We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and a noise term that models the unresolved flow components. As for the classical (deterministic) system, this scheme, referred to as modelling under location uncertainty (LU), conserves the global energy of any realization and provides the possibility to generate an ensemble of physically relevant random simulations with a good trade-off between the model error representation and the ensemble's spread. To maintain numerically the energy conservation feature, we combine an energy (in space) preserving discretization of the underlying deterministic model with approximations of the stochastic terms that are based on standard finite volume/difference operators. The LU derivation, built from the very same conservation principles as the usual geophysical models, together with the numerical scheme proposed can be directly used in existing dynamical cores of global numerical weather prediction models. The capabilities of the proposed framework is demonstrated for an inviscid test case on the f-plane and for a barotropically unstable jet on the sphere.
翻译:我们引入了与物理相关的浅水方程式的物理随机代表,这种衍生主要依赖于一个随机迁移原理,以及流体分解成一个大型部件,以及一个模拟未解决流体元件的噪音术语。关于古典(确定性)系统,这个称为位置不确定情况下建模的系统,保存了任何实现的任何全球能量,并提供了产生与物理相关的随机模拟的组合的可能性,在模型误差代表和共通性分布之间有着良好的权衡。为了保持节能特征,我们将维持基本确定性模型的离散性能量(空间)与基于标准定量体积/差异操作者的随机性术语的近似值结合起来。LU的衍生依据与通常的地球物理模型的非常相同的保护原则,以及拟议的数字计划可以直接用于全球数字天气预测模型的现有动态核心。拟议框架的能力在磁平面和气压空间的反视测试中得到了演示。