Abstract
AbstractA new simple adjoint (SA) method is developed for retrieving three‐dimensional wind from single‐Doppler observations. The method uses the full momentum equations and the mass continuity equation as weak constraints, in addition to the strong constraints of the radial‐wind and reflectivity equations. With these weak constraints, the unknown source term in the previous two‐dimensional SA method is now explicitly estimated in terms of perturbation pressure and buoyancy. This improves the wind retrievals, although the retrieved perturbation pressure and buoyancy may not be accurate. Bi‐spline basis functions are used to express the retrieved fields on coarse finite‐element meshes. The bi‐spline representation filters short‐wave noise and effectively reduces the number of unknowns that need to be retrieved, so the retrievals are further improved. The method is tested with Doppler‐radar data collected during the Phoenix II field experiment. The retrieved winds are very close to the dual‐Doppler observed winds and the difference is about 1.0 m s−1. The retrievals can be further improved by adding smoothness constraints in the cost function, especially when the bi‐spline representation is not used. The robustness of the method is examined in terms of sensitivities to the weights specified for the weak constraints in the cost function.
Published Version
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