excite the bridges by 200 mV, and
the PRTs by 200 mA, every 30 seconds. The program is provided in Appendix D. Related weather
data including solar intensity were gathered from Ithaca Cornell Orchard weather station.59
Sensor Installation and Insulation
For round packages, the µTM was installed into the trees by drilling 1 cm deep holes per-
pendicularly into the tissue below the bark (Figure 2.8-i). The packaged sensors were 9.6 mm in
diameter. A large guide hole was made by using a 10 mm Jobber’s Drill Bit (McMaster), followed
by a grinded-down flat tip 9.5 mm Jobber’s Drill Bit, to create a flat bottom for better contact be-
tween the sensor tip and the tissue. The holes were wetted using tap water after drilling. Since wet
wood shrinks after drilling, the size of the drill bits were selected to fit the size of the packaged
devices without large gaps. The sensors were pressed into the hole gently. After the sensors were
embedded, they were sealed with caulk (McMaster 3008K13) to prevent water loss. The thermal
insulation was done by using 3.18 mm-thick neoprene foam sheets (McMaster 8647K81) tightly
wrapped around the sensors, followed by wrapping the sensor and the tree together using 1.27
51
52
Figure 2.7: Set-up Illustration for Greenhouse Experiments. a. Diagram showing the µTMs used for
the greenhouse experiments. The encapsulation material for all sensors was polyurethane. All wirebonds
were protected by 9001 modified polyurethane material designed for wirebonds. P20 was fully encapsulated
with only poSi exposed in a glass tube, with a ePTFE membrane as a vapor gap between the sample and the
sensor. P176 was only fully encapsulated in a garolite tube. P179 was encapsulated up to the wirebonds,
but the garolite tube covered up to the membrane. P187 was encapsulated up to the wirebonds. M45 was
packaged in a longer tube due to a longer PCB board (the length was not shown here). b. Diagram showing
that M45 was installed in an apple stem in the GH2 experiment. c. Diagram showing that GH4 had six
µTMs. P36 did not have a working bridge, so it only sensed temperature. The sensors on the stem were
installed at 10 to 15 cm of separation from each other, and spiraled around the stem. The MPS-6 and M45
were installed in the soil to monitor soil water potential.
53
cm-thick Ultra-Flexible Foam Rubber (McMaster 9349K2).
Large plastic bags were used to cover the foam as a waterproof layer, and was tightly sealed
using zip-ties against the trees. The whole thermal insulation (about 10 cm-thick) was covered
by aluminum foil as a reflective insulation to prevent sunlight from heating up the sensor and the
insulation system.
Pressure Chamber Measurements
The leaves were wrapped in aluminum foil covered with plastic bags for at least 20 min
before they were cut and pressurized (Figure 2.8-viii). This method gave us stem water potential
measurements.
The pressurization on the leaves were stopped when bubbling started to come out of the cut
stem. The bubbles would usually form a liquid droplet after a couple of seconds. The pressuriza-
tion would be continued if the bubbling stopped and no liquid droplet formed. A pressure bomb
measurement was done on a single leaf for each time point.
Greenhouse Experiment 4 (GH4)
Devices and Data Acquisition
Seven devices were used in GH4, including five micro-tensiometers (P20, P36, P176, P179
and P187) in the tree, and one micro-tensiometer (M45) and one MPS-6 (Decagon) in the soil. The
packaging strategy for the six micro-tensiometers are shown in Figure 2.7. The size of packaged
sensors was 9.6 mm in diameter. Some of the PRTs on the sensors were broken during the em-
bedding because the sensor edge was chipped when the sensor was pressed against the tree. The
installation strategy and packaging should be improved to avoid damaging PRTs in future experi-
ments. The same Schölander pressure chamber was used to measure the stem water potential as a
benchmark for the sensors.
54
Figure 2.8: Photos Showing Micro-Tensiometer Installation and Insulation Steps of GH4. i. A drilled
hole in a living tree; ii. Installation of sensor in a cut branch (a picture of installed sensor in a living tree
was not taken to prevent sensor cavitation due to water loss); iii. Stabilization of sensors using plumber’s
putty and Parafilm; iv. Reinforcing sensor-tissue contact using an elastic band; v. Thermal insulation us-
ing polystyrene foam and polyester fiber wrapped into a large plastic bag; vi. Reflective insulation using
aluminum foil; vii. Opening of a slit using a chisel and a knife for the bare device P187; viii. Bagging a
leaf with aluminum foil covered bags for stem water potential measurements using the Schölander pressure
chamber.
55
The data from the sensors were gathered through CR6 connected with a AM16/32B Relay
Multiplexer (AM) powered by a BP7 battery. One CR6-AM system was able to operate as many as
eight sensors (including one Wheatstone bridge and one PRT per sensor). The MPS-6 was powered
using the switched 12V power supply on CR6. The thermocouple was connected directly to CR6
to prevent errors due to extra wiring between the and CR6 and the AM. A program was written in
CRBasic to run the devices at the same time, and was shown in Appendix D. The data of the µTMs
were taken every 10 seconds as a main program, while the MPS-6 data were taken every 30 s as a
minor program in parallel. The bridge was excited using 50 mV, and the PRT was excited using 20
µ A. Related weather data including solar intensity were gathered from Network for Environment
and Weather Applications (NEWA)59 as in GH2.
Sensor Installation
The µTMs were filled with water at 3.4 MPa for ≥ 6 hours using the HiP high pressure cham-
ber (Figure 2.5), and brought to the greenhouse submerged in water. The sensors were connected to
the CR6-AM in the greenhouse. Data was taken during the entire installation period. For each sen-
sor, a hole of 5 mm depth was drilled using a 9.6 mm diameter Forstner Bits (McMaster 3216A21).
The holes were made in the radial direction with respect to the trunk, and were then wetted using
tap water to prevent drying of the tissue around the hole (Figure 2.8-i). The P187 device was a
bare device with no polyurethane packaging on top of the diaphragm. Therefore, this device was
installed by using a chisel and a blade to open a slit vertically below the bark (Figure 2.8-vii). This
method resulted in less damage to the tissue relative to that induced by the drill. The µTMs were
then inserted into the holes gently (Figure 2.8-ii). After installation, the sensors were stabilized us-
ing Plumber’s Putty sealing cord (McMaster 9408T14), which helped prevent water loss from the
hole (Figure 2.8-iii). Compared to caulk, the sealing cord provided better mechanical stabilization
for the sensors. The sealing cord layer was then wrapped with PARAFILM (Bemis) against the
stem as a further stabilization and waterproofing. The contact between the tubular sensors were
improved by wrapping an elastic band around the sensor and the tree to hold them together (Figure
56
2.8-iv). The sensors were separated about 10 to 15 cm from each other axially along the trunk, and
rotated around the stem to make sure they were not directly on top of one another and blocking
the water flow (Figure 2.7). Thermal insulation was done using 3.18 mm-thick neoprene foam
sheets (McMaster 8647K81), followed by a thick layer of polyester fiberfill (Air Lite 580/6). The
polyester fiber was then used as the second layer of insulation instead of thick foam sheets in GH1
(Figure 2.8-v), because the polyester fiber could be easily shaped to provide more intact insulation
for the complex geometry of the sensors on the stem. The polyester fiberfill was wrapped in a large
plastic bag as in GH4 to prevent water loss from the opened plant tissue. The insulation (about
12 cm-thick) was finished with a layer of aluminum foil, which was also applied to cover the soil
as the last step (Figure 2.8-vi). The soil sensors (M45 and MPS-6) were installed in a 45◦ angle
against the soil surface, to minimize the disturbance on the soil matrix (Figure 2.7c).42 The soil
sensors were installed at the end of the first drought period, as shown in Figure 2.10. Re-watering
after the soil sensors installation improved the soil integrity around the sensors.42
Schölander Pressure Chamber Measurements
The measurement methods were the same as in GH2 except that three pressure bomb repeti-
tions were taken to get a sample of stem water potential measurements at each time point.
Data Analysis Methods
The data were analyzed and plotted using MATLAB (MATHWORKS License 554896). The
offset of the µTMs were calculated and subtracted from the entire data set based on the night water
potential upon two days of watering after the first drought period. The appropriateness of this
correction will be assessed in future experiments.
Simulation – Heat Conduction Between the Tissue and the µTM
To study the temperature difference between the tissue and the sensor discussed in Chapter
IV, a 2D-heat conduction model without internal heat generation was built using Finite Difference
57
Methods. In this model, sensors packaged with air or polyurethane (packaged dimension 10 mm
diameter x 12 mm length) were taken to be in direct contact with the tissue with complete em-
bedding (i.e. the whole sensor tube was inside the tree). The heat flux from plants to the outside
air was calculated using a well-studied 1D cylindrical heat transfer model. The heat conduction
between the tissue and the sensor was simulated using a 2D heat conduction model with top, left
and right, three boundary conditions as fixed tissue temperature (Tp), and the bottom boundary
condition as fixed heat flux to the outside, as calculated using the 1-D heat transfer model in a
cylinder before. We assumed fixed temperature difference between the plant tissue and the outside
air (Tout), therefore
T
θ cavity
−Tout
cavity = T −T represents how close the cavity temperature is to the measuredp out
tissue temperature at steady state. The time scale for to reach steady state heat conduction was also
recorded.
The program of this simulation is provided in Appendix D.
2.5 Results and Discussion
2.5.1 GH2
The purpose of GH2 was to explore installation and insulation strategies, and to compare the
µTM readings with those of the Schölander pressure chamber.
The insulation method was developed in GH2 to prevent water loss from the drilled holes
by using large plastic bags, to minimize the disturbance from the outside temperature variations
by adding thick polystyrene foam around the µTMs, and to prevent sunlight from heating up the
sensors by using aluminum foil as reflective insulation. The final insulation method was explained
in Section.2.4. Even though the greenhouse temperature was controlled, there was still an air
temperature variation of ± 3 ◦ C during the day.
In Figure 2.9, the Schölander reached a peak value at about 11:00 in the morning, while the
58
µTM reached its peak value at about 16:00 in the afternoon, when the on-chip temperature was
increasing at the highest rate. Comparing the midday water potential measured by these two differ-
ence methods, the M45-µTM reported a 15 bar more negative water potential than the Schölander
(Figure 2.9-a). The reason for the mentioned differences might be the vapor psychrometric effect
discussed in Section.2.3 due to a vapor gap and the temperature difference between the µTM and
the tissue. Notice that in GH2, the sensor-tissue contact was not reinforced using the elastic bands
(Figure 2.8-iv), a small vapor gap between the µTM and the tissue could cause significant error (∼
8 MPa/ºC) (Section.2.3).
To study the effect of the vapor psychrometric effect, the possible temperature difference (
∆T ) between the measured sample and the µTM was estimated by subtracting from the current
temperature of the sensor (T) measured by the M45-PRT, the temperature at an earlier time point.
The rational is that when temperature increases at the site of the sensor, we expect that there is a
radial gradient of temperature along which heat flows from outside in. We take the rate of change
in temperature as the radial gradient. The best correlation between the ∆ T and the µTM happened
at a 15 min time difference, as shown in Figure 2.9b, after comparing with the temperature 5 min,
15 min, 25 min and 45 min earlier. The temperature dependence of the µTM was observed in
Figure 2.9b: the stem water potential measured by the µTM varied similarly as the ∆T (−15min) .
Based on the simulation explained in Section.2.4 (code displayed in Appendix D), for a fixed
temperature difference between the plant tissue and the outside air (Tp − Tout ), under steady state
heat conduction, the unaccomplished temperature difference, θcavity ∼ 0.52 for a sensor packaged
in both polyurethane and air. The higher the θcavity , the closer the cavity temperature to the tissue
temperature. We expect a low value of θcavity , if the sensor was not in good contact with the tissue.
This result indicates that a fixed fraction of temperature difference between the sensor and the
tissue, which may have resulted in the 15 bar difference as well as the water potential difference
at other times of the day, always exists. The simulation also indicated that the time scale for the
cavity temperature to reach steady state in polyurethane was one order of magnitude longer than
59
Figure 2.9: GH2–Comparison between the Schölander pressure chamber and the µTM. a. Plot of
M45-µTM measured water potential, Schölander pressure chamber measured potential and temperature
measured by M45-PRT during one diurnal. The left y-axis represents measured water potential (bar). The
right y-axis represents the temperature measured by the sensor M45 and has its positive direction pointing
downwards. The x-axis is the time-scale during the day in hours. The black line represents the data from
M45. The blue circles are Schölander data. The red line is the temperature measured by the M45-PRT. The
stem water potential decreased during the day, and increased at night. b. Plot of the measured water potential
and the time delayed temperature difference that served as a surrogate for the local temperature gradient. The
right y axis is the ∆T = T−15min =T-T(-15min), which was expected to represent the temperature difference
between the µTM and the tissue in direct contact. It has its positive direction pointing downward.
60
that for a sensor packaged with air. Therefore, to make the µTM measurements more accurate,
improving the thermal contact between the sensor and the tissue is crucial. Low profile packaging
strategies with minimum polyurethane were tested below in GH4.
2.5.2 GH4
Previous results in GH2 motivated the use of multiple packaging strategies in GH4, as de-
scribed in Section.2.4, and shown in Figure 2.7.
Figure 2.10 shows the chronological record of the entire experimental period. During the
day, the stem water potential recorded by the sensors decreased. At night, the sensors reported a
higher water potential. The transpiration slowed at night, and the stem water potential increased
to values near those of the soil. The tree went through two drought periods (days 1 - 7; days 8
– 22). Each drought period could be recognized by the decrease in predawn stem water potential
measured by the sensors. After rewatering (day 7 around 3 pm, and day 22 around 11 am), the
predawn stem water potentials of the sensors went back to their offset value.
Figure 2.11 shows the pictures of the tree before (Day 22) and after rewatering (Day 24).
Figure 2.11a shows the status of the tree when its turgor pressure was significantly reduced due to
lack of water. Figure 2.11b shows the status of the tree after its recovery from rewatering. The data
from the sensors were offset corrected based on the predawn water potential measured after three
nights upon rewatering, when the tree recovered from drought responses. The M45 soil sensor
was installed after the first drought period, showed the decrease in soil water potential for the
second drought period progressively, and returned to offset after second rewatering. The following
discussion covers detailed results from the GH4 data.
Figure 2.12 shows the three days when the Schölander pressure chamber data was taken
together with that of the µTMs.
Day 7 (Figure 2.12a) was during the first drought period before rewatering. The plant was
61
Figure 2.10: GH4 Chronological Record of the Entire Experiment Period. This plot includes the entire
data for GH4 experiment. The left y-axis represents the measured stem water potential. The right y-axis
represents the measured sensor temperature with its positive direction pointing downward. The x-axis is the
time-scale based on days after the sensor installation. The red lines represent the temperature measured by
sensors P176 and P179. The black, green, blue, magenta solid lines represent the µTM data from P187, P20,
P176 and P179 respectively (see Figure 2.8 for placement). P20 had a layer of ePTFE membrane between
the plant tissue and the sensor. The black dashed line represents the soil water potential measured by M45.
The blue circles with error bars represent the stem water potential measured by the Schölander pressure
chamber. The dark bars represent the 12-hour dark period from 6pm to 6am. All stem sensors (µTM and
Schölander) show that the stem water potential decreased (more negative) during the day, and increased at
night. The PRTs measured increased temperature during the day and decrease temperature at night. The
first drought period was from day 1 to day 7. On day 7, several Schölander pressure chamber measurements
were done. Rewatering was at 2 pm on day 7. The soil µTM and MPS-6 were installed on day 7 as well.
The second drought period was from day 8 to day 22. Rewatering was done at 11 am on day 22. More
Schölander pressure chamber measurements were done on day 24.
62
Figure 2.11: The Pictures of the Apple Tree Before and After Re-watering. a. Apple tree on Day 22
right before rewatering b. Apple tree on Day 24, two days after rewatering.
63
experiencing large water stress. The Schölander measured a water potential of down to -30 bars,
while the typical range observed in apple trees is -15 to -20 bars.60 Therefore, the apple tree was
experiencing severe stress. The sensors were showing larger tensions than the Schölander (up to
-40 bars). There are two possible reasons for this: 1) the µTM was measuring real tension which
was much higher than the coverage of the pressure chamber (-1 to -40 bar); 2) during the imposed
drought, the sensors and tissue were separated by a larger vapor gap, and resulted in larger vapor
psychrometric effect discussed above.
Day 9 (Figure 2.12b) was two days after rewatering for the first drought period. The P20
sensor, with ePTFE membrane, showed delayed response when the temperature was increasing,
and advanced response when the temperature was dropping. These observations were expected if
the P20 was measuring the vapor psychrometric effect across the ePTFE membrane: when the tem-
perature increases, the sharp decrease in measured water potential was observed. This observation
can be explained by the ”positive” psychrometric effect. It happens when the sensor has a slightly
higher temperature than the tissue. The delayed response could be explained due to the time scale
for heat conduction from the outside environment to the sensor. When the temperature decreases
at night, the sensor is expected to have a slightly lower temperature than the tissue, the vapor
condensates on the poSi membrane, and results in the sharp increase in measured water potential
(”negative” psychrometric effect). P179 delayed its response in a similar way as P20. However, we
expected the other sensors (P187, black curve, and P176, blue curve), which responded faster than
P20, to measure the real stem water potential. Therefore, we hypothesize that the P179 was not in
good contact with the tissue. Since the day 9 was rainy, we expected that the plant did not have
a full transpiration. Nevertheless, the plant should still respond to solar intensity and VPD. These
expectations could explain varying stem water potential measured during the day. P187 and P176
had the closest correlation with the Schölander pressure chamber, but were usually delayed for
about 0.5 to 1 hour. These differences observed for P187 and P176 might be due to the systematic
difference between the leaf stem water potential measured by the pressure chamber and the trunk
stem water potential measured by the µTMs, the vapor psychrometric effect, or the psychrometric
64
Figure 2.12: Comparison between Schölander Chamber and the Micro-Tensiometer. The black line
represents P187. The green line represents P20. The blue line represents P176. The magenta line represents
P179. The line colors are the same for all three subplots. The circles are Schölander Pressure Chamber
measurements. a. Day 7(a sunny day), the Schölander data were measured before rewatering. b. Day 9 (a
rainy day), two days after rewatering for the first drought period. c. Day 24 (a sunny day), two days after
the rewatering for the second drought period on a sunny day.
65
effect specifically due to the xylem tissue in direct contact with the sensors; we favor the hypoth-
esis of a psychrometric effect since the sensors were able to measure the osmotic potential of the
sucrose solution within ± 2 bars of accuracy (Figure 2.6).
Day 24 (Figure 2.12c) was on a sunny day without clouds, and was two days after rewa-
tering for the second drought period. P176 started to read large tensions, about 20 bars more
negative than the Schölander response; this observation suggests that P176 lost contact with the
plant tissue. P187, on the other hand, showed good correlation with the Schölander response, in
distinction from all the other sensors. However, when the day was approaching night, P187 re-
turned more quickly toward zero than the Schölander Pressure Chamber. The reason might be the
accumulation of osmolites in leaves, which resulted in high osmotic potential.61 We expected the
predawn water potential measured by the Schölander Pressure chamber may be the high osmotic
potential discussed. Since the sensors were in direct contact with the tissue, the small molecules
dissolved in xylem sap could get into the sensors, resulting in the insensitivity of the sensor to
osmotic potential. At night, the osmolites inside the µTM might cause the sensors to read positive
pressure due to the opposite direction of diaphragm deflection.
When comparing the behavior of P187 across the three figures in Figure 2.12, the behavior
of P187 appeared to improve progressively during the month, when compared with the Schölander
pressure chamber. The possible reasons for this improvement in P187 could include: 1) the wound
response of the plant resulted in new tissue growing around the sensor, and improved the liquid
and thermal contact between the sensor and the tissue; 2) The embolized xylem elements around
the sensor recovered from cavitation, and improved the sensor-tissue contact; and using a chisel to
open a slit for sensor installation may have caused less damage to the plant than drilling a hole,
because the other sensors installed in drilled holes appeared to progressively lose their contact with
the tissue. However, it was still worth keeping the sensors inside the plant for a longer time to see
how their behavior evolves over longer periods.
Figure 2.13 shows the dependence of plant water potential on the delayed temperature differ-
66
Figure 2.13: Comparison of the µTMs with ∆T−15min, Solar Radiation and Vapor Pressure Deficit. The
black line represents P187. The green line represents P20. The blue line represents P176. The magenta line
represents P179. The circles are Schölander Pressure Chamber measurements. a. Comparison of the µTMs
with ∆T−15min (red line). b. the µTMs vs. Solar Radiation (red line) c. the µTMs vs. VPD (red line)
67
ence (Figure 2.13a), solar intensity (Figure 2.13b) and vapor pressure deficit (VPD) (Figure 2.13c)
on the same rainy day showed in Figure 2.12b. We selected this rainy day because the VPD and
solar intensity varied more significantly than on a normal sunny day, and was helpful for the ob-
servation of the sensor response. It is worth noting that ∆T−15min , VPD, solar intensity, and water
potential measured by the sensors varied in a similar manner. It is hard to determine which one of
the three major factors dominate on the variations of water potential.
Figure 2.13a compared the sensor response to the ”temperature difference” , the 15min tem-
perature difference estimation ( ∆T−15min ) mentioned above. The temperature data were calculated
from P176, due to its position in the center of the sensors installed on the tree.
The sensor still showed a strong correlation with ∆T−15min , as in the GH2 results. This
observation suggests that a psychrometric effect may have affected these measurements as well.
Figure 2.13b compares µTMs’ response to solar intensity. The sensors had a better corre-
spondence on the variations of solar intensity than the Schölander pressure chamber. In particular,
in the region labelled by ”i” , we see a midday drop in the response of the sensors as the solar
intensity dropped. We note though that ∆T−15min also dropped during this period.
Figure 2.13c shows the µTMs’ relationship to VPD. The VPD data were calculated based
on the relative humidity and the temperature data from the Cornell Orchard Weather Station by
assuming near-saturation vapor pressure inside the leaves. The labelled regions (i, ii and iii) in the
plots showed that the midday water potential correlated better with the intensity of solar radiation,
while the variations of the midday water potential correlated with VPD. For example, circle (ii) in
Figure 2.13c shows a correlation between the response of P187 and the VPD variation.
Figure 2.14a compares the responses of the tensiometers to the delayed temperature differ-
ence (∆T ) on day 24 when numerous bomb measurements were performed. The responses from
P20, P176 and P179 were similar, and may follow on the temperature difference, while P187 had
a similar trend as the Schölander pressure chamber data, even though the values were not exactly
68
matched. P20 read close to zero when the Schölander measured -10 to -15 bars of water potential.
The Schölander responses reached plateau while the P20 kept reading more and more negative
water potential. Both P176 and P179 had similar response as P20, but not as extreme. Therefore,
we expected a linear regression if plot P187 against the Schölander data.
Figure 2.14b presents the correlation between the µTMs and the Schölander pressure cham-
ber on day 24. The sensor responses of the four µTMs was plotted against the Schölander data.
P187 had an almost linear correspondence with the Schölander data, and the best fitting quality (
R2 = 0.93 ), compared to R2 ∼ 0.80 of the other sensors.
Figure 2.15 showed the complete data over the second drought period. The soil and stem
water potential during a drought period was theoretically sketched in Figure 1.4a,15 and was tested
experimentally by Gardner and Nieman in 1964 using a pepper plant (Figure 1.4b).28 Compared to
the literature, the data from my experiment indicated close soil and stem water potential at night
when the soil was not under stress. During the drought period, the soil water potential was much
less negative than the stem water potential at night, while the literature showed almost identical
soil and leaf (stem) water potential when the pepper plant was under tension. The possible reasons
were that the soil sensors were not installed deep enough to read the soil sample in direct contact
with the roots. Another possibility was that the pathway from the soil to the sensor generated high
hydraulic resistance during drought period.62 The high resistance could be in the soil, the soil-
root interface, or anywhere in the xylem upstream of the sensor. The generation of high hydraulic
resistance requires further investigation. In addition, the root system of apples has very low density
and are inconsistent in distribution.30 Therefore, the soil sensors may not have measured the soil
water potential that is effective for the apple tree. The predawn Schölander pressure chamber
measured a -5 bar water potential in region (ii), which was much more negative than the sensor
data. Comparing regions (i) and (iv) for well-watered conditions, we note that the offset change
of the sensors was not significant after 12 days. This observation tends to support our decision to
shift the sensor data to zero these pre-dawn responses.
69
Figure 2.14: Linear comparison between the Schölander data and the sensors. a. Chronological Record
on Day 24 with ∆T−15min. The black line represents P187. The green line represents P20. The blue line
represents P176. The magenta line represents P179. The circles are Schölander Pressure Chamber mea-
surements. b. µTM measurements are plotted against the Schölander data. The black line represents 1:1
equal Ψ. The blue line represents the fitting of the correlation. The slopes and the goodness of fit for the
correlation were shown for each sensor.
70
Figure 2.15: GH4-Second Drought Period. The black line represents P187. The green line represents
P20. The blue line represents P176. The magenta line represents P179. The circles are Schölander Pressure
Chamber measurements. Regions i, ii, and iv are well-waterred periods. Region iii is the second dry-down
cycle.
71
Figure 2.16 shows the µTM measurements in the soil. The µTM reported diurnal variations
of the soil water potential. However, we cannot completely exclude the temperature effects on the
diurnal variations. These temperature effects include both the psychrometric effect and the direct
temperature effect on the sensor signal. Additionally, the µTM showed a -14 bar negative water
potential at the end of the second drought period (day 22). This tension was shown relaxed after
the second rewatering on day 22.
Combining the above results, the water potential measured by the µTM showed strong de-
pendence on the "temperature difference", solar intensity and VPD. It has also been shown that,
several weeks after embedding, the P187 had linear correlation with the Schölander pressure cham-
ber. These observations led to the hypothesis that the sensor P187 was measuring real tissue water
potential. Further studies need to be done to test this hypothesis.
The P187, which was the bare device and should have had the best contact with the plant
tissue, showed a linear correlation with the Schölander data after being embedded for almost one
month inside an apple tree. P20 had an ePTFE membrane between the plant tissue and the sensor.
Therefore, P20 has known vapor gap and works as an indicator for the psychrometric effect. If a
µTM behaved in a similar way as the P20, it suggests it has lost contact with the tissue.
The results of GH4 give us preliminary evidence that the packaging strategy of P187 worked
better than other packaging strategies. Nevertheless, some observations were still able to guide us
to further studies and hypotheses. The µTMs were not able resolve the gradient of water potential
in the direction from lower positioned sensor to the higher positioned sensor for small tree sizes,
like the tested apple trees (Figure 2.8-iii). Therefore, a hypothesis is that the radial water potential
gradient dominates when the water stress level is low, due to the small difference in drilled depth
for the sensors. Previous studies have shown radial and axial water potential gradient through a
sap flow meter and measured radial hydraulic resistance in a cut wood stem in laboratory,8 but no
direct measurements have been reported that tested for its existence.
72
Figure 2.16: Soil Water Dynamics by Micro-Tensiometer in Soil.
73
2.6 Conclusion
The development, installation and the in-plant testing of the second generation µTM were
presented in this chapter. The µTM has been shown to be able to measure the plant stem water
potential with high time-resolution, and was able to achieve a linear regression with the widely
accepted Schölander pressure chamber data when being tested in plants.
The µTM was built based on the MVLE theory by connecting the internal liquid to the outside
vapor through a nano-scale porous silicon; this design combined the techniques of MEMS and
piezoresistive pressure sensing to transduce the energy signal to mechanical signal, and eventually
to electronic signal.
Greenhouse experiment 2 (GH2) was conducted to develop the thermal insulation methods
to minimize the thermal noise from the outside environment. From the GH2 results, the sensors
showed much more negative water potential than the pressure chamber measurements (about -15
bar). The hypothesis about the existence of the vapor psychrometric effect due to the sensor-tissue
vapor gap was proposed (7.77 MPa/◦ C) and was tested in the GH4 experiment by trying different
packaging strategies to improve the sensor-tissue thermal contact.
The GH4 experiment showed one device P187 with linear correlation with the Schölander
pressure chamber. This device was a bare device, which should have had direct thermal contact
with the tissue, and was installed with a minimal damage to the plant tissue. The gradual improve-
ment in its measurement might be due to the growing of the wound tissue, or the reconnecting of
the cavitated xylem elements around the sensor. The GH4 also showed strong stem water potential
dependence on solar intensity and vapor pressure deficit (VPD). Based on the GH4 results, a new
hypothesis about the axial and radial gradient of stem water potential will be tested in next step
experiments.
These results proved that a µTM could be used to monitor water potential in real-time in-
side the greenhouse. Further improvement in embedding techniques is necessary to improve the
74
repeatability, and accuracy of the measurements. Additionally, outdoor validation of the micro-
tensiometers is crucial to prove the sensor as a reliable hygrometer, and to open up its application
scope. We will discuss the field measurements on apple, grapevine, and almond, as well as the
circuit models we developed in the following chapters.
75
CHAPTER 3
CONTINUOUS STEM WATER POTENTIAL IN APPLE, GRAPEVINE, AND ALMOND
WITH MICRO-TENSIOMETERS
3.1 Introduction
Vascular plants harvest water from the soil to maintain hydration as they lose water to the
atmosphere during the gas exchange that is required for photosynthesis.63 This flow of water, tran-
spiration travels down a gradient of water potential from the soil to the atmosphere.
Water potential represents the thermodynamic availability of water for chemical and physical
processes. It quantifies water status as a mechanical tension.17 The water potential within the
conductive tissue of plants (xylem) affects growth, yield and quality of crops, and susceptibility to
disease.;64–68 as such, the value of water potential in stems (Ψstem) serves as a preferred measure of
a plant’s water status for studies of physiology and for the guidance of water management.69
Fundamental principles of thermodynamics and fluid mechanics of transpiration date back
to 1890’s based on the work of Dixon and Joly.70 Since the pioneering work of Schölander33 and
coworkers, the community has appreciated the usefulness of in-plant water potential in integrat-
ing plant water status. In 1960, Slatyer introduced the usefulness of water potential as a state
variable.25 Following Slatyer, more advances in models of soil water relations,28 mass and en-
ergy exchange with atmosphere,71,72 stomatal regulation,27 and hydraulics of roots, xylem, and
leaves73 were developed. Despite the emergence of spatially and temporally resolved models of
water within SPAC, e.g., Campbell,73 we have had few opportunities to confront these models with
continuous measurements of dynamics.
Access to the dynamics of Ψstem would open opportunities to access, in-situ, the hydraulic
properties of the plant and soil, the characteristics of stomatal regulation, and the real-time effects
of variations in climate, phenology, and management on plant water status. This information, in
76
turn, would support studies of water stress physiology, predictive models of water relations, and
approaches to manage water efficiently in irrigated agriculture.
To date, tools for the measurement of Ψstem are manual, slow, indirect, and unreliable. These
limitations have hindered the access to the full dynamics of in-plant water potential as a function
of variations in atmospheric conditions (windspeed,vwind; temperature, T ; vapor pressure deficit,
VPD; solar radiation, Qrad; soil water potential, Ψsoil; water inputs from precipitation and irriga-
tion; and biological responses).
Capturing the dynamics of Ψstem (Figure 3.1a) has remained challenging for a variety of
reasons: 1) time-scales of dynamics are too rapid for manual methods (e.g. SPC); 2) the conductive
tissue (xylem) within the stem is buried below the bark; 3) the liquid water moves through the
xylem under metastable state (tension) that is fragile with respect to interventions;70,74,75 and 4)
the water status is close to saturation, in a range that is hard to resolve with many hygrometry
techniques such as resistive and capacitive transducers.14,33,39,42,76
Since its introduction over 60 years ago, a Schölander Pressure Chamber (SPC) has defined
a gold standard for accuracy for both research and water management.22,33,67 This technique in-
volves manual excision of a leaf and takes several minutes per measurement. To date, the SPC
technique remains the most widely accessible method for measuring Ψstem. Previous studies have
shown diurnal measurements of Ψ with the SPC at hourly intervals.67,77,78stem Due to the slow,
manual, destructive nature of this technique, measurements are typically taken infrequently (e.g.
once predawn and once mid-day), such that the full dynamics of plant water status has remained
obscure.66,79,80 Nevertheless, this manual method is trusted as standard for both research and irri-
gation management.
Psychrometry has a long history of use for measurements of the dynamics of in-plant wa-
ter status.22 A thermocouple psychrometer was first introduced in 1950’s and 1960’s by Richards
195881 and Boyer 1965,82 with important advance by Dixon and Tyree22 to correct for strong sen-
77
sitivity to non-isothermal conditions. It shows robust linear calibration of response to change in
water potential under controlled scenarios. It was then used by a number of investigators to pro-
vide time-dependent measurements of stem and leaf water potential over short periods.83–86 For
measurements to show reasonable range of values and responsiveness to perturbations such as pre-
cipitation events, it requires expertise for installation and relatively expensive logging equipment.
Psychrometers can be very accurate. Furthermore, it has proven to be technically challenging to
implement for long-term measurements (days to months) in the field due to its strong sensitivity
to temperature variations, to contamination of the thermocouple surfaces, and the small magnitude
and transient nature of the electrical signal.22,87,88 The group of Simmons has presented a series
of long-term measurements of Ψ with the Dixon psychrometer sold by ICT.89–92stem They have
demonstrated the usefulness of continuous measurements for the refinement of models of stomatal
conductance, and the hydraulics of the SPAC.89–92 However, few examples of long-term (weeks),
continuous measurements of Ψstem have been reported with bench-marked comparison against the
SPC or other techniques.80,93
Scientists have also used indirect measurements to access the dynamics of water potential
in plants, including gas exchange, sap flow, leaf water content, leaf turgor, soil water content, and
trunk diameter fluctuations.28,73,94–103 Gas exchange94,96 and sap flow37 provide estimates for the
rate of transpiration, but one cannot deduce in-plant water status without additional knowledge of
the properties (e.g., resistances) and the state of the SPAC.66,100,104 Further, gas exchange cham-
bers disrupt the effect of wind on the measured tree. Sap flow measurements37 provide in-plant
information, but the readings depend in complicated ways on the depth of embedding, and require
calibration against a lysimeter or gas exchange meter. Furthermore, both gas exchange chambers
and sap flow meters typically function over a short periods of time.96 Dynamics of leaf turgor and
leaf water content of an attached leaf are either complicated and expensive to measure, or hard to
correlate to plant water potential.28,101–103 The use of soil water content or soil water potential to
infer the water status of plants is challenging due to the high spatial variability in the soil and the
potential for large, variable resistances between the soil and the plant, especially for woody peren-
78
nials.73,105 The variations in trunk diameter have been explored as a proxy for plant water stress,
but this technique requires challenging calibration to account for species-to-species variability, as
well as the coupling to the growth of tissue.95,106,107 Moreover, the scalability of this method is
limited by tree-to-tree variations.97
To capture the full dynamics of plant water status, we still lack a robust tool for automated,
continuous, in-situ measurements of Ψstem. We need a new hygrometer that minimizes artifacts
due to environmental perturbations such as temperature fluctuations, operates with standard data
logging equipment, allows for minimally destructive interaction with plant, and provides data over
long periods (months to years) without the need for human intervention.
Regarding the water relations, this new tool will help us understand the drought physiology
of plants by 1) constraining models of hydraulic properties of SPAC; 2) distinguishing the resistive
and capacitive responses of trees to environmental stress; 3) resolving the linear (constant resis-
tance) and non-linear (Ψ-dependent resistance) responses with and without water shortage; and 4)
characterizing the response time of SPAC to evaporative demand from above ground conditions,
and the water supply from below ground water status.
In this chapter, we present the use of a newly developed tool, a micro-tensiometer (µT M,
Figure 3.1b )14,108 for in-situ measurements of Ψstem in a continuous manner. A micro-tensiometer
is a micro-electro-mechanical-systems (MEMS) based microfluidic device designed following the
principles of tensiometry.14,108 After calibration and packaging (Figure 3.1c), we embed the sensor
(µTM) directly below canopy to make liquid contact with water in xylem for reliable measurements
(Figure 3.1d). We report field measurements with thorough bench-marking in three important
woody perennial crops: apple, grape and almond. The field sites include a rainfed wet environ-
ment (apple-central NYS), a rainfed arid climate (grape-CA), and an irrigated arid environment
(almond-CA). We proceed to use these continuous data sets to elucidate important features of the
water relations in these cultivars and environments. We then perform analysis of dynamics across
different time-scales. We conclude with perspectives on the use of micro-tensiometer (µTM) for
79
the study of the physiology of water stress in plants and water management.
3.2 Probing the soil-plant-atmosphere continuum with a micro-tensiometer
A micro-tensiometer (µTM) operates by the same mechanisms as a conventional tensiometer:
an internal cavity filled with pure liquid water couples to the outside environment through a wetted,
porous membrane; and a strain gauge (Figure 3.1) attached to the cavity measures the internal
liquid pressure.109 At equilibrium with a sub-saturated external phase, the hydrostatic pressure
within the cavity (Pcav,liq) is lower than atmospheric (P0). The pressure difference between the
internal liquid and outside is the sensed water potential, Ψ[MPa] = Pcav,liq − P0, and is less than or
equal to zero. The strain gauge then transduces this pressure difference into a voltage signal. This
theory of operation mimics the accepted mechanisms by which vascular plants maintain hydration:
the cohesion-tension theory.70,74,75
Important characteristics of the µTM relative to conventional designs are shown in Figure
3.1b: 1) the micro-electro-mechanical-systems (MEMS) approach was applied for the design and
fabrication of the strain gauge, a Wheatstone Bridge, and to produce many devices in-parallel on
a single silicon wafer bonded to glass;14 2) small volumes of water reservoirs were produced in a
cleanroom environment to minimize nucleation sites for cavitation, a route to phase transition from
liquid to vapor under tension;11 3) the exchange membrane made of mesoporous silicon (poSi, 1-
3 nm) with oxidized surface provides large capillary pressures to suppress air invasion (< −10
MPa);14 and 4) a platinum resistance thermometer (PRT) was fabricated on each sensor for in-situ
temperature sensing. Together, these features allow the µTM to operate across the full range of
water potential commonly encountered in plants (0 > Ψstem > −3 MPa).17 In the current design,
we included microchannels ("Synthetic Xylem" veins) to lower the hydraulic resistance of the
membrane and thus the response time of the sensor to changes in external water potential. These
"Synthetic Xylem" veins mimic the architecture of xylem, and give characteristic response time in
the order of minutes, a ten-fold reduction relative to that of our 1st-generation µTM design.14
80
Figure 3.1c shows a micro-tensiometer mounted onto a customized printed circuit board
(top), and a ready-to-embed micro-tensiometer (bottom). A µTM needs to be packaged to pro-
tect the sensing chip from external mechanical stresses and damage and the electronic elements
from humidity. The electrical connections to a PCB were made via wire-bonds (Figure 3.1c) or
direct solder connections. External wiring is then soldered to the PCB board before encapsulation
with polyurethane in aluminum tubing. The packaged sensor (8-mm in diameter and 12-15 mm
in length), is ready for embedding within plant stems of modest dimension (>25 mm-diameter),
without causing excessive damage (Figure 3.1c). The schematic diagram of a packaged sensor is
shown in Figure 3S.1. The details of packaging can be found in Supporting Information. Before
embedding, the packaged µTMs are calibrated in the laboratory (Figure 3S.2 and 3S.3). The tran-
sient of a small diaphragm µTM (1x2 mm2) is about 1 min, while that for a large diaphragm (2x3.5
mm2) is ∼ 5 min.108
Figure 3.1d shows the interfacing of the µTM with the conductive xylem tissue between
water in the tissue and the water in the µTM cavity. To improve from the embedding technique in
Chapter 2, we filled the interface between the sensor and the tissue with alumina paste to maintain
a direct liquid path and thermal path between the tissue and the µTM; this paste promotes local
equilibrium of both water potential and temperature between the µTM and the xylem, and helps
minimizing the sensitivity of the measurements to thermal gradients. The liquid within the µTM
cavity comes to equilibrium with the reduced pressure that corresponds to the local water potential
in the tissue, such that the voltage output from the strain gauge varies as ∆V ∝ Pcav,liq − P0 =
Ψ .14µT M Figure 3S.4 presents the steps of µTM embedding. We discuss the impact of embedding
depth in Supporting Information (Figure 3S.5 and 3S.6)
81
82
Figure 3.1: Probing the soil-plant-atmosphere continuum with a micro-tensiometer(µTM). a.
Schematic diagram of the Soil-Plant-Atmosphere-Continuum (SPAC). In transpiration (ET), water moves
along a gradient in water potential from the soil (Ψsoil), through the xylem (the water conductive tissue,
Ψstem) and the leaf (Ψlea f ) to the atmosphere with Ψsoil > Ψstem > Ψlea f . Radiation (Qrad), windspeed(vwind),
and the vapor pressure deficit (VPD) are key meteorological variables affecting the ET . The soil is rehy-
drated through precipitation or irrigation (IR). The µTM is embedded in the stem to measure Ψstem. b.
Photos of a µTM. The top view shows the strain gauge and the Platinum Resistance Thermometer (PRT).
The strain gauge measures the deflection of a silicon diaphragm over a cavity in the backside of the silicon
wafer. The bottom view shows this cavity and an array of microchannels ("Synthetic Xylem") leading to-
ward the bottom edge. These channels cross a region of porosified silicon (dark grey zone and expanded
view). The expanded view of the "Synthetic Xylem" show that the channels do not connect to each other
or the edge; liquid must pass through short segments of mesoporous silicon as it flows between the cavity
and the exposed edge. c The top photo shows a µTM that is attached and wire-bonded to a printed cir-
cuit board (PCB). The bottom photo shows a packaged µTM that is ready for embedding. d. A schematic
cross-sectional view of the interface between a µTM and the xylem. The water inside the µTM makes liquid
contact with the active xylem tissue through a layer of alumina paste. The water potential in the xylem Ψstem
is measured as the deviation of hydrostatic pressure (ΨµT M) of liquid water inside the cavity, Pliq,cav from
the reference pressure, usually the atmospheric pressure, P0. The black arrows in xylem shows the water
being pulled upwards, down the gradient of water potential.
