区域三维变分同化中背景误差协方差的模拟

Modeling background error covariance in regional 3D-VAR

背景误差协方差(B)是变分同化中的一个重要部分,极大地影响同化系统输出的分析场。由于计算和指定B中有关统计量需要巨大的资料存储量和计算量,因此进行相关的研究较为困难。本文首先论述了B在变分同化中的重要性以及进行模拟的必要性;接着介绍了美国NMC方法的原理,并研究将其应用到区域三维变分同化中的方法;然后利用WRF模式生成的预报场差值集合对有关统计量进行了估计。揭示了以下结论:通过使用平衡变换和回归系数,控制变量被限制在较小范围内,保证了分析场的质量;流函数第一全局特征向量在200hPa附近的最大分量,表示了急流层中强西风误差;流函数前五个全局特征向量在低层与中高层之间是负相关的;非平衡温度和相对湿度的特征长度尺度比流函数和非平衡速度势的值要小,说明它们是局地性较强的量。流函数和非平衡速度势的特征长度尺度随垂直模态数的增大快速减小,而相对湿度和非平衡温度的特征长度尺度随垂直模态数的变化较为平缓。

Background error covariance （B） is an important part in variational data assimilation （ Var）, which affects the analyses from Var systems greatly. Because the computation and specification of statistics for B needs great data storage and expensive computations, it＇s difficult to perform related research. The present paper at first clarifies the importance of B and the necessity of modeling it. Then the principle and computation steps for American NMC method are introduced in detail and used to demonstrate how to apply it in the regional 3D-Var. Thereafter the statistics of background error covariance are computed by using the forecast data set from WRF model. The results indicate that： making use of balance transforms and regression coefficients, control variables are kept to be small values＇which ensure the quality of analyses. The first global eigenvector has the maximum component nearby 200hPa, where the error of westerly jet exists. There is negative correlation between low and middle-high levels of first five global eigenvectors of stream function. Compared to lengthscales of stream function and unbalanced velocity potential, those of unbalanced temperature and relative humidity are very small, which show that they are local variables. Lengthscales of stream function and unbalanced velocity potential decrease with the number of vertical mode, while those of unbalanced temoerature and relative humidity vary smoothly.