Inflating transform matrices to mitigate assimilation errors with robust filtering based ensemble Kalman filters

Abstract An error covariance matrix plays an important role in maintaining the statistical property of the ensemble in an ensemble Kalman filter method. However, data assimilation filter divergence may occur from an inaccurate estimate of the covariance matrix. In this study, based on an ensemble time‐local H‐infinity filter, which inflates the eigenvalues of the analysis error covariance matrix, a new robust ensemble data assimilation method is proposed, referred to as an inflation transform matrix eigenvalues. By design, new filters may be preferred over other traditional ensemble filters, when model performances are not well known, or change unpredictably. The primary aim is to improve the performance of the assimilation system in the framework of the ensemble filtering, according to the minimum/maximum rule of robust filtering. The proposed estimation method is tested using the well‐known Lorenz‐96 model, in order to investigate how the ensemble time‐local H‐infinity filter method of the inflation transform matrix impacts the robustness of the assimilation system under selected special conditions, such as the assimilation steps, force parameters, ensemble sizes, and observation information. The experiments show that the proposed inflation transform matrix method displays good robustness to the changes in the system's parameters. Also, when compared with the traditional filtering methods, this robust filtering method is found to improve the assimilation performance.