改进三维变分同化模型及应用:动力场数据同化  

Improved three-dimensional variational assimilation model and its application:dynamical field data assimilation

作　　者：李振龙 吴涛[1] 张最 徐猛猛 LI Zhenlong;WU Tao;ZHANG Zui;XU Mengmeng(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《黑龙江大学自然科学学报》2023年第6期631-639,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金(72171002);安徽省级研究生教育教学改革研究项目(2022jyjxggyj135)。

摘　　要：在动力场中,如何消除观测数据受观测条件以及观测仪器误差对仿真物理模型的影响,以获得高精度、高质量的数据至关重要。三维变分作为连续型变分数据同化算法的主流,在融合同化来自动力场的模式和观测值时,其代价函数中构造的背景误差协方差矩阵和观测误差协方差矩阵不可逆,是造成无法使用梯度降低的方式求出其最优估计量问题的原因。对于动力场的数据同化方法,提出了两种改进的三维变分同化模型,不同于优化算法、变量变换、维度分解等其他数学求解方法,所提出的粒度化数据同化和改进三维变分代价函数方法解决了矩阵不可逆导致的算法无法计算的问题。在实证分析中,对于维度差异较高的实验数据和模型仿真数据,这两种方法都具有很好的算法鲁棒性,而且展现出较高的算法精度。In the dynamic field,how to eliminate the error affected by the observation conditions and observation instrument,to obtain high-precision and high-quality data is crucial.However,as the mainstream of continuous variational data assimilation algorithm,when fusing and assimilating the models and observations from the dynamic field,the background error covariance matrix and the observation error covariance matrix constructed in the cost function are irreversible,which is the reason why the optimal estimator cannot be obtained by gradient reduction.For the data assimilation method of the dynamic field,two improved three-dimensional variational assimilation models are proposed,which are different from other mathematical solution methods such as optimization algorithm,variable transformation,dimension decomposition,etc.,and the proposed granular data assimilation and improved three-dimensional variational cost function method solve the problem that the algorithm cannot calculate due to the irreversibility of the matrix.In the empirical analysis,for experimental data and model simulation data with high dimensional differences,these two methods have good algorithm robustness and show high algorithm accuracy.

关 键 词：资料同化技术 三维变分 鲁棒性 代价函数 

分 类 号：O212[理学—概率论与数理统计]