Estimation of the Specific Differential Phase Shift using Kalman Filtering

The specific differential phase shift (K_DP) is defined as the range derivative of the differential phase shift on propagation (Ф_DP). This polarimetric variable depends on the shape, type and concentration of the hydrometeors in a radar resolution volume, and therefore carries valuable information about the characteristics of precipitation. The estimation of K_DP from the measured and noisy total differential phase (ψ_DP) can be affected by significant errors, and especially the high values of KDP can be largely underestimated.

In the present work we propose a Kalman filter (KF) technique to estimate K_DP that relies only on the measured ψ_DP and therefore provides estimate which are fully independent from power-related radar observables. The algorithm aims to provide K_DP estimates at the higher possible resolution, in order to capture the fine scale variation of the precipitation. It takes into account the effect of differential shift upon backscattering (d) and the error structure of the polarimetric phase-based variables, through a parametrization based on simulated radar measurements.

The newly developed algorithm is compared with other two standard algorithms of the same type (i.e., that only use phase-information), that are based on linear interpolation and moving window range derivative. The comparison is carried out by means of simulated DSD fields, which allow to compare “true” and retrieved K_DP values directly. The KF algorithm outperforms the standard ones in terms of Nash Efficiency, Correlation Coefficient, RMSE and mean normalized bias and it is able to improve the estimation of high K_DP values, by reducing their systematic underestimation. It is also shown that the Mean Normalized Absolute Error in the estimation of K_DP for all the methods considered can be as large as 25-30% at the range resolution volume scale.