The Stochastic Dynamics of Biomass and Soil Moisture in Water-Limited Ecosystems

Abstract

This dissertation examines the interaction between soil moisture and vegetation when the system is driven by intermittent, limited rainfall, resulting in a stochastic process. The first chapter introduces analytical techniques for describing this interaction, including a novel solution for the joint probability distribution of biomass and soil moisture. The second chapter applies these techniques to a field site in NW China, and demonstrates that such a model accurately reproduces the observed variability in vegetation over multiple growing seasons. Specifically, it is shown that water is the dominant driver of growth, and that the variability in rainfall can be accurately mapped onto the measured variability in leaf and root biomass via the model given here. The third chapter is devoted to understanding the structures which can arise in the distribution of vegetation in the presence of strong feedbacks with the soil water balance. This culminates in the emergence of bi-modal and multi-modal distributions, along with the conditions under which they occur and new mathematical approaches for describing them, such as exact results for the crossing times between high and low biomass modes. The fourth and final chapter introduces some preliminary work on the application of this model to multi-species ecological competition, namely that between plant species with different transpiration characteristics competing for the same rainfall.