Many submerged plants rely on photosynthesis as a means to obtain sugars and oxygen. Plants that inhabit deeper regions have limited exposure to sunlight, as light irradiance decreases exponentially with increasing distance from the surface. During the winter, ice growth over a lake adds additional light obstruction. Ice sheets may grow to a thickness that reduces light availability to a level that no longer supports photosynthesis. While modeling the growth of ice sheets computationally is not new, there have not been studies linking ice sheet growth with the obstruction of light used for photosynthesis. This study investigates the conditions necessary to grow an ice sheet sufficiently thick to reduce the light irradiance 20 meter below the surface to 10% of the irradiance hitting the surface of the ice.

Our investigation looks at upstate New York and considers a region containing the expanding ice sheet, the water below it, and an insulating 2 centimeter thick layer of snow that only exists when an ice sheet does. To model the growth of the ice sheet we modelled the heat transfer and treated the ice layer as a solid with a no flow liquid water domain underneath. We included Syracuse specific time-dependent air temperature conditions, a convective heat transfer coefficient, radiative flux from sunlight and radiation from the atmosphere at the surface of the lake to mimic common wintertime conditions. We also used zenith angle information from upstate New York latitude and longitudes. A semi-infinite boundary at a constant temperature was established at the bottom of the domain to simulate a deep lake. Additionally, we incorporated water’s temperature dependent density in modeling heat transfer in the domain. Finally, we implemented these design specifications (dimensions, equations, boundary conditions, and physics) in COMSOL software for numeric analysis for the duration of an entire month.

After implementing the model with the above conditions, we were able to show that our model successfully computes the growth and decay of ice over time for small northern lakes. We obtained a model of the temperature variation within the ice layer and water underneath at discrete points in time, as well as the depth of the ice sheet over the course of the time period. Our model demonstrated that ice formation never reached a thickness sufficient to impede photosynthesis in our Syracuse location given normal conditions and moderate future weather shifts. However, our model includes flexibility to incorporate a range of different weather conditions, which may be used to monitor whether climate change can drive ice formation enough to inhibit photosynthesis.