On the treatment of correlated observation errors in data assimilation
On the treatment of correlated observation errors in data assimilation
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发表时间：
2019-11
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通讯作者：
Jemima M. Tabeart
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作者：
Jemima M. Tabeart
数据同化将来自动力系统观测的信息与先前的预报相结合，每项都按其各自的不确定性加权。最近的一个重要研究领域是在数值天气预报系统中引入相关观测误差协方差矩阵。相关的OEC矩阵的好处是多方面的：它们允许使用高密度的观测网络，允许捕获小规模的过程，并帮助最好地利用现有的数据。然而，它们的使用往往与迭代方法的收敛问题有关。在这篇论文中，我们研究了引入相关OEC矩阵对变分资料同化问题的理论影响。我们开发了新的界限的条件数的Hessian两个数据同化配方，并说明我们的研究结果与数值例子在一个理想化的框架。OEC矩阵的最小特征值是这两个问题的关键，这促使使用重处理方法来减少相关矩阵的条件数。我们发展理论的两个修复方法：岭回归和最小特征值法。我们首次表明，这两种方法的标准偏差增加。岭回归降低了绝对相关性，而最小特征值方法对相关性和方差的变化较小。然后，我们提出了第一次深入研究的岭回归方法的业务数据同化系统，使用气象局1D-Var系统。重新调整改善了收敛，但改变了质量控制程序，该程序用于选择适当的观测值进行进一步同化。本文的研究结果为如何在保证计算效率的前提下，在一般变分资料同化问题中包含相关信息提供了指导。
Data assimilation combines information from observations of a dynamical system with a previous forecast, with each term weighted by its respective uncertainty. An important recent area of research has been the introduction of correlated observation error covariance (OEC) matrices in numerical weather prediction systems. The benefits of correlated OEC matrices are multiple: they permit the use of high density observation networks, allow the capture of small scale processes and help make best use of available data. However, their use is often associated with convergence problems for iterative methods. In this thesis we study the theoretical impact of introducing correlated OEC matrices on the conditioning of variational data assimilation problems. We develop new bounds on the condition number of the Hessian for two data assimilation formulations and illustrate our findings with numerical examples in an idealised framework. The minimum eigenvalue of the OEC matrix is a key term for both problems, which motivates the use of reconditioning methods to reduce the condition number of correlation matrices. We develop theory for two reconditioning methods: ridge regression and the minimum eigenvalue method. We show for the first time that standard deviations are increased by both methods. Ridge regression reduces absolute correlations, whereas the minimum eigenvalue method makes smaller changes to correlations and variances. We then present the first in-depth study of the ridge regression method for an operational data assimilation system, using the Met Office 1D-Var system. Reconditioning improves convergence, but alters the quality control procedure, which is used to select appropriate observations for further assimilation. The results in this thesis provide guidance on how to include correlation information in general variational data assimilation problems while ensuring computational efficiency.