The derivation of absolute potential temperature perturbations and pressure gradients from wind measurements in three-dimensional space

A thermodynamic retrieval scheme has been developed by which one can derive the pressure and potential temperature perturbation fields from wind observations detected by remote sensing devices such as Doppler radar. In this method, the technique of variational analysis is applied to seek a set of optimal solutions for the pressure and potential temperature perturbations that, in the least squares sense, will simultaneously satisfy three momentum equations and the thermodynamic equation. The products of the retrieval are the three-dimensional absolute potential temperature fluctuations and the pressure perturbation gradients in any direction. Using artificial datasets generated by a numerical model, a series of experiments is conducted to test the proposed algorithm against various types of degraded input data. These primarily include finite difference approximations of the local temporal derivatives, random errors embedded in velocity observations with significant magnitudes, as well as incomplete data coverage. Improvements in the retrievals are found to be possible if, within a short period of time, wind data are available at multiple time levels. Overall, it has been demonstrated that the absolute potential temperature field and the pressure gradients can be determined with sufficient accuracy in a three-dimensional space. Such a capability is believed to be particularly useful in many meteorological applications.