Reducing the Error in a Time-Split Finite-Difference Scheme Using an Incremental Technique

Abstract

It is shown both in theory and in practice that the accuracy of time-split finite-difference methods may be increased by the very simple device of incrementally adding a portion of the advection term in the adjustment step of the method. In the first part of this study, the theory of the approach is described, and large gains in accuracy are demonstrated by comparison with an exact solution to a forced oscillatory system. The technique is then applied to a considerable number (100) of 48-h forecasts with a barotropic numerical weather prediction (NWP) model using 500-hPa data on the Australian region NWP domain. It is found that the incrementally split scheme is more accurate than the conventional split scheme, which generates more noise and has unrealistically larger values of the root-mean-square ageostrophic wind. A further advantage of the new scheme is that it has superior initialization properties.