A method for solving the balance equation using vector alterations to geostrophic winds

Nondivergent winds that conform to geostrophic winds according to the balance equation are obtained by applying a method of “vector alterations.” the spherical coordinate form of the balance equation (Houghton, 1968) is used. The initial data are expressed as geostrophic wind vectors that may be obtained directly from a grid-point analysis of pressure-height observations. The geostrophic field is used as a first guess that is altered in an iterative manner to give the nondivergent wind field. The method is analogous to the usual solution of the balance equation in terms of a stream function, but does not require boundary conditions. Nondivergent wind fields are illustrated for a strong anticyclonic jet stream, and for a more normal upper-tropospheric flow pattern. The numerical procedure is believed to be relatively accurate since the initial geostrophic fields may be recovered by a reverse calculation. Experimentation indicates that computational convergence occurs for values of geostrophic vorticity somewhat less than –0.5 f.