CMG: Modeling River Basin Dynamics: Parallel Computing and Advanced Numerical Methods

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A fundamental research goal in earth-surface science (geomorphology, hydrology, sedimentology) is to develop mathematical (usually numerical) models that describe the formation of river basins over geologic time and their response to natural and anthropogenic forcing over human time scales. Within the last two decades, the potential for building, testing, and applying such models has advanced significantly thanks to several parallel developments, including (1) cosmogenic nuclide analysis for measuring erosion rates, (2) development of improved rate laws for processes such as soil production, and (3) rapid advances in digital mapping technology, such as LiDAR and the Shuttle Radar Topography Mission (SRTM), that have led to the widespread availability of high-resolution terrain data. However, computational efficiency is now a key limiting factor. Because of nonlinearities in the governing equations, current models cannot, for example, handle an area larger than a few hectares at the resolution of a typical LiDAR image (about1 square kilometer). To address this obstacle, a 4-year collaborative effort between geoscientists and applied mathematiciansis is proposed, aimed at developing efficient and parallelized numerical algorithms for solving the equations that govern the evolution of a topographic surface.River basins and their networks occupy the vast majority of the earth's land surface. Most of us live in a river basin and depend on its ability to gather water over a large area and focus it into a narrow channel.However, the same mechanism gathers sediment and contaminants and can produce natural disasters such as floods and landslides. Efficient and accurate landscape evolution and surface-process models are needed to address numerous environmental problems and many other problems of societal relevance. They also provide outstanding educational and research opportunities that bridge the gap between applied mathematics and geoscience since they embody such a rich variety of challenging mathematical problems. These problems represent exciting intellectual frontiers in both geoscience and mathematics and it is hoped that the proposed collaborative work will attract the attention of mathematicians and lead to further advances.