一种新的基于模糊分析观测信息的局地化方法

地球表层系统是一个极其复杂的巨系统,为了更精确地表达地球表层系统各种过程的动态演进,解决数据同化系统观测误差的估计与处理已经成为地球科学领域备受关注的问题之一。在地球科学系统数值模拟中,一般采用集合数据同化来探讨地学变量预报时的各种误差。集合类卡尔曼滤波通常会由于集合数过小而带来欠采样、协方差低估、滤波发散和远距离虚假相关等问题。针对背景误差协方差被低估问题,局地分析方法（Local Analysis, LA）在一定程度上能起到抑制作用,但无法彻底解决背景误差协方差的虚假相关问题。因此,本文在集合卡尔曼滤波的算法框架下提出了一种与模糊逻辑控制算法相耦合的局地化分析方法（Fuzzy Analysis, FA）。在强非线性Lorenz-96模型中,对不同模型误差下的LA和FA方法进行了性能优劣方面的探讨,并比较分析了2种方法在集合数、观测数和观测位置、放大因子以及强迫参数变化时的同化性能。实验采用均方根误差作为算法评判依据,同时用功率谱密度（Power Spectral Density, PSD）更直接地对2种算法性能优劣作出了评价。结果表明：在完美模型下,FA相对于LA降低了17.5%的均方根误差（Root Mean Square Error, RMSE）;随着模型误差增大,RMSE减小的百分比和减小幅度都在降低;在严重模型误差下,FA降低了8.6%的RMSE。总体而言,新算法FA的有效性和鲁棒性都得到了验证,并且在EnKF同化基础下有效改进了传统的局地化分析方案,优化了观测误差处理,为今后的数据同化研究提供了一个较为全面的观测误差研究平台。

A New Localization Method based on Fuzzy Analysis of Observation Information

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.