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A popular method for obtaining a wind field that satisfies mass continuity and that is consistent with dual-Doppler radial velocity observations is the iterative wind synthesis in Cartesian coordinates. However, in some instances, the iterative method does not converge. Herein, a stability condition is derived for the iterative technique that depends on the horizontal and vertical grid spacings, and the azimuth and elevation angles of the dual-Doppler observations. Alternately, the condition for stability can be expressed as a relationship between the grid box dimensions and the direction of the coplanar arc passing through the grid point. The results of experiments with simulated radar data are consistent with the predicted stability characteristics.
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Dowell et al. (2003) studied this question.
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