Application of Compressive Sensing to Refractivity Retrieval Using Networked Weather Radars

Radar-derived refractivity from stationary ground targets can be used as a proxy of near-surface moisture field and has the potential to improve the forecast of convection initiation. Refractivity retrieval was originally developed for a single radar and was recently extended for a network of radars by solving a constrained least squares (CLS) minimization. In practice, the number of high-quality ground returns can be often limited, and consequently, the retrieval problem becomes ill-conditioned. In this paper, an emerging technology of compressive sensing (CS) is proposed to estimate the refractivity field using a network of radars. It has been shown that CS can provide an optimal solution for the underdetermined inverse problem under certain conditions and has been applied to different fields such as magnetic resonance imaging, radar imaging, etc. In this paper, a CS framework is developed to solve the inversion. The feasibility of CS for refractivity retrieval using single and multiple radars is demonstrated using simulations, where the model refractivity fields were obtained from the Advanced Regional Prediction System. The root-mean-squared error was introduced to quantify the performance of the retrieval. The performance of CS was assessed statistically and compared to the CLS estimates for various amounts of measurement errors, numbers of radars, and model refractivity fields. Our preliminary results have shown that CS can consistently provide relatively robust and high-quality estimates of the refractivity field.