On the foundation and different interpretations of ensemble sensitivity
On the foundation and different interpretations of ensemble sensitivity
复制标题
论系综敏感性的基础及不同解释
DOI：
10.1175/mwr-d-22-0273.1
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发表时间：
2023
影响因子：
3.2
通讯作者：
Hotta Daisuke
中科院分区：
文献类型：
--
作者：
Duc Le;Kawabata Takuya;Hotta Daisuke
在灵敏度分析中，集合灵敏度被定义为响应函数对初始扰动变化的简单线性回归所产生的回归系数。对系综灵敏度的一种解释认为这是基于回归的伴随灵敏度的简化版本，称为单变量系综灵敏度，其推导涉及所谓的对角近似。这种近似将分析误差协方差矩阵替换为具有相同对角线的对角矩阵，有助于避免分析误差协方差的反演，但同时也会给系综灵敏度的理解和实际应用带来混乱。然而，一些作者对这种有争议的解释提出了挑战，他们指出单变量系综灵敏度本质上是多变量的，这就提出了建立系综灵敏度的必要性。在本研究中，我们试图在不依赖有争议的对角假设的情况下，通过建立一个强大的系综灵敏度基础来解决这个困惑。正如在一些研究中所采用的那样，我们通过考虑分析扰动的概率分布，采用基于影响的系综灵敏度定义。数学结果表明，标准化集合灵敏度同时包含三个重要量：1)单个状态变量的标准化变化，2)预测响应与单个状态变量的相关性，3)最敏感的分析摄动。该理论保证了系综灵敏度的有效性，论证了系综灵敏度的多变量性质，并解释了系综灵敏度在实践中的有效性。
In sensitivity analysis, ensemble sensitivity is defined as the regression coefficients resulting from a simple linear regression of changes of a response function on initial perturbations. One of the interpretations for ensemble sensitivity considers this a simplified version of regression-based adjoint sensitivity called univariate ensemble sensitivity whose derivation involves the so-called diagonal approximation. This approximation, which replaces the analysis error covariance matrix by a diagonal matrix with the same diagonal, helps to avoid inversion of the analysis error covariance, but, at the same time causes confusion in understanding and practical application of ensemble sensitivity. However, some authors have challenged such a controversial interpretation by showing that univariate ensemble sensitivity is multivariate in nature, which raises the necessity for the foundation of ensemble sensitivity. In this study, we have tried to resolve the confusion by establishing a robust foundation for ensemble sensitivity without relying on the controversial diagonality assumption. As employed in some studies, we adopt an impact-based definition for ensemble sensitivity by taking into account probability distributions of analysis perturbations. The mathematical results show that standardized ensemble sensitivity carries in itself three important quantities at the same time: 1) standardized changes of the forecast response with one standard deviation changes of individual state variables, 2) correlations between the forecast response and individual state variables, and 3) the most sensitive analysis perturbation. The theory guarantees validity of ensemble sensitivity, demonstrates its multivariate nature, and explains why ensemble sensitivity is effective in practice.