Applications Of Nonlinear Optimization Methods To The Study Of The Four Dimensional Variational Data Assimilation System

In this paper,a further research to the Four Dimensional Variational Data Assimilation System(FDVDAS)is given.By the theorem of the FDVDAS,in order to find the optimal initial fields,a large scale nonlinear optimization problem is needed.But the atmosphere motion patterns are always complicated.The patterns not only have many variables,but also high dimension.So when the pattern is given,whether the problem can be solved accurately and effectively or not,the key point is the efficiency of nonlinear optimization method.A modified conjugate gradient algorithm with inexact line search,for solving large scale nonlinear optimization problem,is described.By virtue of storage saving property and high convergence rate as conventional conjugate gradient methods have,it is a special 2-dimension Quasi-Newton method in essence.However,an important difference is that instead of the new direction being conjugate to the previous direction,it is conjugate to a modified direction(?)_k-1which is perpendicular to the current gradient gk.At last,Lorenz equation is chosen as an example to test the theorem of FDVDAS.And in the process of computing nonlinear optimization problem numerically, the modified conjugate gradient algorithm is applied.