FRG: Collaborative Research: Models of Balanced Multiscale Ocean Physics for Simulation and Parameterization

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。地球气候系统中发生的大范围尺度变化无法在全球气候模型中明确捕获，即使在新兴的千万亿次计算机上也是如此。这个项目将通过以下方式进一步理解物理学在尺度太小而无法用模式对较大气候系统进行分析的情况下的影响：1）探索潜在的新的渐近展开，为三个重要的小尺度过程中的每一个提供简化的单尺度方程：对流、中尺度涡旋和亚中尺度涡旋; 2）扩展渐近展开技术，使其能够显式地导出小尺度流态和大尺度流态之间的耦合关系，3）发展最先进的高性能并行程序，模拟简化的单尺度和多尺度方程; 4）在高性能计算机上进行高分辨率模拟; 5）分析模拟以扩展对每个小尺度过程行为的理解，包括流动动力学，能量学和输运性质;以及6）使用涡流解析模型测试一系列现有的参数化和未解决物理学的超参数化，以了解我们的多尺度方法的范围和影响。发展耦合渐近展开来研究多尺度现象，除了地球科学之外，在许多科学和工程领域都有潜在的应用。本研究旨在展示和应用这种方法的优势，以提高气候系统的数学和计算研究。 在地球科学中，渐近数学方法长期以来一直用于改进计算-第一个数值天气预报是唯一可能的，因为准地转渐近展开。地球科学长期以来也引导了渐近分析;匹配渐近展开的最早例子是对海洋西边界流的研究，如墨西哥湾流和黑潮。最后，这项研究旨在直接改善气候模型对小尺度物理学的表现，这将有助于我们实现改善气候预测和理解以及人类对气候影响的目标。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The vast range of scales occurring in the Earth's climate system cannot be explicitly captured in global climate models, even on emerging petascale computers. This project will further understanding of the effects of physics at a scale that is too small to be resolved by models on the larger climate system by: 1) exploring potentially novel asymptotic expansions that provide reduced single-scale equations for each of the three important small-scale processes: convection, mesoscale eddies, and submesoscale eddies; 2) extending the asymptotic expansion technique to explicitly derive the coupling between small-scale regimes and large-scale flows; 3) developing state-of-the-art high-performance parallel codes to simulate the reduced single-scale and multiscale equations; 4) performing high-resolution simulations on high-performance computers; 5) analyzing the simulations to extend understanding of the behavior of each small-scale process, including flow dynamics, energetics, and transport properties; and 6) testing a range of existing parameterizations and superparameterizations of unresolved physics using eddy-resolving models to understand the scope and impact of our multiscale approach. The development of coupled asymptotic expansions to study multiscale phenomena has potential applications across many fields of science and engineering, in addition to the geosciences. This research is intended to demonstrate and apply the advantages of this approach to improve mathematical and computational study of the climate system. In geosciences, the asymptotic mathematical approach has long been used to improve computation--the first numerical weather forecasts were only possible because of the quasigeostrophic asymptotic expansion. The geosciences have long led asymptotic analysis as well; among the earliest examples of matched asymptotic expansions are studies of oceanic western boundary currents, such as the Gulf Stream and Kuroshio. Finally, the research is intended to directly improve climate models' representation of small-scale physics, which will aid our goals in improved forecasting and understanding of climate and mankind's influence on it.