Deterministic and Stochastic Models of Water Limited Ecosystems: Implications of Pattern Formation, Bifurcations, Model Reduction, and Data

The project consists of three phases. The first is related to analysis of deterministic PDE reaction-advection-diffusion models of vegetation-water interactions. The second project phase relates to stochastic modeling of precipitation in the vegetation models. The third project phase relates to the analysis of satellite data with an aim of better constraining and differentiating between models, as well as informing the modeling efforts. One project area where there is significant work yet to do is in the stochastic modeling aspects of this project. This is a new direction for the PI and the research effort is still gearing up on this phase, although progress has been made by connecting with ecohydrologists who work on this type of precipitation modeling. The PI is continuing with plans to do an inter-model comparison for the deterministic PDE models, where, in collaboration with Dr. Sarah Iams (Harvard) she has constructed models that continuously bridge from one to another in a hierarchy, through parameter changes. In collaboration with Prof. Chad Topaz at Macalester College and Prof. Andrew Bernoff at Harvey Mudd College, there are 4 undergraduates working on the data aspects of the project over summer 2016. This is an exploration that should lead to new modeling efforts. A final overarching challenge for this project is the model reduction aspects that are needed to connect the different modeling frameworks in order to determine their possibly consistency/inconsistency with each other and with available data. An integral part of the research project, particularly in the area of its broader impacts, is the training of PhD students in interdisciplinary applied mathematics research. The PI has two Northwestern PhD students (Mr. Karna Gowda and Ms. Yuxin Chen) whose thesis research is part of this project. The reason for making Northwestern a sub recipient is to be able to cover the student tuition and stipend while they complete their training. This is an essential part of the project