GRAPES全球四维变分同化系统极小化算法预调节  

The Preconditioning of Minimization Algorithm in GRAPES Global Four-dimensional Variational Data Assimilation System

作　　者：张林[1] 刘永柱[1] 

机构地区：[1]中国气象局数值预报中心,北京100081

出　　处：《应用气象学报》2017年第2期168-176,共9页Journal of Applied Meteorological Science

基　　金：公益性行业(气象)科研专项(GYHY201506003);中国气象局数值预报中心GRAPES发展专项(GRAPES-FZZX-2016-04);国家留学人员科技活动择优资助项目"增量四维变分同化方案的优化"

摘　　要：在进行多次外循环更新的增量分析框架下,前一次极小化迭代过程中产生的信息可提供给下一次极小化做预调节。该文在GRAPES全球四维变分同化系统中对极小化算法——L-BFGS算法实施了这种预调节,通过全观测的个例试验和批量试验进行评估,发现进行预调节后L-BFGS算法的收敛效率得到明显提高,而且在1个月的循环试验中表现十分稳定。该工作可以帮助GRAPES全球四维变分同化系统有效减少极小化的迭代次数,有利于满足业务化运行的时效要求。另外,间隔6 h和间隔24 h的两次4DVar分析对应的海森矩阵变化不大,因此,前一时刻极小化过程产生的信息提供给后一时刻的极小化进行预调节也有一定效果。Variational data assimilation is a minimization problem of the cost function.Main characteristics of the problem are that the cost function is quadratic or nearly-quadratic and Hessian matrix of the cost function is sparse,symmetric and positive-definite.Iterative methods are suitable for solving this problem,but the calculation of the cost function and its gradient is very expensive,especially in four-dimensional variational data assimilation（4DVar）.To find an optimal solution and achieve acceptable convergence rate,it is necessary to precondition the minimization algorithm.GRAPES global 4DVar system is developed for the operational use in China Meteorological Administration（CMA）.It solves the minimization using L-BFGS algorithm,which is well known as a practical algorithm for variational data assimilation and originated from the works of Nocedal and Liu et al.It uses the information from the previous m iterations to compute the BFGS matrix which is an approximation to the inverse of Hessian matrix.GRAPES global 4DVar system adopts the incremental approach.In the incremental 4DVar,the inner loop minimization is solved several times with multi-outer-loop updates to find a more accurate solution of the nonlinear problem.It＇s possible to use information from previous minimization to precondition the next minimization.It is also related to the so-called warm-start of L-BFGS.Preconditioned L-BFGS is introduced and impacts of the preconditioning of L-BFGS on the convergence rate in 4DVar experiments of real observations are evaluated.Firstly,a case study is performed with four inner loop minimizations and 50 iterations during each inner loop minimization.Since the preconditioning works from the second inner loop minimization,nonlinear observation terms in the cost function are compared during 50-200 iterations.Results show the preconditioning of L-BFGS is effective,especially during the second inner loop minimization which uses the information from the first inner loop minimization.The scheme which uses info

关 键 词：L-BFGS算法 预调节 四维变分 

分 类 号：P413[天文地球—大气科学及气象学]