GRAPeS三维变分同化系统的理想试验

IDEA EXPERIMENTS OF GRAPES THREE-DIMENSIONAL VARIATIONAL DATA ASSIMILATION SYSTEM

文中介绍了一种新的、适合格点模式的三维变分同化方案GRAPeS 3DVAR。该方案采用相互独立的流函数、非平衡速度势函数、非平衡位势和水汽作为分析变量。通过变量变换对目标函数进行预调节 ,不仅避免了直接计算背景误差协方差逆矩阵的困难 ,而且改善了Hessian矩阵的性状 ,提高了收敛速度。采用EOF分解方法 ,将三维分析变量投影到垂直摸态上 ,分解成为二维场 ;水平方向采用数字 (递归 )滤波器代替矩阵运算 ,实现和简化了方案的求解。此外 ,还考虑了质量场和风场之间的平衡约束关系。理想试验结果表明 ,GRAPeS 3DVAR能够正确地反映多变量之间相互作用关系 ,收敛迅速 。

This paper introduces a new scheme of three-dimensional variational assimilation (GRAPeS-3DVAR), which is suitable for a grid point model. The domain includes China area on horizontal dimension and 15 mandatory levels on vertical dimension . The scheme adopts stream function, unbalanced potential velocity, unbalanced g eopotential height and humidity as analysis variables which are independent of e ach other. The cost function takes the way of incremental method. To solve the p roblems that B -1 are ill conditioned and too large to be computed, the background term is preconditioned using a sequence of variable tra nsform, which improves the convergence in the minimization process and avoids to calculate B -1 directly. EOF decomposition is used as vert ical component of analysis variable transform to project onto vertical modes and separate each three dimensional field into two dimensional field. Recursive filters is used as horizontal component of analysis variable transform. LBFGS m ethod is used on solution of optimization. Simple geostrophic balanced relations hip is used. The system has passed verifications strictly and proved to be credi bility. In order to test the functions of the system, A series of idea experimen ts were made. The results show a reasonable relationship among the multi variab les and a fast convergence in the minimized process.