并行准高斯高阶递归滤波算法研究

三维变分同化系统中一个重要的问题是背景误差协方差矩阵B及其逆的求解.背景误差协方差矩阵的水平变换部分采用递归滤波运算,可以简化矩阵的求解,解决了背景误差协方差矩阵B及其逆难以求解的问题.本文对准高斯高阶递归滤波的算法原理和过程进行了深入研究.因为递归滤波并行的低可扩展性制约了高阶递归滤波算法在三维变分同化系统中的应用,所以本文提出了阶段二维区域剖分并行化方法,实现了并行准高斯高阶递归滤波算法库.数值试验表明,四阶递归滤波1次的效果明显优于一阶4次的滤波效果;并且高阶递归滤波并行算法64核时能达到大约50倍的加速,并行效率高达78%,具有良好的加速效果和较强的可扩展性.

RESEARCH ON PARALLEL ALGORITHM OF QUASI-GAUSSIAN HIGH-ORDER RECURSIVE FILTER

The background error covariance matrix (B) and the calculation of its inverse are an important part of three-dimensional variational assimilation (3DVAR) system. The recursive filter which could simplify matrix calculation is applied to the horizontal transformation of the background error covariance matrix. This paper makes an intensive study of the algorithm principle for quasi-Gaussian high-order recursive filter. Because the parallel design of recursive filter with low extendibility restricts the application of high-order recursive filter in the 3DVAR system, the paper develops a two-dimensional domain decomposition parallel method and designs a parallel algorithm of high-order recursive filter. Numerical experiments show that the filtering effect by using four-order recursive filter only once is better than a continuous four times application of the simple first-order filter, and the parallel algorithm of high-order recursive filter with 78% parallel efficiency could speed up about 50 times when using 64 cores.