On the ergodic properties of climate change with implications for agricultural resilience and sustainability

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Many studies have examined the variability of temperature and precipitation. However, it is not clear what exact trend of variability of climatic variables in the United States is or what this implies for the long run resilience and sustainability of America’s agricultural economy. While grave concerns have been raised about rising temperatures due to greenhouse gas effects, less has been said about changing variance. Our interest is in determining and mapping changes in variance to temperatures and rainfall at monthly aggregates between 1901 and 2020. In this paper, we use three different approaches to calculating the Hurst coefficient of temperature and precipitation: variance ratio, rescaled range, and Vlasicek model. We believe our calculation of the Hurst coefficient from Vlasicek’s mean-reversion econometric model to be original. Our findings that the Hurst coefficient for vast areas of the continental United States is near zero suggesting that between 1901 and 2020 temperatures and precipitation across the US, measured at a monthly scale, are ergodic and have not increased in variance. Some areas reveal a negative Hurst which suggests that variance is decreasing. However, we also find that in many areas of the USA there is evidence of localized climate change that can impact agricultural production and may require resilience interventions. Some effects are substantial. For example, our framework uses pure ergodicity with a Hurst coefficient of 0 as the and find in some areas the measured Hurst is around 0.3. Because variance changes as power law with respect to H, this modest increase implies that over 120 years variance has doubled, or the standard deviation has increased by 41%. This is not, however a sudden shock, but does suggest that in some localized areas (pixels) the phase space defining weather variability is expanding and the strength of mean reversion is weakening. Adaptation strategies should focus on these areas. We also find that climate change has different impacts in different regions of the USA depending on month of year. This suggests that a one-size-fits-all policy will unlikely be successful. Our results suggest that adaptation measures to climate change and changes in climate variability should be local, not national.

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56 pages


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Environment; Ergodic; Hurst exponent; Temperature Variability


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Union Local


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Turvey, Calum G.

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Ortiz-Bobea, Ariel

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Applied Economics and Management

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M.S., Applied Economics and Management

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Master of Science

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Government Document




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dissertation or thesis

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