Optimal reduced space for Variational Data Assimilation
Optimal reduced space for Variational Data Assimilation
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DOI：
10.1016/j.jcp.2018.10.042
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发表时间：
2019-02-15
影响因子：
4.1
通讯作者：
Guo, Yi-Ke
中科院分区：
文献类型：
--
作者：
Arcucci, Rossella;Mottet, Laetitia;Guo, Yi-Ke
数据同化(DA)是一种不确定性量化技术，用于将观测数据合并到预报模式中，以改进数值预报结果。变分DA(VARDA)基于函数的最小化，该函数估计数值结果与观测值之间的差异。业务预报需要实时数据同化。这就要求选择合适的方法来提高VARDA码的效率而不降低精确度。由于预测区域的规模和用于描述物理模型的状态变量的数量，DA是一个大数据问题。本文采用截断奇异值分解(TSVD)来降低空间维度，降低计算量，减小误差。然而，如果截断参数选择不当，则会导致重要信息丢失。我们给出了一种计算最优截断参数的算法，我们证明了最优估计减少了病态，并去除了统计上不太重要的模式，这些模式可能会增加从DA获得的估计的噪声。本文讨论了发展VARDA算法所面临的数值问题，包括背景协方差矩阵的病态、预条件的选择和正则化参数的选择。我们还展示了正则化参数的选择如何影响L-BFGS(Limited-Broyden Fletcher Goldfarb Shanno)计算的Varda最小化的效率。为污染物在城市环境中的扩散提供了实验结果。(C)2018 Elsevier Inc.保留所有权利。
Data Assimilation (DA) is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. Variational DA (VarDA) is based on the minimisation of a function which estimates the discrepancy between numerical results and observations. Operational forecasting requires real-time data assimilation. This mandates the choice of opportune methods to improve the efficiency of VarDA codes without loosing accuracy. Due to the scale of the forecasting area and the number of state variables used to describe the physical model, DA is a big data problem. In this paper, the Truncated Singular Value Decomposition (TSVD) is used to reduce the space dimension, alleviate the computational cost and reduce the errors. Nevertheless, a consequence is that important information is lost if the truncation parameter is not properly chosen. We provide an algorithm to compute the optimal truncation parameter and we prove that the optimal estimation reduces the ill-conditioning and removes the statistically less significant modes which could add noise to the estimate obtained from DA. In this paper, numerical issues faced in developing VarDA algorithm include the ill-conditioning of the background covariance matrix, the choice of a preconditioning and the choice of the regularisation parameter. We also show how the choice of the regularisation parameter impacts on the efficiency of the VarDA minimisation computed by the L-BFGS (Limited - Broyden Fletcher Goldfarb Shanno). Experimental results are provided for pollutant dispersion within an urban environment. (C) 2018 Elsevier Inc. All rights reserved.