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

地球表面科学（地貌学、水文学、沉积学）的一个基本研究目标是建立数学（通常是数值）模型，描述地质时期河流流域的形成及其对人类时间尺度上自然和人为强迫的响应。 在过去的二十年中，由于几个平行的发展，建立，测试和应用这些模型的潜力已经大大提高，包括（1）测量侵蚀速率的宇宙成因核素分析，（2）改进土壤生产等过程的速率定律的发展，以及（3）数字制图技术的快速发展，如LiDAR和航天飞机雷达地形使命（SRTM），这导致了高分辨率地形数据的广泛可用性。然而，计算效率现在是一个关键的限制因素。由于控制方程中的非线性，例如，当前的模型不能以典型的LiDAR图像（约1平方公里）的分辨率处理大于几公顷的区域。为了解决这一问题，地球科学家和应用数学家提出了一个为期4年的合作计划，旨在开发高效的并行数值算法来求解控制地形表面演变的方程。我们大多数人生活在河流流域，依靠其大面积集水并将其集中到狭窄河道的能力，然而，同样的机制也会聚集沉积物和污染物，并可能产生洪水和山体滑坡等自然灾害。 需要有效和准确的景观演变和表面过程模型来解决许多环境问题和许多其他社会相关问题。 它们还提供出色的教育和研究机会，弥合应用数学和地球科学之间的差距，因为它们体现了如此丰富的各种具有挑战性的数学问题。 这些问题代表了令人兴奋的知识前沿，在地球科学和数学，希望拟议的合作工作将吸引数学家的注意，并导致进一步的进展。

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.