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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.

出于概念原因，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了解，例如。关于气候变化。然而，它们也可以成为气候敏感性研究或古气候研究的有用工具，这些领域需要多次或长时间的积分，因此计算效率非常重要。特别是在此类应用中，必须注意的是，未解析尺度的不可避免的亚网格尺度参数化尽可能基于第一原理。随机模态简化（SMR）提供了相应的策略，一旦未解析模态之间的非线性自相互作用被拟合到一个简单的随机过程中，大部分参数化都是在纸上推导出来的。然而，在迄今为止的应用中，所构建的简化模型已经给出了谱公式，其中在全局子网格尺度（SGS）参数化中，所有解析模式彼此相互作用。这限制了该方法对非常低维系统的适用性。为了解决这个问题，最近开发了一种基于网格点的空间离散化的 SMR 实现，从而产生局部随机 SGS 参数化。迄今为止，该策略已在伯格斯方程的框架内进行了测试。在拟议的项目中，将采取重大步骤将当地 SMR 策略应用于大气动力学的现实模型。应为 f 平面上的正压涡度方程和浅水方程构建 SGS 参数化。两个模型都表现出在将局部 SMR 应用于大气动力学一般方程时需要考虑的基本特征。新的 SGS 参数化应满足以下标准：i）它们应在相对少量的基本假设下以系统的方式从模型方程导出 ii）它们应尽可能与模型方程的守恒性质一致 iii）它们应需要最少（如果可能根本不需要）回归拟合已解析的尺度。目前，气候建模需要物理约束和分辨率独立的随机参数化公式。正如这里所提议的，使用 SMR 进行参数化的开发将有助于此类方法。除了气候建模之外，大涡模拟中的湍流建模是另一个可以从此类发展中受益的领域。