基于随机 Lie 输运的 Hasselmann 随机气候建模范式
Hasselmann's Paradigm for Stochastic Climate Modelling based on Stochastic Lie Transport
AI总结：
本文基于 Hasselmann 范式，利用随机 Lie 输运为理想化大气—海洋耦合模型构建 SALT 与 LA-SALT，并证明确定性及随机模型的局部存在性。
摘要：
本文以一个遵循 Hasselmann 随机气候模型范式的理想化大气—海洋模型为例，发展了一种通用的随机气候建模方法。具体而言，通过随机 Lie 输运将随机性引入理想化耦合模型中运动较快的大气分量，而运动较慢的海洋模型则保持确定性。更具体地，随机模型 SALT（stochastic advection by Lie transport，随机 Lie 输运平流）是通过将随机输运引入 Kelvin 环流定理的物质回路而构建的。所得随机模型与底层确定性气候模型一样保持环流。本文还引入了 SALT 的一个变体，称为 LA-SALT（Lagrangian-Averaged SALT，拉格朗日平均 SALT）。在 LA-SALT 中，我们将随机向量场的漂移速度替换为其期望值。LA-SALT 的显著性质是其高阶矩的演化由线性确定性方程控制。我们的建模方法通过建立局部存在性结果得到证实：首先是针对将可压缩大气方程与不可压缩海洋方程耦合的确定性气候模型，其次是针对 SALT 和 LA-SALT 这两个随机模型。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
