A Multigrid Nonlinear Least Squares Four-Dimensional Variational Data Assimilation Scheme With the Advanced Research Weather Research and Forecasting Model

The motions of the atmosphere have multiscale properties in space and/or time, and the background error covariance matrix (B) should thus contain error information at different correlation scales. To obtain an optimal analysis, the multigrid three-dimensional variational data assimilation scheme is used widely when sequentially correcting errors from large to small scales. However, introduction of the multigrid technique into four-dimensional variational data assimilation is not easy due to its strong dependence on the adjoint model, which has high computational costs in data coding, maintenance, and updating, especially for large-scale, complex problems. In this study, the multigrid technique was introduced into the nonlinear least squares four-dimensional variational assimilation (NLS-4DVar) method, which is an advanced four-dimensional ensemble-variational method that can be applied without invoking the adjoint models. The multigrid NLS-4DVar (MG-NLS-4DVar) scheme uses the number of grid points to control the scale, with doubling of this number when moving from coarser to finer grid levels. Furthermore, the MG-NLS-4DVar scheme not only retains the advantages of NLS-4DVar but also sufficiently corrects multiscale errors to achieve a highly accurate analysis. The effectiveness and efficiency of the proposed MG-NLS-4DVar scheme were evaluated by one group of single-observation experiments and one group of comprehensive evaluation experiments using the Advanced Research Weather Research and Forecasting Model. MG-NLS-4DVar outperformed NLS-4DVar, with a lower computational cost.