Problems of Geophysical Fluid Mechanics: Modeling, Theory and Computing

地球物理流体力学问题：建模、理论和计算

• 批准号: 1206438
• 负责人: Roger Temam
• 金额: $ 30.5万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206438&HistoricalAwards=false
• 关键词: Problems; Geophysical; Fluid; Mechanics; Modeling

This project will address problems in mathematical ocean and atmosphere sciences, related to weather and climate prediction. Two classes of problems will be investigated. The first one is that of the boundary conditions for limited area weather models for which physical models do not provide natural boundary conditions. This problem is as old as numerical weather prediction itself, and it is expected that inappropriate boundary conditions will introduce spurious modes, in particular as improved computing capabilities allow better spatial and temporal resolutions. The aim is to derive boundary conditions that lead to mathematically correct problems, and that are computationally satisfactory in the sense that they let the waves move freely inside and outside the domain of computation. The PI will continue his investigations in this direction. The second class of problems is that of moist convection, precipitations and clouds. Our limited understanding of the physics of clouds is one of the primary causes of uncertainty in the current weather and climate predictions. The difficulties are in part due to the large differences in scales, ranging from cloud sizes of hundreds of kilometers to particles (droplets of water, ice or aerosols) of a few microns. There is a similar range of time scales. The project will study this physical problem using mathematical tools from convex analysis and variational inequalities. Numerical multilevel methods will be used as well to study the interaction of clouds and topography near the equator; and finally the tools of convex analysis will also be used for the very modeling of the changes of phase in the clouds. These studies will be conducted in close collaboration with physicists. The project will involve graduate students and post-doctoral associates who will be trained in this important interdisciplinary area. This research project will study fundamental problems in the numerical prediction of weather and climate, as well as problems in the mathematical modeling of clouds and evaporation. The project component related to numerical weather prediction addresses the problem of using information from coarse featured global weather data for fine grained local and regional predictions. If the coarse data are not coupled correctly to the regional model that has higher resolution, then spurious systematic errors (e.g. "ghost" weather fronts) may arise. The project will investigate the mathematical foundations of this problem. The project component on the modeling of clouds and evaporation will use advanced mathematical tools to contribute to the understanding of a set of basic open problems in weather and climate research: Do clouds help cool the planet (because they reflect sunlight) or do they contribute to warming (because they can hold thermal energy)? Weather prediction and climate modeling are objectives with important human, social and economic interest. The project will also train young scientists at the interface of mathematics, geophysical fluid mechanics, and scientific computing.

该项目将解决与天气和气候预测有关的海洋和大气科学数学问题。我们将研究两类问题。第一个是有限区域天气模式的边界条件，其中物理模式不提供自然边界条件。这个问题与数值天气预报本身一样古老，预计不适当的边界条件将引入虚假模式，特别是随着计算能力的提高，可以获得更好的空间和时间分辨率。其目的是推导出边界条件，这些边界条件会导致数学上正确的问题，并且在计算上是令人满意的，因为它们允许波在计算域内外自由移动。私家侦探将继续朝这个方向调查。第二类问题是湿对流、降水和云。我们对云的物理性质了解有限，这是造成当前天气和气候预测不确定的主要原因之一。困难的部分原因在于尺度上的巨大差异，从数百公里的云大小到几微米的颗粒（水滴、冰或气溶胶）。有一个相似的时间尺度范围。该项目将使用从凸分析和变分不等式的数学工具来研究这个物理问题。数值多层方法也将用于研究赤道附近云和地形的相互作用；最后，凸分析的工具也将用于云的相位变化的非常建模。这些研究将在物理学家的密切合作下进行。该项目将涉及研究生和博士后助理，他们将在这一重要的跨学科领域进行培训。这个研究项目将研究天气和气候数值预测的基本问题，以及云和蒸发的数学建模问题。与数值天气预报有关的项目组成部分解决了使用粗特征全球天气数据信息进行细粒度局部和区域预报的问题。如果粗糙数据不能正确地与具有更高分辨率的区域模型耦合，则会产生虚假的系统误差(例如：可能会出现“幽灵”天气锋面。这个项目将研究这个问题的数学基础。云和蒸发建模的项目组成部分将使用先进的数学工具来帮助理解天气和气候研究中的一系列基本开放问题：云是帮助地球降温（因为它们反射阳光）还是有助于变暖（因为它们可以储存热能）？天气预报和气候模拟是具有重要的人类、社会和经济利益的目标。该项目还将培养数学、地球物理流体力学和科学计算领域的青年科学家。