耦合模糊控制算法的数据同化观测误差处理方法

Observation Error Handling Methods of Data Assimilation Coupled with Fuzzy Control Algorithms

针对数据同化过程中集合数目有限情形下的虚假相关问题,通过模糊控制算法判断观测点与状态更新点之间的距离,构造观测位置等价权重,与集合转换卡尔曼滤波方法相结合,提出一种新的数据同化方法。利用经典的Lorenz-96混沌模型,比较分析集合转换卡尔曼滤波(ETKF),局地化集合转换卡尔曼滤波(LETKF)和模糊控制数据同化算法(FETKF)在不同参数变化时的性能,由此探讨3种方法的优劣。研究结果表明:新方法能够使每一步状态更新获得更有效的观测信息,减小因观测数据难以得到有效利用而带来的误差,同时避免了同化过程中的虚假相关问题,从而提高滤波精度。

Observation errors are typically ignored or assumed to be zero correlations in data assimilation for numerical weather prediction,resulting in a loss of information.With regard to spurious correlations in data assimilation with limited ensemble numbers, combined with the traditional Ensemble Transform Kalman Filter,a new method based on fuzzy control algorithms was proposed by calculating observation distances and constructing equivalent observation position weights. Coupled with the standard fuzzy control algo- rithms,a Fuzzy Control Ensemble Transform Kalman Filter （FETKF）was presented and the correspond- ing procedures were given.Within the framework of classical Lorenz-96 chaotic model, we compared the different performances among the following methods,Ensemble Transform Kalman Filter（ETKF）, Local En-semble Transform Kalman Filter（LETKF）,Fuzzy control combined ETKF（FETKF） by changing ensemble sizes, observation numbers, model steps, the inflation factors and the forcing parameters.Comparisons between LETKF localization coefficients and FETKF spatial distance vectors were studied to calculate the corresponding weight function of chaotic model.With the increase of ensemble size, the performances of the three algorithms improved significantly in agreement with typical results from the literature. However, the FETKF was able to meet the demand of the actual assimilation more effectively.In terms of the inflation factors and observation numbers, the estimated value of the modified algorithm was more in line with the requirements of a strongly nonlinear system in a real state.The whole final comparative studies of data as- similation demonstrate that, when observations are randomly located, the new method can eliminate spuri- ous correlations, avoid the long-range observations effects of the state update variables and reduce analysis errors.Meanwhile,the fuzzy control based error handling methods performed robustly under both perfect and imperfect model scenarios in the Lorenz-96 model. However, the application of the methodology to more complex atmospheric or physical models remains to be tested.