Higher-order geostrophic wind approximations
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Two iterative methods are described for obtaining horizontal winds from the pressure-height field by means of higher-order geostrophic approximations for the purpose of improving upon the geostrophic wind. The convergence properties of the iterative methods are discussed; and in a simple theoretical ease, one of the methods is found to diverge with strong cyclonic motion. Both iterative methods were applied to analyzed 500-mb, height charts and obtained from the balance equation. However in a few locations continued iteration led to increasing differences between successively computed winds: i.e., the methods appeared to diverge. In fact, wind values in adjacent areas gradually tended to be corrupted. This lack of convergence, occuring mainly in areas of negative vorticity and additionally in the ease of method II in areas of strong cyclonic vorticity, was associated with the development of excessive horizontal wind divergence, which after three or four iterations sometimes exceeded the relative vorticity. Stream functions were computed by relaxing the relative vorticity of the winds obtained by methods I and II, generally after one iteration. These were compared to the stream function obtained by solving the balance equation and no significant difference were noted. Barotropic forecasts prepared from the streatm functions derived from the two methods are essentially the same as forecasts with the stream function obtained from the balance equation.
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