浅水方程初值问题数据同化的半参数方法  

Semiparametric method of data assimilation for initial value problem of shallow water equations

作　　者：李亚鸣[1] 何幼桦[1] 

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2016年第4期553-560,共8页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11371242)

摘　　要：针对大气海洋方程初值问题的解,通过建立半参数模型,采用局部多项式回归方法,对在不同空间和不同时间点的观测数据进行同化,估计出方程的初始条件.以无粘的浅水方程初值问题为例,通过设计适当的准则,确定最佳估计的窗宽,同时利用完全正交分解对算法进行改进,从而解决了常规非参数估计时投影矩阵接近奇异的问题.最后,将本方法与非参数方法的估计结果进行了比较,由于充分考虑了大气海洋方程解的特点,使得在保持计算量相对较小的同时,估计精度得到提高.For the solutions to atmospheric and oceanic equations, this paper establishes the semiparametric model and applies the local linear regression method to assimilating observational data at different times and different positions, and then the initial value condition of the equations can be estimated. Taking an initial value problem of the non-viscous shallow water equation as an example, the paper proposes an appropriate rule to find the optimal bandwidth. Meanwhile, the paper also applies the complete orthogonal decomposition to improving the algorithms and compares the estimation results of above method with those of nonparametric methods. As this method fully considers the characters of solutions to atmospheric and oceanic equations, it gets better estimation and requires relatively less calculation.

关 键 词：数据同化 半参数模型 局部多项式回归 

分 类 号：O212.1[理学—概率论与数理统计]