论文标题
Hasselmann的范式用于基于随机谎言运输的随机气候建模
Hasselmann's Paradigm for Stochastic Climate Modelling based on Stochastic Lie Transport
论文作者
论文摘要
为理想的大气 - 海洋模型的示例开发了一种通用的随机气候建模方法，该模型基于Hasselmann的随机气候模型的范式。也就是说，通过随机谎言传输方式将随机性纳入了理想化耦合模型的快速大气成分中，而缓慢移动的海洋模型仍然确定性。更具体地说，通过将随机转运引入开尔文循环定理中的材料环中，可以构建随机模型盐（随机对流）。产生的随机模型以及潜在的确定性气候模型也可以保留循环。本文引入了一种称为La-salt的盐（拉格朗日平均盐）。在LA-SALT中，我们通过其预期值代替随机矢量场的漂移速度。 La-salt的显着特性是其较高力矩的演变受线性确定性方程的控制。首先，对于确定性的气候模型，我们的建模方法可以通过建立局部存在结果来证实，该结果将可压缩的大气方程式耦合到不可压缩的海洋方程，其次，对于两个随机盐和LA-salt模型而言。
A generic approach to stochastic climate modelling is developed for the example of an idealized Atmosphere-Ocean model that rests upon Hasselmann's paradigm for stochastic climate models. Namely, stochasticity is incorporated into the fast moving atmospheric component of an idealized coupled model by means of stochastic Lie transport, while the slow moving ocean model remains deterministic. More specifically the stochastic model SALT (stochastic advection by Lie transport) is constructed by introducing stochastic transport into the material loop in Kelvin's circulation theorem. The resulting stochastic model preserves circulation, as does the underlying deterministic climate model. A variant of SALT called LA-SALT (Lagrangian-Averaged SALT) is introduced in this paper. In LA-SALT, we replace the drift velocity of the stochastic vector field by its expected value. The remarkable property of LA-SALT is that the evolution of its higher moments are governed by linear deterministic equations. Our modelling approach is substantiated by establishing local existence results, first, for the deterministic climate model that couples compressible atmospheric equations to incompressible ocean equation, and second, for the two stochastic SALT and LA-SALT models.
