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This paper presents a newly designed thermodynamic retrieval algorithm whereby one can deduce the potential temperature and pressure gradient fields in a three dimensional space using only 3-D wind measurements. The latter can be observed by Doppler radar in real cases. In order to achieve this purpose, all three equations of motion are implemented in a single cost function. Then, given the detailed wind information, and through the process of variational minimization, these equations are solved simultaneously in a least square sense. The products of the approximated solutions are the three dimensional potential temperature, and the pressure gradients along any direction. Some preliminary studies using model-generated data sets show that this is a feasible tool for the retrievals, and satisfactory results can be obtained when the performance of this method against various types of input data errors is investigated. Compared to the traditional method proposed by Gal-Chen, the advantage of this scheme is that the vertical structure of the thermodynamic variables can be determined without requiring a point of independent observation of the pressure and temperature for each layer. In addition, this method can easily be applied to an area with topography. It is believed that this algorithm can be of particularly useful in many Doppler weather radar applications.

Toward Deducing the 3-D Thermodynamic Structure from Only Wind Fields-A Validation Study using Simulated Dataset