83
3.3 Results and Discussion
3.3.1 Dynamic water stress in apple, grapevine and almond.
Accurate and Continuous Measurements of Stem Water Potential
In Figure 3.2a-c, we show measurements from three woody perennials apple (a), grape (b),
and almond (c). We present extended measurements of Ψstem taken with the µTM (blue curves)
along with manual measures performed with the SPC (purple dots). Precipitation and irrigation
are shown in blue bar plots. Measurements with the SPC were performed on bagged leaves to
capture Ψ 66stem.
Before pursuing detailed analysis of these data, we discuss general observations based on
Figure 3.2. Across all three species, we measured the expected diurnal variation of Ψstem (Figure
3.3a-c): the development of stress (decrease of Ψstem) after the stomatal opening in response to
sunrise, and relaxation (increase of Ψstem) when the transpiration decreases with sunset. For all
cases, the range of stresses are reasonable.65,79,110–112 The midday decrease in Ψstem represents the
pressure drop due to flow across the hydraulic resistances of the SPAC. Importantly, the ΨµT M
tracks variations observed with Schölander Pressure Chamber, ΨS PC. We present expanded views
comparing ΨµT M and ΨS PC in Figure 3S.7 and 3S.8.
The continuous nature of µTM readings elucidates the context and species-specific trends
over weeks to months. With regular rain events and water-retentive soil properties at the Cornell
Apple Orchards (Figure 3.2a), most nights the ΨµT M relaxes back to small (non-zero) negative
values (-0.2 to -0.3 MPa); we will discuss the deviations from this behavior below. Despite these
well-watered conditions, ΨµT M descends to substantial midday stresses that vary with weather
conditions.
The full year of data for grapevine (Figure 3.2b) provides an unprecedented opportunity
84
Figure 3.2: Full Dynamics of ΨµT M and Regression Analysis against SPC across Three Species.
a-c. Real-time dynamics measured with the µTM (ΨµT M, solid blue lines) and the SPC (ΨS PC , solid purple
dots) for apple (a), grapevine (b), and almond (c). Water potential is shown on the left-y axis; the rainfall
or irrigation events (IR, blue area plots) are shown on the right-y axis. Shaded grey area indicates nighttime
from 6 pm to 6 am. d-f. Plots of ΨµT M vs. ΨS PC for apple (d), grapevine (c), and almond (f). The black
dots present the mean values of ΨµT M within 20-min window around the time points of SPC measurements
for apple, and 40-min window around the time points of grapevine and almond, against the corresponding
ΨS PC values. The solid black line represents 1:1 correlation as reference. The dashed black line is the linear
regression curve.
85
to observe dynamics across timescales, from hours to seasons. Different from the apple tree,
this mature, unirrigated grapevine in the Davis teaching orchard was in a semi-arid environment
with no irrigation events. We first note trends in ΨµT M with seasonal phenology. The measured
phenological stages included growing seasons, harvest, and defoliation, as indicated in Figure
3.2b. The amplitude of diurnals decreased at the end of the fall from mid-Nov, 2018 to Dec,
1st 2018 during defoliation, and returned to large amplitude diurnals in the Spring of 2019 with
shoot growth. The predawn water potentials increased after the rain season started and reached
a plateau around Dec.1st 2018. This observation indicates the soil was under mild stress due
to continuous loss of water without irrigation or precipitation until the rain arrived during the
late December of 2018. Interestingly, mid-winter diurnal variations in ΨµT M continue to follow a
diurnal pattern of potential transpiration, ET0, despite the complete absence of leaves. Figure 3S.10
shows mid-winter diurnals with weather and ET0. Small positive values of ΨµT M suggest slight
drift of instrument due to the electronics or osmotic contamination of internal volume of liquid.
The reasons of signal drift are discussed in Section 3.5.5. The vine also maintained relatively
consistent, low stress during the night through the Spring, Summer, and Fall when leaves were
present, suggesting that it had a deep, extended root system with access to the water table. Again,
we observed large deviations on nights with large ET0 (red arrows in Figure 3.2b and Figure 3S.10).
Different from both the apple tree and the grapevine, the instrumented almond tree was grown
in a commercial orchard with managed irrigation (Figure 3.2c). We note that the patterns in both
the diurnal maxima (nighttime) and minimum (daytime) were dominated by the irrigation events:
ET0 varied little through Aug.& Sept. (Figure 3S.11), whereas ΨµT M showed clear relaxation of
stress (rising values) after each irrigation event followed by redevelopment of stress (decreasing
values). We also remark that the magnitude of diurnal (Ψmax minstem−Ψstem) changed and grew significantly
with each dry down, even as ET0 remained relatively constant (Figure 3S.11).
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Linear regressions
Figure 3.2d-f show the values obtained with the µTM, ΨµT M, as a function of those measured
with the SPC, ΨS PC, from the data sets presented in Fig. 3.2a-c. The values of ΨµT M reported
are extracted and averaged from 40 min window around the time points of SPC measurements
(±20min). The sensitivity values of the µTM (change of voltage vs. change of water potential)
were those established by laboratory calibrations (Sections 3.5.3 and 3.5.4); in the case of apple
(Figure 3.2a), the voltage offset was shifted based on predawn SPC measurements to correct for a
constant rate of drift in the sensor offset.
All three data sets show linear correlation with slope near 1. The apple data in Figure 3.2d
show some outliers that we will discuss further in the following context. The almond (Figure 3.2f)
shows a 1:1 correspondence between ΨµT M and ΨS PC with data tightly falling onto a best-fit lines
(slopes: 0.96 for apple; 1.23 for grape; 1.02 for almond). Given that the response remains constant
throughout, we have the option to use the SPC measurements to perform an in-situ calibration.
We note that for grape, ΨµT M correlates well with the ΨS PC (Figure 3.2e) both before and after
the winter period, after a full cycle of defoliation and shoot growth. This strong correspondence
between our continuous measurements of Ψstem and those from the SPC suggests the µTM can
serve as an useful tool for long-term tracking of plant water relations.
3.3.2 Detailed dynamics in apple and almond
We now take advantage of continuous nature of our measurements with the µTM to examine
the diurnal and sub-diurnal hydraulic responses of apple (humid/rainfed) and almond (arid/irri-
gated) to the dynamics of the environment and the irrigation (almond). In Figure 3.3, we present
the environmental variables that control potential evaporation along with simple predictions of
ET0 for apple (Figure 3.3a) and almond (Figure 3.3b). We recorded measurements of ΨµT M at high
sampling rates (every 1 min in apple; every 15 min in almond), with sampling of local meteoro-
logical variables (Q −2rad [W m ], VPD [kPa], windspeed [m s−1], precipitation [mm hr−1], and/or
87
irrigation [psi] ) at the same rates. We estimate the vapor pressure deficit (VPD) and the ET0 using
the collected meteorological values (Section 3.5.7).
Rapid response to environmental variables and nighttime water stress in apple
In Figure 3.3a for apple, we observe large variations in environmental variables from day
to day and, on many days, from hour to hour. This variability is the characteristics of New York
State climate during the growing season. We note that the dynamics of ΨµT M undergo fluctuations
that reflect those in ET0, as is particularly evident on a cloudy (low Qrad), humid (low VPD)
day like Sep.14 (Figure 3.3a-i-ii). Clearly, though, the highest frequency dynamics in the micro-
environment are damped out in the in-plant stress, e.g., the short midday spike in Qrad and predicted
ET0 induced a less prominent dip in ΨµT M. We will return to this damping effect below.
In Figure 3.3a, we present a series of days in which there were nighttime periods with non-
zero VPD (Figure 3.3a); on most nights (e.g. Sept.12-15), VPD went to zero, and we observed that
ΨµT M rehydrated to a consistent, constant nighttime value. While the model we have for ET0 does
not predict significant transpiration, we observe significant dips in ΨµT M (red dashed lines in Figure
3.3a). This responsiveness to environmental conditions suggests significant nighttime stomatal
opening. Previous studies have observed nighttime transpiration in multiple woody species.113,114
This nighttime transpiration could facilitate the uptake of water from the soil when the plants are
low on nutrients storage.115,116 It could also prevent the buildup of carbon dioxide due to nighttime
respiration.117
We also note the same strong nighttime responsiveness in grape (red arrows in Figure 3.2b
and Figure 3S.10 with micro-environment data). For apple tree, during the post-harvest period
after Oct. 28th (Figure 3.2a), we observed more significant deviations in nocturnal water potential;
this tendency suggests possible degradation of stomatal regulation at the end of the season.
The ΨµT M brings enhanced sensitivity for the nighttime plant stress, and opens up new pos-
sibilities for studies of nighttime plant behavior that could be crucial for improving irrigation man-
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Figure 3.3: Dynamics of Stem Water Potential with the Meteorological Variables and Transpiration
on Selected Days for Apple and Almond. a-b. For apple (a) and almond (b) the plots, from (top,i) to
(bottom,v), present solar intensity (i; Qrad, kW m−2); vapor pressure deficit (ii; VPD, kPa); windspeed (iii;
m s−1); predicted potential transpiration (iv; ET0, mm hr−1); stem water potential (v-left y) measured with
µTM, Ψstem (MPa); and rain (mm in a-v-right y) or irrigation (pump pressure in psi in b-v-right y). The
dashed black curves in the bottom-most plots are best fit relaxations to the nighttime relaxations (eq.S3.9).
For almond (b-v), the solid black curve represents the response of predawn water potential to irrigation
events.The results of curve fitting, τ ∼ 42 hrs, is shown next to the plot, with the R2 = 0.9932
89
agement for water use efficiency. It is worth noting that this nighttime disequilibrium would be
missed by typical pre-dawn ΨS PC measurements.
Slow dynamics and persistent disequilibrium in almond.
In Figure 3.3b, we see the highly regular diurnal dynamics of environmental variables in
the Central Valley, CA, the location where we collected data in almond. Different from apple and
grapevine, Ψstem in almond never relaxed, showing significant stress both day and night, as noted in
Figure 3.2c, while ET0 remained relatively constant during the time period shown, the amplitude
of diurnals was strongly modulated through the cycles of irrigation, indicating that soil water status
played a dominant defining the dynamics.
As with apple, high frequency environmental signals were damped in the dynamics of ΨµT M
(e.g. Aug.3-5). Distinct from the dynamics in apple, ΨµT M in almond never relaxes to a con-
stant value at night, even on calm nights (low wind) with low VPD and no predicted ET0 (e.g.
Aug.6-15). We observe this nighttime disequilibrium – the continuous increase of ΨµT M implying
continuous rehydration of the almond tree by uptaking water from the soil – throughout our period
of observation (Figure 3.2c).115
Given that VPD goes to zero at night during this period, we interpret this nighttime disequi-
librium as due to the long transient for equilibration between the plant and the soil due to a long
intrinsic response time of the soil-plan system. This lack of equilibrium between the plant and
the soil indicates that the common assumption that pre-dawn measurements of ΨµT M provide an
estimate of Ψsoil may be incorrect for slow-responding plants.115
For comparison, an analysis of baseline water potential,66,67,118 Ψbase is shown in Figure 3S.8
and Figure 3S.11 to represent the Ψstem when soil is saturated with water. The almond ΨµT M tracks
the Ψbase, but deviates to more negative values with a larger diurnal amplitude from the Ψbase after
withholding water for about 10 days. This observation, on the other hand, confirms the increasing
impact of soil stress on both the transients and magnitude of in-plant water status.
90
In addition to the transient of nighttime rehydration represented by the dashed line, we also
observed a multi-day transient (solid black curve in Figure 3.3b-v) of predawn water potential after
irrigation. This slower dynamics represent the response of SPAC to soil water balance between
water supply (irrigation) and water loss (transpiration and drainage), and could provide guidance
for plant-based automated irrigation scheduling.
In Figure 3S.12, we present dynamics of soil water content at the almond orchard from six
soil probes. We note that neither the diurnal dynamics nor the modulation with irrigation are
seen clearly in these soil moisture measurements (Section 3.5.7). This observation illustrates the
challenge of inferring in-plant water status from soil measurements, motivating the use of stem
water potential instead of soil water potential for irrigation scheduling.
3.3.3 Analysis of SPAC hydraulics in apple and almond.
We can now extract more quantitative information about water movement through SPAC
from the measured continuous dynamics in Figure 3.3. For this purpose, we adopt the simple,
coarse-grained representations of the SPAC hydraulics. In the simplest perspective, the hydraulic
resistance and storage of the soil and plant can be lumped together into a single resistance (Rsp)
and capacitance (Csp) as in Figure 3.4a-i; more generally, additional compartments can be added
to account for the distinct water relations of the plant and the soil (Figure 3.4a-ii) or finer details
within each.73
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92
Figure 3.4: Hydraulic Resistance and Response Times of Plants under Wet and Arid Environments.
a. Simple hydraulic circuit models for woody plants: (ai). a 1-compartment model with one hydraulic
resistance Rplant and one hydraulic capacitance Cplant, driven by ET with fixed soil water potential Ψsoil and
variable Ψstem; and (aii). a 2-compartment model with hydraulic resistances of the plant Rplant and the soil
Rsoil, and the capacitances Cplant and Csoil, with one additional dependant variable Ψroot. b. Characteristic
response times of rehydration events, τrd after sunset for apple (solid yellow dots) and almond (solid blue
dots) as functions of their corresponding upper limit of water potential (Ψsoil,lim) of the day. The mean
rehydration time scales are shown for apple and almond displayed in yellow and blue respectively. These
characteristic times were extracted from fits of nighttime relaxation with eq.3.1, as shown in Figures 3.3a-
b(v) (black curves). Linear regressions are performed and shown with dashed lines in yellow and blue for
apple and almond respectively. c. The dependence of the difference between the predawn water potential
Ψpd and midday water potential Ψmd on the daily maximum ET0 for apple (solid yellow dots) and almond
(solid blue dots) under wet and arid environment respectively. Linear regression (dashed yellow line) is
shown for apple. d. The estimated hydraulic resistances of apple Ψapple and almond Ψalmond as functions of
their corresponding predawn water potential Ψpd on left-y axis and right-y axis respectively. The hydraulic
resistances of almond is plotted with a blue colormap corresponding to days after irrigation. Almond data
points from the same rehydration cycle are connected through dashed lines in blue, red, green, and purple.
The equation for estimating the hydraulic resistances, and the mean hydraulic resistance of apple are shown
in the plot in yellow fonts.
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The simplest representation – a single hydraulic resistance and a single capacitance (Figure
3.4a-i) – implies that the dynamics of water potential (and flow) should respond with a single
characteristic time-scale, τrd = RspCsp, such that, on nights with weak ET0, we expect the stem
potential ΨµT M to relax exponentially toward the rehydrated Ψstem in saturated soil (Ψsoil,lim):
Ψ − Ψsd = (Ψ − Ψsd )(1 − e−t/τrdstem stem soil,lim stem ) (3.1)
where Ψsdstem is the water potential at sunset (See Section 3.5.8 for a full discussion of this analysis).
In Figure 3.3a-i&b, we adjust the three parameters τ , Ψsdrd stem and Ψsoil,lim in eq.3.1 to fit
the continuous nighttime values of ΨµT M (dashed black curves). These parameters fit match the
nighttime relaxations satisfactorily (Figure 3S.13 for expanded views of fits), supporting our use of
this simple representation of the effective hydraulics. These fits also provide us with quantitative
estimates of the daily values of the characteristic hydraulic response time τrd (and thus the product,
RspCsp) and the Ψsoil,lim. We can see graphically that apple responds quickly (small τrd) and ΨµT M
converges rapidly to Ψsoil,lim, while almond relaxes slowly (large τrd) such that Ψstem does not have
time to relax to the predicted value of Ψsoil,lim before sunrise, leading to persistent disequilibrium
(see Figure 3S.13), as discussed above.
In Figure 3.4b, we plot these estimates of τrd for apple (yellow dots) and almond (blue dots)
as a function of the estimated soil potential, Ψsoil,lim for calm, humid nights (see Figure 3S.13).
In apple, the response times are short (τ̄rd ∼ 1.2 hr) with little variations over the narrow, high
(wet) range of Ψsoil,lim. This lack of variation indicates that the product, RspCsp, does not vary
substantially under these wet conditions. In almond, in contrast, the response times are longer (5-
15 hrs) and vary substantially, with a trend to smaller values (faster response) in drier soil (lower
Ψsoil). This variation in τrd suggests more complex water relations in this water-limited almond
case relative to those in well-watered apple, with the product RspCsp decreasing with increasing
soil stress.
To continue to explore the effective hydraulic response of these two cases, in Figure 3.4c, we
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turn our attention to the amplitude of the diurnals (∆Ψdstem = Ψpd −Ψmd) as a function of maximum
estimated potential (ET0,max) in apple (yellow dots) and almond (blue dots). Ψpd is the maximum
water potential during a diurnal, while Ψmd is the minimum water potential during a diurnal. In
Figure 3.4d, we plot these data as effective resistance, Rsp = ∆Ψdstem/ET0,max, as a function of the
predawn water potential from the micro-tensiometers, Ψpd.
In apple, the highly variable meteorology created a range of values of ET0 with which ∆Ψdstem
shows a linear trend (R2 = 0.75) and a near zero intercept (Figure 3.4c). This relationship sug-
gests that in this well-watered apple, the hydraulic response of the SPAC is mostly resistive, i.e.,
∆Ψd −1stem ∼ RspET0, where the effective resistance, Rsp ∼ 1.87 MPa hr mm . For a leaf area of
∼ 6 m2, we find an effective resistance, R̄ ' 1 × 1012 Pa s m−3sp for apple. This value is in reason-
able agreement with previous estimates in apple.77 Figure 3.4d shows that daily values of R̄sp vary
around this average value and show no trend with Ψpd. Furthermore, with τrd = RspCsp ∼ 1hr (Fig-
ure 3.4b), we find capacitance Csp ∼ 4 × 10−9m3 Pa−1. This value is about one order of magnitude
larger than the previous literature reported value of 1 ∼ 5× 10−10m3 Pa−1.77 This lower capacitance
value could result from smaller tree size of the measured apple than the literature reported one.
In this well-watered case in apple, our continuous measurements of ΨµT M with the µTM thus
allow for a thorough analysis of the water relations: constant values of hydraulic resistance and
capacitance, a response time (RspCsp) that is long compared to fluctuations in the environment,
but short compared to diurnal forcing, and transpiration that does not deviate significantly from a
simple prediction of potential ET0. In Figure 3S.15, we show that we can use the values of Rsp
and Csp in a simple hydraulic model as in Figure 3.4a-i to capture much of the dynamics of ΨµT M
measured with µTM. Although no previous studies on baseline water potential for apples were
reported, to the best of our knowledge, the success of the simple hydraulic model confirms the
resistive response from the apple tree that coincides with the concept of baseline water potential.
under well-watered conditions.66,67,118
In almond, these simple analyses (Figure 3.4cd) suggest different, more complex water rela-
95
tions than in apple. In Figure 3.4c, we see that, despite a small range of midday values of ET0 (due
to highly regular meteorology), the amplitude of diurnal changes in ΨµT M (∆Ψstem) varied signif-
icantly (∼ 4-fold); unlike in apple, the variations in the diurnal amplitude cannot be attributed to
changes in evaporative demand. When we evaluate the effective resistance, Rsp = ∆Ψ/ET0, (see
Section 3.5.9 for caveats about this analysis), we uncover a strong, complicated dependence on the
state of the soil. The effective resistance is a multi-valued function of soil water potential through a
cycle of irrigation: Rsp grows and plateaus from the first day post-irrigation (dark blue circle) to the
end of the cycle (light green circle) even as Ψsoil varies non-monotonically (increasing for 3 days
before dropping again). Consistent with our analysis of response times in almond (blue circles
in Figure 3.4b), we conclude that the hydraulic properties in this water-limited case vary strongly
with soil water status. The history-dependence of Rsp vs Ψpd (e.g. one day and seven days after
irrigation both showed Ψpd ∼ −0.8 MPa, but Rsp between these two days differed by a factor of
4), reveals the potential hazard in using measurements of Ψpd as a basis for evaluating plant water
status.88,119
Generally, the complexities of the dynamics of stress in almond-failure of pre-dawn equi-
librium (Figure 3.3b), strong variation of hydraulic properties (Figs.3.4cd), and history–dependent
behaviour (Figure 3.4d) – underline the value of the continuous monitoring of stress with the µTM.
Furthermore, this type of data creates an opportunity to develop refined predictive models of SPAC
dynamics that are either mechanistic (i.e., accounting for soil water relations, root characteristics,
stomatal regulation, etc.) or data-driven.73
3.4 Conclusion
We presented the micro-tensiometer as a new robust tool for measuring the dynamics of
water status in plants and analyzing the water relations along the soil-plant-atmosphere continuum
(SPAC).
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Stem water potential measured by the µTMs agreed well with the Schölander pressure cham-
bers (SPC) for three woody species under wet (apple), semi-arid (grapevine), and arid (almond)
environments. The dynamics recorded make qualitative sense when compared to grass reference
transpiration under the three distinct environments. Additionally, we observed nighttime disequi-
librium in stem water potential due to either nighttime transpiration (apple and grapevine), or the
long transients (almond). Some nighttime disequilibrium phenomena could be missed without a
µTM when only conducting point measurements of predawn water potential. The µTM functioned
reliably through 12 months providing a unique opportunity to record the dynamics of water during
the defoliation, dormancy, and shoot development phenological stages of the grapevine.
The continuous nature of dynamic water stress provides an opportunity to dissect the SPAC
water relations as either simple or multiple compartments, under wet (apple) or dry (almond) en-
vironment respectively. Under well-watered conditions, the simplest representation with a single
resistance and a single capacitance can be used to elucidate the water relations of a well-watered
woody plant. The response of the well-watered apple tree to transpiration is mainly resistive. In
contrast, the almond tree showed significant nighttime disequilibrium with the soil, and a longer
rehydration time–scale after irrigation. A simple resistive response to transpiration does not apply
to almond going through drying-cycles due to the complexity of soil hydraulic resistances and ca-
pacitances when dehydrated. The fact that the hydraulic resistance of the SPAC shows complex
dependence on predawn water potential, implies complex water relations induced by the dynamics
of soil water hydraulics with irrigation events. Continuous measurements of in-plant water poten-
tial gives access to a highly relevant measure of soil status based on the plant’s experience of it
through its distributed root system.
Micro-tensiometers with the capability of measuring the dynamics of water status of plants
accurately with high temporal resolution, brings a new approach for studying the transient in
drought responses of plants, including stomatal regulation, root water relations, and the loss of
xylem conductance. Understanding how plants respond to water stress is crucial for better ir-
97
rigation management with increased water productivity.67 This understanding could also aid in
breeding of plants with improved water use efficiency and drought tolerance.120 Furthermore, this
technique can be applied for plant-based irrigation control with better water use efficiency.
3.5 Supporting Information
3.5.1 Fabrication
We have presented the detailed description for the micro-fabrication process of the first and
second generation µTM in references.14,108 Briefly, the micro-fabrication process is described be-
low.
The µTMs are fabricated at the Cornell Nanoscale Facilities (CNF). Figure 3.2b shows the
photos of a micro-tensiometer chip. Silicon and glass wafers were used to fabricate µTMs. The
100 mm silicon wafers were 100-mm, double-side polished, 300-350 µm thick, boron-doped, crys-
tal orientation <111>, and 1-10 Ω − cm resistivity. The Borofloat (SCHOTT) glass wafers were
100 mm in diameter, 500 µm thick, and have one primary flat (WRSMATERIALS). The Wheat-
stone bridge, the strain gauge, and the Platinum Resistance Thermometer (PRT) were obtained by
patterning platinum by lift-off on top of the silicon wafer that was prepared with layers of silicon
dioxide (SiO2-insulator) and poly-silicon (piezoresistor) respectively. The Wheatstone bridge was
positioned on top of the silicon diaphragm above the reservoir to sense its deflection. The PRT was
fabricated above the PoSi membrane, close to the sensing edge, to monitor the thermal status of the
device. A 3 µm-deep reservoir and the vain structure were formed on the bottom side of the wafer
by standard photo-lithography techniques and plasma etching. The mesoporous silicon membrane
(poSi) was patterned through photolithography, and etched through anodization using hydrofluoric
acid (HF). The pore size range was 2-5 µm in diameter.14,121 The reservoir and the vein structure
were then sealed by anodically bonding the silicon and the glass wafers together. The assembled
wafers were diced into 5 mm x 5 mm chips. The transport distance between the bottom of the
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T-vains to external environment (Figure 3.2b) is only 20 µm to minimize the hydraulic resistance
of the membrane and the respone time of the device. The µTM chips were then ready for the
packaging step.
3.5.2 Packaging
Figure 3S.1 shows the cartoon of a packaged micro-tensiometer. The µTMs were packaged
before embedding for protection against mechanical stress and corrosion. The details of packaging
were described previously.108 Figure 3.1 shows the µTM mounted onto the printed circuit board
(PCB) with the electronics side exposed, and then wire-bonded to the PCB. We performed the
wire-bonding using the Westbond 7400A Ultrasonic Wire Bonder at Cornell NanoScale Science
and Technology Facility (CNF). The thin aluminum wires connecting the platinum pads on the
µTM and the copper pads on the custom PCB (OSHPark) were 1.25 mm thick. UV/Visible light-
curable encapsulant (Multi-Cure 9001, DYMAX) was applied on the wire-bonds as protection
against corrosion and mechanical stress during application. The assembled µTM and PCB, after
wiring PCB, were encapsulated with polyurethane (UR5041, Electrolube) while enclosed in alu-
minum tubing. Aluminum is thermally conductive to provide better thermal contact with the plant
tissue. The AWG 28 wires provided connections to our datalogging system (Section 3.5.7). The
potting process was fine-controlled to prevent the Wheatstone bridge and the PRT from touching
the potting material for better thermal equilibrium with the tissue. Additionally, the thermoplas-
tic nature of the polyurethane (UR5041, Electrolube) results in disturbed signal on the Wheatstone
bridge when exposed to complex outdoor environment. Furthermore, the µTMs, made from silicon
and glass, have two orders of magnitude higher thermal conductivity than polyurethane.
We note that, relative to our previously reported methods,108 the flip-chip method was not
used to assemble PCB and µTM, since direct contact between PCB and the Wheatstone bridge
would generate abnormal deflection of the silicon diaphragm, and lead to inaccurate measurements.
Also, different from previous methods,108 the µTM was not attached to copper strips since the
99
Figure 3S.1: Packaged Micro-Tensiometer with Exposed Electronics.
100
mechanical stress during embedding damages the electronics.
3.5.3 Osmotic Calibration
The details of osmotic calibration were shown in our previous publication.108 The major steps
were:
1. The µTMs were first filled with DI water under high pressure. Please refer to Pagay 2014 for
the high pressure filling setup and methods.14 Briefly, the µTMs were kept in liquid water
under 500 psi for 8 hrs to push water through the mesoporous silicon (poSi) membrane.
2. The µTMs were briefly dried and sealed in a glass cap with one end covered with ePTFE
membrane (Porex, PMV10) that only allows the transport of water vapor. The water-filled
µTM was brought to directly contact the ePTFE membrane. This close contact reduced the
air-gap between the membrane and the reference solutions, and therefore, the resistance of
vapor transport.
3. The osmotic calibration was done using urea solutions with water potentials of -5.8 MPa,
-4.2 MPa, -2.1 MPa, -1.4 MPa, and -0.8 MPa (Figure 3S.2a). The water potentials of the
urea solutions were measured with a Chilled-Mirror hygrometer (Decagon WP4C).
4. The µTMs were first kept in the most concentrated solution (-5.8 MPa) for > 8 hrs to
dry the water residues within cap-sealed µTMs. The µTMs were then moved from more
concentrated solutions (more negative water potential values) to less concentrated ones with
a time interval of at least 2 hours.
5. Figure 3S.2 shows the time course of the responses of µTMs during an osmotic calibration.
Figure 3S.2b shows the transient time scale (τ ∼ 1 min) of µTM to step change in osmotic
solutions. It is worth noting here that the µTMs used for grapevine and almond had larger
diaphragm device with a larger internal reservoir of water. These µTMs, therefore, had a
slightly longer response time (4 − 5 min) than the µTM in apple (1 min).108,122 This longer
101
response time was shorter than the response time of the trees (> 5 min), and was, therefore,
fast enough for capturing full dynamics.
6. Figure 3S.2cd shows the calibration curves. The calibrated µTMs shared the same sensitivity
(S ), but different offset (∆V 2out/∆Vin)os. The highly linear correlation (R > 0.99) with the
osmotic water potential (Ψurea) within the general range of plant water potential Ψstem(> −3.0
MPa),17,33 demonstrated the consistency across µTMs for generating reliable measurements.
The variations in µTM offset ((∆Vout/∆Vin)os) likely resulted from the non-uniformity of
poly-silicon deposition using furnace processing that was unavoidable.
102
Figure 3S.2: Osmotic Calibration of Micro-Tensiometer. a. Time course of four µTMs responding to
five urea solutions with potentials of -5.8 MPa, -4.2 MPa, -2.1 MPa, -1.4 MPa and -0.8 MPa from more
concentrated to less concentrated. The µTMs were submerged in each solution for 2 hours. The y-axis
shows the normalized voltage output (∆Vout/∆Vin) from the µTMs. b. Expanded view of the responses of
the µTMs from -5.8 MPa to -4.2 MPa solutions. The averaged time scale is τ ∼1 min. c. The calibration
curves of µTMs against urea solutions. d. Table of calibration parameters for the four sensors.
103
3.5.4 Temperature Calibration
The temperature calibration steps were also described in detail in our previous publica-
tion.108 Briefly, the PRTs of the µTMs were calibrated against a commercial PRT (Model: HSRTD,
OMEGA Engineering, Inc.). The steps were:
1. The packaged µTMs and the commercial thermometer were fully submerged into a temper-
ature controlled water bath (NESLAB RTE-740, Thermo Fisher Scientific).
2. The water bath was set to run at 15◦C, 20◦C, 25◦C, 30◦C, and 30◦C with 150 min intervals
to achieve a thermal equilibrium between the µTMs and the water bath. Figure 3S.3a shows
the PRTs during a full cycle of calibration. The resistance of PRTs and the temperature from
the commercial RTD were measured using the CR6 datalogger (Campbell Scientific). The
data were acquired every 10 seconds. The water bath was controlled using LabVIEW.
3. To ensure consistency, the response from PRTs and the commercial RTD were averaged for
each set temperature by taking 200 data points starting 75 min after the change of temperature
setting. The 75 min is the half-time of each time interval.
4. Figure 3S.3bc show the linear regression performed on the temperature calibration data, and
the corresponding results of calibration. The PRTs show consistent sensitivity to temperature
(S T ), and small differences in offset (PRTos). The R2 →− 1 values show the highly linear
correspondence of the PRTs with the temperature.
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Figure 3S.3: Temperature Calibration of Micro-Tensiometers. a. The PRT resistances of four µTMs
were calibrated against a reference thermometer. The set temperatures were 15 ◦C, 20 ◦C, 25 ◦C, and 30
◦C. b. PRT output from four µTMs are averaged and plotted against reference thermometer’s averaged
measurements. c. Results from linear regression analysis on the correlations shown in b.
105
3.5.5 Embedding
The µTMs were directly embedded into the active xylem region of apple, almond, and
grapevine (Figure 3S.4). Figure 3.2 shows results from µTMs that were radially embedded with
depths of 5mm, 3 mm, 5 mm from the cambium for apple, grapevine, and almond respectively.
This section presents the embedding process in apple. The µTMs in almond and the grapevine
were embedded following a similar procedure.
1. 6.4 mm (1/4") diameter Smooth Finish Drill Bits (McMaster-Carr, Part No.3216A19) were
first used to drill a shallow guide hole which is 3 mm-deep radially into the bark. The hole
was then sprayed with DI water to kill and remove the damaged tissue cells and slow down
the wound response after embedding.
2. A 7.9-mm (5/16") diameter 4-flute End Mill (McMaster-Carr, Part No.3056A64) was then
used to obtain a flat bottom for better contact with the sensing edge of the µTM. The sensing
edge was the cut-edge where the poSi at the interface between the glass and silicon was
exposed to the external environment. This exposed edge was a 800 µ-wide m × 5 mm-long
surface.
3. The wobble of drill bits led to larger holes than the size of the bits themselves. Therefore,
7.9-mm bits were applied for 8-mm diameter µTMs. Drill collars were applied to stabilize
the drill bits, as well as to prevent drilling deeper than desired (10–15 mm).
4. Active xylem is usually located at a depth of 5-20 mm from the outside surface of the tissue
after removing the bark.96 Therefore, the bottom of the drilled hole should had a radial
distance of 10–15 mm from the outside surface either from the drill side of the tree, or
the opposite side of the tree when trees were small. We tried multiple embedding depth to
demonstrate that the outer layer of xylem was more stressed and had higher water transport
rate than the inner layer of the xylem.
5. Besides the active xylem region, the length of a packaged µTM was measured before each
embedding to ensure complete embedding. Complete embedding is important to maintain
106
thermal equilibrium, by reducing the disturbance from varying outside temperature. Figure
3.2c shows the length of packaged µTMs had a range of 12–15 mm, and was within the
requirement of active xylem region.
6. The drilled holes (Figure 3S.4i) were moisturized and cleaned with DI water before µTM
embedding. DI water was used to remove the damaged tissue cells to reduce the wound
response after drilling. After the alumina paste was applied at the sensing edge of the µTMs,
the µTMs were then gently pushed against the bottom of the holes.
7. Aluminum Oxide (alumina) paste (< 50 nm nanopowder, Sigma-Aldrich) was used to im-
prove thermal and liquid contact between xylem and the µTM (Figure 3S.4ii). Alumina has
a high thermcal conductivity (30 W · m−1 · K−1) among oxide-based engineering ceramics
(ASTM D2442), and facilitates the thermal equilibrium between the µTM and the xylem.
Alumina paste comprising < 50 nm nanoparticles was mixed with DI water, and applied at
the interface for all µTMs to facilitate the liquid contact between the poS i and the active
xylem.
8. Figure 3S.4iii shows that Plumber’s putty (McMaster-Carr Part No.3008K11) was used to
mechanically stabilize and seal the µTMs inside the tree hole to slow down the wound re-
sponse and moisture loss from the damaged tissue by enhancing the transport resistance of air
and water vapor. The Parafilm (Bemis Company, Inc.) was wrapped around the plumber’s
putty to stabilize the µTMs around the trunk, and to function as an additional waterproof
layer.
9. Figure 3S.4iv shows that plastic films (ULINE) were applied first around the trunk as mois-
ture insulation against precipitation. Wrap foam and bubble foam (Figure 3S.4v) were ap-
plied layer by layer to provide thermal insulation to the outside complex environment. Elastic
bands were used in-between insulation layers to reinforce the contact between the µTM and
the xylem, while gently protecting the µTM from mechanical damage. A dense foam box
was used as final layer of thermal insulation (Figure 3S.4vi). Aluminum foil was used to
provide reflective insulation to prevent the heating up of sensor under direct sunlight.
107
Figure 3S.4: Embedding Procedure of the Micro-Tensiometer to an Apple Tree.
108
Figure 3S.5: Multiple Micro-Tensiometer at Different Embedding Depth. a. The cross-sectional di-
agram for µTM embedding. b. The extracted data from Figure 3S.5a for µTMs at different embedding
depths:P75, P88, P74, P86, and P96. The values after the µTM labels are the corresponding "r" value. The
ΨS PC is shown as reference. c. The midday Ψstem data from multiple µTMs plotted against the relative
position of embedding (r)
109
Micro-tensiometer offset drift after embedding.
Multiple µTMs were embedded for the apple tree experiment in 2017 to validate the repro-
ducibility of embedding in woody species. Figure 3S.5 shows results from 9 µTMs embedded
into three neighbor apple trees with the same cultivar,training and pruning methods, and growing
conditions. Multiple working µTMs recorded similar dynamics, especially P75, P88 and P83, who
were embedded at similar radial depth.
However, not all µTMs work as long as 2 months, except P75 and P88. The robustness of
µTMs after embedding need to be improved further. We noticed the offset drift in µTMs after
embedding especially the first few days after embedding. The embedding process could have
caused drift in the µTM output due to the mechanical stress from the confined hole and the external
force from either an elastic band or a spring that kept the sensors in contact with the xylem. For
this scenario, we could use the ΨS PC values to define an in-situ calibration curve. Another reason
could be that the moisture insulation may not be perfect. When the environment is stressed during
the day, there could be a small water potential gradient from the xylem to the µTM.
Correction of offset drift
The sensitivity of the µTM (change of voltage vs. change of water potential) we use were
those established by laboratory calibrations (Sections 3.5.3 and 3.5.4); in the case of apple (Figure
3.2a), the voltage offset was shifted based on predawn SPC measurements to correct for a constant
drift due to mechanical stress, or osmotic contamination.
Embedding at different radial depth
We also observed that deeper embedding resulted in higher stem water potential. Figure
3S.6a shows a diagram eclucidating the radial depth of embedding in the stem:
R − Depth
r = (S3.1)
R
110
where R[mm] is the total radius of the embedded trunk; Depth [mm] is the drilled depth; r is a
dimensionless number with its value indicating the relative position of the µTM to the center of the
heartwood.
Multiple µTM measurements from Oct. 5th to Oct. 8th of Figure 3S.5 were extracted and
zoomed in Figure 3S.6b. P75 and P88 were embedded the most shallow. P74 was embedded
deeper into the xylem, and was probably hitting the non-active xylem region.96 P96 was embedded
through the heartwood to the other side of the xylem. P86 was at the center. The deeper embedded
µTMs were showing a delayed midday Ψstem that had a less negative value. The midday values
of µTMs at different embedding depths from the shown three days in Figure 3S.6b were extracted
and plotted as a function of the dimensionless r in Figure 3S.6c. The midday Ψstem showed an
exponential decay with shallower embedding depth, and indicating the outer layer of xylem as
active xylem region.96
Discussion on outliers in Linear Regression between Micro-tensiometer and the Schölander
Pressure Chamber
The outliers in Figure 3.2d can be explained with daily dynamics shown in Figure 3S.7. In
Figure 3S.7, Sep.10 &11 show midday ΨµT M higher than the SPC values. The disagreement was
smaller on Oct.1 & 5. This improved correlation with the SPC possibly indicates the improved
contact with the xylem tissue as time proceeded after embedding due to the limited wound re-
sponse. Oct. 5 shows morning ΨµT M higher than the SPC values. We observed fog happened in
the morning reflected in decreased VPD and fluctuations in shortwave radiation for about 1 hour.
This phenomenon could generate a complex local thermodynamic disequilibrium when the soil,
plant, and atmosphere have different response time scale to the transitions of evaporative demand
with the sunrise-fog-sunrise phenomenon, and result in mismatch between the µTM and the SPC
(Figure 3.2d and Figure 3S.7).
111
Figure 3S.6: Stem Water Potential Changes with Deeper Embedding Depth. a. Cross-sectional diagram
showing the embedding of µTM with dimensionless r = (R − Depth)/R indicating the relative position to
the center of the trunk. R is the radius of trunk. Depth is the embedding depth. b. Expanded view of µTMs
at multiple embedding depth and ΨS PC (blue dots) during Oct.5–8, 2017. The µTMs are: P75 (blue line) at
r = 0.7; P88 (r = 0.8; orange line); P74 (r = 0.2; yellow line); P86 (r = 0; purple line); P96 (r = 0.4; green
line) embedded through the center to the other side of the trunk. c. Extracted stem water potential of the
µTMs during midday plotted against r: P75 (blue dots); P88 (orange dots); P74 (yellow dots); P86 (purple
dots); and P96 (green dots)
112
Figure 3S.7: Comparison of Apple Stress Dynamics with Micro-climatic Variables on Selected Days.
ai-avi. The ΨµT M (blue lines) comparing with the ΨS PC (blue dots). bi-bvi. The calculated grass reference
transpiration (red lines). ci-cvi. The windspeed from the Cornell NEWA weather station. di-dvi. The
shortwave radiation (red line) measured with a pyranometer. ei-eii. The calculated vapor pressure deficit
(VPD, blue lines).
113
3.5.6 Plant Materials
The research was conducted on apple trees at Cornell Orchards in Ithaca (New York
State).The apple trees were semi-dwarf on B.9 rootstock with "Ruby Frost" scion. The orchard
rows were north-south oriented. The soil type was Niagara Silt Loam (NaB). The training system
was Tall Spindle. The spacing between rows and between trees was 3.7 m (12 ft.) and 1.2 m (4 ft.)
respectively. The trunk diameter of tested trees was 4—5 cm. The total leaf area measured at the
end of the experiment was about 6 m2. The apple trees were rainfed without human water supply.
The measured grapevine (Cabernet Sauvignon) was located at the education vineyard of the
Robert Mondavi Institute for Wine and Food Science in Davis, CA. The vines were planted in
2010, and trained with "Geneva Double Curtain". The measured grapevine had a diameter of
about 7.6 cm. The spacing was 3.7 m (12 ft.) between rows, and 2.1 m (7 ft.) between trees. Soils
were deep and could store a lot of water (Discussion with Dr. Ken Shackel). No irrigation events
were launched during the experimental period except one fertilization in Spring 2019.
The measured almond tree (Nonpareil) was planted in 2011, had a diameter of 25.4 cm, and
was trained with minimal pruning. The tree was located at the Done Again Farms (Arbuckle, CA)
where they grow three almond varieties: Nonpareil, Sonara, and Aldrich. The rows are separated
by 6.7 m (22 ft.). The spacing within rows were 4.6 m (15 ft.). No precipitation was observed
during the experimental period. Irrigation events were launched using surface micro-sprinklers,
and micro-sprinklers between each tree down the rows (Discussion with John Monroe).
3.5.7 Scholander Pressure Chamber and Micro-climatic Sensors
Datalogging
Data acquisition was done using the Measurement and Control Datalogger (CR6, Campbell
Scientific). A Relay Multiplexer (AM16/32B, Campbell Scientific) was controlled through the
CR6 to operate up to 8 µTMs at the same time. The µTMs were excited and measured every
114
minute for apple trees. The data acquisition frequency was 15 min for grapevine and almond.
