Abstract
Abstract With the increased density of available observation data, data assimilation has become an increasingly important tool in marine research. However, the success of the ensemble Kalman filter is highly dependent on the size of the ensemble. A small ensemble used in data assimilation could cause filter divergence, undersampling and spurious correlations. The primary method to alleviate these problems is localization. It can eliminate some spurious correlations and increase the rank of the forecast error covariance matrix. The ensemble transform Kalman filter has been widely used in various studies as a deterministic filter. Unfortunately, the covariance localization cannot be directly applied to ensemble transform Kalman filter. The new covariance localization needs to be presented to adapt the ensemble transform Kalman filter. Based on the method of expanded ensemble and eigenvalue decomposition, this study describes a variation of covariance localization that takes advantage of an unbiased covariance matrix from the expanded ensemble. Experiments described herein show that the new method outperforms the localization methods proposed by others when used in the ensemble transform Kalman filter. The new method yields an analysis estimate that is closer to the true state under different experimental conditions.
Highlights
Data assimilation in oceanography and meteorology seeks to provide a current analysis of the state of the atmosphere and ocean, to be used as an initial condition for a forecast
The statistical accuracy of forecast error is extremely important for any ensemble data assimilation scheme, since the forecast error covariance matrix is often estimated from ensemble members
Several experiments were conducted to test the performances of the NCL, P_method and GETKF combined with the ensemble transform Kalman filter (ETKF), respectively
Summary
Data assimilation in oceanography and meteorology seeks to provide a current analysis of the state of the atmosphere and ocean, to be used as an initial condition for a forecast. To overcome the obstacle that covariance localization cannot be applied to the ETKF, Petrie (2008) presented a new approximation of localization in the ETKF It achieved by applying a Schur product between the square root of the correlation function ρ (an n × n -dimensional matrix, where n denotes the number of variables) and a new forecast ensemble perturbation matrix. In the ETKF method, the difficultly of applying the CALECO ensemble is an element-wise product covariance localization is that an n × n -dimensional between one raw ensemble member and one column of the square root of the ECO-RAP matrix. The recognized as a poor method (Bishop et al, 2017) This parameter L represents the number of columns of method has been adapted, using a constant the matrix W, the number of selected eigenvalues inflation factor to obtain an analysis with sufficient from the localization function ρ.
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