A Simple Adjoint Method of Wind Analysis for Single-Doppler Data

A simple adjoint method is developed for retrieving the time-mean winds from a number of consecutive single-Doppler measurements. The method assumes the Lagrangian conservation of reflectivity. Previous methods based on the same advection equation have to deal with problems of nonuniqueness, singularities, or both. These two problems are eliminated by using observations over multiple time levels. The method is tested on artificial data and the results show that using data over multiple time levels not only provides more information and increases the accuracy of the retrieval but also makes the method less sensitive to errors in the observed reflectivity field and errors in the model equation due to the assumed Lagrangian conservation of reflectivity. Because the control equation and its adjoint equation are very simple, the computational cost is very small. It is also found that incorporating the constraint of mass conservation into the method can significantly increase the accuracy of the retrieved winds and reduce the required frequency of observations for retrieving.