Data Assimilation via Error Subspace Statistical Estimation.Part I: Theory and Schemes
Data Assimilation via Error Subspace Statistical Estimation.Part I: Theory and Schemes
复制标题
基于误差子空间统计估计的数据同化第一部分：理论与方案
作者：
Pierre FJ Lermusiaux;A. Robinson
一个合理的方法是用来确定有效的方案，在非线性海洋大气模式的数据同化。条件平均值，几个成本泛函的最小值，被选为最佳估计。在说明目前的目标和描述一些现有的计划，特别是海洋大气数据同化的限制和问题进行了强调。利用地球物理测量和模型的启发式特性，获得了满足目标和解决问题的最佳标准的近似值。这导致了一个不断发展的误差子空间的概念，可变大小，跨越和跟踪的规模和过程中出现的主要错误。定义了误差子空间统计估计的概念。在本最小误差方差方法中，次优准则是基于误差协方差矩阵的维数的连续且能量最优的减少。演化误差子空间的特征在于误差奇异向量和值，或者换句话说，误差主成分和系数。通过ESSE的过滤和平滑方案的推导。数据-预测融合最小化误差子空间中的方差。非线性蒙特卡罗预测在时间上整合误差子空间。平滑是基于统计近似方法。与现有的滤波和平滑程序进行了比较。讨论了ESSE的理论和实践优势。子空间方法引入的概念与实际益处一样有用。的形式主义形成了一个理论基础的相互比较的降维同化方法和验证的具体假设量身定制的应用程序。子空间方法可用于广泛的目的，包括非线性场和误差预测、可预测性和稳定性研究、客观分析、数据驱动模拟、模型改进、自适应采样和参数估计。
A rational approach is used to identify efficient schemes for data assimilation in nonlinear ocean‐atmosphere models. The conditional mean, a minimum of several cost functionals, is chosen for an optimal estimate. After stating the present goals and describing some of the existing schemes, the constraints and issues particular to ocean‐atmosphere data assimilation are emphasized. An approximation to the optimal criterion satisfying the goals and addressing the issues is obtained using heuristic characteristics of geophysical measurements and models. This leads to the notion of an evolving error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. The concept of error subspace statistical estimation (ESSE) is defined. In the present minimum error variance approach, the suboptimal criterion is based on a continued and energetically optimal reduction of the dimension of error covariance matrices. The evolving error subspace is characterized by error singular vectors and values, or in other words, the error principal components and coefficients. Schemes for filtering and smoothing via ESSE are derived. The data‐forecast melding minimizes variance in the error subspace. Nonlinear Monte Carlo forecasts integrate the error subspace in time. The smoothing is based on a statistical approximation approach. Comparisons with existing filtering and smoothing procedures are made. The theoretical and practical advantages of ESSE are discussed. The concepts introduced by the subspace approach are as useful as the practical benefits. The formalism forms a theoretical basis for the intercomparison of reduced dimension assimilation methods and for the validation of specific assumptions for tailored applications. The subspace approach is useful for a wide range of purposes, including nonlinear field and error forecasting, predictability and stability studies, objective analyses, data-driven simulations, model improvements, adaptive sampling, and parameter estimation.