Multigrid methods for improving the variational data assimilation in numerical weather prediction

Two conditions are needed to solve numerical weather prediction models: initial condition and boundary condition. The initial condition has an especially important bearing on the model performance. To get a good initial condition, many data assimilation techniques have been developed for the meteorological and the oceanographical fields. Currently, the most commonly used technique for operational applications is the 3 dimensional (3-D) or 4 dimensional variational data assimilation method. The numerical method used for the cost function minimising process is usually an iterative method such as the conjugate gradient. In this paper, we use the multigrid method based on the cell-centred finite difference on the variational data assimilation to improve the performance of the minimisation procedure for 3D-Var data assimilation.