基于Lorenz-63模型的状态与参数同时估计方法对比研究

Comparison of Methods for Simultaneous States and Parameters Estimation based on Lorenz-63 Model

模型状态同化精度受多种方面因素的影响,针对状态同化中模型参数的不确定性问题,状态与参数同时估计为此提供了一种较好的解决方案,即在进行状态同化的过程中得到合理的参数估计值。在Lorenz-63模型的基础上构建状态与参数同时估计框架,比较分析增广集合卡尔曼滤波(AEnKF,Augmented Ensemble Kalman Filter)、双重集合卡尔曼滤波(DEnKF,Dual Ensemble Kalman Filter)和同时优化与同化方法(SODA,Simultaneous Optimization and Data Assimilation)在集合数、观测误差和观测数不同时的参数和状态估计结果差异,由此探讨3种方法的优劣及适用性。研究结果表明:3种方法都能较好地估计模型的状态和参数,AEnKF的误差在集合数不大于20时最大,随着集合数增加降低的速率最小;3种方法的RMSE值随观测误差的增大而增大,但算法间差异不大;观测数变为1时3种方法的结果都变差,其中AEnKF最明显。

The precision of model states assimilation is affected by various factors. For the problem of the uncertain parameters of the model in the process of states assimilation, simultaneous states and parameters estimation is a preferred approach to solve it which obtains the rational estimation of parameters during states assimilation. Establish the framework of simultaneous estimation based on Lorenz model, and com- pare the differential performances among the following three methods： AEnKF（Augmented Ensemble Kal- man Filter）,DEnKF（Dual Ensemble Kalman Filter） and SODA（Simultaneous Optimization and Data As- similation） by changing ensemble size, observation variance and the number of observation to judge the merits and applicability of these methods. According to the final comparative studies,the RMSE of states in the AEnKF algorithm was the largest one when ensemble size was not more than 20, and decreased slowly along with ensemble size increasing; the RMSE of all the three algorithms added when observation variance increased,but the discrimination among the three is tiny; the results of algorithms got worse for the num- ber of observation turned to one,and this situation was especially obvious in AEnKF.