现代海洋/大气资料同化方法的统一性及其应用进展

The Unification and Application Reviews of ModernOceanic/Atmospheric Data Assimilation Algorithms

海洋 /大气资料同化的理论基础是用数值模式作为动力学强迫对观测信息进行提炼 ,或者说 ,从包含观测误差 (噪声 )的空间分布不均匀的实测资料中依据动力系统自身的演化规律 (动力学方程或模式 )来确定海洋 /大气系统状态的最优估计。本文对主要的现代海洋 /大气资料同化方法 ,包括最优插值 (Optim al Interpolation,简称OI)、变分方法 (3- Dim ensional Variational和 4 - Dimensional Variational,分别简称 3DVAR和 4 DVAR)和滤波方法(Filtering)的原理、算法设计和实际应用进行系统地回顾 ,并对这些资料同化方法的优缺点进行分析和讨论。在滤波框架下 ,所有的现代资料同化方法都被统一了 :OI和 3DVAR是不随时间变化的滤波器 ;4 DVAR和卡曼滤波是线性滤波器 ,即非线性滤波的退化情形 ;而集合滤波能构建非线性的滤波器 ,因为集合在某种程度上体现了系统的非高斯信息。一个非线性滤波器的主要优点是能计算和应用随时间变化的各阶误差统计距 ,如误差协方差矩阵。将非线性滤波器计算的随时间变化的误差协方差矩阵引入到 OI或 4 DVAR中 ,也许能实质性地改进这些传统方法。在实际应用中 ,方法的优劣可能取决于所选用的数值模式和可获得的计算资源 ,因此需针对不同的问题选取不同的资料同化方法。

The fundamentals of modern oceanic/atmospheric data a ssimilation are to extract the observational information by using the numerical model as a dynamic forcing. In this paper,the principle, algorithmic design and application of main data assimilation methods, including optimal interpolation(O I), 3-D and 4-D variational approach (3DVAR and 4DVAR) and fillering method ar e systematically reviewed, and the advantages and disadvantages of these data as similation methods are analysed and discussed. Under the filtering framework, al l modern data assimilation methods can be unified:OI and 3DVAR are stationary fi lter, 4DVAR and Kalman filter are linear filter, and an ensemble of Kalman filte r can construct a nonlinear filter. The main advantage of a nonlinear filter is that the filter can calculate and use the error statistic moments, such as error covariance matrix, and the time-dependent error covariance matrix estimated by a nonlinear fiter can be introduced into OI and 4DVAR to substantially improve these traditional methods.