An Effective Method to Solve the Streamfunction and Velocity Potential from a Wind Field in a Limited Area

The streamfunction and the velocity potential are variables commonly used in the scheme design for atmospheric data assimilation and initial field analysis of numeric weather prediction.They can be obtained in partitioning a wind field by solving the Poisson equations of the vorticity and the divergence of the horizontal components of the wind field. Difference method is usually adopted in a limited area; nevertheless, an obvious departure exits between the original wind field and the reconstructed one from the sum of the streamfunction and velocity potential components in the vicinity of the boundary of the limited area.An effective scheme is designed to solve by difference method the streamfunction and velocity potential of a wind field in an Arakawa-A grid limited area, based on analyzing detailedly the approach and characteristics in the process of the solution. The key techniques in the scheme include the following. Firstly, the solution domain is expanded by two rings by extrapolating linearly the wind field to improve a calculation of boundary values. Secondly, consistent difference schemes are introduced in the solution procedure to enhance the solution precision. And finally only two to three iterations are imposed on incremental corrections to get a satisfactorily accurate result. Experiments are carried out with real wind data and their results indicate that the streamfunction and velocity potential of a wind field can be acquired by the scheme and the reconstructed wind field is reproduced with a very high precision.