标题： 使用随机输运噪声在两层准地转模型中模拟不确定性 显示英文标题

标题： Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model

摘要： 随机变分方法在地球物理流体力学中由Holm（Proc Roy Soc A, 2015）引入，作为推导未解析尺度随机参数化方案的框架。 本文将变分随机参数化应用于一个双层准地转模型，用于β平面通道流配置。 我们提出了一种新的方法，用于估计随机强迫（在参数化中使用），以利用高分辨率确定性模拟的数据来近似未解析成分，并描述了计算随机模型物理一致初始条件的过程。 我们还量化了粗网格模拟相对于细网格模拟的不确定性，在均质（伴随小尺度涡旋）和非均质（具有水平延伸的大尺度急流）流动中进行了分析，并研究了随机解的扩散如何依赖于模型的不同参数。 通过将该参数化与达到某种统计平衡的真实涡旋解析解以及在低分辨率网格上建模的确定性解进行比较来测试该参数化。 结果表明，所提出的参数化显著依赖于随机模型的分辨率，并且在均质和非均质流动中都表现出良好的集合性能，该参数化为数据同化奠定了坚实的基础。 显示英文摘要

摘要： The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic parameterisation in a two-layer quasi-geostrophic model for a beta-plane channel flow configuration. We present a new method for estimating the stochastic forcing (used in the parameterisation) to approximate unresolved components using data from the high resolution deterministic simulation, and describe a procedure for computing physically-consistent initial conditions for the stochastic model. We also quantify uncertainty of coarse grid simulations relative to the fine grid ones in homogeneous (teamed with small-scale vortices) and heterogeneous (featuring horizontally elongated large-scale jets) flows, and analyse how the spread of stochastic solutions depends on different parameters of the model. The parameterisation is tested by comparing it with the true eddy-resolving solution that has reached some statistical equilibrium and the deterministic solution modelled on a low-resolution grid. The results show that the proposed parameterisation significantly depends on the resolution of the stochastic model and gives good ensemble performance for both homogeneous and heterogeneous flows, and the parameterisation lays solid foundations for data assimilation.