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A new thermodynamic retrieval scheme is developed by which one can use the wind fields synthesized from multiple-Doppler radars to derive the three-dimensional thermodynamic fields over complex terrain. A cost function consisting of momentum equations and a simplified thermodynamic equation is formulated. By categorizing the analysis domain into flow and terrain regions, the variational technique is applied to minimize this cost function only within the flow region, leading to the solutions for the three-dimensional pressure and temperature perturbations immediately over terrain. Using idealized datasets generated by a numerical model, an experiment is first conducted to assess the accuracy of the proposed algorithm. The retrieval scheme is then applied to a real case that occurred during the 2008 Southwestern Monsoon Experiment (SoWMEX) conducted in Taiwan. The retrieved thermodynamic fields, verified by radiosonde data, reveal the structure of a prefrontal squall line as it approaches a mountain. The retrieved three-dimensional high-resolution pressure and temperature along with the wind fields not only allow us to better understand the thermodynamic and kinematic structure of a heavy rainfall system, but can also be assimilated into a numerical model to improve the forecast.
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