Conjugate Gradient Algorithm in the Four-Dimensional Variational Data Assimilation System in GRAPES  

作　　者：Yongzhu LIU Lin ZHANG Zhihua LIAN 

机构地区：[1]National Meteorological Center,Beijing 100081

出　　处：《Journal of Meteorological Research》2018年第6期974-984,共11页气象学报（英文版）

基　　金：Supported by the China Meteorological Administration Special Public Welfare Research Fund(GYHY201506003)

摘　　要：Minimization algorithms are singular components in four-dimensional variational data assimilation(4DVar).In this paper,the convergence and application of the conjugate gradient algorithm(CGA),which is based on the Lanczos iterative algorithm and the Hessian matrix derived from tangent linear and adjoint models using a non-hydrostatic framework,are investigated in the 4DVar minimization.First,the influence of the Gram-Schmidt orthogonalization of the Lanczos vector on the convergence of the Lanczos algorithm is studied.The results show that the Lanczos algorithm without orthogonalization fails to converge after the ninth iteration in the 4DVar minimization,while the orthogonalized Lanczos algorithm converges stably.Second,the convergence and computational efficiency of the CGA and quasi-Newton method in batch cycling assimilation experiments are compared on the 4DVar platform of the Global/Regional Assimilation and Prediction System(GRAPES).The CGA is 40%more computationally efficient than the quasi-Newton method,although the equivalent analysis results can be obtained by using either the CGA or the quasi-Newton method.Thus,the CGA based on Lanczos iterations is better for solving the optimization problems in the GRAPES 4DVar system.Minimization algorithms are singular components in four-dimensional variational data assimilation(4DVar).In this paper,the convergence and application of the conjugate gradient algorithm(CGA),which is based on the Lanczos iterative algorithm and the Hessian matrix derived from tangent linear and adjoint models using a non-hydrostatic framework,are investigated in the 4DVar minimization.First,the influence of the Gram-Schmidt orthogonalization of the Lanczos vector on the convergence of the Lanczos algorithm is studied.The results show that the Lanczos algorithm without orthogonalization fails to converge after the ninth iteration in the 4DVar minimization,while the orthogonalized Lanczos algorithm converges stably.Second,the convergence and computational efficiency of the CGA and quasi-Newton method in batch cycling assimilation experiments are compared on the 4DVar platform of the Global/Regional Assimilation and Prediction System(GRAPES).The CGA is 40%more computationally efficient than the quasi-Newton method,although the equivalent analysis results can be obtained by using either the CGA or the quasi-Newton method.Thus,the CGA based on Lanczos iterations is better for solving the optimization problems in the GRAPES 4DVar system.

关 键 词：numerical weather prediction Global/Regional Assimilation and Prediction System four-dimensional variation conjugate gradient algorithm Lanczos algorithm 

分 类 号：P[天文地球]