A fuzzy-logic-based covariance localization method in data assimilation

Abstract

In ensemble data assimilation systems, the impracticalities of full sampling and systematic error often lead to spurious correlations between two variables with low actual correlations. To solve these problems, researchers have previously proposed a covariance localization (CL) method, which mainly involves the Schur product between a state error covariance matrix and a distance-based correlation matrix. Although this CL method can reduce spurious correlations to a certain extent, observational data remain difficult to be used effectively, which results in unreasonable assimilation. In this study, we develop a new CL method coupled with a fuzzy logic control algorithm, which we call the covariance fuzzy (CF) method. The proposed CF method is a distance-based localization method with “fuzzy” vanishing correlations in data assimilation (DA) systems. To verify the effectiveness of the new algorithm, we conducted a set of experiments using an ensemble Kalman filter (EnKF) that combines the nonlinear Lorenz-96 model or the quasigeostrophic (QG) models. First, the performances of the CL and CF methods are discussed with respect to different strength forcings, ensemble sizes, and covariance inflation factors. The experimental results show that the proposed CF method can obtain a more effective observation weight than the CL method and can reduce the errors caused by spurious correlations. Additionally, using power spectral density (PSD) as a performance evaluation index, the robustness of the proposed fuzzy logic localization method is demonstrated. However, the application of the fuzzy logic-based localization methodology to a real atmospheric model remains to be tested.