The Wheatstone bridge was excited by 500 mV for each measurement. The resistance of PRT was
measured through 200 µA of current excitation. Minimum excitation voltage and current were used
to prevent heating up the µTMs while conducting measurements. The output differential voltage
and resistance signals were converted to water potential and temperature by applying calibration
coefficients (FigS:3S.2 & 3S.3). Please refer to Pagay et al. for the theory of operation for the
Wheatstone Bridge.14
Scholander Pressure Chamber
A Schölander pressure chamber (Soilmoisture Equipment Corp.) was used as a benchmark
for stem water potential measurements. For each measurement, a leaf was covered with plastic bags
coated with aluminum foil for at least 10 min before the leaf was cut from the trees. After a leaf was
cut, it was inserted into the specimen holder with the petiole protruding out. After the specimen
was sealed on the gas chamber, the gas flew into the chamber at a controlled rate. The pressure was
then raised until the xylem at the cut surface darkened from a light yellow color to grey and soon
started bubbling. The chamber pressure at this moment was taken as the compensating pressure of
the stem water potential; the stem water potential recorded was the negative of this compensating
pressure.
Leaf Area Meter
LI-3100 Leaf Area Meter Manufactured by LI-COR was used to measure the number of
leaves of tested apple tree at the end of the experiment. All leaves were stripped down from the
apple tree. About 1/6 of total fresh leaves were measured as a sample using LI-3100. Leaves
were dried in 70 °C oven for about 48 hours. The total leaf-area was then calculated based on the
measured sample to the total leaf weight fraction and the sampled leaf area.
115
Figure 3S.8: Comparison Almond ΨµT M ΨS PC , and the Ψbase on Selected Days. Blue line represents the
ΨµT M. Blue dots represents ΨS PC . Blue dashed lines represent Ψbase.
116
Micro-meteorological Sensors
Meteorological sensors were used to record the micro-climatic environment around the mon-
itored apple trees. Meteorological data for grapevine and almond were collected from local weather
stations discussed in detail below. The method of calculating transpiration for all three species us-
ing the meteorological data were shown in Section 3.5.7.
A pyranometer (LI-200R, LI-COR Biosciences) was used to measure the shortwave radia-
tion (W/m2) for the apple tree at Cornell Orchards. A humidity and temperature probe (HMP60,
Vaisala) was used for monitoring the humidity and temperature around the trees. The measured
humidity and temperature were then used to calculate the vapor pressure deficit (VPD). The self-
maintained weather station (LI-200R and HMP60) was positioned 4 meters above ground (1 m
above canopy), for field apple trees. The windspeed and precipitation data for apple trees were
obtained from the weather station operated by Cornell NEWA.59 The full data set was shown in
Figure 3S.9.
The meteorological data (shortwave radiation, precipitation, humidity, temperature, and
windspeed) for the grapevine were obtained from the No.6 weather station operated by CIMIS
in Davis, CA. (https://cimis.water.ca.gov/). The full data set was shown in Figure 3S.10.
The meteorological data (radiation, irrigation, soil water contents, humidity, temperature,
and windspeed) for the almond trees were provided by John Monroe, the owner of the Done Again
Farms in Arbuckle, CA. The irrigation events were quantified using pump pressure (psi). The full
data set was shown in Figure 3S.11.
Soil Stress at Almond Orchard
We show the dynamics of soil stress in Figure 3S.12. Six soil probes were embedded to
depths of 4in, 12in, 24in, 36in, 48in, and 60in, and were programmed to collected the water content
data (θ) every 15 min, same as the µTM (Figure 3S.12a). Change of water content per one hour
117
(area plot in Figure 3S.12b-d) are taken for each probe to elucidate the sensitivity of water content
to irrigation events at different depths. The soil moisture probes show decreasing sensitivity to
irrigation events as embedding depth deepens. Shallow probes (i.e. 4in and 12in) show largest
sensitivity to irrigation events. We note that the probes show diurnal variations that are inserted
relative to those observed in the stem: the apparent water content drops during the night and
recovers during the day. We suspect that this response may be due to a temperature effect. Deep
probes (i.e. 36in, 48in, and 60in) showed gradual depletion at descending rates. The 24in probe
(yellow) that was at an intermediate depth showed early depletion, but maintained its stress level
later. The six soil sensors show complicated water balance for each soil layer, but none of the soil
probes captured the dynamics of the drought stress of the almond tree. This observation highlights
the importance of tools like the µTM to assess in-plant stress directly.
Baseline Water Potential
The concept of baseline Ψstem has been proposed for almond, grapevine, and many other
species to predict the stem water potential under non-soil stressed conditions. When the woody
plants were under "wet" conditions, the Ψstem was observed to decrease linearly with the increase
of VPD [kPa]. The empirical model of the baseline water potential (Ψbase) for multiple woody
species takes the following form:66,67,118
Ψbase[MPa] = −0.12 · VPD[kPa] − 0.41 (S3.2)
The Ψbase was calculated for almond and shown in Figure 3S.11.
Grass Reference ET
We used grass reference transpiration, ET0 to quantify the environmental demand of transpi-
ration. The grass reference ET0 was calculated using the Penman-Monteith equation with param-
eterization based on FAO-56.123
118
Figure 3S.9: Apple: Meteorological Variables, µTM, and Schölander pressure chamber. a. The left
y-axis shows the precipitation in blue lines, while the right y-axis shows the windspeed in yellow line. b.
The shortwave radiation in red line. c. VPD in blue line. d. Grass-reference transpiration in red line. e.
Stem water potential measured by the micro-tensiometer ΨµT M in blue line, and by the Schölander pressure
chamber ΨS PC in purple dots.
119
Figure 3S.10: Grapevine: Meteorological Variables, µTM, and SPC. a. The left-y axis shows precipita-
tion events in blue. The right-y axis shows windspeed in yellow. b. Shortwave radiation in red. c. VPD in
blue. d. Grass reference ET0 in red. e. ΨµT M in blue line and ΨµT M in purple dots.
120
Figure 3S.11: Almond: Meteorological Variables, Micro-Tensiometer and Schölander Pressure
Chamber, and Baseline Prediction. a. The left-y axis shows the irrigation events represented by pump
pressure in blue. The right-y axis shows the windspeed in yellow. b. The shortwave radiation in red line. c.
The VPD in blue line. d. The grass reference ET0 in red. e. The solid blue line represents the ΨS PC . The
dashed blue line represents the baseline water potential Ψbase, based on the formulation by McCutchan et
al.66 The purple dots are the Schölander pressure chamber measurements.
121
Figure 3S.12: Almond: Soil Water Contents. a. Water content measured with soil probes embedded at
6 depths (4 in, 12 in, 24 in, 36 in, 48 in, and 60 in) shown as line-plots with different colors on the left-y
axis. The right-y axis shows the irrigation events represented by irrigation pump pressure in blue bar plots.
b. the rate of change in water contents with 6 hour interval at depths of 4 in and 12 in. c. the rate of change
at depths of 24 in and 36 in. d. the rate of change at depths of 48 in. and 60 in.
122
The FAO-56 proposed grass reference takes the following format:123
S · (R ρaCp·VPD1 n −G) +
ET ra= (S3.3)
λ S + γ(1 + rsr )a
Where λ = 2.2×106[J·kg−1] is the latent heat of vaporization; S [kPa·◦C−1] is the slope of saturation
vapor pressure with respect to temperature; Rn [W · m−2] represents the net radiation at the crop
surface; G[W ·m−2] is the conductive heat loss to the soil; ρa[kg·m−3] = Patm/(287.05·Tair,K)[kg·m−3]
is the dry air density; Cp [J · kg−1 · C−1] = γλ/Patm = 1.01 × 103 [J kg−1] is heat capacity of dry
air; r [s ·m−1a ] is the aerodynamic resistance; rs [s ·m−1] is the stomatal resistance; γ [kPa · ◦C−1]is
the psychrometric constant representing the partial pressure change in water vapor in air per unit
change in air temperature (K or ◦C);  = 0.622 ratio of molecular weight of water vapor to dry
air; R = 287 [J · kg−1 · K−1] is the ideal gas constant; VPD = psat · (100% − RH) [kPa] is
the vapor pressure deficit, RH is relative humidity, psat is the saturated vapor pressure. We used
Rn − G = 0.5 · Qrad based on the FAO-56,123 where Qrad [W · m−2] is the shortwave radiation
measured by the pyranometers.
Parameterization of Grass-Reference ET
Aerodynamic Resistance
Aerodynamic resistance ra represents the heat and vapor transfer resistance from the grass
canopy to air.
ln( zm−d ) · ln( zh−dz )r 0m zoha = k2 (S3.4)Uz
Where zm = 2 [m] height of wind measurements; zh = 2 [m] height of humidity measurements; d =
2/3h [m] zero plane displacement height; zom = 0.123h [m] roughness length governing momentum
transfer; zoh = 0.1zom [m] roughness length governing transfer of heat and vapor; k = 0.41 van
123
Karman’s constant; Uz [m · s−1] windspeed at height zm or zh; h = 0.12 [m] is the crop height taken
from the FAO-56 for ET0 calculations in grapevine and almond123 . This equation is restricted for
neutral stability conditions, where temperature, atmospheric pressure, and wind speed distributions
follow nearly adiabatic conditions. Stability correction is needed for short time periods(hourly or
less), unless the predicted surface is well-watered; the self-maintained weather station was used for
micro-climatic monitoring in the apple tree scenario. The humidity, temperature, and shortwave
radiation data were acquired at 4 m above ground. The approach for aerodynamics calculations by
Dragoni et al. in reference was applied to the potential ET0 calculation in apple trees.124
The final expression of the aerodynamic resistance takes the following form, and applied for
the estimation of almond and grapevine transpiration:
208
ra = (S3.5)Uz
Stomatal Resistance
The stomatal resistance rs is the "bulk" surface resistance representing the resistance of water
vapor transfer from the transpiring crop to the atmosphere.
r
r ls = (S3.6)LAIactive
Where r [s · m−1] = 100 bulk stomatal resistance of the well-illuminated leaf; LAI [m2l active ·
m−2] = 0.5LAI sunlit leaf area index, meaning only the upper half of dense clipped grass is actively
contributing to the surface heat and vapor transfer; LAI = 24 h general equation for LAI; The final
form of stomatal resistance is shown below:
100
r = −1s 0.5 · 24 · = 70 s · m (S3.7)0.12
124
Combining equations S3.4–S3.7 in to eq.S3.3, we have:
0.408 S R 900γVPD Uzn +
ET Tair+273= (S3.8)
S + γ(1 + 0.34Uz)
3.5.8 Nighttime Rehydration Curve Fitting
We analyzed the transient time scale of Ψstem in response to environmental signals by esti-
mating its rehydration time scale after sunset. We fit to the following exponential function:
( x)
y = a · exp − + c (S3.9)
b
where "a = Ψstem − Ψsdstem" is the prefactor of the exponential fit; "b" is the τrd as time scale of
the rehydration; "c" is the maximum achievable water potential, Ψsoil,lim, if the plant keeps getting
rehydrated without transpiration. The results of curve fittings for the apple and almond during
their corresponding full experimental periods where shown in Figure 3S.13ab, with selected values
shown in Figure 3.3a-ii and Figure 3.3b. The further analysis on τrd vs.Ψsoil,lim was performed and
shown in Figure 3.4b.
125
Figure 3S.13: Apple and Almond: Nighttime Rehydration Curve Fitting. a. The curve fittings are
shown in short solid black lines on the left-y axis. The ΨµT M in blue lines, the ΨS PC in blue dots. The
bar-plot of precipitation events is plotted on the right y-axis. b. The curve fittings are shown in short solid
black lines on the left-y axis. The ΨS PC is plotted on the left-y axis. The irrigation events represented by
irrigation pump pressures are shown as bar plots on the right-y axis.
126
3.5.9 Resistance and Capacitance Analysis
As presented in Figure 3.3a-b, the response of apple to transpiration in wet environment is
mainly resistive, whereas in the response of almond under dry conditions is more complex.
The resistive response to transpiration is simulated using simple circuit models proposed
Figure 3S.15. We took values of hydraulic resistance and capacitance from the literature77 with
minor adjustments to achieve a good agreement with the µTM. Figure 3S.15a-i shows the circuit
model with only one resistor (Rsp), and the simulated results are shown in Figure 3S.15a-ii. One
capacitor is added in Figure 3S.15bi, and the simulated results are shown in Figure 3S.15bii. Both
model captured the observed dynamics in micro-tensiometer, and confirms our discussion under
Figure 3.4 that apple in wet environment show resistive response to environmental demand.
Analysis of the relaxation of the simplest two-compartment model (i.e., nighttime relaxation
of almond).
Here, we propose the possibility of using a two-compartment circuit model to elucidate the
dynamic water stress of almond (Figure 3S.14). This additional soil compartment is inspired by
the exponential trend of nighttime rehydration.
The implicit assumption of steady state in the definition of Rsp = ∆Ψdstem/ET0 neglects the
transient nature of almond’s response to both diurnal forcing and irrigation (Figure 3.3b). The
neglect of stomatal regulation as a function of stress in the evaluation of ET0 likely leads to an
overestimate of its value at the lowest water potentials (Ψstem < −2 MPa on Ψcrit in almond). In
Figure 3.4d, this assumption may mean that the values and variations of Rsp are underestimated.
dΨ2 −Ψ2 − ΨC 12 = − ET (S3.10)dt R
127
dΨ
C 1
Ψ2 − Ψ1
1 = (S3.11)dt R
Initial conditions: Ψ2(0) = Ψ02, and Ψ1(0) = Ψ
0
1. Assuming no driving force: ET = 0.
The solutions are:
C
Ψ1(t) = A
2
0 − B0eS t (S3.12)C1
C2 Ψ0+Ψ0 0 0
where A C1 2 1 , B Ψ −Ψ= = 2 1 , and S = − 1 ( 1 + 10 1 C2 0+ 1 C+ 2 R C C ).1 2C1 C1
Two capacitors connected by a single resistor relax with single time constant:
1 1 1
τ2C = ( + ) (S3.13)R C1 C2
The time-scale is donominated by smaller capacitance:
lim = C1 (S3.14)
C1
C →02
We can then recover one compartment’s behavior as C1C →− 0:2
S →− 1
RC1
B0→− (Ψ02 − Ψ0
C
1)
1
C2
C
A 1 0 0 00→− ΨC 1 + Ψ2→− Ψ22
The water potentials then have the following expressions:
t
lim Ψ (t) = Ψ0 − (Ψ0 − Ψ0)e1− RC1 2 2 1 1 (S3.15)C1
C→− 02
lim Ψ (t) = Ψ0
t
2 2 −
C1 (Ψ0 − Ψ0)e1− RC 01 →− Ψ (Constant) (S3.16)
C1→− 0 C 2 1 2C 22
128
Figure 3S.14: Resistance Capacitance Analysis. a. Two compartment RC-circuit model with ET = 0.
b. One compartment RC-circuit model representing the nighttime transient of the plants for rehydration.
c. One compartment RC-circuit model representing the transient of the micro-tensiometer when facing
environmental changes.
129
Figure 3S.15: Apple: Simulated Stem Water Potential vs. Micro-Tensiometer Measurements. ai. The
model that only contains one resistor Rsp and driven by the grass reference ET0. aii. The blue line shows
the simulated results from the model in (ai). The red line represents ΨµT M. bi. The model that contains
both the resistor Rsp and one capacitor Csp driven by the grass reference ET0. bii. The blue line shows the
simulated results with the model in (bi). The red line represents the ΨµT M
130
When R1C1 >> R2C2, and R2C2 << 24 hrs, Ψ2 should relax back to ∼ Ψ1 each night and
follow the predawn trend of Ψ1. The predawn dynamics are then governed by the soil compartment
(Figure 3S.15b).
Analysis on the response dynamics of µTM
If the environmental wafer potential, Ψenv, follows a trigonometric function:
Ψ = Ψ0env envsin(ωt) (S3.17)
Considering the resistance of water transport from inside of the device to the xylem, and the
small volume internal storage, we propose a simple RC circuit model:
dΨ
C µT M − 1 1µ = Ψdt R C µT M + Ψenv(t) (S3.18)µ µ RµCµ
The homogeneous solution is
Ψh (t) = Ψ0 −
t
RµCµ
µT M µT Me (S3.19)
To get the particular solution, we assume:
p
ΨµT M(t) = Acos(ωt + φ) (S3.20)
where φ is a phase lag. We then take a time derivative,
d pΨµT M
= −Aωsin(ωt + φ) (S3.21)
dt
Substituting eq.S3.21 in eq.S3.19, we have
1 Ψ0−Aωsin(ωt env+ φ) + Acos(ωt + φ) = cos(ωt) (S3.22)
RµCµ RµCµ
131
Simplify the left hand side. We get:
− A A Ψ
0
sin(ωt)[Aωcos(φ) + sin(φ)] + cos(wt)[−Aωsin(φ) + cos(φ)] env= cos(ωt) (S3.23)
RµCµ RµCµ RµCµ
At t = 0 and using the initial condition in eq.S3.24, we have:
A
Aωcos(φ) + sin(φ) = 0 (S3.24)
RµCµ
then:
φ = arctan(−ωRµCµ) (S3.25)
ForωRµCµ << 1, φ→− 0, the µTM should achieve high fidelity measurement of the dynamics.
Restating this condition, we have:
1
RµCµ = τµ << (S3.26)
ω
For sunlight driven environmental signal shows f [hr−1] = 124 . ω = 2π f ∼ 0.3 rad/hr. Our osmotic
calibration method shows RµCµ < 5min(∼ 0.08hrs), and 1/RµCµ = 12, such that ωRC = 0.025 ' 0
Since ωRµCµ ∼ 0.025→− 0, φ = arctan(−ωRµCµ) ∼ −ωRµCµ, cos(φ) ∼ 1, sin(φ) ∼ φ such
that we have:
− A Ψ
0
Aωsin(φ) + cos(φ) env= (S3.27)
RµCµ RµCµ
Ψ0
A env= (S3.28)
cos(φ) − ωRµCµsin(φ)
The general solution for the response dynamics of the µTM is then
0 − t Ψ
0
e R C envΨµT M = Ψ µ µµT M + cos(ωt + φ) (S3.29)cos(φ) − ωRµCµsin(φ)
For ωRC << 1,
A 1
0 = ' 1 − (ωRµCµ)
2 ' 1 (S3.30)
Ψenv 1 + (ωRµCµ)
Therefore, we expect the µTM faithfully follows the local dynamics in the stem.
132
CHAPTER 4
MODELING THE WATER DYNAMICS IN APPLE TREES UNDER WELL-WATERED
AND WATER-STRESSED CONDITIONS
4.1 Introduction
Global warming increases the frequency and intensity of environmental extremes in heat and
precipitation, and reduces the availability of fresh water resources,125,126 while human population
is anticipated to reach ∼ 9.7 billion by 2050.127 The growing human population demands more
calories with increasing constraints on fresh water resources. Irrigated agriculture accounts for
over 70% of total water withdrawals by humans.128–131 Understanding the water relations of plants
is crucial for improving the agricultural water use efficiency.12
Plant water stress defines the growth, yield, quality, and susceptibility of trees and crops to
diseases.30,132–135 Stem water potential provides an integrative measure of whole plant water sta-
tus.17,65,67 Accurately predicting the stem water potential is important for increasing the efficiency
of agricultural water management.5,12
Hydraulic circuit models with multiple layers of plant or soil compartments have been em-
ployed for many decades to predict the plant water stress.136–139 However, the equipment used as
experimental validation has lacked the capability of measuring the real time dynamics, or has cap-
tured dynamics with low accuracy or indirectly.80 The micro-tensiometer recently developed by
our lab provides a new method to refine models by providing in-situ accurate dynamical measure-
ments.
In chapter 3, we reported the dynamics of stem water potential using a micro-tensiometer
(µTM) and demonstrated its accuracy. We previewed the possibility of using simple circuit mod-
els to explain the observed responses of stem water potential (Ψstem) to changing environmental
conditions.
133
In this Chapter, we continue our study of simple circuit-based mechanistic models based on
experiments on apple trees under both well-watered and water-stressed conditions. We explore
simple models for apple drought stress prediction by taking advantage of the accurate and con-
tinuous data from the micro-tensiometer (µTM). We compare the relative importance of stomatal
conductance and boundary layer resistance. We emphasize the importance of rhizosphere and
soil hydraulic properties as dry-down proceeds. We demonstrate the opportunities for the use of
micro-tensiometers to refine mechanistic models and explore fundamental questions in plant water
relations.
4.2 Formulation of Circuit Models
Figure 4.1a shows a simple diagram representing the water movement in plants. Transpira-
tion (ET [kg s−1]) is the water flow from the soil through the plants to the atmosphere, driven by
the solar radiation (Q [W m−2rad ]) and the vapor pressure deficit (VPD) of air, and regulated by the
stomatal conductance (gs [m s−1]) and boundary layer resistance (ra(vw) [s m−1]) where vw is the
windspeed. VPD is determined by the relative humidity of air (RH%) and temperature (T [◦C]):
VPD = psat(T )(100% − RH%)/100% [kPa], where psat(T ) [kPa] is saturated vapor pressure of
water at temperature, T [◦C]. Figure 4.1b represents that plants control the rate of water transport
from inside of leaf to the outside atmosphere through stomatal regulation. Stomatal conductance
(gs) is important for determining the ET. Figure 4.1c shows the diagram of root water uptake from
the soil across the roots membrane, and to the root xylem.
Water movement along the soil-plant-atmosphere continuum (SPAC) can be represented us-
ing circuit models with transpiration (ET) as the current source.140 Soil rehydration (I [kg s−1])
happens through precipitation or irrigation. Figure 4.2 shows the schematic diagrams of one com-
partment (1C) model and two compartment (2C) model for well-watered and stressed conditions
respectively.
134
Figure 4.1: Schematic Diagram of Plant Water Relations. a. Diagram showing the water movement
along the soil-plant-atmosphere continuum (SPAC). A micro-tensiometer (µTM) is embedded in the stem
below the canopy to measure the stem water potential. b. Diagram showing the transport of water from leaf
xylem through stomata to the atmosphere. c. Diagram showing the water movement from the soil, across
the root membrane, to the root xylem following the decreasing of water potential. rroot−soil represents the
radial position with respect to the center of the root.
135
Hydraulic capacitance terms (Ct or Cs, kg MPa−1) represent the water storage capacity of
crucial compartments. Here, Ct represents the stem hydraulic capacitance, and Cs is soil hydraulic
capacitance. Hydraulic resistance terms represent the resistances along the soil-plant-atmosphere
continuum. Here, we consider plant (Rt, MPa s kg−1), root-rhizosphere (R , MPa s kg−1r ), and soil
(Rs, MPaskg−1) components. The rhizosphere is the soil zone that is in close contact with the roots,
and accounts for the resistance to water movement from the bulk soil to the root. Soil hydraulic
resistance and capacitance are both non-linear functions of soil water potential (Ψsoil, MPa). Soil
depletion during dry-down with decreasing soil water potential can lead to a significant increase in
soil hydraulic resistance and to non-monotonic variation in soil hydraulic capacitance.
4.2.1 One-compartment circuit model for well-watered conditions
For well-watered conditions, we treat the entire SPAC as being a single compartment. Figure
4.2a shows the one-compartment (1C) model for simulating the dynamic stem water potential
(Ψstem) under well-watered scenarios. For a well-watered case, with nearly saturated soil, we
assume this compartment represents the plant tissue and associate the resistance and capacitance
with the stem (Rt and Ct in Figure 4.2) The non-steady-state governing equation takes the following
form:
dΨstem Ψsoil − ΨC stemt = − ET (4.1)dt Rt
where Ct is the trunk hydraulic capacitance, Rt is the hydraulic resistance along the water move-
ment pathway, and Ψsoil is the fixed soil water potential.
We estimate transpiration (ET) using the Penman-Monteith equation with parameterization
for apple trees71,72,124 (see the transpiration section below).
136
Figure 4.2: One Compartment and Two Compartment Circuit Models. a. One compartment model with
one trunk capacitor and one trunk resistor for simulating the dynamic water stress of well-watered apple tree.
b. Two compartment model with an additional resistor and capacitor represent the soil for simulating the
water-stressed apple tree. This model is the same as the water relations described in Figure 4.2b.
137
4.2.2 Two-Compartment Circuit Model for Drought Stressed Conditions
Plants experience drought either through intense evaporative demand or through depletion
of the soil. To understand the dynamic water stress of plants when the soil is dehydrated, we use
a two-compartment model to capture changes in the state and constitutive properties of the soil.
Figure 4.2b shows the schematic diagram of the two-compartment circuit model. The two coupled
mass balances in terms of the stem water potential (Ψstem) and the soil water potential (Ψsoil) under
non-steady-state are:
dΨ
C stem
Ψsoil − Ψstem
t = − ET (4.2)dt Rt + Rr + Rs
dΨ
C soil −Ψsoil − Ψstems = + I (4.3)dt Rt + Rr + Rs
The parameterization of transpiration (ET), hydraulic resistances (Rt, Rr, and Rs), and hy-
draulic capacitances (Ct, and Cs) is discussed in detail below.
4.2.3 Transpiration
Transpiration (ET) includes the contributions of sunlit leaves and shaded leaves, with an
apple tree based parameterization by Dragoni and Lakso124 and on previous studies of Penman-
Monteith ET and stomatal conductance.71,72,78,141,142 We take the sunlit proportion of the canopy,
f = 40%. Shaded leaves are assumed to receive 10% as much net radiation as the sunlit leaves:124L
ET = ET L + ET S (4.4)
where the sunlit (ET L [kg s−1]) and shaded (ET S [kg s−1]) transpiration take the following forms:
S · R ρC+ pn VPD
ET L = fL · Alea f ·
1 ra (4.5)
λ S + γ(2 + 1g )s·ra
138
1 S · 0
ρC
.1Rn + pr VPDET S a= (1 − fL) · Alea f (4.6)
λ S + γ(2 + 1g )s·ra
where ρ [kg m−3] is the density of dry air, and A 2lea f [m ] is the total leaf area. Parameters in the
above equations are listed and described in Tables 4.1 and 4.2.
4.2.4 Stomatal Conductance
Stomata open in response to sunlight to allow for gas exchange between inside of the leaf
to the outside atmosphere. We use empirical models and parameters for stomatal conductance
from Dragoni,124 Thorpe,141 and Jarvis.78 Dragoni124 and Thorpe141 represent well-watered stom-
atal conductance for field and potted apple, respectively. Jarvis took into account the response of
stomata to plant water potential;78 we adopt this dependence for modeling the drought stressed
conditions. The parameters and their values are provided in Table 4.1.
The stomatal conductance decreases with increasing VPD based on previous empirical stud-
ies. Both Dragoni124 and Thorpe141 use the following form with different values for parameters, αg
and βg, for field and potted scenarios:
gs = gmax(1 − αg · VPD)(1 − β /Q )−1g PAR (4.7)
where gmax [m s−1] represents the stomatal conductance at maximum opening, αg [ kPa−1] is the
parameter that determines the significance of vapor pressure deficit (VPD), β [µmol m−2 s−1g ] de-
termines QPAR [µmol m−2 s−1]; and QPAR is the photosynthetically active radiation.
Jarvis added an additional factor to account for a hypothesized dependence of gs on plant
water potential:
g = g (1 − α · VPD)(1 − β /Q )−1(1 − e−γg(Ψstem−Ψmin)s max g g PAR ) (4.8)
where Ψmin is the wilting point water potential; γg [kPa · ◦C−1] determines the onset of stem water
potential impacts on stomatal conductance as dehydration proceeds, and is estimated to be 4/Ψmin.
139
140
Field Apple Potted Apple
Pars Literature Values 2017 2018 Units
Model 1C 1C 2C
Stomatal Resistance Parameters
A n/a 6 2 2 m2lea f
Potted Apple::0.010141
gmax Field Apple: 0.00625124 0.00625 0.005 0.005 m s
−1
Potted Apple:0.30141
α −1g Field Apple: 0.17124 0.17 0.3 0.3 kPa
β 124,141g 79 µmol m−2s−1
γg 4078 n/a 3 · | 1 1 −1min( | 3 · |ΨµT M) min( | MPaΨµT M)
Ψ 78min -2.4 n/a min(ΨµT M) min(ΨµT M) MPa
30%
fn 6% ∼ 26%113 30% 30% 12%(Ψt,night < −2MPa)
n/a
Table 4.1: Parameters of Stomatal Conductance.
Based on Jarvis, the stomatal conductance does not have a strong dependence on stem water
potential when not stressed. As stress intensifies, the stomata close in response to plant water
potential to prevent further dehydration from damaging the plants.
Despite the dependence shown on solar radiation, VPD, and Ψstem in the empirical models
of stomatal conductance (Eqns.4.7 and 4.8), the determinants of stomatal regulation are still under
investigation.124 We consider the underlying physiological basis of stomatal response to VPD in
this chapter. We also propose a new model of stomatal conductance to account for its dependence
on both VPD and Ψstem in the Jarvis model (eq. 4.8).
Apart from the VPD factor, both the two stomatal conductance models indicate complete
closure at night. However, some studies imply nighttime transpiration in apple trees, and other
woody species.113,143,144 We will investigate the impact of nighttime stomatal opening on dynamic
water stress in this chapter.
4.2.5 Boundary Layer Resistance
Boundary layer resistance is the resistance to heat and water vapor transfer from leaf surface
to the atmosphere. It depends on the windspeed, surface roughness, and the height.
We adopted the expressions of Dragoni124 and Monteith-Unsworth142 for the aerodynamics
resistance for the field and potted conditions, respectively. The Dragoni’s expression takes the
following form:
ln( zm−dz ) · ln(
zh−d
r 0m z
)
oh
a = 2 (4.9)k vw
Where zm [m] is the height of wind measurements; zh [m] is the height of humidity measurements;
d [m] is zero plane displacement height; zom [m] is the roughness length governing momentum
transfer; zoh [m] is roughness length governing transfer of heat and vapor; k = 0.41 is van Karman’s
constant; v −1w [m · s ] is windspeed at height zm or zh; h [m] is the crop height.123
141
We used a simplified expression from Monteith-Unsworth142 for isolated potted apple trees,
since the surface roughness and displacement length cannot be estimated as is required by Drag-
oni’s method. The expression is:
4.72ln( zm 2
r z
)
0m
a = (4.10)1 + 0.54vw
zm = h [m], the height of measured windspeed, where h[m] is the crop height; and z0m = 0.13h [m]
is the displacement height. The parameters and their values of the above two models are provided
in Table 4.2.
4.2.6 Soil Water Transport
Water moves from the bulk soil to the rhizosphere, and then passes into the roots. The process
of root water uptake is driven by the water potential difference between the roots (lower) and the
soil (higher). The water stress of plants depends on the balance between the supply from irrigation
or precipitation and the loss through transpiration (ET).
The constitutive properties of the soil and rhizosphere are nonlinear functions of soil water
potential (Ψsoil), and can be derived from the soil water retention curve (Θ(Ψsoil), eq. 4.11) below.
The soil water retention curve that represents the nonlinear relationship between the effective
water content (Θ, dimensionless) and the soil water potential (Ψsoil, [MPa]):
Θ = [1 + (α · nΨ s )]−mss soil (4.11)
where Θ takes the following form:
θ − θr
Θ =
θs −
(4.12)
θr
where θ [cm3 cm−3] is the dimensionless volumetric soil water content; θ [cm3r cm−3] is the residual
soil water content when the soil is oven dry; Θ [cm3 cm−3] is the saturated soil water content;
αs [cm−1] is defined as the "bubble point", or the inverse of the air invasion pressure limited by the
largest pore size. This number can be converted to MPa−1 using (1 MPa = 10290 cm H2O). ms &ns
142
Pars Literature Values Field Tree Potted Tree Units
Model 1C 1C 2C
Boundary Layer Resistance Parameters
Potted Apple: √40 141vw
Field Apple: ln( zm−d0m )ln( zh−d0h ) 1 2 1 2
r zm−d0m z z 4.72ln(ln( )ln( zh−d0h ) 0m 0h 0.13 ) 4.72ln( 0.13 ) −1a z0m z0h 124 v k2 1 0 m sw + .54vw 1+0.54vw
vwk2
or 4.72ln(
1 2
0.13 ) 146
1+0.54vw
zm 2 5 n/a n/a m
d0m 2/3h 0.8 n/a n/a m
z0m 0.123h 0.123h n/a n/a m
zh 2 5 n/a n/a m
d0h 2/3h 0.8 n/a n/a m
z0h 0.1z0m 0.1z0m n/a n/a m
k 0.41 0.41 n/a n/a n/a
h 0.12 3 n/a n/a m
Table 4.2: Parameters of Boundary Layer Resistance.
143
are empirical constants affecting the shape of the retention curve. Usually, we use the constraint
ms = 1 − 1/n based on Mualem 1976145s for simpler expressions of soil hydraulic conductivity.
Decreasing of soil water potential beyond the air-entry potential (1/αs, Table 4.4) results in
significant increase in resistance and decrease in soil water content.
Following Gardner, we adopt the following form for the dependenc of the rhizosphere resis-
tance, Rr,sat on wafer content:147
R
R r,sat −1r(Ψsoil) = [MPa s kg ] (4.13)
Θ(Ψsoil)
This expression can be interpreted as a "contact" model: Rr,sat is the resistance of the root mem-
brane, and 1/Θ captures the fraction of the root surface that remains in contact with the liquid in
the soil at water content, Θ.
We treat roots as cylinders, and assume water moves radially from bulk soil (r2, m) to the
root surface (r , m).147,1481 The soil resistance (R , MPa s kg−1s ) takes following form:148
ln(r2/r1)Rs = · (4.14)2π Vsoil · RLD · K(Ψsoil)
where V 3soil [cm ] is the volume of bulk soil, RLD, [cm cm−3] is the root length density, and
K(Ψsoil) [kg m−1s−1MPa−1] is the hydraulic conductivity of soil as a function of Ψsoil. The ex-
pression of K(Ψsoil) is shown in eq.S4.6 in Supporting Information 4.5.2.
The soil capacitance (Cs, [kg MPa−1]), derived from the water retention curve, takes the
following form:
dΘ
C ns ns −ms−1 ns−1s = Cs,sat = Cd s,sat
· (1 − ns) · αs · [1 + (αs · Ψsoil) ] · Ψsoil (4.15)Ψsoil
where Cs,sat is a constant representing soil capacitance under saturated conditions. We provide a
derivation of eq. 4.15 in Supporting Information 4.5.2.
The description and the expected range of the parameters in the above equations (eq. 4.1∼eq.
144
4.15) are shown in Tables.4.1-4.4, together with the values used for the models shown below as
comparison.
4.3 Results and Discussion
In this study, we make use of two sets of data acquired in apple with µTM: 1. Field grown
apple trees on B.9 dwarfing rootstock with "Ruby Frost" scion in Niagara Silty Loam in Ithaca, NY
in the late summer of 2017. This site received consistent rain and represents a well-watered case. 2.
Potted apple trees on M.26 semi-dwarfing rootstock with "Royal Gala" scion in an artificial mixture
comprises 2/3 peat moss and 1/3 sand in Ithaca, NY in the early summer of 2018. These potted
trees allowed control of water stress by withholding irrigation, and represent a water-stressed case.
For both experiments, the micro-tensiometer and the micro-meteorological measurements
were acquired by minutes. Micro-meteorological variables include solar radiation (Qrad, kW m−2),
relative humidity(RH%), temperature(T,◦C), and windspeed (vw, m s−1). Precipitation data were
acquired from the Cornell NEWA (newa.cornell.edu), or through measurements with a digital
scale. The micro-meteorological variables were used for estimating transpiration (ET) shown in
the figures. VPD is calculated from the measured relative humidity and temperature.124 The details
of data acquisition is shown in Supporting Materials.
4.3.1 Evaluation of Circuit Model for Well-Watered Apple Tree
Figure 4.3a presents the dynamics of ΨµT M (a-i, blue curve) together with Ψ1C−stem (a-i, red
curve), the residual between the measured and modelled water potential (a-ii, RES = Ψ1C−stem −
ΨµT M), transpiration(ET, a-iii), windspeed (a-iv), Qrad (a-v), and VPD (a-vi) over a five days period
(Sep.7 to 12, 2017).
Driven by solar radiation, ΨµT M (Figure 4.3a-i) showed the expected diurnal variations: de-
creasing and increasing in water potential with amplitude that follows that of the transpiration
145
(ET, Figure 4.3a-i). ΨµT M returned rapidly to near zero values at night, due to the fast rehydration
process from the soil after sunset.
The Sep.8 in Figure 4.3a presents the dynamics of water potential on a rainy day of 2017
Field Apple Experiment. The increase of cloud coverage (decrease in solar radiation, Qrad, Figure
4.3b) and VPD in the mid-afternoon, reduced environmental demand of transpiration (ET). The
increase in solar radiation after precipitation resulted in short period of increased in ET, as well as
a decrease in measured ΨµT M.
On days with large ET, for example, Sep.10 and Sep.11, the midday ΨµT M shows low water
potential, indicating the enhanced water stress with large evaporative demand. Similarly, when
ET was small, the ΨµT M showed less tension. Both ΨµT M and ET showed smallest quantitative
values on Sep.9 and largest values on Sep.11. This observation indicates the resistive nature of the
responding of stem water potential to transpiration.
To further elucidate this resistive correlation, we extracted the midday values of ΨµT M and the
peak values of transpiration (ETmax) and performed a linear regression analysis in Figure 4.3b to
compare the lowest water potential of the day with the largest evaporative demand. The measured
midday values of stem water potential Ψmid show linear correspondence with ETmax. This obser-
vation coincides with the concept of baseline water potential,66,67,118 where stem water potential is
assumed to correlate linearly with VPD when soil is saturated with water.
This linear correlation and the nearly purely resistive behavior it implies indicate that other
modes of regulation of water flow through plants (such as by stomata closing, or increasing hy-
draulic resistance of soil due to dehydration) were not active. We conclude that evaporative demand
was not high enough to dehydrate the root-zone to limit the water flow through the SPAC. The dy-
namic water stress developed in trees was entirely controlled by environmental demand in this
regime.
146
Figure 4.3: Example of Well-Watered Dynamics from the 2017 Field Apple Experiment. a. The plots
show the dynamics of drought stress and environmental variables from Sep.7th to Sep.12th 2017. (i) Stem
water potential measured by the micro-tensiometer (blue line), modelled stem water potential using the one-
compartment model (red line), and the precipitation events (blue bar plot). (ii) Residual calculated with
Ψ1C−stem −ΨµT M in blue line. (iii) Transpiration calculated with the Penman-Monteith equation.71,72,124 (iv)
Measured windspeed in yellow line. (v) Shortwave radiation in red line. (vi) Calculated vapor pressure
deficit (VPD) in blue line. b. Midday water potentials from the ΨµT M (blue dots) and the Ψ1C−stem (red
dots), and the peak value of calculated transpiration (ETmax) were extracted from data in Figure 4.3a. Linear
regressions of ΨµT M (dashed blue line), Ψ1C−stem (dashed red line) against (ETmax), and the r-squared values
of fittings are shown inside the plot.
147
We thus explore the use of the simple, single-compartment SPAC model in Figure 4.2a, to
elucidate our dynamic water potential under well-watered conditions.
A simple 1C-model with 3 parameters including Ψsoil, Rt and Ct adjusted within the expected
range was applied to capture the dynamic water stress of trees under well-watered conditions.
We included a capacitor to capture the observed filtering of high frequency disturbances in Ψstem
(Figure 4.3a-i) relative to those in ET0 (Figure 4.3a-iii).
Since the soil water supply was not limited under well-watered conditions, we assumed the
soil hydraulics does not impact the stem water potential. The Ψsoil was assigned to be a fixed value
of −0.1 MPa, a value slightly higher than the previous reported predawn stem water potential
(∼ −0.2 MPa) under well-watered conditions.111 Reasonable values within the range of previous
empirical studies were assigned to C and R .77,149t t The values are shown in Table.4.3.
The red curve in Figure 4.3a-i presents the predictions of such a model in which we adjusted
Rt, Ct, and Ψsoil to minimize the residuals (Figure 4.3b). The residual calculated as Ψ1C−stem−ΨµT M
is mostly within ±0.2 MPa with largest values as −0.5 MPa. The modelled Ψ1C−stem tracked the
dynamics of ΨµT M on Sep.8, the rainy day with complex weather variations. As shown in Figure
4.3b, the midday water potential of Ψ1C−stem against ETmax (red dashed line) coincide with the
linear behavior observed with the ΨµT M (blue dashed line) with comparable regression parameters.
The simulation for the entire 60 days of 2017 Field Apple experiment is shown in Figure
4.4. The best fit value of R-C gives the response time of plant, τ = RtCt ∼ 10 min. The predicted
(Ψ1C−stem) and measured (ΨµT M) stem water potential are validated against each other regarding
both the dynamics and accuracy regarding middy values and dynamics. The residuals (Figure 4.5b)
show good agreement except in the morning and evening. This disagreement could result from the
thermodynamic disequilibrium between the µTM and the xylem tissue due to temperature rise and
decrease during sunrise and sunset. Under well-watered conditions, we only need 3 parameters to
predict the dynamics of stem water potential.
148
Figure 4.4: Overview of 60-day Simulation of Well-Watered Dynamics from 2017 Field Apple. a.
Full dynamics of simulation (Ψ1C−stem, red line), and measured stem water potential (ΨµT M, blue line). b.
Residual (RES = Ψ1C−stem − ΨµT M) throughout the 60 days.
149
4.3.2 Nighttime Stomatal Opening and Boundary Layer Resistance
For some days of the well-watered experiment, we observed nighttime disequilibrium in
ΨµT M. Previous studies have reported nighttime transpiration,113 and showed that the nighttime
transpiration can reach up to 25% of peak rate ET for apple trees. Here, we introduce nighttime
stomatal opening to the 1C-model to capture the nighttime dynamics.
Figure 4.5a shows the simulated stem water potential using the 1C-model with gs,night as 0%,
30%, and 50% of gmax as nighttime stomatal opening, as well as allowing gs = gmax. The expression
of stomatal conductance that allows nighttime transpiration is:
gs = gmax(1 − αg · VPD)(1 − βg/QPAR + 1/ f −1night) (4.16)
where fnight represents the fraction of stomatal opening at night.
Transpiration (ET ) and residuals (Figure 4.5c, RES = Ψ1C−stem − ΨµT M) for each stomatal
opening scenarios are also shown. The inverse of boundary layer resistance (1/ra) is compared
with different level of stomatal conductance to estimate the dominate resistance for transpiration.
