保持结构的随机参数化：一种耦合海洋-大气模型的Ornstein-Uhlenbeck噪声应用
Structure-preserving stochastic parameterization of a barotropic coupled ocean-atmosphere model with Ornstein--Uhlenbeck noise
AI总结：
本文首次将随机对流由Lie传输框架应用于简化耦合海洋-大气系统，通过随机拉格朗日动力学假设推导出随机流体方程，保持几何结构，并用Ornstein-Uhlenbeck噪声替代白噪声，提升预测性能。
摘要：
我们首次将随机对流由Lie传输框架（SALT）应用于简化耦合海洋-大气系统。SALT在随机拉格朗日动力学假设下，从哈密顿变分原理推导出随机流体方程，从而保持底层确定性方程的几何结构——Kelvin环流定理、Lie导数对流算子和局部守恒定律。大气部分被随机化，而海洋保持确定性，遵循Hasselmann的快速随机大气驱动慢气候的范式。空间相关向量通过高分辨率模拟中的Lagrangian轨迹差的EOF分析估计。主要贡献是将标准白噪声时间模型替换为Ornstein-Uhlenbeck（OU）过程，受主导EOF模式中强自相关（退相关时间50-150时间步）的启发；OU过程是唯一能用单个参数捕捉这种时间记忆的平稳高斯马尔可夫过程。集合预报在10-15时间单位内表现出良好的发散-误差一致性。通过连续排名概率分数——严格性质分评分规则评估，随机集合优于匹配大小的确定性集合，尽管其RMSE更高。耦合随机系统的良好性被识别为一个重要开放问题。
英文摘要：
We present the first application of the stochastic advection by Lie transport (SALT) framework to an idealized coupled ocean-atmosphere system. SALT derives stochastic fluid equations from Hamilton's variational principle under a stochastic Lagrangian kinematic assumption, thereby preserving the geometric structure -- Kelvin circulation theorem, Lie-derivative advection operators, and local conservation laws -- of the underlying deterministic equations. The atmospheric component is rendered stochastic while the ocean remains deterministic, following Hasselmann's paradigm of a fast stochastic atmosphere driving a slow climate. The spatial correlation vectors encoding unresolved subgrid transport are estimated from high-resolution simulations via EOF analysis of Lagrangian trajectory differences. A central contribution is the replacement of the standard white-noise temporal model with Ornstein-Uhlenbeck (OU) processes, motivated by strong autocorrelation (decorrelation times of 50-150 time steps) in the dominant EOF modes; the OU process is the unique stationary Gaussian Markov process capable of capturing this temporal memory with a single parameter. Ensemble forecasts exhibit good spread-error agreement over 10-15 time units. Evaluated via the Continuous Ranked Probability Score -- a strictly proper scoring rule measuring discrepancy between the forecast measure and the true conditional distribution -- the stochastic ensemble consistently outperforms a size-matched deterministic ensemble, despite carrying higher RMSE. Well-posedness of the coupled stochastic system is identified as an important open problem.
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