Application of compressive sensing to refractivity retrieval using networked weather radar

The radar-derived refractivity field can be used as a proxy of near-surface moisture field and has the potential to improve the forecast of convective initialization. The refractivity retrieval was originally developed for the use of single radar, and was recently extended for a network of radars by solving a constrained minimization of mean-square-errors (MSE). In practice, the number of high quality clutter returns can be often fewer than the number of retrieved refractivity points and the retrieval problem becomes ill-defined. In this work, an emerging technology of compressive sensing (CS) is proposed to retrieve refractivity field using a network of radars. It has been shown that CS can provide optimal solution for an underdetermined inverse problem if the conditions of sufficient sparsity and incoherence property are met. For example, CS has been proven to be advantageous over other least mean-square-errors (MSE) based methods if the number of measurements is much fewer than the dimension of signals to be retrieved.

In this work, the relationship between the refractivity field and the phases measured from multiple radars is represented by a linear model. A CS framework with discrete cosine transform (DCT) was used to solve the inversion. The application of CS to refractivity retrieval using single and multiple radars is demonstrated using simulations. In simulation, the model refractivity field was calculated from numerical weather model. Subsequently, the radar-measured phases from randomly located clutters were generated by integrating refractivity along the ray path. The performance of CS was quantified statistically for various conditions such as the amount of measurement errors, the number of high quality clutter returns, and radar locations. Further, the performance of CS was compared to the method that was developed previously using a MSE approach with smoothness constrain. Our preliminary results have shown that CS can provide relatively robust and high quality estimates of refractivity field for most cases.