We used Thorpe’s model, eq. 4.7, to calculate stomatal conductance, gn0 with zero nighttime
stomatal opening forces no transpiration at night: gn0 represents the original results from eq. 4.7.
gn30 allows 30% of nighttime stomatal opening and is the fraction of opening ( fn, dimensionless)
used for the results shown in Figure 4.3a, Figure 4.4, and Figure 4.7a below. This is the closest
to the literature proposed nighttime ET as 25% of peak ET. The nighttime ET does not include
solar radiation, but is only related to the VPD and windspeed. Therefore, this 25% could have
underestimated the real nighttime stomatal conductance. In the third case, gn50 allows 50% of
nighttime opening as a comparison for the gn30. Finally, gmax is an extreme scenario that has the
stomata remain open throughout. This full opening was also compared with the boundary layer
resistance for their influence on ET and Ψstem (Figure 4.5d).
150
Figure 4.5: Modelled Stem Water Potential, and transpiration with Different Degree of Stomatal
Opening. a. The plot compares ΨµT M (blue line) with the modelled stem water potential with nighttime
stomatal conductance of 0% (red line), 30% (yellow line), 50% (purple line), and 100% (green line) of
maximum. b. The plot shows the transpiration modelled with different degrees of stomatal conductance
plotted in the same color as in (a). c. Calculated residual for the modelled Ψ1Cs in (a) using RES =
ΨµT M −Ψ1C . d. Comparison of the stomatal conductance (left y-axis) for the modelled Ψ1C in (a) with same
color specification, and the inverse of the boundary layer resistance (1/ra, right y-axis)
151
Figure 4.5 shows ΨµT M (blue line) with other simulated Ψ1C−stem using different stomatal
models; Ψ1C−gn0 (red line), Ψ1C−gn30 (yellow line), Ψ1C−gn50 (purple line) give the expected overlap-
ping day-time dynamics, while Ψ1C−gmax (green line) does not have stomatal regulation in response
to VPD and solar radiation, and is expected to predict more negative stem water potential than the
previous three. It is worth noting that, by allowing stomata to open fully, the predicted midday wa-
ter potential Ψ1C−gmax is only about 0.2 MPa more negative than with regulation. This observation
suggests that under this well-watered condition, stomatal regulation did not play an important role
in controlling ET and the associated development of stress.
When gs,night = gn0 = 0, stomata close fully at night, and therefore, results in nighttime
ET = 0 and Ψ1C−stem→− Ψsoil. However, this is not what we observe with the ΨµT M. By allowing
stomata to remain partially open at night in the model, during the nights of Sep.28, Sep.29, and
Sep.30, Ψ1C−gn30, Ψ1C−gn50, and Ψ1C−gmax show nighttime water stress, with the Ψ1C−gmax being the
lowest. In fact, Ψ1C−gmax shows the best correspondence with the ΨµT M, as seen in the residual
(Figure 4.5c). This observation suggests that stomata did not fully close in this tree and that the
common method of measuring the predawn water potential to determine the drought stress of soil
may not be accurate, since its value will be lower even in saturated soil when the predawn ET is
not zero.115,150,151 Continuous measurement of nighttime water potential will be more informative
regarding soil stress by showing contrasting timescales of response to temporary environmental
demand, or prolonged build up of soil water stress. Moreover, monitoring the dynamic water stress
at night can facilitate management of irrigation, or selection of cultivars with better water use
efficiency during the mostly ignored nighttime period.
Figure 4.5d shows that, under high windspeed conditions, the boundary layer conductance,
or the inverse of boundary layer resistance (r−1a , light blue line, right y-axis) is significantly higher
than the stomatal resistances (left y-axis). When comparing the scale of the left and right y-axes,
the boundary layer conductance (1/ra) can be 100 times higher than the stomatal conductance.
The difference among all simulated Ψ1C at night is most siginificant on Sep.28, 2017. Midnight of
152
Sep.28 shows that the Ψ1C−gmax has lowest stem water potential among the cases simulated. There-
fore, when the plant is facing large evaporative demand, either through large stomatal opening, or
experiencing high VPD and high windspeed, the nighttime disequilibrium in stem water potential
is more obvious.151 On most nights, the stomatal conductance limits the transpiration. However,
with high windspeed and high VPD, the low stomatal conductance cannot prevent nighttime tran-
spiration from happening.
4.3.3 Evaluation of Circuit Model for Water-Stressed Apple Tree
Since the field apple tree does not often experience severe drought in upstate New York, we
used a potted apple tree with controlled irrigation to create water-limited conditions. We withheld
water to generate drought stress in the tested apple trees and then re-watered them to acquire
dynamic water stress during dry-down cycles.
A 1C-model was first tried for simulating the dry-down dynamics with a fixed value of Ψsoil
(Figure 4.6). Values of parameters are shown and compared in Table.4.3. The 1C-model failed
to capture the dry-down dynamics since the soil compartment is not considered. During the well-
watered range, the 1C-model predicts the stem water potential well.
Based on this failure of the 1-C model, we hypothesized that a significant increase of soil
and rhizosphere hydraulic resistance during the dry-down. A two-compartment (2C) model with a
soil compartment was applied to capture the dry-down dynamics measured by ΨµT M. Figure 4.2b
shows the schematic diagram of the circuit model. We simulated the stem water potential using
equations 4.2 and 4.3, by adjusting parameters of resistances and capacitances to within expected
range to achieve the desired trend of dynamic water stress.
Figure 4.7a-i-vi show measured (blue), and modelled (red) stem water potential, the residual
of the modelled stem water potential, transpiration (ET), windspeed (vw), photosynthetically active
radiation (QPAR), and vapor pressure deficit (VPD) over 12 days from June 6 to June 18, 2018.
153
Figure 4.6: One Compartment Model for Simulating the Drought Stress in 2018 Potted Apple Experi-
ment. a. Stem water potential measured by the micro-tensiometer (blue line), modelled stem water potential
using an one-compartment model (red line), and the irrigation events (blue bar plot). b. Residual calculated
with RES = ΨµT M − Ψ2C−stem in blue line. c. Transpiration calculated with the Penman-Monteith equa-
tion71,72,124 in blue line. d. Windspeed in yellow line. e. Shortwave radiation is in red line. f. Calculated
vapor pressure deficit (VPD) in blue line.
154
Irrigation events are shown in blue bar plots in Figure 4.7a-i on right y-axis. Measurements from
the micro-tensiometer (ΨµT M) and other micro-meteorological sensors, as mentioned before, were
acquired every minute. A digital scale was used to monitor the real transpiration (ET) and irrigation
events. Since the pots were covered with plastic films and aluminum foil, irrigation was the only
water supply to the system.
Same as before, the ET was estimated using the Penman-Monteith equation 4.4. Stomatal
conductance was modelled with eq. 4.8 to account for the impact of Ψstem under drought. Boundary
layer resistance was calculated based on eq. 4.10, since the potted tree was located in an open space
surrounded by buildings on four sides, the surface roughness and displacement length could not be
easily estimated.
Figure 4.7a shows one full cycle of dry-down starting from the last flood irrigation event on
June 6 2018 until the re-watering event on June 13 2018. Multiple irrigation events were launched
after the re-watering to keep the plant well-watered. During water withholding, the predawn water
potential continuously decreased, indicating the depletion of the water stored in the soil.
Starting on June 11, the predawn ΨµT M (Figure 4.7a-i; blue) began to decrease more rapidly
and the amplitude of the diurnal variations in ΨµT M increased. This observation follows the pre-
dicted trend of the soil water potential (Figure 4.7a-i; yellow). After the soil water potential de-
creased below the air entry potential indicated by αs (1/αs = 0.02 MPa), the Ψsoil decreases more
rapidly with each step change in soil water content (Θ). This predawn water potential could help
us back out a root-zone water retention curve.
The recovery of ΨµT M starts soon after re-watering by flood irrigation on June 13, and ΨµT M
increased to the well-watered range within about 6 hours. This time interval for recovery gives us
the rehydration time scale of the root-zone after severe drought.
The amplitude of diurnals of windspeed, photosynthetically active radiation (PAR), and va-
por pressure deficit (VPD) are comparable from day to day during the dry-down process, while
155
Figure 4.7: Example of Drought-stressed Dynamics from the 2018 Potted Apple Experiment. a. Dy-
namics of drought stress and environmental variables from June 6th to June 18th, 2018. (i) Stem water
potential measured by the micro-tensiometer (blue line), predicted stem water potential using the two-
compartment model (red line), predicted soil water potential (yellow line), and the irrigation events (blue
bar plot). (ii) Residual (blue line) calculated as RES = ΨµT M − Ψ2C−stem from (a). (iii) Transpiration (blue
line) calculated with the Penman-Monteith equation 4.4.71,72,124 (iv) Measured windspeed (yellow line). (v)
Shortwave radiation (red line). (vi) Calculated vapor pressure deficit (VPD, blue line) b. Correlation be-
tween the extracted midday water potential and the peak value of calculated transpiration (ETmax) from the
ΨµT M (circles connected by dashed black line), and the Ψ2C−stem (circles connected by solid black line). The
circles are shown in colormap to indicate the number of days after withholding water.
156
the measured stem water potential keeps decreasing. The estimated transpiration (ET) shows a
decreasing trend due to the stomatal closure as stem water potential decreases. This effect explains
the reduced amplitude of diurnal of ΨµT M as drought stress develops.
Figure 4.7b compares the lowest water potential (Ψmid) of the day with the largest evaporative
demand (ETmax) as presented in Figure 4.3b for the well-watered case. The measured Ψmid is shown
as circles connected by solid black line. Different from well-watered conditions (Figure 4.3b),
ΨµT M decreased in response to increase of ET at the beginning, but then continued to decrease
even as ETmax decreased.
The trend of midday water potential Ψmid indicates the development of drought stress from
well-watered, to mild-stress, to severe stress. Drought developed in trees triggers stomatal closure
(eq. 4.8) and results in decreasing of ETmax as drought proceeds. Without re-watering, the tran-
spiration keeps depleting the plant regardless of the partial stomatal closure, and the stem water
potential keeps on decreasing due to the soil dehydration. After re-watering, both the Ψmid and
ETmax increase to the well-watered range under high evaporative demand from the environment.
The parameters with Ψsoil dependence bounce back to their well-watered range. The hydraulic
resistances Rr and Rs decrease, while the soil hydraulic capacitance Cs increases.
The modelled stem water potential from the 2C-model is shown in Figure 4.7a with solid red
line. Different from the 1C-model in Figure 4.2a, the soil water potential is not a fixed parameter,
but a dependent variable.
The digital scale recorded transpiration is shown in Figure 4.9. Due to the wind disturbance,
the digital scale recorded ET was noisy, but still functioned as a comparison for the estimated ET
(eq. 4.4).
The modeled and measured dynamics of stem water potential follows the same trend of de-
hydration. The residual (RES) is calculated and shown in Figure 4.7a. During the dehydration, the
RES is within ±0.5 MPa, with a maximum value of −2 MPa. This peak deviation occurred at the
157
Figure 4.8: Dynamic Hydraulic Resistances for Dry-down Simulation. The resistances of trunk (Rt),
root (Rr), and soil (Rs) are shown in blue, red, yellow lines respectively.
158
time of re-watering on June 13, this discrepancy could come from the time lag in measured and
modelled stem water potential when responding to a flood irrigation event. Another possible rea-
son is the assumption of unchanged root-zone soil hydraulics during the dry-down process when
simulating the root water transport. The root-zone soil hydraulics could change due to, for exam-
ple, the dehydration of root exudates could change the water retention properties of rhizosphere by
forming a hydrophobic coating around the roots and protect the tree from the drying soil.152
Table.4.3 compares the parameters across 1C-well-watered, 1C-stressed, and 2C-stressed.
In all cases, we held the parameters of the plant compartment constant (Rt and Ct), because we
assumed no cavitation in xylem elements under the studied stress level. The value of Ct was smaller
for the potted cases because the apple tree was smaller in height and diameter when compared with
the field apple tree. The value of Rt was slightly larger than the field tree but of the same order of
magnitude. The value of Rt was also related to the xylem anatomy as the cross-sectional area of
active xylem should be reduced for a smaller tree. The plants were grown in a soil mixture of peat
moss and sand. The water retention parameters (ns, ms, Θ, θr, Ks,sat) were acquired from pressure
plate experiment performed on the soil mixture. The soil parameters are shown in Table.4.4. We
calculated Rr, Rs, and Cs base on equations 4.13, 4.14, and 4.15 respectively. The mathematical
derivation is shown in Supporting Material. The value of Rr,sat was estimated based on previous
empirical studies.77 Roots in potted soil were considered as one layer of root-soil interaction with
Vsoil = V 148 −3 96pot. The root length density (RLD) was estimated to be 0.1 cm · cm . The fine root
diameter r1 was assumed to be 0.1 cm based on previous studies.153 The radial location of bulk soil
√
relative to root xylem was estimated as r2 = 1/ π · RLD by assuming roots were cylindrical tubes
aligned in parallel.148
When comparing the quantitative values of resistances and capacitances, we observed Ct is
the same for both 1C-stressed and 2C-stressed models; and Rt was close to the summation of Rt
and Rr,sat. When comparing the results of 1C (Figure 4.6) and 2C (Figure 4.7), the 1C-model failed
to capture the dry-down dynamics since the soil compartment is not considered. During the well-
159
Field Apple Potted Apple
Pars Literature Values 2017 2018 Units
Model 1C 1C 2C
Circuit Model Parameters
Ψt0 n/a -0.60 -0.40 -0.40 MPa
1
Ψs0 − −1
− 1 Ψ (Θ = 0.5) Ψ (Θ = 0.5)
αs (Θ
ms
0 − 1) ns -0.10
soil 0 soil 0
= −0.1 = −0 MPa.1
potted apple:77
2 ∼ 5 × 104
R 3t field apple:77 2.8 × 10 1 × 10
4 4 × 103 MPa s kg−1
4 × 103
potted apple: 0.02
C −1t field apple: 0.22 0.2 0.1 0.1 kg MPa
potted apple:77
4 ∼ 10 × 104
Rr,sat field apple:78 n/a n/a 4 × 10
3 MPa s kg−1
5 × 103
R R = R /Θ77r r r,sat n/a n/a Rr MPa s kg−1
R ln(r2/r1) 147 −1s 2π·RLD·Vsρw·K K n/a n/a Rs MPa s kgs r
Cs,sat ρw · Vs · (θs − θr) n/a n/a C kg MPa−1s,sat
C Cs,sat ·(1−n )·α
ns
s s −1
s [1+(αs·Ψsoil)ns ]ms+1 n/a n/a Cs kg MPa
Root Architecture Parameters
r1 <= 0.1 n/a n/a √0.1 cm
r2 0.1 ∼ 0.15153 n/a n/a 1/ π · RLD cm
RLD 0.05 ∼ 0.25 × 103 154 n/a n/a 0.1 cm cm−3
Θ0: effective soil water content
ρw: liquid water density
Table 4.3: Comparison of Parameters for the Two Circuit Models.
160
Pars Literature Values Potted Apple 2018 Units
Peat Moss Mix∗: 36.29
αs Silt Loam: 209.8 42.79 MPa
−1
ns n/a 1.538 n/a
ms 1-1/n 145s 1-1/ns n/a
l 0.5145s 0.5 n/a
Θ n/a 0.48 n/a
θr n/a 0.20 n/a
K n/a 10−2.158s,sat kg m−1s−1MPa−1
1 1
K ms 2r Θ 2 [1 − (1 − Θms ) ] Kr
field apple:ds = 40 cm154
Vs rs = 1/2Ls πr2s d
3
s cm
Ls: in-row spacing
rs[cm]: soil pot size
ds[cm]: soil pot depth
Table 4.4: Soil Hydraulic Parameters.
161
Figure 4.9: Comparison of Measured and Modelled transpiration. The measured transpiration with a
digital scale (blue line), and the predicted transpiration (red line) with the Penman-Monteith equation71,72,124
are shown on the left y-axis. Irrigation events (purple bar plots) are shown on the right y-axis.
162
watered range, the 1C-model predicted the stem water potential well. The RES values showed the
deviation of 1C-model from the ΨµT M happened as soil dries down.
Figure 4.8 compares the hydraulic resistances for the 2C-model during the dry-down cycle
in Figure 4.7a. As mentioned before, the stem hydraulic resistance was held constant. The rhizo-
sphere hydraulic resistance (Rr) remained the highest during the entire dehydration process, and it
changed inversely with the soil water potential. The soil hydraulic resistance (Rs) increased by 5
orders of magnitude during the dehydration process and surpassed the stem hydraulic resistance.
Furthermore, as expected, the soil hydraulic resistance showed the highest sensitivity to irrigation
events. We note that Rt, Rr, and Rs all contribute to the predicted response and thus cannot be
ignored for predicting plant drought behavior. This 2C-model gives reasonable prediction of stem
water potential during dry-down with RES →− 0 throughout (Figure 4.7a-ii), except the moment of
re-watering.
4.3.4 A New Stomatal Conductance Model under Drought
Figure 4.10 compares predicted stomatal conductance under well-watered (Thorpe model,
eq. 4.7, red line) and water-stressed conditions (Jarvis model, blue line). Parameters for VPD and
solar radiation were taken from Thorpe’s model for potted apple trees specifically.141 Additionally,
we consider a new stomatal conductance model that aims to replace VPD dependence in the 2C-
model. We hypothesize the stomata closure responds to Ψstem instead of VPD. This new model
takes the following form:
β
g −1
Ψstem Ψstem
sΨ = gmax(1 + ) (1 − · exp(1 − )) (4.17)Qrad Ψmin Ψmin
During the well-watered period (June 6-8), all three models agree (Figure 4.10, because
neither the VPD-dependence (eq. 4.7) nor the Ψstem-dependence (eq. 4.17) were important during
this period. Similar to the 1C-model, a 30% of nighttime stomatal opening was introduced for all
three studied stomatal models. During the dry-down process, gs,Jarvis decreases and deviates from
163
gs,Thorpe. Assuming extensive stomatal closure would happen and take up to 24 hours to recover
after severe drought stress, an extended period of 12% nighttime stomatal opening is introduced
to the Jarvis model for the 2C from the noon of June 12 to the night of June 14. For the diurnal
dynamics of stomatal conductance, due to the lack of VPD-dependence, gs,Ψstem increases as stem
water potential recovers in the afternoons. This phenomenon did not happen for the other two
models. Figure 4.11a shows the predicted Ψstem with the new stomata conductance model. Instead
of relaxing back to less negative values as ΨµT M and ΨS PC, the new predicted Ψ2C−stem (red line)
decreased to a more dehydrated status until the stomata were forced to close by sunset from June 8
to 10. This observation suggests the direct VPD-dependence in the Thorpe and Jarvis models may
indeed be important.
4.4 Conclusion
In this chapter, we developed circuit models to capture the dynamic water stress of apple
trees under well-watered and water stressed scenarios. The field apple tree tested in late Summer
of 2017 did not experience drought stress, and was used to represent well-watered conditions. The
potted apple tree went through dry-down cycles was tested in early Summer of 2018, and was taken
to represent water-stressed conditions.
Transpiration, estimated with the Penman-Monteith equation, functions as the main driving
force for the circuit models. The stomatal conductance with well-watered model, water-stressed
model, and nighttime opening, and their impact on stem water potential was studied.
For the parameterization of circuit models, we used constant values of resistance and ca-
pacitance near the values reported by previous literature for the trunk compartment for all circuit
models, as the drought stress experienced was not severe enough to cause cavitation or the loss of
xylem conductance. For the soil compartment, the root-rhizosphere resistance (Rr), soil hydraulic
resistance (Rs), and soil capacitance (Cs) were derived from soil water retention curve with value
164
Figure 4.10: Comparison of Stomatal Conductance Models. Jarvis model (eq. 4.8; blue line). Thorpe
model (eq. 4.7; red line). The Jarvis model with dependence on stem water potential (eq. 4.17; yellow line)
165
Figure 4.11: Simulation of Drought Stress with the Modified Model of Stomatal Conductance. a.
Stem water potential measured by the micro-tensiometer (blue line), modelled stem water potential using
the two-compartment model (red line) comprising the modified stomatal model (eq. 4.17), and irrigation
events (blue bar plot). b. Residual calculated with RES = ΨµT M − Ψ2C−stem in blue line. c. Transpiration
calculated with the Penman-Monteith equation71,72,124 (blue line). d. The measured windspeed (yellow
line). e. Shortwave radiation (red line). f. Vapor pressure deficit (VPD; blue line).
166
measured independently.
We showed that the well-watered dynamics of the apple tree can be captured using a simple
one-compartment model with three parameters (Rt, Ct, and a fixed Ψsoil). Models with nighttime
stomatal opening tracked the nighttime water stress better. However, when well-watered, even full
opening of stomata does not generate significant stress in midday water potential, suggesting that
the stomatal regulation is not important for plant water relations in saturated soil.
We captured the drought-stressed dynamics of the apple tree by adding a soil compartment to
our circuit model. The predicted rhizosphere resistance was the highest among all three hydraulic
resistances in the model and increased with drought stress. The soil hydraulic resistance increased
most significantly during the dehydration process. A new stomatal conductance model that only
depended on the stem water potential, instead of VPD, was proposed and tested for the dry-down
simulation. The disagreement between the simulated Ψstem and the
µT M
Ψstem suggests that the stomata
do respond to VPD possibly through changing the leaf water potential.
The circuit models and the micro-tensiometer validated each other on measuring and model-
ing the dynamics of stem water potential. The model elucidated the captured nighttime water stress
recorded by the micro-tensiometer. The patterns of plant water stress were different when facing
short-term high frequent environmental demand, and long-term soil dehydration and re-saturation.
Previous studies have used predawn water potential to evaluate the drought stress of plants, but the
continuous dynamics is significantly more informative regarding the type of stress developed, and
whether an irrigation decision should be made. Both the models and the micro-tensiometer will
function as useful tools to enhance our understanding of drought responses of plants, as well as
improving the efficiency of agriculture water management.
167
4.5 Supporting Information
4.5.1 2017 and 2018 Experimental Materials and Methods
Plant Materials
The field experiment was conducted in 2017 on apple trees at Cornell Orchards in Ithaca
(New York State). The apple trees were on B.9 dwarfing rootstock with "Ruby Frost" scion. The
orchard rows were north-south oriented. The soil type was Niagara Silt Loam (NaB). The training
system was Tall Spindle. The spacing between rows and between trees were 3.7 m (12 ft.) and
1.2 m (4 ft.) respectively. The trunk diameter of tested trees was 4—5 cm. The total leaf area
measured with an leaf area meter (LI-3100, LI-COR) at the end of the experiment was about 6 m2.
The apple trees were rainfed without human water supply.
The dry-down experiment was conducted in 2018 on potted apple trees is the courtyard of
the Cornell Guterman Bioclimatic Laboratory. The apple trees were on semi-dwarf M.26 rootstock
with "Royal Gala" scion. The trees, planted in 5-gal pots with artificial mixture comprises 2/3 peat
moss and 1/3 sand, were 3 to 4 meters tall, and 3-4 cm diameter stems below the canopy. The total
leaf area measured at the end of the experiment was ∼ 3.3 m2.
Micro-Tensiometer Measurements
Micro-tensiometers were directly embedded into the trunk below canopy for stem water
potential measurements. The methods of fabrication, packaging, and embedding are described in
detail in our previous study.108 Briefly, the micro-tensiometers were fabricated at the cleanroom
of Cornell Nanoscale Facilities. The details of fabrication protocol are described and shown in
Appendix I. Micro-tensiometers were mounted onto PCB boards with connections through wire-
bonding. The mounted sensors were then packaged using polyurethane in an aluminum tubing. A
shallow hole (5 ∼ 7 mm) from was drilled radially towards the center of the stem from the outer
surface. A micro-tensiometer was then embedded into the trunk with aluminum oxide paste applied
168
in between for better thermal and liquid contact. Measurements were triggered and recorded with
CR6 data-loggers (Campbell Scientific).
Schölander Pressure Chamber Measurements
Benchmark stem water potentials were measured using a Schölander pressure chamber (Soil-
moisture Equipment Corp.), a widely accepted manually operated tool.33
Digital Scale
Water loss from the potted apple trees were recorded using a digital scale with an accuracy of
±1 g (WBK-70aH, Adam Equipment). The digital scale data were acquired every 1 minute using a
datalogger (CR6, Campbell Scientific). The data acquisition code is shown in Appendix II. Due to
the wind disturbance for the potted tree in outdoor environment, the digital scale show noisy signal
with a clear trend.
Windspeed Sensor
The windspeed around the potted apple tree was monitored using a C2192 anemometer sen-
sor (adafruit.com). Data were collected each minute via a CR6 logger.
Photosynthetically Active Radiation
Photosynthetically active radiation (PAR) data were acquired from the outdoor weather sta-
tion from the Cornell Greenhouses.
Leaf Area Meter
Leaf areas for the 2017 and 2018 Apple experiments were measured using a LI-3100 leaf
area meter. For both experiments, about 1/6 of total fresh leaves were measured as a sample with
the leaf area meter. Both the sampled leaves, and the rest of the unmeasured leaves were dried in
an 70◦C oven for at least 48 hours. The total leaf area was then calculated based on the measured
169
sample to the total leaf dry-weight fraction.
4.5.2 Soil Compartment Formulation
Soil Hydraulic Capacitance
The soil hydraulic capacitance (Cs) can be derived from eq. 4.10 based on the van Genuchten
1980 formula.155 The soil water content is by definition:
W
Vw ρw
θ = = (S4.1)
Vs Vs
where Vw [cm3] is the volume of water in the soil matrix; V [cm3s ] is the total volume of the soil
matrix; W [kg] is the weight of water in the soil matrix; ρw = 1000 [kg/m3] is the density of water.
The saturated soil hydraulic capacitance Cs,sat = ρwVs(θs − θr) The soil hydraulic capacitance is
defined by the change in stored water per unit change in soil water potential, and expressed as:77
dW
Cs = (S4.2)dΨsoil
Using van Genuchten’s form of θ, the expression of the soil hydraulic capacitance (Cs) is
then:
Cs = Cs,sat · (1 − n) · αn · [1 + (α · Ψ )n]−m−1 · Ψn−1soil soil (S4.3)
Rhizosphere Hydraulic Resistance
The rhizosphere resistance for the water-stressed plant increases as soil gets stressed. Based
on the Contact Model previously proposed, the rhizosphere resistance depends on the effective soil
170
water content (Θ), which directly relates to the soil water content (Ψstem) through eq. 4.14:147
R
Rr( )
r,sat
Ψsoil = (S4.4)
Θs(Ψsoil)
The Rr,sat is the root-zone hydraulic resistance for potted apple tree under drought stress.
Bulk-Soil Hydraulic Resistance
The steady state radial flux density (q [kg s−1]) takes the following form:
dΨ
q soil= −2πrl · K(Ψsoil) (S4.5)dr
The hydraulic conductivity (K(Ψsoil)) takes the following form:
K(Ψsoil) = Ks,satKr(Ψsoil) (S4.6)
where Ks,sat [kg m−1 s−1 MPa−1] is the saturated soil hydraulic conductivity, and Kr is the dimen-
sionless relative soil hydraulic conductivity.
Following van Genuchten, the relative hydraulic conductivity takes the following form:
1 1
Kr = Θ 2 [1 − (1 − Θms )ms]2 (S4.7)
where ms = 1− 1/n 145s and 0 < ms < 1. Considering eq. 4.14, the hydraulic condictivity takes the
following form:
[1 − (α Ψ )ns−1s soil [1 + (αsΨ ns −ms 2K soil) ] ]r = (S4.8)
[1 + (α Ψ )n
ms
s soil s] 2
At steady state, we have: ∫ Ψ
2πl soil K(Ψ)dΨ Ψ − Ψ
q − Ψr ≡ − soil r= (S4.9)
ln(r2/r1) Rs
171
where r1 [cm] is the fine root radius, r2 [cm] is the half distance between roots, l [cm] is the root
length, Rs [MPa s kg−1] is the soil hydraulic resistance, Ψsoil [MPa] here represents water potential
of bulk soil, and Ψr [MPa] is the water potential of root-zone soil. After reformatting, the Rs has
the following expression:
≡ ln(r2/r1)(ΨR ( ) ∫soil − Ψr)s Ψsoil,Ψr (S4.10)Ψ
2π · Vs · RLD · soil K(Ψ)dΨΨr
The form in eq. S4.10 is challenging to evaluate, so it is often approximated by neglecting
the variation of K(Ψsoil) as:
ln(r /r )
Rs(
2 1
Ψsoil) = (S4.11)2π · Vs · RLD · K(Ψsoil)
We used this simplified form in our SPAC model.
172
CHAPTER 5
RESPONSE OF WATER STRESS IN APPLE TREE TO INTERMITTENT IRRIGATION
EVENTS
5.1 Introduction
Previous chapters elucidated the functionality of a micro-tensiometer as a robust and accurate
hygrometer for continuous measurements of drought stress in woody species. In chapter 3, we
demonstrated the micro-tensiometer for the measurements of water stress in woody species under
wet (apple), semi-arid (grapevine), and arid (almond) environments. In chapter 4, we developed
circuit models with minimized number of parameters to validate the observed dynamics for well-
watered field apple tree and water-stressed potted apple tree using experimental data from 2017
and 2018.
As discussed before, this new technique not only opens up new possibilities to study the
transient in physiological responses of plants to drought stress, but also provides a tool to monitor
the drought stress for better water management. The models developed in chapter 4 could function
as virtual tools for the prediction of plant water stress using weather forecast. The models and
the micro-tensiometer together provide an unique opportunity for the model predictive control of
irrigation156 to achieve fine maintenance of plant water stress for the mild stress requirement at
different phenological stages.
In this chapter, we present my exploration of the response of plant water stress to a series of
well-controlled irrigation events, as a preliminary study of the predictive control of irrigation with
micro-tensiometers. Furthermore, we investigate the timing and amount of irrigation for less water
loss through drainage and evaporation, and more efficient water uptake by plants.
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Figure 5.1: Schematic Diagram of Irrigation.a. Top view of the layout of four drippers and a soil sensor
in the pot. b. Side view of the relative position of the apple roots and drippers.
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5.2 Experiment Setup of Controlled Irrigation
A simple irrigation control system was set-up using Raspberry Pi as a micro-controller to
launch irrigation events with control valves on potted apple trees. A digital scale was used to mea-
sure the amount of irrigation and rate of transpiration from the measured apple tree, while covering
the pot with a waterproof board. The dynamic water stress of apple trees while responding to both
small irrigation events and large irrigation events at different timings of the day were measured.
The "small" and "large" are defined in comparison with the cumulative evapo-transpiration (ET)
of the measured apple tree on sunny days.
Figure 5.1 shows the top view (Figure 5.1a) and the side view (Figure 5.1b) of the pot of
the measured apple tree. As previous chapters described, the micro-tensiometers were embedded
into the trunk of these trees (Figure 3.1). Four drippers were inserted into the soil pot about 10 cm
deep. A soil stress sensor was used to record the water potential of soil and to capture the response
of soil water potential to irrigation events.
The impact of different amounts of irrigation at a variety of time-points during the day is
discussed below. The water flow rate of each dripper is ∼ 0.038 L min−1 before the soil started
draining through the bottom of the pots (Figure 5.2). Figure 5.2 shows the weight of the potted
tree from the start of irrigation at midnight to 6 am of Aug. 17 2019. The irrigation rate is close to
∼ 0.15 L min−1, four times the rate of each dripper, as the total weight of soil and plant increases
after irrigation starts. When the total weight stops changing, water starts to drain from the bottom
of the pot, meaning the soil is close to saturation.
Based on our pre-experiment testing, 1.5 Liters is close to the measured accumulated evapo-
transpiration using the digital scale on a sunny day. This volume corresponds to about 10 min of
irrigation with four drippers at the same time. Following discussions will use minutes of irrigation
to quantify the irrigation amount.
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Figure 5.2: Irrigation of Apple Tree from Midnight to 6am. The left y-axis shows the weight output from
the digital scale (blue line). The right y-axis shows the irrigation rate extracted as a discrete time derivative
of the weight change every 10 data points with data acquisition interval as 5 seconds.
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5.3 Results and Discussion
Figure 5.3 shows the full response of the stem water potential to irrigation events from Aug.
18 to Sep. 12, together with the evapo-transpiration and the measured soil water potential. Figure
5.3 also shows the soil water potential from the micro-tensiometer embedded tree (Ψsoil,embedded,
blue line), and the neighbor tree (Ψsoil,neighbor, red line). It is worth noting that a fertilization event
with an equivalent supply of water for 16 min was performed around the noon of Aug. 23. Both
trees were irrigated with the same amount of water at the same time. It is obvious that, the response
of the soil sensors depends on their relative locations to the drippers embedded, especially when a
small irrigation volume was supplied. Despite the long response timescale of plants based on our
previous discussions, the micro-tensiometer is able to show real response of plants to irrigation,
dynamics that cannot be tracked using a soil stress sensor.
Root water uptake is not as effective during the day.
Figure 5.4 shows a preliminary experiment with on/off control with a threshold of −2.1 MPa.
Figure 5.4a from the top to bottom shows the measured Ψstem with a micro-tensiometer, together
with irrigation events on the right y-axis; the evapo-transpiration calculated using the Penman-
Monteith equation (ETPM); the vapor pressure deficit (VPD); and the shortwave radiation (Qrad).
The ETPM is compared with the digital scale monitored ETDS in Figure 5.5. Irrigation events were
launched 6 times with 5 min intervals every 3 min until it is programmed to stop. The irrigation
amount was about 3 times as much as the daily accumulated ET (ETcum, ∼ 10 min of irrigation)
under full sun conditions.
On Aug. 5 shown in Figure 5.4, the measured apple tree responded to irrigation events by
showing increasing water potential when the evapo-transpiration, the solar radiation, and the VPD
were all increasing, but not yet at their daily maximum. The plant started to respond about 30
min after the onset of irrigation, but only rehydrated to −2.5 MPa from -2.7 MPa after three times
of ETcum was delivered. Interestingly, due to the irrigation event, the nighttime water potential
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Figure 5.3: Overview of Stem Water Potential, Evapo-transpiration, and Soil Water Potential. The
y-axis from top to bottom shows stem water potential from the micro-tensiometer (blue line), the Penman-
Monteith evapo-transpiration (blue line), and the soil water potential from the embedded apple tree (blue
line), together with the neighbor apple tree (red line) with same irrigation events. The right y-axis of the top
plot shows the irrigation events in purple line. The black arrows distinguish the irrigation events during the
day. The blue numbers are predawn events. The purple number shows the water from a fertilization event.
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Figure 5.4: Dynamics of Stem Water Potential with Irrigation under On-Off Control. a. Plots from top
to bottom show stem water potential with a micro-tensiometer (Ψstem, blue line), Penman-Monteith evapo-
transpiration (ETPM, blue line), vapor pressure deficit (VPD, blue line), and shortwave radiation (Qrad, blue
line) on Aug. 5. The right y-axis of the top plot shows the rate of irrigation in purple line. b. Zoom-in
dynamics from 9:00 am to 18:00 pm of a.
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Figure 5.5: Comparing the Digital Scale Measured Evapo-transpiration and Penman-Monteith Pre-
dicted Evapo-transpiration. The digital scale extracted evapo-transpiration is shown in blue line. The
Penman-Monteith predicted evapo-transpiration is shown in red line.
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increased by 0.5 MPa when compared with the previous night.
This observation indicates the apple tree does not respond instantaneously to irrigation events
despite the significant water stress (-2.7 MPa) and the significant amount of water (3x ETcum)
supplied. We hypothesize that the trees may not uptake water effectively during the day, and
daytime irrigation may not be efficient. The plant-based on-off irrigation control approach without
considering the large timescale of daytime water uptake could result in significant water loss.
Small amount daytime irrigation events
The data shown in Figures 5.6, 5.8, and 5.9 were selected from the complete experimental
period shown in Figure 5.3. Figure 5.7 verifies that the micro-tensiometer (ΨµT M) has comparable
results with the Schölander pressure chamber (ΨS PC).
Figure 5.6 shows the response of the apple tree to small irrigation events during the daytime.
The top plot shows the Ψstem from the micro-tensiometer. The bottom plot shows the predicted
evapo-transpiration (ETPM). One obvious dry-down process is shown from Aug. 25–26 with
irrigation events on Aug. 26. Two 1-min irrigation events and three 2-min irrigation events (black
arrows with numbers) were launched at different times during the day. A total of 8-min (80%
ETcum) irrigation was launched during the day. However, no obvious response to these irrigation
events from the apple tree was observed. We note that Ψstem mainly follows the variations in
the evapo-transpiration (ETPM). This observation confirms, again, the measured apple tree does
not uptake water effectively during the day. The reason could be that the timescale for roots to
respond to irrigation events is long due to their shrinkage under stress when transpiring during the
daytime.147
Small nighttime irrigation events.
In Figure 5.8, we show the response of the measured tree to small irrigation events at night
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Figure 5.6: Apple Tree under Water Stress Shows No Response to Small Irrigation Events during
Daytime. The plots show stem water potential (blue line), irrigation events (purple line), and Penman-
Monteith evapo-transpiration (blue line) from Aug. 25 to Aug. 27. Five irrigation events with small amounts
during the daytime are highlighted with blue boxes on Aug. 26 with first two as 1 min, and the following
three as 2 min.
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Figure 5.7: Comparison between Stem Water Potential Measured by Micro-tensiometer and Schö-
lander Pressure Chamber. The blue line represents stem water potential from the micro-tensiometer. The
purple dots represent measurements from the Schölander pressure chamber (SPC).
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Figure 5.8: Apple Tree under Water Stress Responds to Small Irrigation Events during Nighttime.a.
The plots show stem water potential (blue line), irrigation events (purple line), and Penman-Monteith evapo-
transpiration (blue line) from Aug. 21 to Aug. 28. Five irrigation events with small amounts during the
nighttime are highlighted with blue boxes on Aug. 21, 22, 23, 25, and 27, with 2 min, 3 min, 3 min, 1 min,
and 1 min respectively.
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when not transpiring. As in Figure 5.6, the top plot shows the ΨµT M, and the bottom plot shows
ETPM. The black arrows with the number of minutes are representing the launched nighttime
irrigation events.
The nighttime irrigation events on Aug. 21 and 25 with 2-min and 1-min of irrigation events
respectively resulted in non-observable response from the Ψstem, when the apple tree was not under
severe stress. Irrigation events were launched on Aug. 22, 23, and 27 with 3-min, 3-min, and
1-min respectively when the trees were under mild-severe stress. When compared with the evapo-
transpiration, all three events show response to irrigation with increasing stem water potential
while the ET remained constant or close to zero. More surprisingly, the Ψstem responds to the 1-
min event on Aug. 27 when nighttime water potential was about -1.7 MPa, indicating severe stress.
This observation indicates the roots can uptake water more effectively during the night when none
or low rate of transpiration was happening. It also indicates the time-scale of response by roots is
shorter during the night than daytime.
Large irrigation events during daytime
Figure 5.9 shows two trials of large irrigation events (12 min) when the Ψstem is lower than
-3 MPa. These irrigation events were about 120% of ETcum. We observed about +1 MPa of rehy-
dration before sunset. The 1st step rehydration was followed up by a more significant rehydration
event after sunset. This two-step rehydration indicated that the stored water in the soil after irri-
gation was subsequently absorbed by the roots at night. The transient of water uptake by roots
depends on the stress level of roots.
Predawn Irrigation Events
Based on the previous discussion, the timing of irrigation is important. The roots uptake
water more effectively at night than during the day, meaning a shorter transient to irrigation events
at night than during the day.
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Figure 5.9: Apple Tree under Water Stress Shows Two-Step Response to Large Irrigation Events dur-
ing Midday. The plots show stem water potential (blue line), irrigation events (purple line), and Penman-
Monteith evapo-transpiration (blue line) from Sep. 5 to Sep. 12. Two irrigation events with large amounts
during the nighttime are highlighted with blue boxes on Sep. 7 and 10, with both 12 min.
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Figure 5.10 shows the response of Ψstem to predawn irrigation events. Although the nighttime
water potential was close to -1 MPa, same as on Aug. 22, Ψstem with irrigation amount of 8 min
and 5 min on Sep. 4 and 5 respectively did not induce significant post-irrigation responses. These
irrigation amounts were estimated by calculating the ETcum based on the weather forecast. The
method is shown in Appendix C and Appendix D. Even though we cannot tell exactly whether the
roots uptake the irrigated water efficiently at predawn, the apple tree only shows -2 MPa of midday
stress.
5.4 Conclusion
In this chapter, we measured the drought response of a potted apple tree to intermittent drip
irrigation events and explored the impact of timing and amount of irrigation to the drought response
of the plant.
We conclude that the roots have different rehydration timescales during the day or at night.
This transient timescale of water uptake mainly depends on the root-zone drought stress level.
During the day, the measured apple tree did not uptake water efficiently when actively transpiring,
even if the plant was under severe stress. At night, the relaxed roots were more effective with
water uptake, as seen in the larger responses to similarly small volumes of irrigation. Water that
was not absorbed during the day due to this delay appeared to be absorbed at night in a two-step
response. When compared with the measured soil water potential, the measured dynamic stem
water potential reflected the real response of trees to stress and irrigation events, even for the
highly localized drip irrigation events.
Considering the soil drainage in field conditions, we recommend the irrigation of trees and
crops at night or predawn instead of during the day, to avoid water loss to drainage as a result of
the inefficient root water uptake efficiency.
The results of this experiment implies new opportunities to understand plant water relations
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Figure 5.10: Apple Tree Responds to Predawn Irrigation with Replacement Cumulative ET. The
plots show stem water potential (blue line), irrigation events (purple line), and Penman-Monteith evapo-
transpiration (blue line) from Sep. 3 to Sep. 6. Two irrigation events with predicted cumulative ET at the
predawn of Sep. 4 and 5 are highlighted with blue boxes, with 8 min and 5 min respectively.
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for better water management: 1) the response time-scale of roots to irrigation events under different
drought level; 2) the minimum amount of irrigation, to rehydrate the plant back to the desired
Ψstem from different stress level, while considering the variations of the evaporative demand; 3) the
impact of different irrigation techniques on water management; and 4) if the geographic location
allows drought studies in field conditions, the relationship between the timing and the amount of
irrigation to different levels of drought stress for field trees by considering the soil water balance.
