Direct Computation of Geostrophic Winds from Observed Winds Using the Balance Equation

In certain meteorological problems it is desirable to make a grid-point analysis of observed winds. In order to combine a wind analysis with other quantities, or to use the wind analysis in a numerical model, one may wish to know the geostrophic winds (or the heights) that conform to the analyzed winds. Many previous studies have shown that the balance equation accurately describes relationships between winds and the height field. In this paper the balance equation is used to equate geostrophic vorticity at each grid point to a sum of terms evaluated from the wind analysis. Then the geostrophic winds are found by altering an initial guess field of zonal and meridional wind components until the geostrophic vorticity and divergence required at each point are met within a close tolerance. The final wind vectors are a geostrophic field that conforms to the original wind analysis according to the balance equation. Typical examples are shown of geostrophic wind vectors computed by this method in a sloping planetary boundary layer, and in the upper troposphere. In addition, geostrophic departures are compared with irrotational winds calculated for the same cases.