Date of Award:


Document Type:


Degree Name:

Master of Science (MS)


Mathematics and Statistics

Committee Chair(s)

Luis F. Gordillo


Luis F. Gordillo


Brynja Kohler


Patrick Belmont


Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming these regions into deserts. Many mathematical models have been developed for purposes of analyzing vegetation-water interactions, particularly in semi-arid landscapes. Most models are based on the average behavior of the system as a whole, and how it is influenced by external changes. These models may be termed "macro-scale" models. Other models have concerned themselves with the interactions between individuals, in this case the interactions between individual plants and the available water. These models may be termed "micro-scale" models. In this thesis we present a model for vegetation-precipitation interactions which is intermediate between these two types of models. This "meso-scale" model, also known as a stochastic model, has the advantage of incorporating the behavior of the system as a whole, while still retaining the "noise" (or internal influences) from the individual interactions. Extensive simulations with this model suggest that persistence in current trends of precipitation decline in semi-arid landscapes may expedite desertification processes by up to several decades.