5.5 Supporting Information
Plant Material
The potted apple trees used for this experiment are from the trees used in Chapter 2 of this
dissertation after three more years of growth.
Method of Irrigation Control
Four drippers were deployed in the soil surrounding the stem as shown in Figure 5.1a. The
drippers were inserted into the soil to a depth of 10-cm. Each pressure compensated dripper has a
flow rate of 0.0378 kg min−1. Four drippers has a total flow rate of 0.15 kg min−1.
A Raspberry Pi model 3B+ was programmed to turn on/off the solenoid valves (24V, SS-25J-
24VDC) to launch irrigation events. Hoses were connected from the main water supply through
the valves, to the trees that need to be irrigated. Hologram NOVA 3G dongle was installed onto
the Raspberry Pi to allow for wireless communication between the Raspberry Pi and an online IoT
(Internet of Things) platform, as well as the PC.
We used "ssh" to communicate wirelessly from the PC to the Hologram through "Remote.it"
for launching Python programs on the Raspbian system of the Raspberry Pi.
Programs written in Python were used to launch irrigation events, monitor the time interval of
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each irrigation event, acquire data from the CR6 datalogger through serial communication, fetch
the irrigation data and datalogger data to Ubidots, an online IoT platform. These programs are
attached to Appendix C.
Micro-tensiometer
Micro-tensiometers were fabricated, packaged, calibrated, and embedded below canopy into
the stem of the potted apple trees. The cleanroom fabrication process is described in Appendix A.
The packaging, calibration, and embedding processes are discussed in detail in chapters 2 and 3.
A CR6 datalogger (Campbell Sci) is used to measure the micro-tensiometers by the minute.
Micro-meteorological and Soil Water Potential Measurements
A micro-climatic station for measurements of solar radiation (LI-200R, LI-COR), relative
humidity and temperature (HMP-60, Vaisala), and windspeed (C2192) around the potted apple
tree are taken using a CR6 datalogger (Campbell Sci.) as well by the minute. One CRBasicEdi-
tor program was used to take measurements from the micro-tensiometers and the micro-climatic
weather station. It is shown in Appendix B.
Soil sensors (Watermark 200 Model 253) were used to monitor the soil conditions of the
potted apple trees. We used a CR6-datalogger with a Multiplexer (AM16/32B, Campbell Sci.) to
measure the soil sensors by programming the datalogger with the CRBasicEditor.
We also transmitted the micro-tensiometer and micro-meteorological data from the CR6 dat-
aloggers to the Raspberry Pi through serial communication using CRBasicEditor. The program is
shown in Appendix B. as well.
A program was written in MATLAB to upload data from the PC to the IoT platform when
Raspberry Pi was down due to lack of power supply. This was one technical problem that will be
further discussed below.
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Cumulative Evapo-Transpiration
We acquire weather forecast data from "atmosim.com". The Python for data acquisition
was from Marty Sullivan. The Python codes are shown in Appendix C. The weather forecast data
include solar radiation, relative humidity, temperature, and windspeed. Penman-Monteith equation
shown in previous chapters was used for to predict the evapo-transpiration for the following 24
hours by using the forecast data. The cumulative ET (ETcum) was then calculated, and converted
to irrigation time based on the water flow rate of drippers. The MATLAB program for this part of
calculation is shown in Appendix D.
Improvement Suggestions for the Current System
We successfully operated the setup of controlled irrigation experiment throughout 2019 Sum-
mer, but this system needs further improvement.
We replied on one Raspberry Pi to control irrigation and operate data transmission. We had
one solar panel to generate power for four 24V solenoid valves, as well as the Raspberry Pi itself.
This system had the following problems:
Due to the lack of sunlight for some days in Ithaca, NY., this solar panel did not generate
enough energy for the valves to operate throughout the night. This problem made predawn or
early morning irrigation trails challenging. More solar panels or backup batteries are suggested
for future experiment. Besides, lack of power required reboots of the Raspbian, and restarts of
all the Python programs that had been running and uploading data regularly. The lost data during
power outage needed to be collected from CR6, and uploaded manually from the PC using the data
uploading MATLAB program shown in Appendix D.
The launch of irrigation with 24-Volt valves could disturb the sensor signals through the
Raspberry Pi. This problem suggests separating the data acquisition systems of micro-tensiometers
and irrigation control.
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We still used one CR6 datalogger to measure all micro-tensiometers and the weather station.
We used another CR6 to operate all soil sensors. The crossing of wires at the experiment site
generate a potential trip-hazards. It would be beneficial to have individual datalogger for each tree
for measurement of soil water potential and stem water potential. The weather station would be
purely operated by the CR6 datalogger.
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CHAPTER 6
MEASUREMENT OF WATER DYNAMICS IN MAIZE (ZEA MAYS L.)
6.1 Introduction
Maize is one of the most important cereal crops in the world and supplies 50% of world
calories.157 It is also a major resource for biofuel and livestock feed. With the predicted growth of
global population to 9.7 billion by 2050,127 the demand on grain production will increase globally,
and double for developing countries.158
Water stress in maize determines its growth, yield, disease tolerance and mortality by con-
trolling the rate of efficiency assimilation and nutrient uptake.120,159–163 A drought stressed maize
produces kernel with low weight and number. More specifically, water stress of maize impacts
the nutrient uptake by affecting the stomatal conductance, leaf elongation, root density, and root
distribution. Due to the intensified influence from climate change, studies have shown increased
sensitivity of maize to drought stress.164
Water potential quantifies the water stress as mechanical tension. Many techniques (Schö-
lander pressure chamber, infrared thermometry,165 and leaf psychrometry37) have been applied to
measure the in-plant water potential of maize. Among all techniques, the Schölander pressure
chamber (SPC) has been the mostly widely adopted, especially for woody perennials and is accu-
rate tool to access in-plant water potential based on excision of leaves.
To improve the crop yield, fine-tuned management of drought stress, meaning maintaining
a reasonable level of water stress at specific phenological stages of plant growth (e.g. flowering
or grain filling), can improve water use efficiency (WUE) and crop quality.120,166 Continuous mea-
surements of drought stress of maize is important for more efficient stress management. As the
most widely adopted tool, however, the destructive, dis-continuous, and labor-intensive nature of
SPC measurements presents challenges for the current demand of efficient management of water
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stress with both high temporal resolution and accuracy.
Under usual conditions, stem water potential lies in between roots and leaf, shows less vari-
ations with evaporative demand from the environment than leaves do, and provides information on
the root water potential or the rhizosphere stress level. Certain physiological responses of plants,
like leaf elongation and stomatal conductance,68,167–169 are more sensitive to root or soil water po-
tential than the more measurable leaf water potential.159,161,162 However, accessing the stem water
potential of maize remains a challenge. A variety of models that integrate the water relations of
multiple layers of soil and the crop were developed to predict the stem or root water potential of
maize plants.170–172 Nonetheless, these hydraulic models need a reliable validation.
In this chapter, we introduce the application of the micro-tensiometer in maize (Figure
6.1a-c) for continuous measurements of stem water potential. We have demonstrated the micro-
tensiometer as a reliable tool to monitor the stem water potential in a variety of woody species:
apple, almond, and grapevine. Here, we present the first trial of micro-tensiometer on an herba-
ceous plant.
We show one complete dry-down of potted maize followed up with a watering event, together
with a digital scale monitored transpiration in a greenhouse. Photosynthetically active radiation
(PAR), vapor pressure deficit (VPD), and soil water potential (Ψs) were measured. We compare
the monitored stem water potential with the Schölander pressure chamber (SPC) as benchmark for
midday measurements (Ψmid). We then generate a root-zone soil retention curve using the predawn
water potential Ψpd extracted from the micro-tensiometer, and the effective water content based on
the water retention curve of the dual-porosity Turface soil (Figure 6.1d).
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6.2 Results and Discussion
6.2.1 Embedding of the micro-tensiometer into the maize stem
Figure 6.1 shows the experimental setup for the embedding of micro-tensiometers into maize
stem.38 Figure 6.1a presents a diagram indicating the position of embedding. The maize plant had
16 nodes with the bottom two as roots, and a total of 12 leaves at the time of embedding. The
micro-tensiometer was embedded between the 5th and 6th nodes. Three leaves were removed to
allow for enough space of insulation, leaving in total at the time of embedding. Figure 6.1b shows
the schematic diagram of the micro-tensiometer after packaging. The methods of fabrication and
packaging were the same as presented in previous chapters. Figure 6.1c shows the dual-porosity
Turface soil for the maize being tested. The water retention curve inferred from measurements of
stem water potential is compared with a previous study on Turface soil in the following sections.
Figure 6.1d shows a potted maize on a digital scale with micro-tensiometer embedded and insulated
with the maize stem. Windspeed, humidity and temperature sensor, and photosynthetically active
radiation (PAR) with the instruments specified in the "Supporting Information" section.
6.2.2 Measured dynamics of the dry-down cycle
Figure 6.2 shows, from top to bottom, the measured Ψstem (MPa) and Ψlea f (MPa) with ir-
rigation events, measured transpiration (ET, kg hr−1), vapor pressure deficit (VPD, kPa), photo-
synthetically active radiation (PAR, µmolm−2 s−1), and measured soil water potential (Ψsoil, MPa).
The monitored stem water potential is shown on the left y-axis of the first plot using a micro-
tensiometer (ΨµT M) with the blue line. The leaf water potential was measured using a Schölander
pressure chamber (SPC) on the embedded plant (ΨS PC,embedded solid red dot), and the neighbor plant
(ΨS PC,neighbor solid blue dot) for comparison.
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Figure 6.1: Measurements of Maize Water Stress Dynamics Using A Micro-tensiometer. a. A
schematic diagram of the measured maize with 16 nodes and 9 leaves after embedding. b. A schematic
diagram of a packaged micro-tensiometer with the sensor mounted onto a printed circuit board, connected
through wire-bonding, and encapsulated in aluminum tubing using polyurethane. c. A schematic diagram
representing the dual porosity of the Turface soil38 with inter-aggregates; the intra-aggregates are formed of
smaller particles. d. A photograph of the experimental setup with instrumented maize plant positioned on a
digital scale, with the micro-climatic weather instruments nearby (not shown).
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Figure 6.2: Dry-Down Cycle of Corn Stem Water Potential. a. Full dynamics of water potential mea-
sured by a micro-tensiometer (solid blue line), Schölander pressure chamber measured leaf water potential
of the instrumented maize plant in solid red dots and in the neighbor maize plant in solid blue dots. b. Digital
scale measured transpiration (solid blue line). c. Vapor pressure deficit calculated from the measured hu-
midity and temperature. d. Photosynthetically active radiation (solid red line) measured by the PAR sensor.
e. Soil water potential (solid blue line) measured by the soil sensor.
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Transpiration
Transpiration (ET) and the amount of irrigation (IR) were calculated from the pot weight
measured continuously with a digital scale (Figure 6.3). The pot was covered during the dry-down
cycle so the ET only occurred through the plant. The digital scale data were acquired every 1
minute, while the ET and irrigation were calculated on a time interval of 15 minutes.
The measured ET has a close coupling to the diurnal of PAR on the well-watered days. No
nocturnal transpiration was observed based on the digital scale data, except the midnight of day 9,
when the plant was stressed down to -1.4 MPa. The nocturnal transpiration could facilitate the nu-
trient uptake at night without significant water loss to the environment, as dehydration could cause
insufficient nutrient uptake from the soil that usually happens together with water uptake.173,174
When stem and leaf water potential reached the lowest value of about -1.5 MPa (day 10), the
ET showed a smaller peak value compared the other days with similarly high VPD and PAR. The
stomata could have closed partially in response to drought stress to prevent significant water loss
from the maize plant. This observation is similar to the previous study by Beadle 1973:175 maize
stomata close when leaf water potential is lower than -1 MPa. On day 10 before re-watering, even
though the demand from the environment was high, the ET was low, and Ψstem did not decrease
further.
Dynamic water Stress
After an irrigation event on day 1, we withheld water from day 2 to 10; on day 10, we
re-watered at 3:30pm. Predawn data on day 16 is close to the ΨµT M, indicating that the micro-
tensiometer did not drift significantly during the experimental period.
From day 1 to 7, the maize plant was not watered, but was not under stress either. Figure 6.4
shows an expanded view of the dynamics of maize from day 3 to 7 to better elucidate the behavior
in the well-watered range of maize. During the well-watered period (days 1-7), we observe the
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Figure 6.3: Weight Measurements from a Digital Scale.
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Ψstem decreased in response to the onset of transpiration at 6am, when greenhouse lights came on
or after sunrise. At approximating 6pm, the ΨµT M reached a plateau around -0.35 MPa. When the
light was turned off around 10pm, the Ψstem relaxed back to a higher water potential value (-0.2
MPa); we interpret this maximum potential at night as the effective representation of water stress
in the rhizosphere. When well-watered and under low evaporate demand (days 3-7), the diurnal
amplitude in Ψsoil was about -0.15 MPa; this value is not significant when compared to Ψlea f . On
day 2 and 13 (Figure 6.2), there were obvious deviations in values of Ψlea f from the Ψstem when
evaporative demand from the environment is high, as indicated by the large peak values of PAR.
The instrumented maize plant started to show drought on day 7, the sixth day after the water
withholding. On day 6, the drop in Ψsoil indicates the onset of dehydration in soil. During days
7-10 (Figure 6.2), the measured Ψlea f showed the same trend as the Ψstem when the plant was
stressed. We note that the measured peak ET is higher on days 7-10 than the other days with
SPC measurements. Based on Neumann 1973, the leaf water potential varies linearly with the
transpiration rate. The Ψlea f is more sensitive to the variations of ET than stem or root water
potential.176 The water potential difference between Ψlea f and Ψstem is smaller on days with low ET
(days 3-9).
Daily rehydration of maize can be seen in the increase of ΨµT M at night (Figure 6.2). The
nighttime rehydration stops after the ΨµT M drops below -1.5 MPa (day 10). The failure of rehy-
dration could result from the lack of water flow from the soil to the root, as well as the nocturnal
transpiration observed in ET (Figure 6.2c). The hydraulic conductance in rhizosphere and soil
decrease as water loss continues, as implied by their hydraulic properties.153
ΨµT M starts to respond about 30 minutes after the watering event on day 10. The ΨµT M takes
about 8 hours to relax from -1.4 MPa to about -0.2 MPa. This rehydrated water potential is the
about the same as the nighttime water potential before dry-down. The 8 hours represent the time
scale of rehydration for the whole soil volume and plant to a large flood irrigation event.
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Figure 6.4: Well-watered Dynamics of Maize Water Potential from Days 3 to 7. a. Dynamics of water
potential measured by a micro-tensiometer (solid blue line), Schölander pressure chamber measured leaf
water potential of the instrumented maize plant in solid red dots and of the neighbor maize plant in solid
blue dots. b. Digital scale measured transpiration (solid blue line). c. Vapor pressure deficit calculated from
the measured humidity and temperature. d. Photosynthetically active radiation (solid red line) measured by
the PAR sensor. e. Soil water potential (solid blue line) measured by the soil sensor.
201
On days 12 and 14, Ψstem increased to higher water potential than before dry-down in re-
sponse to irrigation events in the morning, then continued to decrease after that. This observation
is the same as what was shown in Neumann 1974.176 It suggests that the root water uptake is more
rapid than the transpiration, and results in a temporary rehydration.
A phase shift of ΨµT M relative to the environmental variables is observed. VPD, PAR or ET
reaches their maximum in the early afternoon around 3pm, while Ψstem reaches its lowest value
around 6pm. This phase delay indicates the ΨµT M is coupled to a hydraulic storage reservoir that is
preventing rapid responses to the fast dynamics of the environmental demand. This phenomenon
suggests the Ψstem below canopy is reflecting the root water potential which is closely coupled to
the soil.
6.2.3 Water Retention Curve of the Rhizosphere
Figure 6.5 compares the rhizosphere water retention curve generated using extracted predawn
micro-tensiometer measurements with the soil water retention based on the theory of dual-porosity
Turface soil and the data series in Figure 6.1ab and Figure 6.3.38
The soil water content (θ) for generating the rhizosphere water retention curve was calculated
based on the water balance of the soil:
Vpot · θi − ∆W/ρw,l
θ = (6.1)
Vpot
Where Vpot (cm3) represents the pot size; θ (cm3cm−3i ) represents the initial water content of
the soil at the beginning of the dry-down cycle; ∆W (kg) is the water loss through transpiration
measured using the digital scale; and ρ (kgm−3w,l ) represents liquid water density.
The effective water content (Θ) takes the following form, as mentioned in Chapter 5:
θ − θr
Θ =
θs −
(6.2)
θr
202
Figure 6.5: Modeled and Empirical Water Retention Curve. a. Modeled water retention curve (solid
blue dots connected by blue line) using the hydraulic parameters of the Turface soil, and the empirical
water retention (solid black dots connected by black line) curve generated from the extracted predawn water
potential from the ΨµT M and the water balance of soil. b. Comparing the modelled and empirical soil water
retention curve after the initial water content (θi) is shifted from 0.75 to 0.28, and the gap between the
empirical water potential at saturation is shifted upwards by 0.15 MPa.
203
where the saturated water content is θs = 0.75 (cm3cm−3), while the residual water content is
θr = 0.011 (cm3cm−3) for Turface.38
We use the following expression for the effective soil water content:38
Θ = w · [1 + (α · |Ψ |)−n1]−m1 + w · [1 + (α · |Ψ |)−n2)]−m2d 1 1 s 2 2 s (6.3)
In this expression for a dual porosity soil, w1 and w2 are unitless weighting factors of inter-
aggregate and intra-aggregate pores respectively; α −1 −11 (MPa ) and α2 (MPa ) are the inverse of
air entry potentials; n1, n2, m1, and m2 are factors that determine the shape of the water retention
curve.
Predawn water potential is extracted by taking average of micro-tensiometer measurements
from 5:30 am to 5:40 am daily during the entire dry-down period. Here, we are assuming that the
stem is not in equilibrium with the soil at pre-daawn, as we have discussed in Chapters 3 and 4,
this assumption may breakdown as the soil reached lower water potentials during dry-down.
Figure 6.5a compares the water retention curves of experimentally generated micro-
tensiometer based (black dots connected by a solid black line), and theoretically based using the
dual-porosity theory (blue dots connects by a solid blue line, 6.3) by assuming the initial water
content is at the saturated water content (θi = θs = 0.75) with respect to the inter-aggregate pores.
The rhizosphere water retention curve follows the similar trend as the theory-based water retention
curve, but with significant shifts with respect to both Θ and Ψs.
Figure 6.5b shows the shifted ΨµT M-based water retention curve (black dots connected by
a solid black line) in both the initial water content, and the saturated value of water potential.
The initial water content θi is changed from 0.75, the initial water content determined by inter-
aggregates, to 0.28, the one determined by intra-aggregates. The ΨµT M in saturated range is shifted
towards less negative by 0.15 MPa. This shift of -0.15 MPa corresponds to the pre-dawn value
of Ψstem observed during the well-watered period (days 1-6; Figure 6.2) and may be due to an
204
Pars Units Values Description
θs cm3cm−3 0.75 Saturated Water Content
θ cm3cm−3r 0.011 Residual Water Content
Inter-aggregate Pores
w1 n/a 0.56 Macropore Fraction
α1 MPa−1 2.75 Inverse of air entry potential
n1 n/a 2.78 Retention Curve Shape Factor
m1 n/a 1 − 1/n1 Retention Curve Shape Factor
Intra-aggregate Pores
w2 n/a 0.44 Micropore Fraction
α MPa−12 37.8 Intra-aggregate Pores
n2 n/a 1.73 Retention Curve Shape Factor
m2 n/a 1 − 1/n2 Retention Curve Shape Factor
Table 6.1: Parameters for Dual-Porosity Soil Retention Curve.38
205
osmotic potential in the soil. Surprisingly, the shifted experiment-based and the model-based soil
water retention curve (blue dots connects by a solid blue line) coincide with each other. This
correspondence between experiment and theory supports the assumption that the pre-dawn stem
water potential tracks the water stress of root and root-zone soil. ΨµT M can represent dynamic
water stress of the root-zone soil.
6.3 Conclusion
In this study, we demonstrated the micro-tensiometer as a potential tool for the measurements
of stem water potential in maize. A micro-tensiometer (µTM) was used to monitor the dynamic
stem water potential in maize during a dry-down and re-watering cycle, with the Schölander pres-
sure chamber (SPC) as benchmark. The predawn water potential was extracted from ΨµT M and
interpreted as water potential of the root-zone soil. These values allowed us to build an effective
water retention curve for the soil that correspond well with the theoretical water retention curve
for Turface soil.
Different from the leaf water potential that varies rapidly with changing environmental de-
mand, the stem water potential provides an assessment of the water stress of maize roots and
root-zone soil; water status in the root zone is challenging to measure by other means.
The application of micro-tensiometer in maize opens new opportunities for the study of
physics and biology of water relations in maize and other herbaceous plants. For example, the time
scale of physiological responses to drought stress could be addressed with this micro-tensiometer.
We could understand the transient response of stomatal conductance better. The pattern of dry-
down of stem water potential could help screen for drought tolerant cultivars and root phenotypes
for plant breeding. The dynamic water stress could be used to improve current multi-layer hy-
drological models for efficient water management and serve as ground-truth for remote sensing
technologies.
206
6.4 Supporting Information
Plant material
The maize (Zea mays L.) was planted in pots on December 21st, 2017 in Turface Soil. The
pots had a diameter of 10.5 inch, and a height of 9 inch. Turface soil in the pots had a height of
6.75 inch. The greenhouse light was turned on everyday at 6:00 am and off at 10:00 pm.
Micro-tensiometer
The micro-tensiometers were fabricated, packaged, and calibrated in the same manner as
described in previous chapters. Two micro-tensiometers were embedded in two adjacent maize
plants with the plants have 16 nodes and 12 leaves. One of the micro-tensiometers had a broken
wire after embedding. This maize plant is labeled as the “neighbor” plant. The other one survived
the entire experiment period, and is labeled as the “instrumented” plant.
Schölander pressure chamber
After embedding, each maize plant had 9 remaining leaves. Since the number of leaves was
limited, for each data point, only one leaf from each plant was taken for measurement from 13:00
to 15:00 most days during the dry-down process. Each sampled leaf was encapsulated in a plastic
bag and cut from the leaf tip for a length of about 20 cm. The midday stem water potential was
then measured using a Schölander pressure chamber (SPC).
The impact of cut leaves on maize water relations was minimal. Since there was no noctur-
nal transpiration at during the experiment except day 10, the most drought stressed day, minimal
amount of water was lost due to the cut of the maize leaves for pressure chamber measurements.
This phenomenon is probably because the menisci recedes back into the veins of the leaf after
cutting. The menisci connect to the outside across a tube(vein) filled with water saturated air. The
saturated air functions as a good barrier of water vapor transport. The wound response of maize
could be another reason.
207
Micro-meteorological measurements
The micro-climate weather station was placed within 2 meters of measured maize plant,
without shading from the other plants. A CR6 (Campbell Scientific, Inc) was used for datalog-
ging from the micro-tensiometers and the micro-climatic sensors. The datalogging programs are
shown in Appendix B. LI-193 spherical PAR Sensor supplier was used for the measurements of
photosynthetically active radiation. HMP60 supplier was used for the measurement of humid-
ity and temperature. A digital scale (WFK 75H, Adams Equipment) was used to measure the
maize plant weight together with soil for the calculations of irrigation and transpiration. MPS6
(Decagon Devices, Inc) was used to measure soil water potential. The windspeed sensor (C2192,
elecmaker.com), as expected, showed zero wind in the greenhouse.
208
CHAPTER 7
SUMMARY AND CONCLUSION
Climate change induced global warming results in uneven distribution and frequency of pre-
cipitation globally, increased the global demand of evaporation, and therefore, reduced the fresh-
water resources. Irrigated agriculture consumes up to 70% of water withdrawal by human but only
supplies 40% of global demand of calories. With the growth of population approaching 9.7 billion,
it is important for us to develop strategies to manage water use more efficiently.
My research emphasized the development of a new hygrometer, a micro-tensiometer, for in
situ monitoring of stem water potential in trees and crops with high accuracy and high temporal res-
olution. This new tool could open new opportunities for studies of drought response and tolerance
of plants, as well as developing plant-based irrigation control for enhanced water use efficiency. To
the best of our knowledge, no existing hygrometers could provide in situ measurements of plant
water stress under outdoor scenarios reliably, accurately, and continuously.
Micro-tensiometer development and first trials in greenhouses
In Chapter 2, we described the design ideas of the micro-tensiometer by combining the tra-
ditional tensiometry approach with the cutting-edge micro-electro-mechanical systems (MEMS)
technique. When compared with the 1st version,14 we: 1) implemented a "synthetic tree" approach
to shorten the response time of sensors from hours to a couple of minutes; 2) designed patterned
mesoporous silicon membrane that could enhance stability of the sensors, while also facilitate
shortening the response time; 3) reduced the form factor from 12x10 to 5x5 mm×mm; 4) changed
the electronics from aluminum to platinum for anti-corrosion in outdoor scenarios; and 5) designed
the platinum resistance thermometer (PRT) for in situ temperature measurements. Besides the im-
provement on the fabrication, we also developed the osmotic calibration methods, as well as the
anti-corrosion packaging strategies for outdoor applications.
209
We conducted preliminary experiments on apple trees inside greenhouses, showed compara-
ble water stress measurements from the micro-tensiometers and the Schölander pressure chamber
(SPC), a widely accepted ex situ manual-operated hygrometer, and discovered that the "psychro-
metric effect" could be the major source of error when the sensor and the tissue in contact cannot
reach thermal equilibrium. Building the liquid and thermal contact between the tissue and sensor
is crucial for accurate measurements.
Measurements of Dynamic Water Stress on Trees and Crops under Well-Watered and Water
Stressed Conditions
After the greenhouse testing of micro-tensiometer in Chapter 2, we moved the testing of
micro-tensiometers to outdoor environment. In Chapter 3, we showed the micro-tensiometer mea-
surements on apple, grapevine, and almond under rainfed, semi-arid and arid scenarios respec-
tively. Accurate monitoring by the micro-tensiometer could last as long as 12 months. The mea-
surements are comparable with the SPC measurements. Nighttime water stress occurred in both
apple and grapevine when the windspeed and vapor pressure deficit are high during the night.
Moreover, we observed that the water stress of plants showed multiple timescales that we inter-
preted as reflecting multiple compartments along the soil-plant-atmosphere continuum (SPAC).
The response time of soil grows as the lack of water supply proceeds. The response timescale of
plants is more rapid to environmental demand, while the upper limit of their nighttime rehydration
is constrained by the soil stress level. The idea of using circuit models177 to interpret the observed
dynamics in water stress is proposed in this chapter.
In Chapter 5, we presents measurements of stem water potential in maize inside the green-
house. This is the first trial of micro-tensiometer in herbaceous plants. We used the µTM to record
one dry-down cycle of maize. Again, the Schölander pressure chamber (SPC) was used to validate
the water potential of maize, although only leaf water potential could be measured when using
SPC. ΨS PC was closer to ΨµT M on rainy and cloudy days, but more negative on sunny days. This
difference suggests a large hydraulic resistance between the stem and the leaf. Considering the
210
small amplitude of diurnals sensed with the µTM, we suggest that the ΨµT M tracks the integration
of the root-rhizosphere water potential. A water retention curve was generated based on the soil
water balance and ΨµT M. Surprisingly, this water retention curve coincides with the one generated
based on the soil hydraulic parameters from the Turface soil.38 This observation demonstrates the
potential of micro-tensiometers as hygrometer for the measurement of dynamic root-zone water
stress for herbaceous plants.
Modeling the Observed Dynamic Water Stress from Apple Trees
The idea of using circuit analog to represent plant water relations has been initiated decades
ago.177 However, few examples exist in the literature of measurements of dynamic water stress. As
mentioned in Chapter 3, we would like to use circuit models to interpret the dynamic water stress
we observed in woody plants.
Empirical data from two experiments were used to compare with the models developed:
the 2017 Field Apple experiment under well-watered conditions, and the 2018 Potted Apple dry-
down experiment under water-stressed conditions. One resistor-capacitor (RC) compartment (1-
RC) model with fixed soil water potential, driven by the predicted transpiration with the Penman-
Monteith equation,124 is sufficient for capturing the dynamic water stress during 2017 Field Apple
experiment. By allowing the stomatal to be partially open at night, we was able to make sense of
the observed nighttime water stress. We also showed that 2-RC circuit model with five parameters
was sufficient for simulating the dynamic water stress during the dry-down cycle of 2018 Potted
Apple under outdoor scenario. Compared to the 1-RC model, the soil water potential is determined
by the water retention properties of soil as dry-down proceeds.
By taking advantage of the continuous data from the micro-tensiometers, we propose circuit
models with minimized number of parameters to predict the dynamic water stress under both well-
watered and water-stressed conditions. The models could be used to develop a predictive control
system for plant-based irrigation to optimize the water use efficiency. They could also be a tool
211
for further exploring the drought response of trees such as stomatal regulation and the hydraulic
architecture of roots.
Response of an Apple Tree to Controlled Irrigation Events
To move forward on the path of developing plant-based irrigation control, a controlled irriga-
tion experiment was conducted to explore the response of stem water potential to irrigation events
with different amount of water at different time of the day. The details are discussed in Chapter 6.
Potted apple trees with embedded micro-tensiometers were drip-irrigated under the control
of solenoid valves operated using a Raspberry Pi. Python programs were launched on Raspberry
Pi to determine the time and amount of irrigation. Weather forecast was used to estimate the
cumulative transpiration for the upcoming day. Digital scale was used to monitor the real water
loss and amount of irrigation to the potted apple tree.
My main discoveries are: 1) the tree did not respond to midday irrigation events unless more
than 120% of cumulative ET (ETcum) was irrigated when the tree was severely stressed. We suggest
that the reason could be the disconnection between active roots and retrievable water during active
transpiration due to root shrinkage; 2) during the following night, the tree that did not respond to
daytime irrigation rehydrates to a higher water potential value when compared to the preceding
night, due to the further absorbance of water stored in the soil; 3) the tree responded to even
10% of ETcum at night with increasingly strong response when the tree became more stressed;
and 4) predawn irrigation with forecasted ETcum prevented dehydration of the tree during the day,
although no significant response to irrigation events was observed.
The above discoveries emphasize the importance of understanding the response timescale of
roots to irrigation events at different time of the day, as well as the soil water balance. My results
suggest launching irrigation in field scenarios during the night or at predawn with predicted total
water loss of the following day to prevent dehydration of trees, since the root-soil disconnection
during the day could result in water loss through drainage. Furthermore, it costs significant amount
212
of water to improve the root-soil contact during the day.
Future Opportunities with the Micro-tensiometer
With this dissertation, we demonstrated micro-tensiometer as a new tool for sensing the
dynamic water stress of trees and crops, developed models to validate the observed dynamic water
stress, and then explored the complexity of controlled irrigation for trying to maintain plant under
mild stress. The micro-tensiometer opens up opportunities for both fundamental studies on water
relations of plants and for applications for more efficient management of agricultural water use.
Monitoring the dynamic water stress of plants provides an opportunity to enhance our un-
derstanding of plant water relations by reinforcing the time factor of drought response of plants.
Problems regarding the timescale of stomatal regulation and of root water uptake could be ad-
dressed. Moreover, nighttime dynamic water stress can be further studied without the constraints
from human labor. The pattern of dynamic water stress during dehydration could be closely related
to the hydraulic architecture of roots and to the water retention properties of rhizosphere. With
more efficient method of fabrication and embedding, the micro-tensiometers could be applied for
plant breeding to select drought tolerant genotypes.
Along the path of plant-based irrigation control using the micro-tensiometer, more studies
and experiments are required to develop models and strategies to maintain the plants at certain mild
stress level. For a certain crop species, the method of irrigation, water retention properties of soil,
the response time of plants to irrigation and the timing of irrigation are crucial factors. Among
all important determinants, the varying response timescale of root and rhizosphere to different
amount of irrigated water at different stress level of plants is the most challenging for developing
an efficient controlled irrigation system.
213
APPENDIX A
MICRO-TENSIOMETER MASK DESIGN WITH L-EDIT CAD
214
Figure A.1: Layers of Micro-fabrication for Micro-tensiometers.
215
Figure A.2: Design of Piezo-resistors.
216
Figure A.3: Micro-Tensiometer 1x2 Cavity.
217
Figure A.4: Micro-Tensiometer 1.5x3 Cavity.
218
Figure A.5: Micro-Tensiometer 2x3.5 Cavity.
219
Figure A.6: Micro-Tensiometer 3.5x4 Cavity.
220
Figure A.7: Micro-tensiometer Double Wheatstone Bridge.
221
APPENDIX B
CRBASICEDITOR PROGRAMS FOR DATA COLLECTION
B.1 Data Acquisition of the Micro-tensiometers and Micro-climatic
Weather Station, and Transmission to the IoT platform Ubidots
’CR6 Series
’Created by Short Cut (3.1)
’Author Siyu Zhu
’Declare Variables and Units
’ P21 P47
’ HMP60 for RH and Room T: brown 12V; clear and blue: G; Temp: black-U7:
↪→ RH: while-U8
’ Windspeed: sensor-brown-red: 12 V; sensor-black-black: G; sensor-blue-
↪→ white: signal-U4
’ PAR: blue: low-U12; green: high-U11;
’ Solar Intensity:
’ Digital Scale 35: Red: RX-C1; Green: TX-C2; Black: G.
’ Digital Scale 75: Red: RX-C3; Green: Tx-C4; Black: G.
’ Soil Sensor: white: power; red: C3 signal; bare: G
’ micro-tensiometer: V73 V75 V95 M75 M81
Const snum = 5
Const scaninterval = 60
Dim i
Public BattV
222
Public PTemp_C
Public LCount
Public FullBR(snum)
Public Psensor(snum)
Public Tsensor(snum)
Public Resist(snum)
Public SlrkW
Public SlrMJ
Public roomT
Public roomRH
Public PAR_Den
’Public PAR_Tot
Public Windspeed
Public Pin(8)={11,12,13,14,15,16,17,18}
’ micro-tensiometer: V73 M75 M73 M81 M80
Public mprt(snum) ={4.142364948, 4.869566821, 4.867016274, 4.936455461,
↪→ 4.912980414}
Public bprt(snum) ={1389.163979, 1681.306589, 1685.188278, 1690.470989,
↪→ 1701.958853}
Public mbrt(snum)= {-0.001479959, -0.014763669, -0.014672959,
↪→ -0.013760097, -0.016604648}
Public bbrt(snum) ={-2.298574629, 5.000137849, 4.292633931, 3.904577519,
↪→ 5.63353644}
Public mbrp(snum) ={0.030514041, 0.027390138, 0.030394168, 0.030478299,
↪→ 0.033496951}
223
Public bbrp(snum) ={-0.513319294, -0.044215941, -0.063313505, 0.002192339,
↪→ 0.06310442}
Public offset(snum) = {380,3,0,75,-45}
Units BattV=Volts
Units PTemp_C=Deg C
Units FullBR=mV/V
Units Resist = ohm
Units Psensor = bar
Units Tsensor = Deg C
Units roomT = Deg C
Units roomRH = %RH
Units SlrkW=kW/m^2
Units SlrMJ=MJ/m^2
Units PAR_Den=umol/s/m^2
’Units PAR_Tot=mmol/m^2
Units Windspeed = m/s
’Define Data Tables
DataTable(SZ072619,True,-1)
DataInterval(0,scaninterval,Sec,10)
Average(1,Psensor(1),IEEE4,False)
Average(1,Psensor(2),IEEE4,False)
Average(1,Psensor(3),IEEE4,False)
Average(1,Psensor(4),IEEE4,False)
Average(1,Psensor(5),IEEE4,False)
’ Average(1,Psensor(6),IEEE4,False)
224
’ Average(1,Psensor(7),IEEE4,False)
’ Average(1,Psensor(8),IEEE4,False)
Average(1,Tsensor(1),IEEE4,False)
Average(1,Tsensor(2),IEEE4,False)
Average(1,Tsensor(3),IEEE4,False)
Average(1,Tsensor(4),IEEE4,False)
Average(1,Tsensor(5),IEEE4,False)
’ Average(1,Tsensor(6),IEEE4,False)
’ Average(1,Tsensor(7),IEEE4,False)
’ Average(1,Tsensor(8),IEEE4,False)
Average(1,FullBR(1),IEEE4,False)
Average(1,FullBR(2),IEEE4,False)
Average(1,FullBR(3),IEEE4,False)
Average(1,FullBR(4),IEEE4,False)
Average(1,FullBR(5),IEEE4,False)
’ Average(1,FullBR(6),IEEE4,False)
’ Average(1,FullBR(7),IEEE4,False)
’ Average(1,FullBR(8),IEEE4,False)
Average(1,Resist(1),IEEE4,False)
Average(1,Resist(2),IEEE4,False)
Average(1,Resist(3),IEEE4,False)
Average(1,Resist(4),IEEE4,False)
Average(1,Resist(5),IEEE4,False)
’ Average(1,Resist(6),IEEE4,False)
225
’ Average(1,Resist(7),IEEE4,False)
’ Average(1,Resist(8),IEEE4,False)
EndTable
DataTable(SZ072619vpdsli,True,-1)
Average(1,BattV,IEEE4,False)
Average(1,PTemp_C,IEEE4,False)
Average(1,roomT,IEEE4,False)
Average(1,roomRH,IEEE4,False)
Average(1,SlrkW,IEEE4,False)
’ Average(1,SlrMJ,IEEE4,False)
Average(1,PAR_Den,IEEE4,False)
’ Totalize(1,PAR_Tot,IEEE4,False)
Average(1,Windspeed,IEEE4,False)
EndTable
’Main Program
BeginProg
’ Main Scan
Scan(scaninterval,Sec,1,0)
’ Default Datalogger Battery Voltage measurement ’BattV’
Battery(BattV)
’ Default Wiring Panel Temperature measurement ’PTemp_C’
PanelTemp(PTemp_C,60)
’ measure humidity and temperature from HMP60
VoltSe(roomT,1,AutoRange,U7,False,0,60,0.1,-40)
VoltSe(roomRH,1,AutoRange,U8,False,0,60,0.1,0)
226
’ measure solar intensity using LI200
VoltDiff(SlrkW,1,mV200,U9,True,0,60,1,0)
If SlrkW<0 Then SlrkW=0
SlrMJ=SlrkW*0.0006642753
SlrkW=SlrkW*0.1328551
’ run spherical solar sensor LI193
VoltDiff(PAR_Den,1,mV200,U11,True,0,60,1,0)
’ If PAR_Den<0 Then PAR_Den=0
PAR_Den=PAR_Den*101.66 ’ the wrong number was 245.6423
’ run windspeed sensor
VoltSe(Windspeed,1,mV5000,U4,True,10000,60,0.02025,-8.1)
’ Collect Data from Micro-Tensiometers
’ Turn on Muxselect
PortSet(U2,1)
Delay(0,150,mSec)
LCount = 1
SubScan(0,uSec,snum)
PulsePort(U1,10000)
BrFull(FullBR(LCount),1,mV5000,U5,U3
↪→ ,1,500,1,1,10000,60,1,0)
LCount = LCount + 1
NextSubScan
LCount = 1
PortSet(U2,0)
Delay(0,150,mSec)
227
MuxSelect(U1,U2,5,8,1)
LCount = 1
SubScan(0,uSec,snum)
’Switch to next AM16/32 Multiplexer channel
PulsePort(U1,10000)
’Generic Resistance measurements ’FullBR()’ on the AM16/32 Multiplexer
Resistance(Resist(LCount),1,mV5000,U5,U3
↪→ ,1,200,1,1,10000,60,1,0)
LCount=LCount+1
NextSubScan
’Turn AM16/32 Multiplexer Off
PortSet(U2,0)
Delay(0,150,mSec)
LCount = 1
’Test Code with Assigned Data
’convert the direct measurements into water potential and bars
Tsensor() = (Resist()-bprt())/mprt()
Psensor() = (FullBR()-mbrt()*Tsensor()-bbrt()-bbrp())/mbrp()
↪→ -offset()
’Call Data Tables and Store Data
CallTable SZ072619
228
CallTable SZ072619vpdsli
’Send data to Raspberry Pi
SerialOpen (ComC3,4800,16,0,50,2)
’BattV
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"BattV ="&";","",0,100)
SerialOut (ComC3,BattV&",","",0,100)
’TimeStamp
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"TimeStamp ="&";","",0,100)
SerialOut (ComC3,SZ072619.TimeStamp(1,1)&",","",0,100)
’TestPin
SerialOut (ComC3,"Pin="&";","",0,100)
For i=1 To snum Step 1
SerialOut (ComC3,Pin(i)&",","",0,100)
’Resist
Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"Resist="&";","",0,100)
For i=1 To snum Step 1
SerialOut (ComC3,Resist(i)&",","",0,100)
229
’FullBr
Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"FullBr="&";","",0,100)
For i=1 To snum Step 1
SerialOut (ComC3,FullBR(i)&",","",0,100)
’Tsensor
Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"Tsensor="&";","",0,100)
For i=1 To snum Step 1
SerialOut (ComC3,Tsensor(i)&",","",0,100)
’Psensor
Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"Psensor="&";","",0,100)
For i=1 To snum Step 1
SerialOut (ComC3,Psensor(i)&",","",0,100)
’PAR
Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"PAR="&";","",0,100)
SerialOut (ComC3,PAR_Den&",","",0,100)
230
’SlrkW
’ Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"SlrkW ="&";","",0,100)
SerialOut (ComC3,SlrkW&",","",0,100)
’Windspeed
’ Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"Windspeed ="&";","",0,100)
SerialOut (ComC3,Windspeed&",","",0,100)
’roomT
’ Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"roomT ="&";","",0,100)
SerialOut (ComC3,roomT&",","",0,100)
’roomRH
’ Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,"roomRH ="&";","",0,100)
SerialOut (ComC3,roomRH&",","",0,100)
’ Next
SerialOut (ComC3,";","",0,100)
SerialOut (ComC3,CHR(10),"",0,100)
231
NextScan
B.2 CRBasicEditor Program for Data Acquisition of Digital Scale
’For programming tips, copy this address to your browser
’search window:https://www.campbellsci.com/videos/datalogger-programming
’CR6 Series Datalogger
’Program author: Siyu Zhu
Public PTemp, Batt_volt
’Define Data Tables
DataTable (Test,1,-1) ’Set table size to # of records, or -1 to
↪→ autoallocate.
