混合误差协方差用于集合平方根滤波同化的试验

The Suitability Test of Ensemble Square Root Filter with Hybrid Background Error Covariance

在集合卡尔曼滤波方法中,根据预报集合统计提供的依流型而变的预报误差协方差对同化起到决定性的作用。但在集合样本容量不足及模式存在系统误差时,由预报集合估计的预报误差协方差会出现明显偏差。既要减小这种估计偏差对同化产生的影响而又不增加计算量,一种可供选择的方法是将定常或准定常的高斯型预报误差协方差和由预报集合估计的预报误差协方差加权平均用于集合卡尔曼滤波同化。利用浅水方程模式,通过观测系统模拟试验检验在不同的模式误差、集合成员数以及观测密度条件下,将这种混合预报误差协方差矩阵用于在集合平方根滤波的效果。试验结果表明,当预报集合成员数较多而模式又无误差时,不必采用混合的预报误差协方差矩阵,否则,采用混合的预报误差协方差矩阵都有可能改进分析和预报。混合预报误差协方差的最优的权重系数与模式误差关系密切,模式误差越大,定常预报误差协方差的权重越大。最优的权重系数与集合成员数及观测密度也有一定关系。

The flow-dependent background error covariances produced with ensemble forecast statistics play an important role in the Ensemble Kalman Filter （EnKF） assimilation. But the accuracy of the forecast error covariance is reduced by both limited forecast ensemble size and forecast model system error significantly. A possible method to reduce the negative effect from the bias of the forecast error covariance - without additional computing cost is discussed. A hybrid forecast error covariance by weighting mean of the sample covariance matrix of the forecast ensemble and the static or quasi static covariance matrix is employed in Ensemble Square Root Filter （EnRSF） data assimilation. The hybrid scheme is tested by a set of Observing System Simulation Experiments （OSSE） with different model errors, ensemble sizes, and observation densities, using the shallow water model. The preliminary results show that the hybrid scheme is no need for big ensemble size and perfect model situation. Otherwise, the hybrid scheme could reduce forecast and analysis error. The optimal weighting coefficient in the hybrid scheme is depend on the model error distinctly and the weight of static error covariance will grow with model error. Ensemble slze and observation density also influence the optimal weighting coefficient.