A Numerical Procedure for Computing Fields of Stream Function and Velocity Potential

Abstract

A numerical procedure is described for computing a stream-function field from the vorticity of the horizontal wind field. The method was developed for use in meteorological studies which require analyses based solely on wind observations, or for use in the construction of balanced fields of winds and heights. The boundary of the net region is treated by specifying the gradients of the stream function normal to the boundary. The solution for the stream-function field is achieved relatively quickly by the iterative process known as the implicit alternating-direction method. The same procedure is also used to calculate a velocity-potential field from the divergence of the wind field. The computations are performed on a spherical net and have been tested on wind fields over both the United States and the Caribbean. The computed stream-function fields have been found to provide reliable and sufficiently accurate representations of the non-divergent wind field.