DataInterval (0,15,Sec,10)
Minimum (1,batt_volt,FP2,False,False)
Sample (1,PTemp,FP2)
EndTable
’Main Program
BeginProg
Scan (1,Sec,0,0)
PanelTemp (PTemp,15000)
Battery (Batt_volt)
’Enter other measurement instructions
232
’Call Output Tables
’Example:
CallTable Test
NextScan
EndProg
B.3 CRBasicEditor Program for Soil Water Potential Monitoring
’CR6 Series
’Created by Short Cut (4.1)
’Author: Siyu Zhu
’Declare Variables and Units
Dim LCount
Public BattV
Public PTemp_C
Public Temp
Public kohms(10)
Public WP_kPa(10)
Const scanfreq = 60 ’sec
Const R_0 = 100
’for RPI
Public Pin(10) = {21,22,23,24,25,26,27,28,29,30}
Dim i
Const snum = 10
233
Units BattV=Volts
Units PTemp_C=Deg C
Units Temp= Deg C
Units kohms=kilohms
Units WP_kPa=kPa
’Define Data Tables
DataTable(SZ071819SL,True,-1)
DataInterval(0,scanfreq,Sec,10)
Average(1,Temp,IEEE4,False)
Sample(1,kohms(1),IEEE4)
Sample(1,kohms(2),IEEE4)
Sample(1,kohms(3),IEEE4)
Sample(1,kohms(4),IEEE4)
Sample(1,kohms(5),IEEE4)
Sample(1,kohms(6),IEEE4)
Sample(1,kohms(7),IEEE4)
Sample(1,kohms(8),IEEE4)
Sample(1,kohms(9),IEEE4)
Sample(1,kohms(10),IEEE4)
’ Sample(1,kohms(11),IEEE4)
’ Sample(1,kohms(12),IEEE4)
Sample(1,WP_kPa(1),IEEE4)
Sample(1,WP_kPa(2),IEEE4)
Sample(1,WP_kPa(3),IEEE4)
Sample(1,WP_kPa(4),IEEE4)
Sample(1,WP_kPa(5),IEEE4)
234
Sample(1,WP_kPa(6),IEEE4)
Sample(1,WP_kPa(7),IEEE4)
Sample(1,WP_kPa(8),IEEE4)
Sample(1,WP_kPa(9),IEEE4)
Sample(1,WP_kPa(10),IEEE4)
’ Sample(1,WP_kPa(11),IEEE4)
’ Sample(1,WP_kPa(12),IEEE4)
EndTable
’Main Program
BeginProg
’Main Scan
Scan(scanfreq,Sec,1,0)
’Default CR6 Datalogger Battery Voltage measurement ’BattV’
Battery(BattV)
’Default CR6 Datalogger Wiring Panel Temperature measurement
↪→ ’PTemp_C’
PanelTemp(PTemp_C,60)
’Generic Resistance measurements ’Temp’
Resistance(Temp,1,mV5000,U11,U9,1,200,True,True
↪→ ,10000,60,1,0)
PRTCalc(Temp,1,Temp/R_0,1,1,0)
’Turn AM16/32 Multiplexer On
PortSet(U2,1)
Delay(0,150,mSec)
LCount=1
SubScan(0,uSec,12)
235
’Switch to next AM16/32 Multiplexer channel
PulsePort(U1,10000)
’253 Soil Moisture Sensor measurements ’kohms()’ and
↪→ ’WP_kPa()’ on the AM16/32 Multiplexer
BrHalf(kohms(LCount),1,mV200,U5,U3,1,200,True
↪→ ,0,15000,1,0)
’Convert resistance ratios to kilohms
kohms(LCount)=1.8*kohms(LCount)/(1-kohms(LCount))
LCount=LCount+1
NextSubScan
’Convert kilohms to water potential
For LCount=1 To 12
WP_kPa(LCount)=(100+(1.8*Temp+32)-69.8)/100*kohms(
↪→ LCount)
If kohms(LCount)<=1 Then
WP_kPa(LCount)=-(20*kohms(LCount)-11)
Else
WP_kPa(LCount)=-(-0.00279*kohms(LCount)
↪→ ^3+0.19109*kohms(LCount)^2+3.71485*kohms
↪→ (LCount)+6.73956)
EndIf
Next
’Turn AM16/32 Multiplexer Off
PortSet(U2,0)
Delay(0,150,mSec)
’Call Data Tables and Store Data
CallTable SZ071819SL
236
’ Send Data to RPI
SerialOpen(ComC3,4800,16,0,50,2)
’BattV
SerialOut(ComC3,";","",0,100)
SerialOut(ComC3,"BattV ="&";","",0,100)
SerialOut(ComC3,BattV&",","",0,100)
’SoilTemp
SerialOut(ComC3,";","",0,100)
SerialOut(ComC3,"Temp ="&";","",0,100)
SerialOut(ComC3,Temp&",","",0,100)
’TimeStamp
SerialOut(ComC3,";","",0,100)
SerialOut(ComC3,"TimeStamp = "&";","",0,100)
SerialOut(ComC3,SZ071819SL.TimeStamp(1,1)&",","",0,100)
’TestPin
SerialOut(ComC3,"Pin="&";","",0,100)
For i = 1 To snum Step 1
SerialOut(ComC3,Pin(i)&",","",0,100)
Next
’kohm
SerialOut(ComC3,"kohms="&";","",0,100)
237
For i = 1 To snum Step 1
SerialOut(ComC3,kohms(i)&",","",0,100)
Next
’WP_kpa
SerialOut(ComC3,"WP_kpa="&";","",0,100)
For i = 1 To snum Step 1
SerialOut(ComC3,WP_kPa(i)&",","",0,100)
Next
238
APPENDIX C
PYTHON PROGRAMS FOR IRRIGATION CONTROL
C.1 Program for launching irrigation events
Check Internet Connection
’’’Checks every ten minutes is the raspberry pi is connected to internet,
if yes, uploads to ubidots the connection status,
if not disconnect and reconnect to internet running two bash commands.’’’
import os
from time import sleep
from ubidot_save import post_request
experiment_running=True
myCmd1= ’sudo hologram modem disconnect’ #a bash command to disconnect
↪→ from internet
myCmd2 = ’sudo hologram modem connect’ #a bash command to connect to
↪→ internet
#These commandes will only work with the hologram nova 3g dongle.
#In the case where a wifi is around or another kind of 3g dongle is being
↪→ used
#this is not necessary
while experiment_running:
received=False
payload={’signal’: []}
try:
payload[’signal’].append({"value":1})
post_request(payload,"signal")
239
except:
os.system(myCmd1)
os.system(myCmd2)
sleep(600) #wait 10 minutes
save Data from Dataloggers
@Save Data from the CR6 Datalogger.
from Datalogger.CR6_com import get_all_data_sensor
from time import sleep
from ubidot_save import post_request
import numpy as np
from datetime import datetime, timedelta
delta_upload_data=timedelta(minutes=5) #Upload data every 30 minutes
experiment_running=True
number_of_points=0
time_start=datetime.now()
l=-1
payload={}
payload_weather={}
payload_CR6={}
while experiment_running:
received=False
while received==False:
try:
received,dic_CR6=get_all_data_sensor()
240
except:
sleep(10)
print(received, l)
timestamp=dic_CR6[’timestamp’].timestamp()*1000
number_of_points
if payload=={}:
for i in range(5):
for data in [’Resist’,’FullBr’,’Tsensor’,’Psensor’]:
payload[data+str(dic_CR6[’pin’][i])]=[]
for i in range(5):
for data in [’Resist’,’FullBr’,’Tsensor’,’Psensor’]:
if np.isnan(dic_CR6[data][i]):
payload[data+str(dic_CR6[’pin’][i])].append({"value":0, "
↪→ timestamp": timestamp})
else:
payload[data+str(dic_CR6[’pin’][i])].append({"value":dic_CR6
↪→ [data][i], "timestamp": timestamp})
if payload_weather=={}:
for data in [’PAR’,’SlrkW’,’Windspeed’,’roomT’,’roomRH’,’VPD’]:
payload_weather[data]=[]
for data in [’PAR’,’SlrkW’,’Windspeed’,’roomT’,’roomRH’,’VPD’]:
payload_weather[data].append({"value":dic_CR6[data],"timestamp":
↪→ timestamp})
if payload_CR6=={}:
for data in [’BattCR6’]:
payload_CR6[data]=[]
for data in [’BattCR6’]:
241
payload_CR6[data].append({"value":dic_CR6[data],"timestamp":
↪→ timestamp})
if datetime.now()>=time_start+l*delta_upload_data:
print(’saving data’)
for i in range(5):
for data in [’Resist’,’FullBr’,’Tsensor’,’Psensor’]:
try:
L=np.load(’Data/’+data+str(int(dic_CR6[’pin’][i])))
except:
np.save(’Data/’+data+str(int(dic_CR6[’pin’][i])),[])
L=np.load(’Data/’+data+str(int(dic_CR6[’pin’][i]))+’.npy
↪→ ’)
liste_completed=np.concatenate((L,payload[data+str(dic_CR6[’
↪→ pin’][i])]))
np.save(’Data/’+data+str(int(dic_CR6[’pin’][i])),
↪→ liste_completed)
print("Uploading Data")
try:
post_request(payload,"sensors")
post_request(payload_weather,"weather")
post_request(payload_CR6,"Info_CR6")
payload={}
payload_weather={}
payload_CR6={}
except:
sleep(10)
l+=1
242
sleep(10)
Launch Irrigation
import RPi.GPIO as GPIO
import time
from datetime import datetime
from get_sensor_data import get_sensor_data
GPIO.setmode(GPIO.BCM)
GPIO.setup(22, GPIO.OUT) # tree4 not working to tree1 and tree2
GPIO.setup(27, GPIO.OUT) # tree1 to tree4
GPIO.setup(17, GPIO.OUT) # tree5
GPIO.output(22,False)
GPIO.output(27,False)
GPIO.output(17,False)
Check Irrigation
import RPi.GPIO as GPIO
from datetime import datetime, timedelta
from time import sleep
from ubidot_save import post_request
GPIO.setmode(GPIO.BCM)
pins=[22,27,17]
delta_upload_data=timedelta(minutes=5) #Upload data every 5 minutes
experiment_running=True
time_start=datetime.now()
for pin in pins:
GPIO.setup(pin,GPIO.OUT)
243
def check_irrigation():
opened={}
for pin in pins:
state = 1-GPIO.input(pin)
opened[pin]={’value’ : state, ’timestamp’ : int(datetime.now().
↪→ timestamp()*1000)}
return(opened)
payload={}
l=0
while experiment_running:
opened=check_irrigation()
if payload=={}:
for pin in opened.keys():
payload[’valve’+str(pin)]=[]
for pin in opened.keys():
payload[’valve’+str(pin)].append(opened[pin])
if datetime.now()>=time_start+l*delta_upload_data:
print("Uploading Data",datetime.now())
try:
post_request(payload,"irrigation")
payload={}
payload_weather={}
payload_CR6={}
print("finish",datetime.now())
except:
sleep(1)
244
l+=1
sleep(15)
Launch Irrigation at Desired Time
import RPi.GPIO as GPIO
import time
from datetime import datetime
from get_sensor_data import get_sensor_data
GPIO.setmode(GPIO.BCM)
GPIO.setup(22, GPIO.OUT)
GPIO.setup(27, GPIO.OUT)
GPIO.setup(17, GPIO.OUT)
GPIO.output(22,True)
GPIO.output(27,True)
GPIO.output(17,True)
experiment_running = True
while experiment_running:
now = datetime.now(tz=None)
print(now)
if datetime(2019,8,17,0,0,0) <= now <= datetime(2019,8,17,0,1,10) :
#if current is under a certain threshold
for i in range(1):
245
print("start continuous irrigation") #irrigate for 2 minutes
GPIO.output(22,True) # tree 1 & 2
GPIO.output(27,False) # tree4
GPIO.output(17,True)# tree 5
time.sleep(7*60*60)
GPIO.output(22,True)
GPIO.output(27,True)
GPIO.output(17,True)
print("stop continuous irrigation")
time.sleep(60)
Fetch Data to the IoT Platform
import time
import requests
import random
’’’see ubidots API documentation to understand better what’s happening’’’
TOKEN = "BBFF-x5U0hl4eYphqtNNjra0JKhr0yq2WYM" # Put your TOKEN here
def post_request(payload,device_label):
# Creates the headers for the HTTP requests
url = "http://things.ubidots.com"
url = "{}/api/v1.6/devices/{}".format(url, device_label)
headers = {"X-Auth-Token": TOKEN, "Content-Type": "application/json"}
# Makes the HTTP requests
req = requests.post(url=url, headers=headers, json=payload)
status = req.status_code
246
# Processes results
if status >= 400:
print("[ERROR] Could not send data after 1 attempts, please check \
your token credentials and internet connection")
return False
print("[INFO] request made properly, your device is updated")
return True
Weather Forecast Data Acquisition
from Weather.weather_forecast import *
from Weather.atmosim_API import *
from datetime import datetime, timedelta, timezone
from pandas import DataFrame
elements_forecast=[
’rhm’, #Relative Humidity
’temp’, #Temperature
’sky’, #Cloud coverage
’wspd’, #Windspeed
]
elements_rtma=[
’temp’, #temperature
’sky’, #Cloud coverage
’wspd’, #Windspeed
]
247
coordinates=[42.4, -76.5] #Coordinate of the experimental site
#Time_zone_delta compare to UTC
current_timezone=’America/New_York’
time_zone_delta=timezone(timedelta(hours=-4))
dic_weather={}
dic_weather=update_forecast(coordinates,current_timezone,elements_forecast
↪→ ,dic_weather)
dic_weather=update_observation(coordinates,current_timezone,elements_rtma,
↪→ dic_weather)
dic_weather[’temp’]
help(get_Temp_forecast)
date = datetime(2019,10,1,23,0,0)+timedelta(hours=1)
#date=datetime.now()+timedelta(hours=1)
Temp=get_Temp_forecast(24,date,dic_weather[’temp’])
print(Temp)
RH=get_RH_forecast(24,date,dic_weather[’rhm’])
print(RH)
WS=get_WS_forecast(24,date,dic_weather[’wspd’])
print(WS)
248
help(get_Qrad_forecast)
Qrad,times=get_Qrad_forecast(24,date,dic_weather[’sky’],coordinates,
↪→ time_zone_delta)
print(Qrad,times)
#returns kW/m^2
#Timestamps is a number of microsecond since a given origin of time : see
↪→ https://en.wikipedia.org/wiki/Unix_time
df = DataFrame({’timestamp’:times,’Temp’:Temp,’RH’:RH, ’WS’:WS,’Qrad’:Qrad
↪→ })
df.to_excel(r’C:\Users\tang7\Dropbox\1-Data\Data 2019\2019
↪→ _08_06_Irrigation_Data_Analysis\wfsz.xlsx’)
C.2 Supportive Python Programs
CR_com.py
import time
import json
import numpy as np
from datetime import datetime
#import serial
string_test = ’;BattV =;12.97138,;TimeStamp =;07/13/2019 00:21:00,Pin
↪→ =;2,3,4,17,5,6,7,;Resist=;NAN,1432.885,-3909.159,NAN
↪→ ,1412.76,1416.836,-66.13998,;FullBr
249
↪→ =;-1.978689,-4.408078,87.87556,-2.640025,-3.76715,-4.449905,5.014434,;
↪→ Tsensor=;NAN,12.79603,-1295.349,NAN,20.58054,17.99043,-381.9137,;
↪→ Psensor=;NAN,1.630483,33351.32,NAN,-40.49984,6.721006,-144.8095,;PAR
↪→ =;2000,;SlrkW =;1000,;Windspeed =;5,;roomT =;25,;roomRH =;100,;\n’
A=-1.044e4
B=-11.29
C=-2.7e-2
D=1.289e-5
E=-2.478e-9
F=6.456
def get_all_data_sensor():
# ser = serial.Serial(
# port=r’/dev/ttyS0’,
# baudrate = 4800,
# parity=serial.PARITY_NONE,
# stopbits=serial.STOPBITS_ONE,
# bytesize=serial.EIGHTBITS,
# timeout=1.0)
# x= ser.readline()
# x=ser.readline().decode(’utf8’)
## x=ser.readline().decode(’utf8’)
# ser.close()
x=string_test
dic_data={}
# FullBr=np.array(liste[5].split(","))[:8].astype(np.float)
# print(pin,Resist,FullBr)
if len(x)==0:
250
return(False,dic_data)
else:
liste=x.split(";")
dic_data[’BattCR6’]=float(liste[2][:-1])
timestring=liste[4]
month=int(timestring[0:2])
day=int(timestring[3:5])
year=int(timestring[6:10])
hour=int(timestring[11:13])
minute=int(timestring[14:16])
second=int(timestring[17:19])
date=datetime(year,month,day,hour,minute,second)
dic_data[’timestamp’]=date
dic_data[’BattV’]=float(liste[2][:-1])
# dic_data[’Ptemp_C’]=float(liste[6][:-5])
dic_data[’pin’]=np.array(liste[5].split(","))[:7].astype(np.float)
dic_data[’Resist’]=np.array(liste[7].split(","))[:7].astype(np.
↪→ float)
dic_data[’FullBr’]=np.array(liste[9].split(","))[:7].astype(np.
↪→ float)
dic_data[’Tsensor’]=np.array(liste[11].split(","))[:7].astype(np.
↪→ float)
dic_data[’Psensor’]=np.array(liste[13].split(","))[:7].astype(np.
↪→ float)
dic_data[’PAR’]=float(liste[15].split(’,’)[0])
dic_data[’SlrkW’]=float(liste[17].split(’,’)[0])
dic_data[’Windspeed’]=float(liste[19].split(’,’)[0])
251
dic_data[’roomT’]=float(liste[21].split(’,’)[0])
dic_data[’roomRH’]=float(liste[23].split(’,’)[0])
Te=dic_data[’roomT’]
RH= dic_data[’roomRH’]
SVD = 5.018+0.32321*Te+8.1847e-3*Te**2+3.1243e-4*Te**3
VD=RH/100*SVD
dic_data[’VPD’]=SVD-VD
return(True,dic_data)
# return(pin,Resist,FullBr)
get_sensor_data.py
"""definition of a function to access sensor data"""
import numpy as np
def get_sensor_data(numsensor,data):
’’’A function to access sensor data
Args:
numsensor : int associated with the sensor (nothing to do with the
↪→ Valve)
data : name of the data among (FullBr, Psensor, Tsensor, Resist)
Returns:
(array) : the array of all the last measured value with their
↪→ timestamp’’’
L=np.load(’Data/’+data+str(numsensor)+".npy")
return(L)
atmosim_API.py
252
’’’Most of that code come from Marty Sullivan : please ask him if any
↪→ issue is
met with his API’’’
import gzip
import json
from os import environ
from time import sleep
from urllib.request import HTTPError, Request, urlopen
from datetime import datetime
def update_forecast(coord,timezone,elems,dic_forecast):
’’’Update the dictionnary with hourly weather with the latest weather
↪→ forecast
Args :
coord (list) : coordinate [lat,long]
timezone (str) : string corresponding to the Timezone
elems (list) : list of string corresponding to wanted elements
: see "ndgd-elements.txt to know what’s available
dic_forecast (dictionnary) : dictionnary with hourly weather datas
↪→ that has
to be updated
Returns :
None
’’’
#Initialize the dictionnary if needed
253
for element in elems:
if element not in dic_forecast.keys():
dic_forecast[element]={}
# Relevent API URIs
environ["DOMAIN_NAME"]="atmosim.com"
environ["TEST_API_KEY"]="c285c856-5bdf-4e8d-acf3-a845535d32ea"
QUERY_URI = ’https://{0}/api/query’.format(environ[’DOMAIN_NAME’])
RESULTS_URI = ’https://{0}/api/results/{{QueryId}}’.format(environ[’
↪→ DOMAIN_NAME’])
query_data = dict(
category=’forecast’,
dataset=’ndfd’,
grid=’conus’,
elements=elems,
coordinates=[coord],
timezone=timezone,
output=’JSON’,
)
try:
# Prepare the query initialization request with the data above
# Sets the x-api-key header to TEST_API_KEY environment variable
# Print out your query_id
query_req = Request(QUERY_URI)
query_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
query_req.method = ’POST’
254
query_req.data = json.dumps(query_data).encode(’utf-8’)
with urlopen(query_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_id = resp[’query_id’]
print(’QueryId: ’ + query_id)
# Poll the results API call every five seconds until the query
↪→ succeeds or fails
# Raise an exception if the query fails (should not ever happen)
’’’Don’t worry too much about all that part, I copy pasted it from
Marty’s code : there is no need to understand everything about it’’’
query_status = ’SUBMITTED’
results_req = Request(RESULTS_URI.format(QueryId=query_id))
results_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
while query_status not in [’SUCCEEDED’, ’FAILED’, ’CANCELLED’]:
sleep(5)
with urlopen(results_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_info = resp[’query_info’]
query_status = query_info[’query_status’]
print(’QueryStatus: ’ + query_status)
if query_status in [’FAILED’, ’CANCELLED’]:
255
raise RuntimeError(’Query Failed!’)
# Concatenate all of the rows from the 1+ output files
result_rows = []
for result_url in query_info[’query_results’]:
with urlopen(result_url) as compressed_results:
gz_results = gzip.open(compressed_results, ’rt’, encoding=’utf
↪→ -8’)
result_rows.extend(gz_results.readlines())
# Parse and update the dic with each JSON row
for row in result_rows:
row = json.loads(row)
dic_forecast[row[’element’]][datetime.strptime(row[’forecast_time’]
↪→ \
,’%Y-%m-%dT%X.000-04:00’)]=row[’value’]
#All of this is a way to catch exception to be sure that the code
#doesn’t stop but still inform about what’s happening
except KeyError as e:
print(’ERROR: Make sure you have set the system environment variables
↪→ DOMAIN_NAME and TEST_API_KEY’)
except HTTPError as e:
try:
errors = json.loads(json.loads(e.read().decode(’utf-8’))[’errors’])
256
for err in errors:
print(’ERROR: ’ + err)
except:
print(’ERROR: Server Error’)
return(dic_forecast)
def update_observation(coord,timezone,elems,dic_forecast):
’’’Update the dictionnary with hourly weather with the latest ’
↪→ observation’
which are here the RTMA initialisation grid
Args :
coord (list) : coordinate [lat,long]
timezone (str) : string corresponding to the Timezone
elems (list) : list of string corresponding to wanted elements
: see "ndgd-elements.txt to know what’s available
dic_forecast (dictionnary) : dictionnary with hourly weather datas
↪→ that has
to be updated
Returns :
None
’’’
for element in elems:
if element not in dic_forecast.keys():
dic_forecast[element]={}
# Relevent API URIs
environ["DOMAIN_NAME"]="atmosim.com"
257
environ["TEST_API_KEY"]="c285c856-5bdf-4e8d-acf3-a845535d32ea"
QUERY_URI = ’https://{0}/api/query’.format(environ[’DOMAIN_NAME’])
RESULTS_URI = ’https://{0}/api/results/{{QueryId}}’.format(environ[’
↪→ DOMAIN_NAME’])
query_data = dict(
category=’forecast’,
dataset=’rtma’,
grid=’conus’,
elements=elems,
coordinates=[
[42.4, -76.5],
],
# coordinates=coord,
timezone=timezone,
output=’JSON’,
)
try:
# Prepare the query initialization request with the data above
# Sets the x-api-key header to TEST_API_KEY environment variable
# Print out your query_id
query_req = Request(QUERY_URI)
query_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
query_req.method = ’POST’
query_req.data = json.dumps(query_data).encode(’utf-8’)
258
with urlopen(query_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_id = resp[’query_id’]
print(’QueryId: ’ + query_id)
# Poll the results API call every five seconds until the query
↪→ succeeds or fails
# Raise an exception if the query fails (should not ever happen)
query_status = ’SUBMITTED’
results_req = Request(RESULTS_URI.format(QueryId=query_id))
results_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
while query_status not in [’SUCCEEDED’, ’FAILED’, ’CANCELLED’]:
sleep(5)
with urlopen(results_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_info = resp[’query_info’]
query_status = query_info[’query_status’]
print(’QueryStatus: ’ + query_status)
if query_status in [’FAILED’, ’CANCELLED’]:
raise RuntimeError(’Query Failed!’)
# Concatenate all of the rows from the 1+ output files
result_rows = []
259
for result_url in query_info[’query_results’]:
with urlopen(result_url) as compressed_results:
gz_results = gzip.open(compressed_results, ’rt’, encoding=’utf
↪→ -8’)
result_rows.extend(gz_results.readlines())
# Parse and pretty-print each JSON row
for row in result_rows:
row = json.loads(row)
dic_forecast[row[’element’]][datetime.strptime(row[’forecast_time’]
↪→ \
,’%Y-%m-%dT%X.000-04:00’)]=row[’value’]
# print(json.dumps(row, indent=2))
except KeyError as e:
print(’ERROR: Make sure you have set the system environment variables
↪→ DOMAIN_NAME and TEST_API_KEY’)
except HTTPError as e:
try:
errors = json.loads(json.loads(e.read().decode(’utf-8’))[’errors’])
for err in errors:
print(’ERROR: ’ + err)
except:
260
print(’ERROR: Server Error’)
return(dic_forecast)
atmosim-test.py
import gzip
import json
from os import environ
from time import sleep
from urllib.request import HTTPError, Request, urlopen
def get_Forecast(coordinates,timezone,elems):
dic_forecast={}
for element in elems:
dic_forecast[element]=[]
# Relevent API URIs
environ["DOMAIN_NAME"]="atmosim.com"
environ["TEST_API_KEY"]="c285c856-5bdf-4e8d-acf3-a845535d32ea"
QUERY_URI = ’https://{0}/api/query’.format(environ[’DOMAIN_NAME’])
RESULTS_URI = ’https://{0}/api/results/{{QueryId}}’.format(environ[’
↪→ DOMAIN_NAME’])
#
# POST data below requests:
# 1. a forecast dataset
# 2. the ndfd dataset
# 3. the conus grid
# 4. the maxt + mint elements
# 5. the lat/lon points (42.0, -76.0) and (42.1, -76.1)
261
# 6. sets output timestamps (ISO Format) to the America/New_York tz (
↪→ https://en.wikipedia.org/wiki/List_of_tz_database_time_zones)
# 7. sets the output data type to JSON (can also set to TEXTFILE for
↪→ csv output but this script only works with JSON)
#
query_data = dict(
category=’forecast’,
dataset=’ndfd’,
grid=’conus’,
elements=[
’rhm’,
’temp’,
’sky’,
’wspd’,
],
coordinates=[
[42.4, -76.5],
],
timezone=’America/New_York’,
output=’JSON’,
)
try:
# Prepare the query initialization request with the data above
# Sets the x-api-key header to TEST_API_KEY environment variable
262
# Print out your query_id
query_req = Request(QUERY_URI)
query_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
query_req.method = ’POST’
query_req.data = json.dumps(query_data).encode(’utf-8’)
with urlopen(query_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_id = resp[’query_id’]
print(’QueryId: ’ + query_id)
# Poll the results API call every five seconds until the query
↪→ succeeds or fails
# Raise an exception if the query fails (should not ever happen)
query_status = ’SUBMITTED’
results_req = Request(RESULTS_URI.format(QueryId=query_id))
results_req.add_header(’x-api-key’, environ[’TEST_API_KEY’])
while query_status not in [’SUCCEEDED’, ’FAILED’, ’CANCELLED’]:
sleep(5)
with urlopen(results_req) as req:
resp = json.loads(req.read().decode(’utf-8’))
query_info = resp[’query_info’]
query_status = query_info[’query_status’]
print(’QueryStatus: ’ + query_status)
263
if query_status in [’FAILED’, ’CANCELLED’]:
raise RuntimeError(’Query Failed!’)
# Concatenate all of the rows from the 1+ output files
result_rows = []
for result_url in query_info[’query_results’]:
with urlopen(result_url) as compressed_results:
gz_results = gzip.open(compressed_results, ’rt’, encoding=’utf
↪→ -8’)
result_rows.extend(gz_results.readlines())
# Parse and pretty-print each JSON row
for row in result_rows:
row = json.loads(row)
dic_forecast[row[’element’]].append((row[’value’],row[’
↪→ forecast_time’]))
print(json.dumps(row, indent=2))
except KeyError as e:
print(’ERROR: Make sure you have set the system environment variables
↪→ DOMAIN_NAME and TEST_API_KEY’)
except HTTPError as e:
try:
errors = json.loads(json.loads(e.read().decode(’utf-8’))[’errors’])
264
for err in errors:
print(’ERROR: ’ + err)
except:
print(’ERROR: Server Error’)
weather_forecast.py
from datetime import timedelta
import numpy as np
import pandas as pd
from Weather.Weather_constants import *
from pvlib.location import Location
# larson et. al. use offset = 0.35 : value used to compute Qrad from cloud
↪→ cover
offset=0.35
def get_Temp_forecast(H,startdate,dic):
#Returns the temperature forecast in degree C.
Args:
H (int) : number of hours ahead of forecast needed
265
startdate(datetime) : datetime object to represent the time to
↪→ start giving forecasts
dic (dictionnary) : dictionnary containing the brute weather
↪→ forecast from the forecast API
Returns:
(array) : length H array with the forecast for the H next hours
↪→ after startdate’’’
T=[]
for i in range(H):
date= startdate + timedelta(hours=i)
temp = dic[date.replace(minute=0,second=0, microsecond=0)]
T.append((float(temp)-32)*(5/9))
return(np.array(T))
def get_RH_forecast(H,startdate,dic):
’’’Returns the Relative Humidity forecast in %.
Args:
H (int) : number of hours ahead of forecast needed
startdate(datetime) : datetime object to represent the time to
↪→ start giving forecasts
dic (dictionnary) : dictionnary containing the brute weather
↪→ forecast from the forecast API
Returns:
(array) : length H array with the forecast for the H next hours
↪→ after startdate’’’
266
RH=[]
for i in range(H):
date= startdate + timedelta(hours=i)
rh = dic[date.replace(minute=0,second=0, microsecond=0)]
RH.append(float(rh))
return(np.array(RH))
def get_WS_forecast(H,startdate,dic):
’’’Returns the Windspeed forecasts in m/s.
Args:
H (int) : number of hours ahead of forecast needed
startdate(datetime) : datetime object to represent the time to
↪→ start giving forecasts
dic (dictionnary) : dictionnary containing the brute weather
↪→ forecast from the forecast API
Returns:
(array) : length H array with the forecast for the H next hours
↪→ after startdate’’’
WS=[]
for i in range(H):
date= startdate + timedelta(hours=i)
ws = dic[date.replace(minute=0,second=0, microsecond=0)]
WS.append(float(ws))
return(np.array(WS))
def get_Qrad_forecast(H,startdate,dic,coordinates,time_zone_delta):
’’’Returns the Qrad forecasts in W/m^2.
267
Args:
H (int) : number of hours ahead of forecast needed
startdate(datetime) : datetime object to represent the time to
↪→ start giving forecasts
dic (dictionnary) : dictionnary containing the brute weather
↪→ forecast from the forecast API
coordinates(list) : the coordinate of the place where Qrad is
↪→ needed
time_zone_delta (timezone) : the timezone of the place where Qrad
↪→ is needed
Returns:
(array,list) : length H array with the forecast for the H next
↪→ hours after startdate
and list of length H with timestamps corresponding to this
↪→ forecasts’’’
Qrad=[]
times=[]
#Setting the location in the right format for pvlib
Loc=Location(coordinates[0],coordinates[1],tz=’America/New_York’)
for i in range(H):
date= startdate + timedelta(hours=i)
date=date.replace(minute=0,second=0, microsecond=0)
#get the Qrad of a clearsky for this time of the day at that
↪→ location
clrsky=Loc.get_clearsky(pd.DatetimeIndex([date.replace(tzinfo=
↪→ time_zone_delta)]))[’ghi’][0]
#get the total solar irradiance after having used the cloud
268
↪→ coverage factor
#Look at the pvlib documentation for better understanding of what’s
↪→ happening
ghi = (offset + (1 - offset) * (1 - float(dic[date])/100)) * clrsky
Qrad.append(ghi/1000)
times.append(date.timestamp())
return(np.array(Qrad),times)
Weather_constants.py
import numpy as np
alphaD = 0.3e-3 #0.17e-3; %Pa-1 0.3e-3
betaD = 79 #umol/s-m^2
betaD=betaD*0.219/1000 #transform to kW.m^-2
AVPD=17.2693882; #Constant for calculating Psat
BVPD=35.86; #Constant for calculating Psat
CVPD=0.61078 #Constant for calculating Psat in kPa
gmaxD = 0.005 #m/s*1.88
lambd=2.260e6 #J/kg
cp=1.01e3# %heat capacity of air
#psychrometric constant
269
gamma=66 # %Pa/K
gammags= 0.1026
betaD=betaD*0.219/1000 #transform to kW.m^-2
270
APPENDIX D
MATLAB PROGRAMS FOR SIMULATION AND DATA TRANSMISSION
D.1 One Compartment RC Circuit Model
% This code combines multiple data files.
% Before this code
% 1. Soil data RN should be corrected to real time, and also delete extra
↪→ text
% on non-data columns.
% 2. In case running in different systems, for Mac, the importdata command
% load the timestamp column as well; for Win10, the importdata command
↪→ does
% not load the timestamp.
clear
clc
close all
SZColor = {[0 0.4470 0.7410]
[0.8500 0.3250 0.0980]
[0.9290 0.6940 0.1250]
[0.4940 0.1840 0.5560]
[0.4660 0.6740 0.1880]
[0.3010 0.7450 0.9330]
[0.6350 0.0780 0.1840]};
lwidth = 1;
271
pftsize = 14;
markersize = 15;
% Directions for the Program
formac = 0; % 1 use mac system for 1, 0 use win system
forghws = 1; % 1 use guterman data, 2 for newa weather station
runorg = 0; % 1 use original dataset, 0 for load imported data including
↪→ modeled data
ename = ’OR17’;
stdatenum = datenum(’09/04/2017’);
stdatetime = datetime(2017,9,4,19,40,0);
% Basic Information for experiments
enum = 4; % the total number of experiments
PSIColor = {[0 0 0],[0 0 0.5],[0.5 0 0],[0 0.5 0.5],[0.8 0.4 0.0],[1 0
↪→ 1],[0.8 0.5 0.8],[0.5 0.8 0]};
timeofs = [];
timeofs(1) = 19+40/60;
timeofs(2) = 18+58/60;
timeofs(3) = 18+25/60;
timeofs(4) = 18+27/60;
snum(1) = 6;% number of sensors for OR4
snum(2) = 8;% number of sensors for OR5
snum(3) = 8;% number of sensors for OR6
snum(4) = 8;% number of sensors for OR7
if runorg == 1
% load original data file collected by CR6. Be careful regard to the soil
272
% data loading.
