数据同化系统中的集合时间局地化鲁棒滤波方法

针对传统的卡尔曼滤波方法对不确定因素不具备鲁棒性问题,在集合鲁棒滤波的基础上,提出一种从观测角度构建优化数据同化的方法,称之为放大观测协方差矩阵的集合时间局地化鲁棒滤波,并推导了新方法的算法准则和递归公式。利用非线性系统Lorenz-96模型,基于性能水平系数、驱动参数、观测数目和集合数目变化的条件,对新方法和集合卡尔曼滤波方法的鲁棒性和同化精度进行比较。结果表明:集合卡尔曼滤波方法的均方根误差大于时间局地化鲁棒滤波的;在观测数或集合数较少的情况下,集合卡尔曼滤波出现了滤波发散问题,而鲁棒滤波的均方根误差波动较小;相较于传统的集合卡尔曼滤波算法,观测角度构建的时间局地化的H_∞滤波方法对系统参数的变化更具鲁棒性,滤波精度更高。

小集合数条件下的数据同化策略研究

基于集合的数据同化方法近年来得到广泛的重视和研究,已经逐步实验在业务大气数据同化系统中来替代变分类方法。集合Kalman滤波方法高度依赖于集合的大小,集合数过小会带来欠采样,协方差低估,滤波发散和远距离的虚假相关等问题。局地化技术可以有效改善小集合带来的相关问题。在Lorenz-96模型的基础上,研究有无局地化的效果差异,探讨小集合条件下的局地化技术的优劣性;提出一种基于功率谱密度(PSD)判断集合数据同化效果的办法。实验证明:在有限集合数下,采用Kalman增益值和PSD可以评价同化效果,结合局地化技术,可以获得效率更高的同化算法。

Impacts of Stochastic Forcing on Ensemble Prediction Effect

Based on the dynamic framework of Lorenz 96 model,the ensemble prediction system(EPS)containing stochastic forcing has been developed.In this system,effects of stochastic forcing on the model climate state and ensemble mean prediction have been studied.The results show that the climate mean and standard deviation provided by a new computing paradigm by means of introduction of the proper stochastic forcing into numerical model integration process are closer to that of the true value than that made by the non-stochastic forcing.In other words,numerical model integration process with stochastic forcing has positive effect on the model climate state,and the effect is found to be positive mainly in the long lead time.Meanwhile,with respect to ensemble forecast effect yielded by white noise stochastic forcing,most results are better than those provided by no-stochastic forcing,and improvements pertaining to white noise stochastic forcing vary non-monotonically with the increase of the size of white noise.Moreover,the effects made by the identical white noise stochastic forcing also are different in various non-linear systems.With respect to EPS effect yielded by red noise stochastic forcing,most results are better than those provided by no-stochastic forcing,but only a part of ensemble forecast effect influenced by red noise is superior to that influenced by white noise.Finally,improvements pertaining to red noise stochastic forcing vary non-symmetrically and non-monotonically with the distribution of coefficientΦ.Besides,the selection of correlation coefficientΦis also dependent on non-linear models.

观测误差协方差估计下的集合鲁棒滤波数据同化方法

在数据同化方法中,观测误差协方差矩阵是相关的,且与时间和状态有一定的依赖性。针对这种相关特性,将鲁棒滤波方法与观测误差协方差估计方法相结合,得到随状态时间变化的观测误差协方差,提出一种带有观测误差估计的鲁棒数据同化新方法,更新观测误差协方差,改善估计效果。从分析误差协方差,转移矩阵特征值放大等角度优化同化方法。利用非线性Lorenz-96混沌系统,对三种不同优化角度下带有观测误差估计的鲁棒滤波和原鲁棒滤波方法的鲁棒性和同化精度进行评估,并比较分析了两种方法在模型误差、观测数目和性能水平系数变化时的性能。结果表明:观测误差估计技术能够提高状态估计的精确性,带有观测误差估计的鲁棒滤波对系统参数变化具有较好的鲁棒性。