Simple Adjoint Methods for Single-Doppler Wind Analysis with a Strong Constraint of Mass Conservation

Abstract

Three schemes are developed to incorporate a strong constraint of (incompressible) mass conservation into the basic scheme (scheme B) of the simple adjoint method of Qiu and Xu for retrieving the time-mean wind field from a sequence of single-Doppler scans. In the first scheme (S1), the two-dimensional wind field on a surface normal to the radar beam is partitioned into an irrotational component expressed by the velocity potential and a nondivergent component expressed by the streamfunction. The velocity potential can be obtained directly from single-Doppler observations, and the streamfunction is retrieved by the adjoint method. In this way, the retrieved wind field satisfies the mass conservation equation precisely. The second scheme (S2) is the same as scheme S1 except that a spectral expression is used to replace the grid representation of the streamfunction. The third scheme (S3) imposes a strong mass conservation constraint through a postadjustment after the wind field is retrieved by scheme B with a weak mass conservation constraint. These schemes are tested with artificial data. Their relative merits and disadvantages are examined and compared in terms of accuracy, convergence rate, sensitivity to errors, and computational efficiency.