matrix{1,1} = importdata(’CR6Series_5690_OR4_0904.xlsx’);
matrix{1,2} = importdata(’CR6Series_5690_OR4_0904_vpdsli.xlsx’);
matrix{1,3} = importdata(’CR6Series_5690_OR4_0904_sl.xlsx’);
matrix{2,1} = importdata(’CR6Series_5690_OR5_0925.xlsx’);
matrix{2,2} = importdata(’CR6Series_5690_OR5_0925_vpdsli.xlsx’);
matrix{2,3} = importdata(’CR6Series_5690_OR5_0925_sl.xlsx’);
matrix{3,1} = importdata(’CR6Series_5690_OR6_1002.xlsx’);
matrix{3,2} = importdata(’CR6Series_5690_OR6_1002_vpdsli.xlsx’);
matrix{3,3} = importdata(’CR6Series_5690_OR6_1002_sl.xlsx’);
matrix{4,1} = importdata(’CR6Series_5690_OR7_1020.xlsx’);
matrix{4,2} = importdata(’CR6Series_5690_OR7_1020_vpdsli.xlsx’);
matrix{4,3} = importdata(’CR6Series_5690_OR7_1020_sl.xlsx’);
save(’datamatrix.mat’,’matrix’);
else
load(’datamatrix.mat’)
load(’PCM.mat’)
load(’tCMh.mat’)
load(’tCMd.mat’)
load(’ET1.mat’) % L/hour
load(’timeM.mat’) % time (hours)
timeMday = timeM./24;
load(’gsD.mat’) % get stomatal conductance m/s
load(’rtRp.mat’)
273
load(’rtimeRp.mat’)
load(’Rp1.mat’)
end
if runorg ==1 && formac == 1
for maini = 1:enum
sdata{maini} = matrix{maini,1}.data(5:end,2:end);
edata{maini} = matrix{maini,2}.data(5:end,2:end);
ldata{maini} = matrix{maini,3}.data(5:end,2:end);
end
else
for maini = 1:enum
sdata{maini} = matrix{maini,1}.data(5:end,:);
edata{maini} = matrix{maini,2}.data(5:end,:);
ldata{maini} = matrix{maini,3}.data(5:end,:);
end
end
% load manual pressure bomb data
% load data from original data set
matrix{7,1} = importdata(’PB_OR4.xlsx’);
matrix{7,2} = importdata(’PB_OR5.xlsx’);
matrix{7,3} = importdata(’PB_OR6.xlsx’);
matrix{7,4} = importdata(’PB_OR7.xlsx’);
for i = 1:enum
pbdata = matrix{7,i}.data;
274
timePB{i} = (pbdata(:,1)-1).*24+pbdata(:,2)+pbdata(:,3)./60;
for j = 1:size(pbdata,1)
PB_avg(j,1) = -nanmean(pbdata(j,4:end));
PB_max(j,1) = -min(pbdata(j,4:end));
PB_min(j,1) = -max(pbdata(j,4:end));
end
PB{i} = PB_avg;
PBneg{i} = PB_min-PB_avg;
PBpos{i} = PB_max-PB_avg;
clearvars PB_avg PB_max PB_min
end
matrix{5,1} = importdata(’GS_OR4.xlsx’);
matrix{5,2} = importdata(’GS_OR5.xlsx’);
matrix{5,3} = importdata(’GS_OR6.xlsx’);
matrix{5,4} = importdata(’GS_OR7.xlsx’);
for i = 1:enum
gsdata = matrix{5,i}.data;
timeGS{i} = (gsdata(:,1)-1).*24+gsdata(:,2)+gsdata(:,3)./60;
for j = 1:size(gsdata,1)
GS_avg(j,1) = nanmean(gsdata(j,4:end));
GS_max(j,1) = min(gsdata(j,4:end));
GS_min(j,1) = max(gsdata(j,4:end));
end
GS{i} = GS_avg;
GSneg{i} = GS_min-GS_avg;
275
GSpos{i} = GS_max-GS_avg;
clearvars GS_avg GS_max GS_min
end
%% Load Porometer data
matrix{8,1} = importdata(’Porometer_OR4.xlsx’);
matrix{8,2} = importdata(’Porometer_OR5.xlsx’);
matrix{8,3} = importdata(’Porometer_OR6.xlsx’);
matrix{8,4} = importdata(’Porometer_OR7.xlsx’);
A = 0.61121;
B = 18.678;
C = 257.14;
D = 234.5;
for i = 1:enum
podata = matrix{8,i}.data;
timePO{i} = (podata(:,1)-1).*24+podata(:,2)+podata(:,3)./60;
POrh{i} = podata(:,4);% RH in Percentage
POSLI{i} = podata(:,5); % Solar in umol/m^2-s
POgs{i} = podata(:,6);% cm/s
POET{i} = podata(:,7);% ug/m^2-s
POTL{i} = podata(:,8);% DegC
POTC{i} = podata(:,9);% DegC
TK0 = 273.15;
POTLK{i} = POTL{i}+TK0;
276
POTCK{i} = POTC{i}+TK0;
POPsat{i} = A*exp((B-POTCK{i}./D).*(POTCK{i}./(POTCK{i}+C)));% gives
↪→ kPa
POVPD{i} = (100-POrh{i})./100.*POPsat{i};% kPa
end
%% Load CR6-Environmental Data for Every Orchard Experiment
for maini = 1:enum
clearvars X Y
X = sdata{maini};
Y = edata{maini};
% Load Environmental Data
time{maini} = X(:,1)/60; % convert time to hours from RN wo timeofs
RN{maini} = Y(:,1);
Te{maini}= Y(:,2); % DegC
RHe{maini} = Y(:,3);
SLIkW{maini} = Y(:,4); % kW/m^2
SLIW{maini} = SLIkW{maini}.*1000; % convert to W/m^2
SLIq{maini} = SLIkW{maini}.*10^3./0.101.*0.2;% Convert to Quantum
↪→ units
SLIJ{maini} = Y(:,5); %
PAR{maini} = Y(:,6)./6.74; % umol/s/m^2 didnt put in cfactor 6.74
↪→ in CR6
end
% Retrieve Soil Data and interpolate soil data
for maini = 1:enum
277
Z = ldata{maini};
soil = Z;
run(’analysis_soil_data_interpolate.m’)
Z = soil;
RNl{maini} = Z(:,1);
timel{maini} = RNl{maini}./60; % convert from min to hours
Pl{maini} = Z(:,2)./100; % convert from kPa to bars
Tl{maini} = Z(:,3);
end
%% Weather Station Data
% Guterman Greenhouse Real-time PAR, Precipitation, and Windspeed Data
if runorg == 1
matrix{6,1} = importdata(’GHWS_OR4.xlsx’);
matrix{6,2} = importdata(’GHWS_OR5.xlsx’);
matrix{6,3} = importdata(’GHWS_OR6.xlsx’);
matrix{6,4} = importdata(’GHWS_OR7.xlsx’);
GHWS = [];
if runorg == 1 && formac == 1
for maini = 1:enum
GHWS{maini} = matrix{6,maini}.data(:,2:end);
end
else
for maini = 1:enum
GHWS{maini} = matrix{6,maini}.data;
end
end
278
save(’GHWS.mat’,’GHWS’)
else
load(’GHWS.mat’)
end
for maini = 1:enum
clearvars X Y Z
X = GHWS{maini}(:,1);
Y = GHWS{maini}(:,2);
Z = GHWS{maini}(:,3);
PARgh{maini} = X(timeofs(maini)*60+1-60:timeofs(maini)*60+length(RN{
↪→ maini}-60));
Y(Y == 0) = 10^(-20);
WSgh{maini} = Y(timeofs(maini)*60+1-60:timeofs(maini)*60+length(RN{
↪→ maini})-60);
PCPgh{maini} = Z(timeofs(maini)*60+1-60:timeofs(maini)*60+length(RN{
↪→ maini})-60);
end
% NEWA Weatehr Station Data; Windspeed and Pricipitation
clearvars X Y Z X1 Y1 X_new Y_new
if runorg == 1
matrix{7,1} = importdata(’OR4-5-6 Weather Data.xlsx’);
if runorg == 1 && formac == 1
NEWA = matrix{7,1}.data(:,2:end);
else
279
NEWA = matrix{7,1}.data;
end
save(’NEWA.mat’,’NEWA’)
else
load(’NEWA.mat’)
end
X = NEWA(:,7)*0.447; % convert from mile per hour to m/s
Y = NEWA(:,3)*25.4; % load precipitation convert from inches to mm
timen = (1:length(X))*60;
X1 = flipud(X);
Y1 = flipud(Y);
X_new = [];
for j = 1:length(timen)-1
for r = timen(j):1:timen(j+1)
X_new(r) = X1(j)+(r-timen(j))*(X1(j+1)-X1(j))/(timen(j+1)-timen(j))
↪→ ;
Y_new(r) = Y1(j)+(r-timen(j))*(Y1(j+1)-Y1(j))/(timen(j+1)-timen(j))
↪→ ;
end
end
% Convert time to real time
rtime{1} = timeofs(1)+time{1};
rtimel{1} = timeofs(1)+timel{1};
rtimePB{1} = timePB{1};
280
rtimeGS{1} = timeGS{1};
rtimePO{1} = timePO{1};
for maini = 2:enum
clearvars X Y
X = rtime{maini-1};
Y = rtimel{maini-1};
rtime{maini} = floor(X(end)/24)*24+timeofs(maini)+time{maini}; % Put
↪→ time in series
rtimel{maini} = floor(Y(end)/24)*24+timeofs(maini)+timel{maini};% Put
↪→ soil time in series
rtimePB{maini} = floor(X(end)/24)*24+timePB{maini}; % Put PB time in
↪→ series
rtimeGS{maini} = floor(X(end)/24)*24+timeGS{maini}; % Put GS time in
↪→ series
rtimePO{maini} = floor(X(end)/24)*24+timePO{maini};
end
% Getting the minute based time start from the real start of the OR4;
for maini = 1:enum
rtimemin{maini} = round((rtime{maini}-timeofs(1))*60+1); % convert from
↪→ real time hours to minutes
end
%% Clip the Interpolated NEWA data to match the size of the dataset
for maini = 1:enum
clearvars X Y Z
if maini == 1
281
X = X_new(timeofs(maini)*60+1:timeofs(maini)*60+length(RN{maini}))’;
X(X == 0) = 10^(-20);
WSn{maini} = X;
PCPn{maini} = Y_new(timeofs(maini)*60+1:timeofs(maini)*60+length(RN{
↪→ maini}))’;
else
Z = rtime{maini-1};
a1 = floor(Z(end)/24)*24*60+timeofs(maini)*60+1;
a2 = floor(Z(end)/24)*24*60+timeofs(maini)*60+length(RN{maini});
X = X_new(a1:a2)’;
X(X == 0) = 10^(-20);
WSn{maini} = X;
PCPn{maini} = Y_new(a1:a2)’;
end
end
%%
% Retrieve Sensor data
for maini = 1:enum
X = sdata{maini};
for j = 1:snum(maini)
Psi{j,maini} = -X(:,j+1); % Change sign for Water Potential (bars)
Temp{j,maini} = X(:,j+9);% units in degree C
end
end
% Get the predawn water potential
282
clearvars A
A(1,2) = PB{1}(1);
A(1,1) = rtimePB{1}(1);
A(2,2) = PB{2}(2);
A(2,1) = rtimePB{2}(2);
A(3,2) = PB{3}(1);
A(3,1) = rtimePB{3}(1);
A(4,1) = rtimePB{1,3}(13);
A(4,2) = PB{1,3}(13);
if enum == 4
A(5,1) = rtimePB{4}(1);
A(5,2) = PB{4}(1);
end
Predawn = A;
pd = Predawn(:,2);
tpd = Predawn(:,1);
clearvars A
% Offset correction based on the first predawn measurement
for j = 3:4
q = 1;
X = rtime{1};% use only the predawn measurement in the if first
↪→ expe
Y = Psi{j,1};
x1 = round((Predawn(1,1)-timeofs(1))*60-10);
x2 = round((Predawn(1,1)-timeofs(1))*60+10);
283
y = mean(Y(x1:x2));
ycor = y-Predawn(1,2);
for maini = 1:enum
Psi{j,maini} = Psi{j,maini}-ycor;
end
end
%% Combine Data Files into One
t = [];
tl = [];
tPB = [];
tGS = [];
tPO = [];
% Combine time into one
for maini = 1:enum
t = [t;rtime{maini}];
tl = [tl;rtimel{maini}];
tPB = [tPB;rtimePB{maini}];
tGS = [tGS;rtimeGS{maini}];
tPO = [tPO;rtimePO{maini}];
end
% Combine environmental variables
RNC = [];
TeC = [];
RHeC = [];
284
SLIkWC = [];% LI200R
SLIWC = [];% LI200R (W/m^2-s)
SLIqC = [];% LI200R unit conversion (umol/m^2-s)
SLIJC = [];% LI200R joules accumulation over time
SLIgC = [];% guterman PAR (umol/m^2-s)
PARC = [];% LI193 Spherical Quantum Sensor (umol/m^2-s)
PARghC = [];
WSghC = [];
PCPghC = [];
WSnC = [];
PCPnC = [];
POVPDC = [];
POSLIC = [];
POgsC = [];
PBC = [];
GSC = [];
Psi3 = [];
Psi4 = [];
T3 = [];
T4 = [];
Tsoil = [];
PBnegC = [];
PBposC = [];
GSnegC = [];
GSposC = [];
285
PlC = [];
PsiDC = [];
PsiTC = [];
for maini = 1:enum
RNC = [RNC;RN{maini}];
TeC = [TeC;Te{maini}];
Tsoil = [Tsoil;Tl{maini}];
RHeC = [RHeC;RHe{maini}];
SLIkWC = [SLIkWC;SLIkW{maini}];
SLIWC = [SLIWC;SLIW{maini}];
SLIqC = [SLIqC;SLIq{maini}];
SLIJC = [SLIJC;SLIJ{maini}];
PARC = [PARC;PAR{maini}];
PARghC = [PARghC;PARgh{maini}];
WSghC = [WSghC;WSgh{maini}];
PCPghC = [PCPghC;PCPgh{maini}];
WSnC = [WSnC;WSn{maini}];
PCPnC = [PCPnC;PCPn{maini}];
PBC = [PBC; PB{maini}];
GSC = [GSC; GS{maini}];
286
Psi3 = [Psi3;Psi{3,maini}];
Psi4 = [Psi4;Psi{4,maini}];
T3 = [T3;Temp{3,maini}];
T4 = [T4;Temp{4,maini}];
PBnegC = [PBnegC;PBneg{maini}];
GSnegC = [GSnegC;GSneg{maini}];
GSposC = [GSposC;GSpos{maini}];
PBposC = [PBposC;PBpos{maini}];
PlC = [PlC; Pl{maini}];
POVPDC = [POVPDC;POVPD{maini}];
POSLIC = [POSLIC;POSLI{maini}];
POgsC = [POgsC;POgs{maini}];
end
%% Choose Windspeed Source for Next Step Calculation
wvC = WSghC;
rainC = PCPghC;
%% VPD, Psychrometric Constant(gamma), and dew T calculation
AVPD = 0.61121;
BVPD = 18.678;
CVPD = 257.14;
DVPD = 234.5;
287
TK0 = 273.15;
TeK = TeC+TK0;
% Calculate Saturated Vapor Pressure Using Arden Buck Equation
Psat = AVPD*exp((BVPD-TeC./DVPD).*(TeC./(TeC+CVPD)));% gives kPa
VPDkPa = (100-RHeC)./100.*Psat;% kPa
VPDPa = VPDkPa.*1000; % Pa
gamma = log(RHeC./100)+(BVPD-TeC./DVPD).*(TeC./(TeC+CVPD));
dewT = CVPD*gamma./(BVPD-gamma);
run(’analysis_0_offset_shift.m’)
%%
clc
close all
avgnum = 10;
gfactor = 1.5;%[1.88 1.5 1.3 ]; % factor for the maximum stomatal
↪→ conductance for Thorpe
fcuticle = 0.3;%0.05;%0.5;
afactor = 0;
% Choose Range of Data
selectrange = 0; % 0 select range 1 do not select range
if selectrange == 1
stday = 1; % day stday
stdatenumM = stdatenum+stday;
edday = 20;%stday+floor(time(end)/24)-1;% to the end of edday-2
288
eddatenumM = stdatenum+edday;
stpoint = round(((stday-1)*24+24)*60-timeofs(1)*60);% first numb = 0
↪→ means from the 12:00am of Day 1
edpoint = round(((edday-1)*24+24)*60-timeofs(1)*60);
lastday = ceil(edpoint-stpoint)/60/24;
else, if selectrange == 0
stpoint = 1;
edpoint = length(t);
end
end
datalength = floor((edpoint-stpoint)/avgnum);
edpoint = stpoint+datalength*avgnum-1;
% Load Data and Choose Data Range
PM1 = transpose(sum(reshape(Psi3aftC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); %bar
timeMhr = transpose(sum(reshape(t(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);% in hours
timeMdayr = timeMhr./24;
time0 = timeMhr(1);
timeMh = timeMhr-timeMhr(1);
timeMday = timeMh/24;
timeM=timeMh*3600; %convert to seconds
timeMhT = timeMh’;
timeMsT = timeMhT*3600;% convert to seconds
modelDT = datetime(2017,9,4,0,0,0)+hours(timeMhr);
289
expDT = datetime(2017,9,4,0,0,0)+hours(t);
pbDT = datetime(2017,9,4,0,0,0)+days(tPBday);
tickDT = datetime(2017,9,4,0,0,0):days(1):expDT(end);
PARM = transpose(sum(reshape(PARghC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); % umol/m^2-s
SLIqM = PARM;
SLIkWM = transpose(sum(reshape(SLIkWC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); %kW/m^2
SLIWM = SLIkWM.*1000;
airTM = transpose(sum(reshape(TeC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);%degrees C
airTKM = airTM+273.15; %convert room temperature to Kelvin
airRHM = transpose(sum(reshape(RHeC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); %Relative Humidity
wvM = transpose(sum(reshape(wvC(stpoint:edpoint),[avgnum,(edpoint-stpoint
↪→ +1)/avgnum]),1)./avgnum); %m/s
As = 120/2*370/2;% % Effective Soil Area cm^2
PCPnMmmhr = transpose(sum(reshape(PCPnC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);% mmhr
PCPnM = transpose(sum(reshape(PCPnC(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum)./3600.*(As*100)./1000; % Amount of
↪→ Irrigation in kg/s
VPDkPaM = transpose(sum(reshape(VPDkPa(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);
VPDPaM = transpose(sum(reshape(VPDPa(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);
290
%% Adjustable Variables
% Calculation of Boundary Layer Resistance for Grass Reference ET
hgr = 0.12;%0.12; %m
dgr = 2/3*hgr;
zgr0m = 0.123*hgr;
zgr0h = 0.1*zgr0m;
zgrm = 3.5;% meter
zgrh = zgrm;
karman = 0.41;
ragrfactor = log((zgrm-dgr)/zgr0m)*log((zgrh-dgr)/zgr0h)/karman^2;
% Calculation of Boundary Layer Resistance for Dragoni Reference ET
hDR = 3;%0.12; apple tree canopy height in meters
dDR = 0.8;%2/3*hDR; 0.8 m is Dragoni’s calculation
zDR0m = 0.123*hDR;
zDR0h = 0.1*zDR0m;
zDRm = 5;% meter
zDRh = 5;% humidity sensor position
karman = 0.41;
raDfactor = log((zDRm-dDR)/zDR0m)*log((zDRh-dDR)/zDR0h)/karman^2;
raD = raDfactor./(wvM); % Dragoni
gmaxD=0.00625; %m/s*1.88
alphaD = 0.17e-3; %Pa-1 0.3e-3 Dragoni’s Constant
betaD=79; %umol/s-m^2
291
%slope of saturation pressure curve Pa/K
S=CVPD*(273.15*AVPD-AVPD*BVPD)./(airTKM-BVPD).^2 ...
.*exp(AVPD.*(airTKM-273.15)./(airTKM-BVPD))*1000;
rho=(1.01*10^5)./(287.05.*airTKM); %calculate density of air
cp=1.01e3; %heat capacity of air
% stomatal conductance time constant
x = 15;% 15 minutes
tau=x*60;
%psychrometric constant
gamma=66; %Pa/K
%latent heat of vaporization
lambda=2.260e6; %J/kg
%build set point vector for Test model of stomatal conductance
gsD=gmaxD.*(1-alphaD*VPDkPaM)./(1+betaD./PARM);
% gsD=gmaxD./(1+betaD./PARM);
gsD(gsD<=0.3*gmaxD) = gmaxD*0.3;
% gsD = gmaxD.*ones(size(VPDkPaM));
rsD=1./gsD;
rsgf0 = 70; % s m^-1
ragf0 = ragrfactor./wvM;% 208./wvM; % s m^-1
292
epsilon = S/gamma;
omega = (epsilon+2)./(epsilon+2+rsD./raD);
ETD_SL=(1/lambda)*(S.*0.5.*SLIWM.*raD+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raD+gamma.*rsD)*6; % kg/s
ETD_USL = (1/lambda)*(S*0.1.*0.5.*SLIWM.*raD+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raD+gamma.*rsD)*6;% kg/s
ETD = 0.4*ETD_SL+0.6*ETD_USL; % kg/s
ETDRmmhr = ETD./6.*3600; % mm/hr
figure
plot(ETD)
legend(’ETD’)
%%
figure
plot(timeMday,rsD./raD)
ylabel(’r_s / r_a’)
xlabel(’time(days)’)
ax = gca;ax.FontSize = 14;
% ax.YLim = [0 2];
% hold on
% plot(timeMday,1./rsD)
% hold off
% ax = gca;
% ax.YLim = [0 gmax];
293
%% Plant Hydraulic Conductance Based On Dragoni
clc
lwidth = 1;
pftsize = 14;
markersize = 15;
PM_pd = zeros(size(tickDT));
PM_md = PM_pd;
ET_min = PM_pd;
ET_max = PM_pd;
pdDT = tickDT;
mdDT = tickDT;
for i = 2:length(tickDT)
pdDT(i) = tickDT(i)+hours(5.5);
mdDT(i) = tickDT(i)+hours(14.5);
PM_pd(i) = mean(PM1(modelDT>tickDT(i)+hours(5) & modelDT<tickDT(i)+
↪→ hours(6)));
PM_md(i) = mean(PM1(modelDT>tickDT(i)+hours(14) & modelDT<tickDT(i)+
↪→ hours(15)));
ET_min(i) = mean(ETDRmmhr(modelDT>tickDT(i)+hours(4) & modelDT<tickDT(i
↪→ )+hours(5)));
ET_max(i) = mean(ETDRmmhr(modelDT>tickDT(i)+hours(14) & modelDT<tickDT(
↪→ i)+hours(15)));
end
dlim1 = 12;dlim2 = 16;
294
DTD927 = modelDT(modelDT>tickDT(24)+hours(dlim1) & modelDT<tickDT(24)+
↪→ hours(dlim2));
PMD927 = PM1(modelDT>tickDT(24)+hours(dlim1) & modelDT<tickDT(24)+hours(
↪→ dlim2))./10;% MPa
ETD927 = ETDRmmhr(modelDT>tickDT(24)+hours(dlim1) & modelDT<tickDT(24)+
↪→ hours(dlim2));
nlim1 = 0; nlim2 = 4;
DTN928 = modelDT(modelDT>tickDT(25)+hours(nlim1) & modelDT<tickDT(25)+
↪→ hours(nlim2));
PMN928 = PM1(modelDT>tickDT(25)+hours(nlim1) & modelDT<tickDT(25)+hours(
↪→ nlim2))./10;% MPa
ETN928 = ETDRmmhr(modelDT>tickDT(25)+hours(nlim1) & modelDT<tickDT(25)+
↪→ hours(nlim2));
figure,
set(gcf,’Position’,[100 100 800 500])
plot(PMN928,ETN928,’.’,’MarkerSize’,markersize)
f1 = fit(PMN928,ETN928,’poly1’);
hold on
fit1 = plot(f1);
fit1.LineWidth = lwidth;
fit1.Color = SZColor{1};
MBfit1 = coeffvalues(f1);
str1 = sprintf(’y = %6.4f x - %6.4f’,MBfit1(1),abs(MBfit1(2)));
plot(PMD927,ETD927,’.’,’MarkerSize’,markersize)
f2 = fit(PMD927,ETD927,’poly1’);
295
fit2 = plot(f2);
fit2.LineWidth = lwidth;
fit2.Color = SZColor{2};
MBfit2 = coeffvalues(f2);
str2 = sprintf(’y = %6.4f x - %6.4f’,MBfit2(1),abs(MBfit2(2)));
hold off
ax = gca;
ax.FontSize = pftsize;
text(5/10*(max(xlim)-min(xlim))+min(xlim),9/10*(max(ylim)-min(ylim))+min(
↪→ ylim),str1,’FontSize’,pftsize,’Color’,SZColor{1})
text(5/10*(max(xlim)-min(xlim))+min(xlim),8.5/10*(max(ylim)-min(ylim))+min
↪→ (ylim),str2,’FontSize’,pftsize,’Color’,SZColor{2})
xlabel(’\Psi_{\muTM} (MPa)’)
ylabel(’ET_0 (mm/hr)’)
legend({’0-4am Sep.28’,’fit 0-4am’,’12-4pm Sep.27’,’fit 12-4pm’},’FontSize
↪→ ’,pftsize,’Location’,’EastOutside’)
grid on
figure,
plot(PMN928,ETN928,’.’,’MarkerSize’,markersize)
f1 = fit(PMN928,ETN928,’poly1’);
hold on
fit1 = plot(f1);
fit1.Color = SZColor{1};
fit1.LineWidth = lwidth;
MBfit1 = coeffvalues(f1);
str1 = sprintf(’y = %6.4f x + %6.4f’,MBfit1(1),MBfit1(2));
296
hold off
ax = gca;
ax.FontSize = pftsize;
ax.XLabel = [];
ax.YLabel = [];
grid on
gmd = ET_max./(PM_md-PM_pd);
gpd = ET_min./(PM_pd);
dPsi = PM_md-PM_pd;
%%
figure,
plot(ET_max,PM_md./10,’.’,’MarkerSize’,markersize,’Color’,’k’);
hold on
[f3,gof3] = fit(ET_max(~isnan(ET_max))’,PM_md(~isnan(ET_max))’./10,’poly1
↪→ ’);
fit3=plot(f3);
fit3.Color = ’k’;
fit3.LineWidth = lwidth;
MBfit3 = coeffvalues(f3);
str3 = sprintf(’y = %6.4f x - %6.4f \n R^2 = %6.4f’,MBfit3(1),abs(MBfit3
↪→ (2)),gof3.rsquare);
ax = gca;
ylabel(’\Psi_{\muTM} (MPa)’);
xlabel(’ET_{Dragoni} (mm/hr)’);
297
ax.FontSize = pftsize;
grid on
text(1/20*(max(xlim)-min(xlim))+min(xlim),1/10*(max(ylim)-min(ylim))+min(
↪→ ylim),str3,’FontSize’,pftsize,’Color’,’k’)
legend({’ET_{md} vs \Psi_{md}’,’fit-md’},’FontSize’,0.8*pftsize,’Location
↪→ ’,’NorthEast’)
%% Start The One Compartment Model
ET = ETD’;% kg/s5
PMT = PM1’;% bars
MDL = 1;% if MDL = 2 run 2 compartment model
Nf = size(timeMh,1);
diffM = timeMh(2:end)-timeMh(1:end-1);
intv = find(diffM>0.5);
% Irrigation
PCPnM(isnan(PCPnM)) = 0;
timeI = avgnum*60;% irrigation time interval in seconds
%% Constants
% initial conditions
Pt0 = -6;
Ps0 = -1;
Ct = 0.02;% trunk capacitance 0.02 works well
Rt = 28000;
run(’analysis_1_model_1C_part2.m’)
298
clearvars PCM
PCM = Pt’;
tCMh = timeMh+time0;
tCMd = tCMh./24;
save(’PCM.mat’,’PCM’)
save(’tCMh.mat’,’tCMh’)
save(’tCMd.mat’,’tCMd’)
save(’ET.mat’,’ET’)
save(’PMT.mat’,’PMT’)
%% calculate mean root squared
sig = std(Pt’);
RMSele = 1/sig^2.*(Pt’-PMT’).^2;
RMS = sqrt(sum(RMSele)/size(PMT’,2));
save(’RMS.mat’,’RMS’)
%% Print Parameters to an Excel File
filename = ’Adjusted_Parameters_for_the_1C_Model.xlsx’;
clearvars A
counter = 1;
sheet = 1;
A{counter} = {’Maximum Stomatal Conductance(m/s)’,gmaxD};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Cuticle Conduntance factor’,fcuticle};xlrange = sprintf
↪→ (’A%d’,counter);xlswrite(filename,A{counter},sheet,xlrange);
299
↪→ counter = counter+1;
A{counter} = {’Initial Pt0(bars)’,Pt0};xlrange = sprintf(’A%d’,counter)
↪→ ;xlswrite(filename,A{counter},sheet,xlrange);counter = counter
↪→ +1;
A{counter} = {’Initial Ps0(bars)’,Ps0};xlrange = sprintf(’A%d’,counter)
↪→ ;xlswrite(filename,A{counter},sheet,xlrange);counter = counter
↪→ +1;
A{counter} = {’RMS (bars)’,RMS};xlrange = sprintf(’A%d’,counter);
↪→ xlswrite(filename,A{counter},sheet,xlrange);counter = counter+1;
winopen(filename)
D.2 Two Compartment RC Circuit Model
% This Code Load and Analyzes the GH8 Data
% Calculate the transpiration Using Penman-Monteith
% Simulates the stem water potential
clear
clc
close all
% Set-up Figure Characteristics
positionvec = [50 50 800 400];
SZColor = {
[0 0.4470 0.7410]
[0.8500 0.3250 0.0980]
[0.9290 0.6940 0.1250]
300
[0.4940 0.1840 0.5560]
[0.4660 0.6740 0.1880]
[0.3010 0.7450 0.9330]
[0.6350 0.0780 0.1840]};
markersize = 30;
lwidth = 1.5;
fsize = 14;
pftsize = 14;
% What to run for the code
runporo = 1;% 1 means load the porometer data
ra_ind = 1;
WW = 0; % 0 Means Using the Jarvis Stomatal Conductance under Water Stress
↪→ Model
stday = 0;
edday = 30;% timeday(end) = 32.3875
% Experiment Start Time
timeofs = 18+32/60; % hour of the day for entire data set
% Load all data
load(’matrix.mat’)
% Time
RN = matrix{1,1}(:,1);
timehr = RN./60+timeofs;
timeday = timehr./24;
301
ticknum = round(timeday(1)):1:round(timeday(end));
strealtime = datetime(2018,5,24,18,32,0);
exprealtime = strealtime+hours(timehr);
% Sensors
channel = 8;
for i = 1:channel
Psi{i} = -matrix{1,1}(:,i+1);
Temp{i} = matrix{1,1}(:,i+1+channel);
V{i} = matrix{1,1}(:,i+1+channel*2);
PRT{i} = matrix{1,1}(:,i+1+channel*3);
end
% Pressure Chamber
clear X; X = matrix{3,1};
clear Y; Y = matrix{4,1};
timePB35hr = X(:,1)*24+X(:,2)+X(:,3)./60;
timePB75hr = Y(:,1)*24+Y(:,2)+Y(:,3)./60;
timePB35day = timePB35hr./24;
timePB75day = timePB75hr./24;
timerealPB35 = strealtime+days(timePB35day);
timerealPB75 = strealtime+days(timePB75day);
PsiPB35L = -(X(:,4)+X(:,5))./2;
PsiPB35S = -(X(:,6)+X(:,7))./2;
PsiPB75L = -(Y(:,4)+Y(:,5))./2;
PsiPB75S = -(Y(:,6)+Y(:,7))./2;
clear X Y
302
%% Porometer
clear X; X = matrix{5,1};
clear Y; Y = matrix{6,1};
timegs35hr = X(:,1)*24+X(:,2)+X(:,3)./60;
timegs75hr = Y(:,1)*24+Y(:,2)+Y(:,3)./60;
timegs35day = timegs35hr./24;timerealgs35 = strealtime+hours(timegs35hr);
timegs75day = timegs75hr./24;timerealgs75 = strealtime+hours(timegs75hr);
gs35 = X(:,6)./100; % convert from cm/s to m/s
gs35(gs35 == 0 | gs35>0.003) = NaN;
gs75 = Y(:,6)./100;
gs75(gs75 == 0 | gs75>0.003) = NaN;
PAR35 = X(:,5); % umol/m^2-s
RH35 = X(:,4); % %
Tl35 = X(:,8); % degC
Tc35 = X(:,9); % degC
PAR75 = Y(:,5);
RH75 = Y(:,4);
Tl75 = Y(:,8); % degC
Tc75 = Y(:,9); % degC
%% Remove Error Values from Sensor Data
clear Y; Y = Psi{3};
clear X; X = find(Y>50);
for counter = 1:size(X,1)
Y(X(counter)) = Y(X(counter)-1);
303
end
Psi{3} = Y; clear X Y
Putm = Psi{3};
save(’Putm.mat’,’Putm’)
save(’timeday.mat’,’timeday’)
clear i
for i = 1:length(timePB75hr)
tst = timePB75hr(i)-5/60;
ted = timePB75hr(i)+5/60;
PmPB(i) = mean(Putm(timehr>tst & timehr<ted));
end
clear i
ix = find(isnan(PsiPB75S));
figure,
plot(PsiPB75S,PmPB,’.’,’MarkerSize’,markersize)
f1 = fit(PsiPB75S([1:ix-1,ix+1:end]),PmPB([1:ix-1,ix+1:end])’,’poly1’);
MBPB = coeffvalues(f1);
strm = sprintf(’m = %4.4f’,MBPB(1));
strb = sprintf(’b = %4.4f’,MBPB(2));
text(-20,-20,strm,’FontSize’,fsize)
text(-20,-22,strb,’FontSize’,fsize)
hold on
plot(f1,’k’)
hold off
xlabel(’Sch\"{o}lander Pressure Bomb (bars)’)
304
ylabel(’\Psi_{\muTM} (bars)’)
title(’Micro-Tensiometer vs. Sch\"{o}lander Pressure Chamber’)
grid on
ax = gca;
ax.FontSize = fsize;
ax.YLim = [min(ylim),1];
savefig(’Figure2c’)
%% Load Microclimate Data
Te = matrix{2,1}(:,2);
RHe = matrix{2,1}(:,3);
PAR1 = matrix{2,1}(:,10); % PAR data from greenhouse measurements
PAR2 = matrix{2,1}(:,4); % PAR data from our micro-climate station
PAR = PAR1;
WS = matrix{2,1}(:,5);WS(WS <= 0) = 1e-6;
W35 = matrix{2,1}(:,6);
W75 = matrix{2,1}(:,7);
%% Calculate VPD
TK0 = 273.15;
TeK = Te+TK0;
AVPD=17.2693882; %Constant for calculating Psat
BVPD=35.86; %Constant for calculating Psat
CVPD=0.61078; %Constant for calculating Psat in kPa
Psat=CVPD*exp(AVPD*(TeK-273.15)./(TeK-BVPD)); %kPa Teteus Equation
VPDkPa=(100-RHe)./100.*Psat; %kPa
VPDPa=VPDkPa.*10^(3); %Pa
305
VPDPa(VPDPa<0) = 0;
%% ET and Irrigation Calculation
% Clear errors from the weight measurement
W35(W35>10000 | W35<1000) = NaN;
W75(W75>10000 | W75<1000) = NaN;
X = find(isnan(W35));
for counter = 1:size(X)
if X(counter) == 1
W35(X(counter)) = W35(X(counter)+1);
else, if X(counter) == size(W35,1)
W35(X(counter)) = W35(X(counter)-1);
else
W35(X(counter)) = (W35(X(counter)-1)+W35(X(counter)+1))/2;
end
end
end
clear X
X = find(isnan(W75));
for counter = 1:size(X)
if X(counter) == 1
W75(X(counter)) = W75(X(counter)+1);
else, if X(counter) == size(W75,1)
W75(X(counter)) = W75(X(counter)-1);
else
306
W75(X(counter)) = (W75(X(counter)-1)+W75(X(counter)+1))/2;
end
end
end
clear X
ETdiff35 = zeros(size(W35));
ETdiff75 = zeros(size(W75));
diff = 10;
ETdiff35(1+diff:end) = -(W35(1+diff:end)-W35(1:end-diff)); % g
ETdiff75(1+diff:end) = -(W75(1+diff:end)-W75(1:end-diff)); % g
%% Irrigation Data
wateringlimit = 100;
X = find(ETdiff35<-wateringlimit);
IW35 = zeros(size(ETdiff35));% g
IW35(X) = abs(ETdiff35(X))./diff;
Ii35 = IW35./1000; % kg
clear X
X = find(ETdiff75<-wateringlimit);
IW75 = zeros(size(ETdiff75));% g
IW75(X) = abs(ETdiff75(X))./diff; % g/min
Ii75 = IW75./1000; % kg
clear X
% Clear errors from the weight measurement
307
X = find(isnan(ETdiff35));
for counter = 1:size(X)
if ~isnan(ETdiff35(X(counter)-1))
ETdiff35(X(counter)) = ETdiff35(X(counter)-1);
else
ETdiff35(X(counter)) = (ETdiff35(X(counter)-1)+ETdiff35(X(counter)
↪→ +1))/2;
end
end
clear X
X = find(isnan(ETdiff75));
for counter = 1:size(X)
if ~isnan(ETdiff75(X(counter)-1))
ETdiff75(X(counter)) = ETdiff75(X(counter)-1);
else
ETdiff75(X(counter)) = (ETdiff75(X(counter)-1)+ETdiff75(X(counter)
↪→ +1))/2;
end
end
clear X
% Y = find(isnan(ET));
ET35 = ETdiff35./(diff/60)./3.6e6; % kg/s
ET75 = ETdiff75./(diff/60)./3.6e6; % kg/s
ET35(ET35<0 | ET35>0.5e-3) = 0;
ET75(ET75<0 | ET75>0.5e-3) = 0;
308
windowSize = 40;
b = 1/windowSize*ones(1,windowSize);
a = 1;
ET35flt = filter(b,a,ET35);
ET75flt = filter(b,a,ET75);
Ii35flt = filter(b,a,Ii35);
Ii75flt = filter(b,a,Ii75);
fdelaymin = (windowSize-1)/2;
fdelayhr = fdelaymin/60;
fdelayday = fdelayhr/24;
clear a b
%% Variables for Model
MDL = 2;% Choose 1C 2C or 3C Model
avgnum = 10;% Take Average for Every 10 Data Points
% Choose Data Range for Simulation
selectrange = 1; % 0 select range 1 do not select range
if selectrange == 1
stday = 12;%12;%13; % day stday
edday = 31;%31;%24;%stday+floor(time(end)/24)-1;% to the end of edday-2
stpoint = round(((stday-1)*24+24)*60-timeofs*60);% first numb = 0 means
↪→ from the 12:00am of Day 1
edpoint = round(((edday-1)*24+24)*60-timeofs*60);% in minutes
lastday = ceil(edpoint-stpoint)/60/24;
309
else, if selectrange == 0
stpoint = 1;
stday = round(timeday(stpoint));
edpoint = length(timeday);
edday = round(timeday(edpoint));
end
end
datalength = floor((edpoint-stpoint)/avgnum);
edpoint = stpoint+datalength*avgnum-1;
% Load Data and Choose Data Range
PM1 = transpose(sum(reshape(Psi{3}(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); %bar
timeMh = transpose(sum(reshape(timehr(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);% in hours
timeMrh = timeMh;
timeMrt = strealtime+hours(timeMh);
timeMrday = timeMrh/24;
timeMh = timeMh-timeMh(1);
timeMday = timeMh/24;
timeM = timeMh*3600; % convert to seconds
timeMhT = timeMh’;
timeMsT = timeMhT*3600;% convert to seconds
PARM = transpose(sum(reshape(PAR(stpoint:edpoint),[avgnum,(edpoint-stpoint
↪→ +1)/avgnum]),1)./avgnum); % umol/m^2-s
310
SLIkWM = PARM*0.219./1000; %kW/m^2
airTM = transpose(sum(reshape(Te(stpoint:edpoint),[avgnum,(edpoint-stpoint
↪→ +1)/avgnum]),1)./avgnum);%degrees C
airRHM = transpose(sum(reshape(RHe(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum); %Relative Humidity
wvM = transpose(sum(reshape(WS(stpoint:edpoint),[avgnum,(edpoint-stpoint
↪→ +1)/avgnum]),1)./avgnum); %m/s
PCPnM = transpose(sum(reshape(Ii75(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum)./60; % Amount of Irrigation in kg/s
PCPnM(isnan(PCPnM) | PCPnM<0.8e-3) = 0;
PCPnM(timeMday>(17-stday+1) & timeMday<(17.8-stday+1)) = 0;
VPDkPaM = transpose(sum(reshape(VPDkPa(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);
VPDPaM = transpose(sum(reshape(VPDPa(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);
Nf = size(timeMh,1);
diffM = timeMh(2:end)-timeMh(1:end-1);
intv = find(diffM>0.5);
% Unit Conversions
SLIqM = PARM;
SLIWM = SLIkWM.*10^3;
airTKM = airTM+273.15; %convert room temperature to Kelvin
%% Calculate ET with the Penman-Monteith Equation
311
gfactor = 1;%[1.88 1.5 1.3 ]; % factor for the maximum stomatal
↪→ conductance for Thorpe
fcuticle = 0.3;%0.05;%0.5;
fcuticled = 12/30*fcuticle;
leafA = 2; % leaf area in m^2
% Windspeed and boundary layer resistance
% raD = 25.5783./(1+0.54.*(1+0.54.*wvM)); % miscalculated denominator(
↪→ Yunusa 2000)
raDtp = 40./sqrt(wvM); % Thorpe 1980
raDdr = 40./wvM; % Dragoni 2003 does not work due to infinite resistance
↪→ when wv is close to zero.
raDyu = 4.72*(log(1/0.13))^2./(1+0.54.*wvM);
ra_ind = 3;
if ra_ind == 1
raD = raDtp;
raDMDL = ’Thorpe 1980’;
else if ra_ind == 2
raD = raDdr;
raDMDL = ’Dragoni 2003’;
else
raD = raDyu; %(Yunusa 2000, Monteith and Unsworth 1990)
raDMDL = ’Yunusa 2000’;
end
end
312
% gs modeling Thorpe
gmax = 0.005; %m/s*1.88
alphags = 0.3e-3;%0.17e-3; %Pa-1 0.3e-3
betags = 79; %umol/s-m^2
gammags = 3*abs(1/min(Psi{3}));% inverse of abs(-6 bars) a turning point
↪→ of the role of SWP
% Stomatal Conductance Modeling
gmaxD=gmax; %m/s*1.88
alphaD = alphags; %Pa-1 0.3e-3
betaD=betags; %umol/s-m^2
%slope of saturation pressure curve Pa/K
S=CVPD*(273.15*AVPD-AVPD*BVPD)./(airTKM-BVPD).^2 ...
.*exp(AVPD.*(airTKM-273.15)./(airTKM-BVPD))*1000;
rho=(1.01*10^5)./(287.05.*airTKM); %calculate dry air density
cp=1.01e3; %heat capacity of air
%psychrometric constant
gamma=66; %Pa/K
%latent heat of vaporization
lambda=2.260e6; %J/kg
%build set point vector for Test model of stomatal conductance
313
% gsspD=gmaxD.*(fcuticle+(1-alphaD.*VPDPa)./(1+betaD./(SLIqM))); %*ones(
↪→ size(VPDPa));%*m/s
if WW == 1
gsspD=gmaxD.*((1-alphaD.*VPDPaM)./(1+betaD./(PARM)));
else
% gsspD=gmaxD./(1+betaD./(PARM)).*(1-exp(gammags.*(-PM1+min(Psi{3}))));%
↪→ no VPD term
gsspD=gmaxD.*((1-alphaD.*VPDPaM)./(1+betaD./(PARM))).*(1-exp(gammags.*(-
↪→ PM1+min(Psi{3}))));%
% Jarvis
end
gsspD(PM1>-15 & PARM<200) = fcuticle*gmaxD;
gsspD(PM1<-20 & PARM<100) = fcuticled*gmaxD;
gsspD(950:1144) = fcuticled*gmaxD;
gsspavgD=mean(gsspD);
rsspavgD=1/gsspavgD;
rsD=1./gsspD;
save(’rsD.mat’,’rsD’)
save(’raD.mat’,’raD’)
%Evaporation rate for model 2 for shaded and unshaded leaves
ETvargs2UNSHADED=(1/lambda)*(S.*SLIWM.*0.5.*raD+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raD+gamma.*rsD);
ETvargs2SHADED=(1/lambda)*(0.1.*S.*SLIWM.*0.5.*raD+(rho.*cp).*VPDPaM)
↪→ ./(...
314
(S+2.*gamma).*raD+gamma.*rsD);
Sf1 = 60/100; % Shaded leaf percentage
USf1=1-Sf1;
ETgstot1=(USf1*ETvargs2UNSHADED+Sf1*ETvargs2SHADED)*leafA;% Measured leaf
↪→ area
ETPM = ETgstot1;
ET = ETPM;
ETtp = Sf1*(1/lambda)*(S.*SLIWM.*0.5.*raDtp+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDtp+gamma.*rsD)+USf1*(1/lambda)*(0.1.*S.*SLIWM.*0.5.*
↪→ raDtp+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDtp+gamma.*rsD);
ETdr = Sf1*(1/lambda)*(S.*SLIWM.*0.5.*raDdr+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDdr+gamma.*rsD)+USf1*(1/lambda)*(0.1.*S.*SLIWM.*0.5.*
↪→ raDdr+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDdr+gamma.*rsD);
ETyu = Sf1*(1/lambda)*(S.*SLIWM.*0.5.*raDyu+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDyu+gamma.*rsD)+USf1*(1/lambda)*(0.1.*S.*SLIWM.*0.5.*
↪→ raDyu+(rho.*cp).*VPDPaM)./(...
