Compressed Dual-Polarimetry for Meteorological Radars

Many modern weather radars are polarization agile. That is, they can transmit both horizontal and vertical polarized electromagnetic waves independently, and the radar receiver/processor processes the two polarization echoes independently. From such measurements, the determination of dual-polarized products such as reflectivity (Z_dr), copolar correlation coefficient (ρ_hv) and differential propagation phase (φ_dp) follows. Proper interpretation of these products provides estimates on the size, shape, and type of hydrometeors.

In recent years, the compressed sensing (CS) technique has received much attention in several disciplines. In some instances, CS allows significant lower sampling rates compared to traditional techniques, but without compromising data quality. Conventional weather radars dwell on its target to achieve a desired signal-to-noise ratio. This limits the radar scan rate. We hypothesize that CS-based weather radars may allow for higher scan rates while preserving the quality of the radar products. We previously demonstrated recovery of a precipitation scene (obtained through CS) by reconstruction of a single-polarization radar reflectivity product (Z_h) using low-rank matrix completion algorithms.

Here we extend that work to dual-polarization estimates of precipitation. We use data collected with the Iowa X-band Polarimetric (XPOL) radars to test and demonstrate our techniques. Application of CS requires sparsity or sparse approximation for the radar signals. Unlike hard point targets, precipitation echoes are not sparse in conventional dictionaries such as time and frequency. However, the motion among the precipitation scatterers is small compared to the radar wavelength. With typical sampling rates their relative positions produce highly correlated echoes from sample to sample. These highly-correlated precipitation echoes can be modeled as a low-rank matrix. Leveraging recent advances in matric completion techniques, we reconstruct the full matrix and produce estimates of the dual-polarization products.