CMG COLLABORATIVE RESEARCH: Novel Mathematical Strategies for Superparameterization in Atmospheric and Oceanic Flows

提高我们对大气和海洋环流的理解和模拟能力对人类社会产生了非常直接的影响。然而，大气和海洋的流动涵盖了广泛的尺度，从10000公里量级的行星尺度到几毫米量级的微观尺度。这对全球气候模拟提出了一个特别的挑战，即使使用最强大的计算机，也不能直接解决几公里以下的尺度。拟议的项目将开发新的方法，通过超参数化来表示大气和海洋模式中未解决尺度对直接模拟尺度的影响。（SP），广义地定义为一套通用的技术，通过这些技术，小尺度动力学可以用数学和数值方式表示为嵌入式子网格模型。超参数化是一种相对较新的方法，在云的参数化方面取得了巨大成功，但尚未应用于气候模式中的许多其他相关问题。本项目将应用新颖的sp技术，准确地将大气和海洋模式中各种尚未解决的重要过程的影响结合起来。我们的研究将集中于SP策略在高度相关和困难的地球物理问题上的应用，包括大气中的湿对流、海洋中尺度和亚中尺度涡旋以及与中纬度天气系统相关的湿地转湍流，该系统结合了湿对流和地转湍流的元素。我们用一个系统的三步SP过程来处理这些不同的问题：(1)建立物理问题的多尺度方程；(2)对波动使用周期逼近；(3)利用间断性以简化模型取代波动动力学，这种简化模型可以通过廉价的数值方法或解析解来解决。我们的目标是在一组理想模型中开发和测试这种SP方法，并最终提供新的参数化算法，这些算法可能会被纳入可操作的全球气候模型中。

Improving our understanding of, and ability to model atmospheric and oceanic circulation impacts human society in a very direct way. Atmospheric and oceanic flows, however, encompass a wide range of scales, from the planetary scale, of order 10000km, to the microscale, on the order of a few millimeters. This raises a particular challenge for global climate simulations, which cannot directly resolve scales below a few kilometers at best, even with the most powerful computers. The proposed project will develop novel methods to represent the effects of unresolved scales on directly simulated scales in atmospheric and oceanic models through ʻsuperparameterizationʼ (SP), defined broadly as a general set of techniques by which small-scale dynamics can be represented mathematically and numerically as an embedded sub-grid model. Superparameterization is a relatively new approach that has had great success in the parameterization of clouds, but has yet to be applied to many other relevant problems in climate models. The present project will apply novel SPtechniques to accurately incorporate the effects of a wide variety of important unresolved processes in atmospheric and oceanic models.Our research will focus on the application of SP strategies to highly relevant and difficult geophysical problems, including moist convection in the atmosphere, mesoscale and submesoscale eddies in the oceans, and moist geostrophic turbulence associated with the midlatitude weather system, which combines elements of both moist convection and geostrophic turbulence. We approach these diverse problems with a systematic, three step SP process: (1) the development of multi-scale equations for the physical problem;(2) the use of a periodic approximation for the fluctuations; and (3) exploitation of intermittency to replace fluctuating dynamics with reduced models that may be solved by either inexpensive numerical methods or by analytic solutions. Our goals are to develop and test this SP approach in a set of idealized models, and ultimately to provide new parameterization algorithms that may be incorporated in operational global climatemodels.