(S+2.*gamma).*raDyu+gamma.*rsD);
if WW == 1
save(’ETPM_WW.mat’,’ETPM’)
else
save(’ETPM_WS.mat’,’ETPM’)
315
end
save(’ETPM.mat’,’ETPM’)
figure(’Position’,positionvec)
plot(timeMrday,raDtp)
hold on
plot(timeMrday,raDdr)
plot(timeMrday,raDyu)
plot(timeMrday,rsD)
plot(timegs75day,1./gs75,’.’,’MarkerSize’,20)
hold off
ax = gca;
ax.FontSize = pftsize;
ax.XTick = 0:5:ticknum(end);
set(gca,’xticklabel’,[])
ax.XLim = [stday edday];
ax.YLim = [0 1e4];
ax.XMinorGrid = ’on’;
hold on
bar(ticknum,max(ylim)*ones(size(ticknum)),0.5,’FaceColor’,’k’,’
↪→ FaceAlpha’,0.05,’EdgeAlpha’,0.05);
hold off
ylabel(’ra or rs (s/m)’)
legend(’ra_{Thorpe}’,’ra_{Dragoni}’,’ra_{Yunusa}’,’rs’)
figure(’Position’,positionvec)
plot(timeMrday,ETtp)
316
hold on
plot(timeMrday,ETdr)
plot(timeMrday,ETyu)
hold off
ax = gca;
ax.FontSize = pftsize;
ax.XTick = 0:5:ticknum(end);
set(gca,’xticklabel’,[])
ax.XLim = [stday edday];
ax.XMinorGrid = ’on’;
hold on
bar(ticknum,max(ylim)*ones(size(ticknum)),0.5,’FaceColor’,’k’,’
↪→ FaceAlpha’,0.05,’EdgeAlpha’,0.05);
hold off
ylabel(’ET (kg/s)’)
legend(’ET_{raThorpe}’,’ET_{raDragoni}’,’ET_{raYunusa}’)
figure(’Position’,positionvec)
plot(timeMrday,ET)
hold on
plot(timeday,ET75flt)
hold off
ax = gca;
ax.FontSize = pftsize;
ax.XTick = 0:5:ticknum(end);
set(gca,’xticklabel’,[])
ax.XLim = [stday edday];
317
ax.XMinorGrid = ’on’;
hold on
bar(ticknum,max(ylim)*ones(size(ticknum)),0.5,’FaceColor’,’k’,’
↪→ FaceAlpha’,0.05,’EdgeAlpha’,0.05);
hold off
ylabel(’ET(kg/s)’);
str = sprintf(’The gmax is %2.4f m/s. The raD model is %s’,gmax,raDMDL);
title(str)
%% Simulating Plant Psi
% Parameters
rhow = 1; % density of water 1 g/cm^3
% vG-Mualem parameters keep all root dimensions in cm
n = 1.5380;
m = 1-1/n;
as = 3.6292+0.6+0.05; % from m to bar (1/"bubble point") soil (1/bar)
↪→ (0.01 1/cm = 10 1/bar) van Genuchten Silty Loam
Ks = 10^(-6.158)*10^4;% from m/s kg/(m s bar)to at saturated conditions
l = 0.5;
thetar = 0.2; % cm^3/cm^3
thetas = 0.48; % cm^3/cm^3
Theta0 = 0.5;
RLD = 0.1; % cm/cm^3
r1 = 0.1;% root radius in cm
r2 = 1/sqrt(pi*RLD);% half distance between roots in cm
318
% Effective Soil Dimensions and Hydraulic Properties
rs = 16; % cm 32 cm in diameter of pots
ds = 35.56; % cm 35.56 in depth pot size
As = pi*rs^2;
Vs = pi*rs^2*ds;% cm^3 assume cylindrical
Cs = rhow*Vs/1000*(thetas-thetar); % saturated rhizosphere hydraulic
↪→ capacitance [kg/bar]
Is = PCPnM; % Irrigation directly on Soil with kg/s
Is(1300:1360) = 0;% Digital Scale Error
% Effective Rhizosphere Dimensions and Hydraulic Properties
ar = as; %1/7; % (1/"bubble point") rhizosphere (1/bar)
Vr = RLD*Vs*pi*(r2^2-r1^2);% cm^3 assume cylindrical
Cr = rhow*Vr/1000*(thetas-thetar); % rhizosphere hydraulic capacitance [kg
↪→ /bar]
Ir = Is;
% plant hydraulic parameters
Ct = 0.01;%0.02;% trunk capacitance kg/bar 0.01 for contact model
Rr = (2+2)*10^4;%8000;% 5000 for contact model
Rt = 1*10^4;
% Initial Conditions
Pt0 = -4;% -2 for contact model
Ps0 = -((Theta0^(-1/m)-1).^(1/n))/as;
319
% Real Time
t2CMh = transpose(sum(reshape(timehr(stpoint:edpoint),[avgnum,(edpoint-
↪→ stpoint+1)/avgnum]),1)./avgnum);
t2CMd = t2CMh./24;
run(’analysis_1_2Cv3.m’)
P2CM = Pt’;
P2SM = Ps’;
% save simulation results
save(’P2CM.mat’,’P2CM’)
save(’P2SM.mat’,’P2SM’)
save(’t2CMh.mat’,’t2CMh’)
save(’t2CMd.mat’,’t2CMd’)
save(’ET.mat’,’ET’)
save(’PM1.mat’,’PM1’)
%% Statistical Analysis
sig = std(Pt’);
RMSele = 1/sig^2.*(Pt’-PM1).^2;
RMS = sqrt(sum(RMSele)/size(PM1,2));
save(’RMS.mat’,’RMS’)
filename = ’Adjusted_Parameters_for_the_Model.xlsx’;
clearvars A
counter = 2;
sheet = 1;
320
A{counter} = {’Maximum Stomatal Conductance(m/s)’,gmax};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Cuticle Percentage Opening at Night’,fcuticle};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Cuticle Percentage Opening at Night Drought’,fcuticled};
↪→ xlrange = sprintf(’A%d’,counter);xlswrite(filename,A{counter},
↪→ sheet,xlrange);counter = counter+1;
A{counter} = {’Root Diameter(cm)’,r1};xlrange = sprintf(’A%d’,counter);
↪→ xlswrite(filename,A{counter},sheet,xlrange);counter = counter+1;
A{counter} = {’Half Distance Between Roots (cm)’,r2};xlrange = sprintf
↪→ (’A%d’,counter);xlswrite(filename,A{counter},sheet,xlrange);
↪→ counter = counter+1;
A{counter} = {’RLD (cm/cm^3)’,RLD};xlrange = sprintf(’A%d’,counter);
↪→ xlswrite(filename,A{counter},sheet,xlrange);counter = counter+1;
A{counter} = {’Plant Hydraulic Resistance (bar-s/kg)’,Rt};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Rhizosphere Resistance-sat (bar-s/kg)’,Rr};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Plant Hydraulic Capacitance (kg/bar)’,Ct};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Soil Pot Radius(cm)’,rs};xlrange = sprintf(’A%d’,counter
↪→ );xlswrite(filename,A{counter},sheet,xlrange);counter = counter
321
↪→ +1;
A{counter} = {’Soil Pot Depth(cm)’,ds};xlrange = sprintf(’A%d’,counter)
↪→ ;xlswrite(filename,A{counter},sheet,xlrange);counter = counter
↪→ +1;
A{counter} = {’Soil Capacitance-sat (kg/bar)’,Cs};xlrange = sprintf(’A%
↪→ d’,counter);xlswrite(filename,A{counter},sheet,xlrange);counter
↪→ = counter+1;
A{counter} = {’Soil Hydraulic Conductance-sat (bar-s/kg)’,Ks};xlrange =
↪→ sprintf(’A%d’,counter);xlswrite(filename,A{counter},sheet,
↪→ xlrange);counter = counter+1;
A{counter} = {’Initial Pt0(bars)’,Pt0};xlrange = sprintf(’A%d’,counter)
↪→ ;xlswrite(filename,A{counter},sheet,xlrange);counter = counter
↪→ +1;
A{counter} = {’Intial Theta0(bars)’,Theta0};xlrange = sprintf(’A%d’,
↪→ counter);xlswrite(filename,A{counter},sheet,xlrange);counter =
↪→ counter+1;
A{counter} = {’Initial Ps0(bars)’,Ps0};xlrange = sprintf(’A%d’,counter)
↪→ ;xlswrite(filename,A{counter},sheet,xlrange);counter = counter
↪→ +1;
A{counter} = {’residual water content’,thetar};xlrange = sprintf(’A%d’,
↪→ counter);xlswrite(filename,A{counter},sheet,xlrange);counter =
↪→ counter+1;
A{counter} = {’saturated water content’,thetas};xlrange = sprintf(’A%d
↪→ ’,counter);xlswrite(filename,A{counter},sheet,xlrange);counter =
↪→ counter+1;
A{counter} = {’VG-n’,n};xlrange = sprintf(’A%d’,counter);xlswrite(
↪→ filename,A{counter},sheet,xlrange);counter = counter+1;
322
A{counter} = {’VG-m’,m};xlrange = sprintf(’A%d’,counter);xlswrite(
↪→ filename,A{counter},sheet,xlrange);counter = counter+1;
A{counter} = {’VG-alpha-soil(1/bar)’,as};xlrange = sprintf(’A%d’,
↪→ counter);xlswrite(filename,A{counter},sheet,xlrange);counter =
↪→ counter+1;
A{counter} = {’RMS (bars)’,RMS};xlrange = sprintf(’A%d’,counter);
↪→ xlswrite(filename,A{counter},sheet,xlrange);counter = counter+1;
% winopen(filename)
D.3 Data Submission to the IoT platform
% Send Data to Ubidots.
% posixtime submitted to Ubidots have to be in UTC, not in New York local
% time.
clc
api = ’http://things.ubidots.com’;
options = weboptions(’RequestMethod’,’post’,...
’Timeout’,120,’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’MediaType’,’application/json’);
%% upload MATLABSoilSensors/soilwp and soiltemp
api = ’http://things.ubidots.com’;
options = weboptions(’RequestMethod’,’post’,...
’Timeout’,120,’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
323
’MediaType’,’application/json’);
run(’analysis_soilsensors.m’)
posix_sl = posixtime(soilrealtime+hours(4)).*1000;% Convert from absolute
↪→ NewYorkTime to UTC
trees = {’tree1sl’,’tree2sl’,’tree3sl’,’tree4sl’,’tree5sl’};
treedata = {tree1wpkPa tree2wpkPa tree3wpkPa tree4wpkPa tree5wpkPa};
stsltime = datetime(2019,9,20,12,40,0,’TimeZone’,’America/New_York’);
edsltime = datetime(2019,9,28,14,0,0,’TimeZone’,’America/New_York’);
posixstsl = posixtime(stsltime).*1000;
posixedsl = posixtime(edsltime).*1000;
posix_slrg = posix_sl(posix_sl>posixstsl & posix_sl<posixedsl);
soiltemp_rg =soiltemp(posix_sl>posixstsl & posix_sl<posixedsl);
tlength = length(posix_slrg);
pagesize = 10;
pagenum = ceil(tlength/pagesize);
for i = 1:pagenum
fprintf(’Round %d out of %d \n’,i,pagenum)
tic
% tree_soil_range
for j = 1:5
url = [api ’/api/v1.6/devices/MATLABSoilSensors/’ trees{j} ’/
↪→ values’];
clear value T dataarray tree_slrg
324
tree_slrg = treedata{j}(posix_sl>posixstsl & posix_sl<posixedsl)
↪→ ;
value = tree_slrg;
if i < pagenum
T = table(value((i-1)*pagesize+1:i*pagesize),posix_slrg((i
↪→ -1)*pagesize+1:i*pagesize),’VariableNames’,{’value’,’
↪→ timestamp’});
else
T = table(value((i-1)*pagesize+1:end),posix_slrg((i-1)*
↪→ pagesize+1:end),’VariableNames’,{’value’,’timestamp’})
↪→ ;
end
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
end
% soiltemp
url = [api ’/api/v1.6/devices/MATLABSoilSensors/soiltemp/values’];
clear value T dataarray
value = soiltemp_rg;%(timestamp>(posixtime(datetime
↪→ (2019,8,16,10,15,0)).*1000));
if i < pagenum
T = table(value((i-1)*pagesize+1:i*pagesize),posix_slrg((i-1)*
↪→ pagesize+1:i*pagesize),’VariableNames’,{’value’,’timestamp
↪→ ’});
else
325
T = table(value((i-1)*pagesize+1:end),posix_slrg((i-1)*pagesize
↪→ +1:end),’VariableNames’,{’value’,’timestamp’});
end
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
toc
end
%% Update devices/sensors
api = ’http://things.ubidots.com’;
options = weboptions(’RequestMethod’,’post’,...
’Timeout’,120,’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’MediaType’,’application/json’);
CR6import = importdata(’5690_SZ072619.dat’);
clc
tsCR6x = CR6import.textdata(5:end,1);
tsCR6 = datetime(tsCR6x,’InputFormat’,’MM/dd/yyyy HH:mm’,’TimeZone’,’
↪→ America/New_York’);
varall = CR6import.data(:,2:end);
varall(isnan(varall)) = 0;
startts = datetime(2019,9,26,6,55,0,’TimeZone’,’America/New_York’);
stopts = datetime(2019,9,26,15,20,0,’TimeZone’,’America/New_York’);
timestamp_rg = tsCR6(tsCR6>=startts & tsCR6<=stopts);
326
tposix_rg = posixtime(timestamp_rg).*1000;
varall_rg = zeros(length(timestamp_rg),20);
for i = 1:size(varall,2)
clear x
x = varall(:,i);
varall_rg(:,i) = x(tsCR6>=startts & tsCR6<=stopts);
end
for i = 1:5
varname{i} = sprintf(’fullbr1%2.1f’,i);
varname{i+5} = sprintf(’psensor1%2.1f’,i);
varname{i+10} = sprintf(’resist1%2.1f’,i);
end
% ts_slt =
tlength = length(timestamp_rg);
pagesize = 10;
pagenum = ceil(tlength/pagesize);
for i = 1:pagenum
fprintf(’Round %d out of %d \n’,i,pagenum)
tic
for j = 1:5
% fullbr
url = [api ’/api/v1.6/devices/sensors/’ varname{j} ’/values’];
clear value T dataarray
327
value = varall_rg(:,j+10);%(timestamp>(posixtime(datetime
↪→ (2019,8,16,10,15,0)).*1000));
if i < pagenum
T = table(value((i-1)*pagesize+1:i*pagesize),tposix_rg((i-1)*
↪→ pagesize+1:i*pagesize),’VariableNames’,{’value’,’timestamp’})
↪→ ;
else
T = table(value((i-1)*pagesize+1:end),tposix_rg((i-1)*pagesize+1:
↪→ end),’VariableNames’,{’value’,’timestamp’});
end
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
% Psensor
url = [api ’/api/v1.6/devices/sensors/’ varname{j+5} ’/values’];
clear value T dataarray
value = varall_rg(:,j);%(timestamp>(posixtime(datetime
↪→ (2019,8,16,10,15,0)).*1000));
if i < pagenum
T = table(value((i-1)*pagesize+1:i*pagesize),tposix_rg((i-1)*
↪→ pagesize+1:i*pagesize),’VariableNames’,{’value’,’timestamp’})
↪→ ;
else
T = table(value((i-1)*pagesize+1:end),tposix_rg((i-1)*pagesize+1:
↪→ end),’VariableNames’,{’value’,’timestamp’});
end
dataarray = table2struct(T);
328
response = webwrite(url,dataarray,options);
% resist
url = [api ’/api/v1.6/devices/sensors/’ varname{j+10} ’/values’];
clear value T dataarray
value = varall_rg(:,j+15);%(timestamp>(posixtime(datetime
↪→ (2019,8,16,10,15,0)).*1000));
if i < pagenum
T = table(value((i-1)*pagesize+1:i*pagesize),tposix_rg((i-1)*
↪→ pagesize+1:i*pagesize),’VariableNames’,{’value’,’timestamp’})
↪→ ;
else
T = table(value((i-1)*pagesize+1:end),tposix_rg((i-1)*pagesize+1:
↪→ end),’VariableNames’,{’value’,’timestamp’});
end
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
end
toc
end
% Update devices/weather
api = ’http://things.ubidots.com’;
options = weboptions(’RequestMethod’,’post’,...
329
’Timeout’,120,’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’MediaType’,’application/json’);
clc
CR6wsimport = importdata(’5690_SZ072619vpdsli.dat’);
tswsx = CR6wsimport.textdata(5:end,1);
tsws = datetime(tswsx,’InputFormat’,’MM/dd/yyyy HH:mm’,’TimeZone’,’America
↪→ /New_York’);
varwsall = CR6wsimport.data(:,4:end);
varwsall(isnan(varwsall)) = 0;
SVD = 5.018+0.32321.*varwsall(:,1)+8.1847e-3.*varwsall(:,1).^2+3.1243e-4*
↪→ varwsall(:,1).^3;
VD=varwsall(:,2)./100.*SVD;
VPDcb = SVD-VD;
varwsall = [varwsall VPDcb];
% strg = [datetime(2019,8,14,6,15,0,’TimeZone’,’America/New_York’);...
% ];
% edrg = [datetime(2019,8,14,10,13,0,’TimeZone’,’America/New_York’);...
% ];
% for im = 1:length(strg)
% startts = strg(im);
% stopts = edrg(im);
330
tsws_rg = tsws(tsws>=startts & tsws<=stopts);
tswsposix_rg = posixtime(tsws_rg).*1000;
varwsnames = {’roomt’,’roomrh’,’slrkw’,’par’,’windspeed’,’vpd’};
varwsall_rg = zeros(length(tsws_rg),length(varwsnames));
for i = 1:length(varwsnames)
clear x
x = varwsall(:,i);
varwsall_rg(:,i) = x(tsws>=startts & tsws<=stopts);
end
tlength = length(tswsposix_rg);
pagesize = 10;
pagenum = ceil(tlength/pagesize);
for i = 1:pagenum
fprintf(’Round %d out of %d \n’,i,pagenum)
tic
for j = 1:length(varwsnames)
clear value T dataarray
url = [api ’/api/v1.6/devices/weather/’ varwsnames{j} ’/values
↪→ ’];
value = varwsall_rg(:,j);
if i < pagenum
331
T = table(value((i-1)*pagesize+1:i*pagesize),tswsposix_rg((i
↪→ -1)*pagesize+1:i*pagesize),’VariableNames’,{’value’,’
↪→ timestamp’});
else
T = table(value((i-1)*pagesize+1:end),tswsposix_rg((i-1)*
↪→ pagesize+1:end),’VariableNames’,{’value’,’timestamp’})
↪→ ;
end
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
end
toc
end
% end
%% upload pressure chamber data.
run(’DataManual.m’)
api = ’http://things.ubidots.com’;
options = weboptions(’RequestMethod’,’post’,...
’Timeout’,120,’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’MediaType’,’application/json’);
clc
load(’SPCtree.mat’);
for j = 1:5
tic
332
clear varname value ts_SPC T dataarray
varname = sprintf(’treepb%d’,j);
url = [api ’/api/v1.6/devices/manual/’ varname ’/values’];
ts_SPC = posixtime(SPCtree{j,1}).*1000;
value = -SPCtree{j,2};
T = table(value,ts_SPC,’VariableNames’,{’value’,’timestamp’});
dataarray = table2struct(T);
response = webwrite(url,dataarray,options);
toc
end
D.4 Data Acquisition from the IoT platform
% % This code Retrieves Data from Ubidots.
% All Ubidots Data once collected are lastest data first. All datatable
% need to be fliped.
% Experiment Period1 From July 28th to August 9th, 2019
timestposixms = sprintf(’%d’,posixtime(timest)*1000);
timeedposixms = sprintf(’%d’,posixtime(timeed)*1000);
numofdata = sprintf(’%d’,2*floor(minutes(timeed-timest)));% As long as
↪→ this number is larger than the dataset
numofdatair = sprintf(’%d’,2*floor(seconds(timeed-timest)/5));
api = ’http://industrial.api.ubidots.com’;
namesensors = {’fullbr11.0’;’fullbr12.0’;’fullbr13.0’;’fullbr14.0’;’
↪→ fullbr15.0’;...
333
’resist11.0’;’resist12.0’;’resist13.0’;’resist14.0’;’resist15.0’;...
’psensor11.0’;’psensor12.0’;’psensor13.0’;’psensor14.0’;’psensor15
↪→ .0’;...
’tsensor11.0’;’tsensor12.0’;’tsensor13.0’;’tsensor14.0’;’tsensor15
↪→ .0’;...
’new-variable-2’;...
’new-variable-3’;...
’new-variable-14’;...
’new-variable-15’;...
};
nameweather = {’par’;’roomrh’;’roomt’;’slrkw’;’vpd’;’windspeed’};
nameirrigation_Period1 = {’valve17’;’valve2’;’valve3’;’valve4’};
nameirrigation_Period2 = {’valve17’;’valve22’;’valve27’};
UbidotsData = {};
%% Start Data Retrieve
% Retrieve Micro-tensiometer Original Data
for i = 1:size(namesensors,1)
% url = [api ’/api/v1.6/devices/sensors/’ namesensors{i} ’/values/?
↪→ page_size=’ numofdata];
url = [api ’/api/v1.6/devices/sensors/’ namesensors{i} ’/values/?page_size
↪→ =’ numofdata ’/?token=BBFF-x5U0hl4eYphqtNNjra0JKhr0yq2WYM&start=’
↪→ timestposixms ’&end=’ timeedposixms];
options = weboptions(’RequestMethod’,’get’,...
’Timeout’,30,’UserAgent’,[’MATLAB’ ’R2019a’],...
334
’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’ContentType’,’json’);
clear X
Xload = webread(url,options);
if i<=5
clear nameX resultsX valueX
nameX = sprintf(’utmV%d’,i);
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i>5 && i<=10
clear nameX resultsX valueX
nameX = sprintf(’utmPRT%d’,i-5);
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i>10 && i<=15
clear nameX resultsX valueX
nameX = sprintf(’Putm%d’,i-10);
335
resultsX = Xload.results;
valueX = -flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i>15 && i<=20
clear nameX resultsX valueX
nameX = sprintf(’Tutm%d’,i-15);
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i == 21
clear nameX resultsX valueX
nameX = sprintf(’Tutm%dc’,5);
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i == 22
clear nameX resultsX valueX
nameX = sprintf(’Putm%dc’,5);
336
resultsX = Xload.results;
valueX = -flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
clear Xstruct timeX_millis timeX_s
Xstruct = Xload.results;
timeX_millis = extractfield(Xstruct,’timestamp’)’;
timeX_s = timeX_millis./1000;
realtime1 = flipud(datetime(timeX_s,’ConvertFrom’,’posixtime’,’TimeZone
↪→ ’,’America/New_York’));
end
if i == 23
clear nameX resultsX valueX
nameX = sprintf(’Putm%dNC’,1);
resultsX = Xload.results;
valueX = -flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
end
if i == 24
clear nameX resultsX valueX
nameX = sprintf(’Putm%dNC’,5);
resultsX = Xload.results;
337
valueX = -flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
clear Xstruct timeX_millis timeX_s
Xstruct = Xload.results;
timeX_millis = extractfield(Xstruct,’timestamp’)’;
timeX_s = timeX_millis./1000;
realtimeutm = flipud(datetime(timeX_s,’ConvertFrom’,’posixtime’,’
↪→ TimeZone’,’America/New_York’));
end
end
% Retrieve Weather Station Data
for i = 1:size(nameweather,1)
% url = [api ’/api/v1.6/devices/weather/’ nameweather{i} ’/values/?
↪→ page_size=’ numofdata];
url = [api ’/api/v1.6/devices/weather/’ nameweather{i} ’/values/?page_size
↪→ =’ numofdata ’/?token=BBFF-x5U0hl4eYphqtNNjra0JKhr0yq2WYM&start=’
↪→ timestposixms ’&end=’ timeedposixms];
options = weboptions(’RequestMethod’,’get’,...
’Timeout’,30,’UserAgent’,[’MATLAB’ ’R2019a’],...
’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’ContentType’,’json’);
338
clear Xload nameX resultsX valueX Xstruct timeX_millis timeX_s realtimews
Xload = webread(url,options);
nameX = nameweather{i};
nameXT = [nameweather{i} ’t’];
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
Xstruct = Xload.results;
timeX_millis = extractfield(Xstruct,’timestamp’)’;
timeX_s = timeX_millis./1000;
realtimews = flipud(datetime(timeX_s,’ConvertFrom’,’posixtime’,’
↪→ TimeZone’,’America/New_York’));
assignin(’base’,nameXT,realtimews);
end
% Retrieve Irrigation Data
for i = 1:size(nameirrigation_Period2,1)
url = [api ’/api/v1.6/devices/irrigation/’ nameirrigation_Period2{i} ’/
↪→ values/?page_size=’ numofdatair ’/?token=BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM&start=’ timestposixms ’&end=’
↪→ timeedposixms];
options = weboptions(’RequestMethod’,’get’,...
’Timeout’,30,’UserAgent’,[’MATLAB’ ’R2019a’],...
339
’KeyName’,’X-Auth-Token’,’KeyValue’,’BBFF-
↪→ x5U0hl4eYphqtNNjra0JKhr0yq2WYM’,...
’ContentType’,’json’);
clear Xload nameX resultsX valueX timeX_millis timeX_s
Xload = webread(url,options);
nameX = nameirrigation_Period2{i};
resultsX = Xload.results;
valueX = flipud(extractfield(resultsX,’value’)’);
assignin(’base’,nameX,valueX);
UbidotsData = [UbidotsData nameX];
timeX_millis = extractfield(resultsX,’timestamp’)’;
timeX_s = timeX_millis./1000;
realtimeir = flipud(datetime(timeX_s,’ConvertFrom’,’posixtime’,’
↪→ TimeZone’,’America/New_York’));
assignin(’base’,[’timeir’ nameirrigation_Period2{i}],realtimeir);
end
%%
save(’SZData190726_to_190923’)
Prediction for Cumulative ET
% This Code Calculates Forecast Cumulative ET.
wfmatrix = importdata(’wfsz.xlsx’);% Downloads Data from ACIS (Applied
↪→ Climate Information System)
340
wfdata = wfmatrix.data;
%%
wfrealtime = datetime(wfdata(:,2),’ConvertFrom’,’posixtime’,’TimeZone’,’
↪→ America/New_York’);
wftimehrs = hours(wfrealtime-wfrealtime(1))+hour(wfrealtime(1));
wftemp = wfdata(:,3);% degree C
wfrh = wfdata(:,4);% percentage
wfqrad = wfdata(:,6); % kw/m^2
wfws = wfdata(:,5);% m/s
wfpar = wfqrad*1000/0.219;% umol/m^2-s
%%
% VPD
TK0 = 273.15;
TeK = wftemp+TK0;
AVPD=17.2693882; %Constant for calculating Psat
BVPD=35.86; %Constant for calculating Psat
CVPD=0.61078; %Constant for calculating Psat in kPa
wfPsat=CVPD*exp(AVPD*(TeK-273.15)./(TeK-BVPD)); %kPa Teteus Equation
wfVPDkPa=(100-wfrh(1:size(wftemp)))./100.*wfPsat; %kPa
wfVPDPa=wfVPDkPa.*10^(3); %Pa
wfVPDPa(wfVPDPa<0) = 0;
figure
plot(wfrealtime,wfVPDkPa)
title(’VPDkPa’)
341
% ra
wv = wfws;
naturalwv = 1e-10;
wv(wv<=naturalwv) = naturalwv; % m/s
ra_ind = 2;
wfratp = 40./sqrt(wv); % Thorpe 1980
wfradr = 40./wv; % Dragoni 2003 does not work due to infinite resistance
↪→ when wv is close to zero.
wfrayu = 4.72.*(log(1/0.13))^2./(1+0.54.*wv);
figure
plot(wfrealtime,wfws)
if ra_ind == 1
wfra = wfratp;
raDMDL = ’Thorpe 1980’;
else, if ra_ind == 2
wfra = wfradr;
raDMDL = ’Dragoni 2003’;
else
wfra = wfrayu; %(Yunusa 2000, Monteith and Unsworth 1990)
raDMDL = ’Yunusa 2000’;
end
end
342
figure
plot(wfrealtime,wfra)
title(’ra s/m’)
% gs or rgs
gmax = gsmmol2ms(226); %m/s*1.88
alphags = 0.3e-3;%0.17e-3; %Pa-1 0.3e-3
betags = 79; %umol/s-m^2
gammags = 3*abs(1/35);% inverse of abs(-6 bars) a turning point of the
↪→ role of SWP
fcuticle = 0.3;
% Putmgs = interp1(realtimeutm,Putm,wfrealtime);
% % Calculation of Stomatal Conductance
gsww=gmax.*((1-alphags.*wfVPDPa)./(1+betags./(wfpar)));
gsww(wfpar<200) = fcuticle*gmax;
gs = gsww;
rgs=1./gs;
% ET
%slope of saturation pressure curve Pa/K
S=CVPD*(273.15*AVPD-AVPD*BVPD)./(TeK-BVPD).^2 ...
.*exp(AVPD.*(TeK-273.15)./(TeK-BVPD))*1000;
rho=(1.01*10^5)./(287.05.*TeK); %calculate dry air density
cp=1.01e3; %heat capacity of air
gamma=66; % psychrometric constant Pa/K
lambda=2.260e6; %%latent heat of vaporization J/kg
343
leafA = 1; % m^2
Sf1 = 60/100; % Shaded leaf percentage
USf1=1-Sf1;
% wfqrad(wfqrad>2)=0;
%Evaporation rate for shaded and unshaded leaves
wfETUNSHADED=(1/lambda)*(S.*wfqrad.*1000*0.5.*wfra+(rho.*cp).*wfVPDPa)
↪→ ./(...
(S+2.*gamma).*wfra+gamma.*rgs);
wfETSHADED=(1/lambda)*(0.1.*S.*wfqrad.*1000*0.5.*wfra+(rho.*cp).*wfVPDPa)
↪→ ./(...
(S+2.*gamma).*wfra+gamma.*rgs);
wfET=(USf1*wfETUNSHADED+Sf1*wfETSHADED)*leafA;% Measured leaf area
wfETphr = wfET*3600;
cumwfET = trapz(wftimehrs,wfETphr);
irrate = 0.15;% kg/min/tree
ir_min = cumwfET/irrate;
figure,plot(wfrealtime,wfETphr)
xlabel(’time of day’)
ylabel(’WeatherForcastET (kg/hr)’)
titlestr = sprintf(’CumET is %4.4f kg with ir time %d min. ’,cumwfET,
↪→ ir_min);
title(titlestr)
save(’wfET.mat’,’wfET’)
D.5 Heat Transfer Simulation
344
% 2D finite difference model for heat transfer simulation
% Complete embedding of sensor filled completely with urethane
% a + chip only embedding
tic
clear
close all
clc
change_to_air = 1; % 0 means the material around the chip is polyurethane;
↪→ 1 means it is air
T_ind = 0.1;
tube_length = 12e-3; % [m] length of the tube
tube_diameter = 10e-3; % [m] diameter of the sensor+tubing
% materials information
% silicon
k_si = 130; % thermal conductivity W/m-K
d_si = 2330; % density kg/m^3
C_si = 0.81*1000;% specific heat capacity J/kg-K
alpha_si = k_si/(d_si*C_si);% thermal diffusivity m^2/s
% UR5041 packaging material
k_u = 0.25;
d_u = 1180;
C_u = 1800;
alpha_u = k_u/(d_u*C_u);
345
% air
k_a = 0.026;
d_a = 1.1839;
C_a = 1010;
alpha_a = k_a/(d_a*C_a);
%overall heat transfer coefficient
r_1 = 1.5e-2; %[m]
r_2 = 10e-2; %[m]
h_air = 10; % W/m^2-K forced convection, low speed of flow over a surface
U_overall = 1/(r_1/k_u*log(r_2/r_1)+r_1/r_2*1/h_air);% (W/m^2-K)
if change_to_air == 1
k_u = k_a;
d_u = d_a;
C_u = C_a;
alpha_u = alpha_a;
end
% Inputs
s_length= 5e-3; % [m] depth of the drilled hole in meter
s_thickness = 0.8e-3; % [m] thickness of the sensor
alpha = tube_length/tube_diameter; % alpha = L/W of tube L = 15 cm; W = 10
↪→ cm
346
beta = s_length/tube_length; % beta = sL/L = sensor length / Length of
↪→ tube
lamda = s_thickness/tube_diameter;
minnodes_x = 3; % minimum number of nodes for the device
minnodes_y = 5;
% m = number of ndx across the sensor
% ndx is the distance between nodes in x direction ( cross-section of the
% sensor)
% n = number of ndx on both sides of the sensor
m = minnodes_x;
n_is_an_integar = 0; % 0 means no, 1 means yes
while n_is_an_integar == 0
if abs(((1-lamda)/2)/(lamda/m)-round(((1-lamda)/2)/(lamda/m)))<1e-15
n_is_an_integar = 1;
n = round(((1-lamda)/2)/(lamda/m));
else
m = m + 1;
end
end
ndx = lamda/m;
a = minnodes_y;
b_is_an_integar = 0;
while b_is_an_integar == 0
if abs((1-beta)/(beta/a)-round((1-beta)/(beta/a)))<1e-15
b_is_an_integar = 1;
347
b = round((1-beta)/(beta/a));
else
a = a + 1;
end
end
ndy = beta/a;
%% Create T Matrix and Indexes
X = (-(n+m/2)*ndx:ndx:(n+m/2)*ndx)*tube_diameter;
Y = (0:ndy:(a+b)*ndy)*tube_length;
T = zeros(a+b+1,m+2*n+1);
T(2:a+1,n+1:n+m+1) = 1;
g = ndx/ndy;
x = size(T,2);
y = size(T,1);
%%
if g>1
dt = (ndy)^2/(alpha_si*5);
else if g<=1
dt = (ndx)^2/(alpha_si*5);
end
end
% create index matrix
row = 0;
s_row = 0;
348
sl_row = 0;
sr_row = 0;
sb_row = 0;
st_row = 0;
for i = 2:y-1
for j = 2:x-1
if T(i,j) == 0
row = row + 1;
u_ind(row)=i+(j-1)*size(T,1);
end
% top side of silicon
if T(i,j) ==1 && T(i,j-1) == 1 && T(i,j+1) == 1 && T(i+1,j) == 1 &&
↪→ T(i-1,j) == 0
st_row = st_row + 1;
s_ind_t(st_row) = i + (j-1)*size(T,1);
end
% top left corner
if T(i,j) ==1 && T(i,j-1) == 0 && T(i,j+1) == 1 && T(i+1,j) == 1 &&
↪→ T(i-1,j) == 0
s_ind_tlc = i + (j-1)*size(T,1);
end
% top right corner
if T(i,j) ==1 && T(i,j-1) == 1 && T(i,j+1) == 0 && T(i+1,j) == 1 &&
↪→ T(i-1,j) == 0
s_ind_trc = i + (j-1)*size(T,1);
end
% internal silicon
349
if T(i,j) ==1 && T(i,j-1) == 1 && T(i,j+1) == 1 && T(i+1,j) == 1 &&
↪→ T(i-1,j) == 1
s_row = s_row + 1;
s_ind(s_row) = i + (j-1)*size(T,1);
end
% left side of silicon
if T(i,j) == 1 && T(i,j-1) == 0 && T(i,j+1) == 1 && T(i+1,j) == 1
↪→ && T(i-1,j) == 1
sl_row = sl_row + 1;
s_ind_l(sl_row) = i+(j-1)*size(T,1);
end
% right side of silicon
if T(i,j) == 1 && T(i,j-1) == 1 && T(i,j+1) == 0 && T(i+1,j) == 1
↪→ && T(i-1,j) == 1
sr_row = sr_row + 1;
s_ind_r(sr_row) = i+(j-1)*size(T,1);
end
% bottom side of silicon
if T(i,j) == 1 && T(i,j-1) == 1 && T(i,j+1) == 1 && T(i+1,j) == 0
↪→ && T(i-1,j) == 1
sb_row = sb_row + 1;
s_ind_b(sb_row) = i+(j-1)*size(T,1);
end
% bottom left corner
if T(i,j) == 1 && T(i,j-1) == 0 && T(i,j+1) == 1 && T(i+1,j) == 0
↪→ && T(i-1,j) == 1
s_ind_blc = i+(j-1)*size(T,1);
350
end
% bottom right corner
if T(i,j) == 1 && T(i,j-1) == 1 && T(i,j+1) == 0 && T(i+1,j) == 0
↪→ && T(i-1,j) == 1
s_ind_brc = i+(j-1)*size(T,1);
end
end
end
% bottom boundary condition of the system
bound_b = 0;
for j = 2:size(T,2)-1
bound_b = bound_b+1;
b_ind(bound_b) = a+b+1+(j-1)*size(T,1);
end
% top and sides boundary conditions
bound_t = 0;
for j = 2:x-1
bound_t = bound_t+1;
t_ind(bound_t) = 1+(j-1)*y;
end
bound_r = 0;
bound_l = 0;
for i = 2:y-1
bound_l = bound_l+1;
bound_r = bound_r+1;
l_ind(bound_l) = i;
r_ind(bound_r) = i+(x-1)*y;
351
end
tlc_ind = 1;
blc_ind = y;
trc_ind = 1+(x-1)*y;
brc_ind = x*y;
%% Dimensionless Conditions
% dimensionless initial and boundary conditions
T_p = 1;
T_inf = 0;
T(:,:) = T_inf; %[C] Define Initial Conditions
T(1,:) = T_p; %[C] Define Boundary Conditions
T(:,1) = T_p; %[C] left top
T(:,end) = T_p; %[C] Right top
%% RUN
t = 0;
stop_sim = 0;
ind = 1;
T_diff(ind) = 0;
g = ndx/ndy;
Fo_u = alpha_u*dt/(ndx^2);
Fo_si = alpha_si*dt/(ndx^2);
Bi = U_overall*ndx/k_u;
while stop_sim ==0
t = t + dt;
352
ind = ind+1;
% top boundary condition
%T(t_ind) = T(t_ind)+Fo_u*(T(t_ind+y)+T(t_ind-y)-2*T(t_ind))+2*Fo_u*g
↪→ ^2*(T(t_ind+1)-T(t_ind));
%left side boundary condition
%T(l_ind) = T(l_ind)+Fo_u*g^2*(T(l_ind+1)+T(l_ind-1)-2*T(l_ind))+2*Fo_u
↪→ *(T(l_ind+y)-T(l_ind));
%right side boundary condition
%T(r_ind) = T(r_ind)+Fo_u*g^2*(T(r_ind+1)+T(r_ind-1)-2*T(r_ind))+2*Fo_u
↪→ *(T(r_ind-y)-T(r_ind));
% top left corner
%T(tlc_ind) = T(tlc_ind)+2*Fo_u*(T(tlc_ind+y)-T(tlc_ind))+2*g^2*Fo_u*(T
↪→ (tlc_ind+1)-T(tlc_ind));
%bottom left corner
%T(blc_ind) = T(blc_ind)+2*Fo_u*(T(blc_ind+y)-T(blc_ind))+2*g^2*Fo_u*(T
↪→ (blc_ind-1)-T(blc_ind));
% top right corner
%T(trc_ind) = T(trc_ind)+2*Fo_u*(T(trc_ind-y)-T(trc_ind))+2*g^2*Fo_u*(T
↪→ (trc_ind+1)-T(trc_ind));
% bottom right corner
%T(brc_ind) = T(brc_ind)+2*Fo_u*(T(brc_ind-y)-T(brc_ind))+2*g^2*Fo_u*(T
↪→ (brc_ind-1)-T(brc_ind));
% bottom boundary condition
T(b_ind) = Fo_u*(T(b_ind-y)-2*T(b_ind)+T(b_ind+y))+2*g^2*Fo_u*(T(b_ind
↪→ -1)-T(b_ind))+2*g*Bi*Fo_u*(-T(b_ind))+T(b_ind);% changed T-p to
↪→ T(u_bound)
% urethane part
353
T(u_ind) = Fo_u*(T(u_ind-y)-2*T(u_ind)+T(u_ind+y))+Fo_u*g^2*(T(u_ind-1)
↪→ -2*T(u_ind)+T(u_ind+1))+T(u_ind);
%T(u_ind) = Fo_u*(T(u_ind)+T(u_ind-y)+g^2*T(u_ind-1)+g^2*T(u_ind+1))
↪→ -((2+2*g^2)*Fo_u-1)*T(u_ind);
% silicon part
T(s_ind) = Fo_si*(T(s_ind-y)-2*T(s_ind)+T(s_ind+y))+Fo_si*g^2*(T(s_ind
↪→ -1)-2*T(s_ind)+T(s_ind+1))+T(s_ind);
% silicon top side
T(s_ind_t) = T(s_ind_t)+Fo_si*(T(s_ind_t-y)-2*T(s_ind_t)+T(s_ind_t+y))
↪→ +2*k_u/k_si*g^2*Fo_si*(T(s_ind_t-1)-T(s_ind_t))+2*g^2*Fo_si*(T(
↪→ s_ind_t+1)-T(s_ind_t));
% silicon top left corner
T(s_ind_tlc) = T(s_ind_tlc)+4*Fo_si*k_u/k_si*(T(s_ind_tlc-y)-T(
↪→ s_ind_tlc))+2*Fo_si*(T(s_ind_tlc+y)-T(s_ind_tlc))+4*k_u/k_si*
↪→ Fo_si*g^2*(T(s_ind_tlc-1)-T(s_ind_tlc))+2*Fo_si*g^2*(T(s_ind_tlc
↪→ +1)-T(s_ind_tlc));
% silicon top right corner
T(s_ind_trc) = T(s_ind_trc)+4*Fo_si*k_u/k_si*(T(s_ind_trc+y)-T(
↪→ s_ind_trc))+2*Fo_si*(T(s_ind_trc-y)-T(s_ind_trc))+4*k_u/k_si*
↪→ Fo_si*g^2*(T(s_ind_trc-1)-T(s_ind_trc))+2*Fo_si*g^2*(T(s_ind_trc
↪→ +1)-T(s_ind_trc));
% silicon left
T(s_ind_l) = T(s_ind_l)+2*Fo_si*k_u/k_si*(T(s_ind_l-y)-T(s_ind_l))+2*
↪→ Fo_si*(T(s_ind_l+y)-T(s_ind_l))+g^2*Fo_si*(T(s_ind_l-1)-T(
↪→ s_ind_l))+g^2*Fo_si*(T(s_ind_l+1)-T(s_ind_l));
% silicon right
354
T(s_ind_r) = T(s_ind_r)+ 2*Fo_si*(T(s_ind_r-y)-T(s_ind_r))+g^2*Fo_si*(T
↪→ (s_ind_r-1)-2*T(s_ind_r)+T(s_ind_r+1))+2*k_u/k_si*Fo_si*(T(
↪→ s_ind_r+y)-T(s_ind_r));
% silicon left bottom corner
T(s_ind_blc) = T(s_ind_blc)+4*Fo_si*(T(s_ind_blc-y)-T(s_ind_blc))+4*g
↪→ ^2*k_u/k_si*Fo_si*(T(s_ind_blc+1)-T(s_ind_blc))+2*g^2*Fo_si*(T(
↪→ s_ind_blc-1)-T(s_ind_blc))+2*Fo_si*(T(s_ind_blc+y)-T(s_ind_blc))
↪→ ;
% silicon right bottom corner
T(s_ind_brc) = T(s_ind_brc)+2*Fo_si*(T(s_ind_brc-y)-T(s_ind_brc))+2*
↪→ Fo_si*g^2*(T(s_ind_brc-1)-T(s_ind_brc))+4*Fo_si*k_u/k_si*(T(
↪→ s_ind_brc+y)-T(s_ind_brc))+k_u/k_si*g^2*4*Fo_si*(T(s_ind_brc+1)-
↪→ T(s_ind_brc));
% silicon bottom side
T(s_ind_b) = T(s_ind_b)+Fo_si*(T(s_ind_b-y)-2*T(s_ind_b)+T(s_ind_b+y))
↪→ +2*Fo_si*g^2*(T(s_ind_b-1)-T(s_ind_b))+2*Fo_si*g^2*(k_u/k_si)*(T
↪→ (s_ind_b+1)-T(s_ind_b));
T_diff(ind) = T(round(a+b/2),round(n+m/2));
% if ind > 40000 && abs(T_diff(ind)-T_diff(ind-1))<=1e-8 && T_diff(ind)>1e
↪→ -3
% stop_sim = 1;
% else
% stop_sim = 0;
% end
if ind > 550000 && abs(T_diff(ind)-T_diff(ind-1))<=1e-20
355
stop_sim = 1;
else
stop_sim = 0;
end
if mod(ind,10000) == 0
clc
figure(1)
plot(t/60,T_diff(ind),’ob’)
hold on
xlabel(’time(min)’)
ylabel(’Temp(Cavity)’)
figure(2)
surf(T)
drawnow
fprintf(’time passed:\n %8.4f min \n’,t/60)
fprintf(’temperature difference between cavity and sample:\n %8.4f
↪→ fraction of (T-plant - T-outside) \n’,T_diff(ind))
end
end
%%
figure(3)
surf(X,Y,T)
fprintf(’time interval: \n %8.4f s \n’,dt)
fprintf(’tube length: \n %8.4f mm \n’,tube_length*1000)
356
fprintf(’complete time passed:\n %8.4f min \n’,t/60)
fprintf(’final temperature difference between cavity and sample:\n %8.4f
↪→ fraction of (T-plant - T-outside) \n’,T_diff(end))
toc
357
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