Conditioning of hybrid variational data assimilation
Conditioning of hybrid variational data assimilation
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DOI：
10.1002/nla.2534
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发表时间：
2023-09
影响因子：
4.3
通讯作者：
Shaerdan Shataer;A. Lawless;Nancy K. Nichols
中科院分区：
文献类型：
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作者：
Shaerdan Shataer;A. Lawless;Nancy K. Nichols
在变分同化中，先验和似然的高斯假设下动态系统的最可能状态可以通过解决最小二乘最小化问题来找到。近年来，我们看到混合变分数据同化方法在数值天气预报中的流行。在这些方法中，先验误差协方差矩阵是气候部分和流相关集合部分的加权和，后者是秩亏的。变分数据同化的非线性最小二乘问题是使用迭代数值方法解决的，Hessian 矩阵的条件数可以很好地代表此类方法的收敛行为。在本文中，我们通过建立 Hessian 条件数的界限来研究混合四维变分数据同化 (Hybrid 4D-Var) 方案中最小二乘问题的条件。特别是，我们考虑先验协方差的系综分量对系统调节的影响。数值实验表明，所获得的界限可用于预测真实条件数的行为和迭代算法的收敛速度
In variational assimilation, the most probable state of a dynamical system under Gaussian assumptions for the prior and likelihood can be found by solving a least‐squares minimization problem. In recent years, we have seen the popularity of hybrid variational data assimilation methods for Numerical Weather Prediction. In these methods, the prior error covariance matrix is a weighted sum of a climatological part and a flow‐dependent ensemble part, the latter being rank deficient. The nonlinear least squares problem of variational data assimilation is solved using iterative numerical methods, and the condition number of the Hessian is a good proxy for the convergence behavior of such methods. In this article, we study the conditioning of the least squares problem in a hybrid four‐dimensional variational data assimilation (Hybrid 4D‐Var) scheme by establishing bounds on the condition number of the Hessian. In particular, we consider the effect of the ensemble component of the prior covariance on the conditioning of the system. Numerical experiments show that the bounds obtained can be useful in predicting the behavior of the true condition number and the convergence speed of an iterative algorithm