Classification of Polarimetric Radar Data in Rayleigh and non-Rayleigh Scattering to Improve Detection of Hail and Tornado Debris

Polarimetric radar data such as differential phase and its range derivative specific differential phase (K_DP) contain weather information that can be used to improve microphysics retrievals and quantitative precipitation estimation (QPE). However, the usefulness of current operational estimates of K_DP is limited by artifacts resulting from the presence of differential scattering phase and measurement error. Recent studies have shown that an accurate estimation of differential propagation phase can be obtained via linear programming specifically when performed within regimes of Rayleigh scattering. This estimation of the differential propagation phase can then be interpolated to adjacent non-Rayleigh scattering regimes and by taking the difference between the differential phase and the estimation of differential propagation phase, we can get estimates of differential scattering phase which has shown to have potential utility toward identifying non-Rayleigh scatterers such as hail and tornado debris. The crux of this process thus relies on the accurate classification of Rayleigh scattering regimes.

Empirical methods exist for classifying Rayleigh scatterings regimes by implementing thresholds for reflectivity, cross-correlation coefficient, signal to noise ratio, and standard deviation of differential phase. Simply put, if the values of the polarimetric measurements meet the criteria of these thresholds for a given range gate, that gate would be classified as a Rayleigh regime gate. However, while the process is useful for exhibiting the utility of Rayleigh scattering regimes for the purpose of isolating differential propagation phase, it is not perfect because measurements contain statistical errors. The variability in radial profiles of polarimetric products is often such that this process will exclude gates that would have otherwise been manually classified or leads to false positives in noisy, non-Rayleigh scattering regions.

We therefore believe it is imperative to study more robust statistical methods for the classification of Rayleigh and non-Rayleigh scattering regimes. In this study we will examine and compare a few different methods of this this classification. A manual classification has been performed by utilizing the available polarimetric data with our understanding of physical meteorological processes and scattering theory. This will be used as our 'ground truth.' We then utilize joint probability density functions of Rayleigh and non-Rayleigh scatters to employ a Bayesian classification at every gate. Further, we will also investigate machine learning approaches to improve the classification as these approaches can make use of not only the information at given gate but also correlations among different radar variables and that among adjacent gates. By improving the classification of Rayleigh and non-Rayleigh scattering regimes, we expect to improve our estimations of specific differential phase which, in turn, leads to improved QPE and microphysics retrievals as well as improving our estimates of differential scattering phase which should improve the detection of hail and tornado debris.