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Local stochastic subgrid-scale modeling in efficient simulations of geophysical fluid dynamics

地球物理流体动力学高效模拟中的局部随机亚网格尺度建模

基本信息

批准号：
251091552
负责人：
Dr. Stamen Dolaptchiev
金额：
--
依托单位：
Institut für Atmosphäre und Umwelt (IAU)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2014
资助国家：
德国
起止时间：
2013-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/251091552?language=en
关键词：
Local stochastic subgrid scale modeling

项目摘要

Efficient models of the atmosphere are already interesting for conceptual reasons, as they can yield deepened insight into dynamic mechanisms, e.g. with regard to climate variability. They can, however, also be a helpful tool in climate-sensitivity studies, or in investigations of paleoclimate, where many or long integrations are needed, and thus computational efficiency is a matter of importance. Especially in such applications care has to be taken that as much of the inevitable subgrid-scale parameterizations of unresolved scales are based on first principles as possible. Stochastic mode reduction (SMR) offers a corresponding strategy, where most of the parameterization is derived on paper, once the nonlinear self-interactions between the unresolved modes have been fitted to a simple stochastic process. In applications so far, however, the constructed reduced model has been given a spectral formulation, where in the global subgrid-scale (SGS) parameterization all resolved modes interact with each other. This limits the applicability of this approach to very low-dimensional systems. To circumvent this problem, recently an implementation of the SMR to grid-point-based spatial discretizations has been developed which results in a local stochastic SGS parameterization. This strategy has so far been tested within the framework of the Burgers equation. In the proposed project significant steps will be taken towards the application of the local SMR strategy to realistic models of atmospheric dynamics. SGS parameterizations should be constructed for the barotropic vorticity equation and for the shallow water equations on an f-plane. Both models exhibit essential features to be taken into account in the application of the local SMR to the general equations of atmospheric dynamics.The new SGS parameterizations should fulfill the following criteria: i) they should be derived from the model equations in a systematic way under a relatively small number of basic assumptions ii) they should be as consistent as possible with the conservation properties of the model equations and iii) they should require minimal (if possible none at all) regression fitting of the resolved scales. Currently, there is a need in climate modeling for physics constrained and resolution independent formulations of stochastic parameterizations. The development of parameterizations using SMR, as proposed here, will contribute to such methods. Besides climate modeling, turbulence modeling in large eddy simulation is another field, which can benefit from such developments.

由于概念上的原因，有效的大气模型已经很有趣，因为它们可以加深对动态机制的洞察，例如关于气候变异性的。然而，在气候敏感性研究或古气候研究中，它们也可以是一个有用的工具，因为在这些领域需要许多或长期的积分，因此计算效率是一个重要的问题。特别是在这样的应用中，必须注意，尽可能多的未分辨尺度的不可避免的次网格尺度参数化是基于第一原理的。随机模式减缩(SMR)提供了一种相应的策略，其中，一旦未分辨模式之间的非线性自相互作用被拟合为一个简单的随机过程，则大部分参数都是在纸上推导出来的。然而，到目前为止的应用中，所构造的简化模型已经给出了谱公式，其中在全球亚网格尺度(SGS)的参数化中，所有可分辨的模式相互作用。这限制了这种方法在非常低维的系统中的适用性。为了避免这一问题，最近发展了一种基于网格点的空间离散的SMR实现，其结果是局部随机SGS参数化。到目前为止，这一战略已经在Burgers方程的框架内进行了测试。在拟议的项目中，将在将当地SMR战略应用于实际的大气动力学模型方面采取重大步骤。对于正压涡度方程和f平面上的浅水方程，应构造SGS参数化格式。这两个模式在将局地SMR应用于大气动力学一般方程时都显示出需要考虑的基本特征。新的SGS参数化应满足以下标准：i)它们应在相对较少的基本假设下系统地从模式方程中导出；ii)它们应尽可能与模式方程的守恒性质相一致；iii)它们应要求对所分解的尺度进行最小(如果可能的话)回归拟合。目前，在气候模拟中需要物理约束和分辨率无关的随机参数化公式。本文提出的使用SMR的参数化的发展将有助于这些方法的发展。除了气候模拟之外，大涡模拟中的湍流模拟是另一个可以从这些发展中受益的领域。