关键词: 数据同化, 集合卡尔曼滤波, 局地化分析, 模糊分析, 模糊逻辑控制算法, 均方根误差, 功率谱密度

Abstract:

In numerical simulations of the earth system, ensemble data assimilation methods are commonly used to study the various observation errors in predicting geological variables. In this regard, the widely used Ensemble Kalman Filter (EnKF) may suffer from a series of problems such as undersampling, covariance underestimation, filter divergence, and distanced spurious correlations, when the ensemble size is small. In particular, implementing the traditional Local Analysis (LA) method by the distance-based Gaspari and Cohn (GC) function can reduce the underestimation of background error covariance to some extent, but cannot completely eliminate the spurious correlation problem. In this study, a Fuzzy Analysis (FA) localization method coupled with the fuzzy logic control algorithm was proposed in the framework of the EnKF assimilation algorithm. In the design of the fuzzy logic controller, the distance between observation points and the corresponding status update points is taken as the fuzzy inputs. Through a series of fuzzy inference, more accurate fuzzy weight coefficients can be obtained as the control outputs, so as to reduce the observation error and improve the assimilation accuracy. Based on the Lorenz-96 model, the effectiveness of LA and FA under different model errors was compared; and the robustness of the two methods under ensemble numbers, observation numbers, and observation space, covariance inflation factor, and forced parameter change was discussed and analyzed. Meanwhile, Root Mean Square Error (RMSE) and Power Spectral Density (PSD) were used as performance indexes to evaluate the performance of the two algorithms. The experimental results show that the new localization method can correct the background error covariance matrix by constructing the corresponding equivalent weight of observation position to update local coefficient based on EnKF. To some extent, it can effectively eliminate the remote correlation between observations and state, and the observation data can be effectively utilized in the local scope. The FA algorithm can reduce the observation error, and the effectiveness and robustness of the new method was proved in nonlinear chaotic systems. These schemes illustrate that the new localization method based on Fuzzy Analysis of observation information can lead to a systematic improvement of the data assimilation performance. However, the determination of fuzzy distance and the calculation of fuzzy equivalent weight coefficient take extra long time; how to combine parallel computation with fuzzy control for improving assimilation efficiency remains to be further studied.

Key words: data assimilation, Ensemble Kalman Filter, local analysis, fuzzy analysis, fuzzy logic control algorithm, Root Mean Square Errorpower spectral density