Spatial patterns and processes characterizing geographical entities and phenomena, such as drainage basins, systems of cities, and flows of information, often show a remarkable mix of organization and complexity. These arise from a large number of interactions that are spatially distributed and characterized by non-linear processes involving stochastic effects and instabilities. The dominant objective of this research is to refine and extend a family of physically based models for simulating key aspects of drainage basin evolution. The project will incorporate theoretical, computational, and field-based investigations to accomplish the following: (1) apply emerging methodologies for characterizing the qualitative behavior of infinite-dimensional, non-linear dynamical systems in explaining the emergence of spatial patterns in the evolution of drainage basins; (2) demonstrate that such methods must be used in conjunction with traditional methods in developing a full characterization of the evolution of fluvial land surfaces and an understanding of various scaling laws; (3) develop additional tools for such analyses and apply them to other examples of complex geographic phenomena; and (4) disseminate an understanding of these methods and their value. The mathematical and modeling results will provide a basis for qualitative and quantitative predictions that may be compared with observations on real landscapes, and ultimately, models of analogous geographic phenomena, such as population movements, diffusion of innovations, and information flows can be developed based on this understanding.
