An Inverse Mapping Table Method for Raindrop Size Distribution Parameters Retrieval Using X-band Dual-Polarization Radar Observations

Abstract

An inverse mapping table (IMT) method is proposed in this article to retrieve the raindrop size distribution (RSD) parameters from X-band polarimetric weather radar data. In the IMT method, a forward mapping database from three parameters of a gamma-type RSD to polarimetric radar variables is first built based on the scattering simulations under ideal atmospheric conditions, and then an inverse mapping database is derived. In particular, given a fixed shape parameter ( $\mu $ ) of RSD, the intersection of horizontal reflectivity ( $Z_{\text {H}}$ ) and differential reflectivity ( $Z_{\text {DR}}$ ) contour lines is first obtained in the domain of total number concentration ( $N_{\text {T}}$ ) and median volume diameter (MVD) $D_{0}$ ; and the inverse mapping relationship between $Z_{H}$ and $Z_{\text {DR}}$ to $N_{T}$ and $D_{0}$ at a fixed $\mu $ value is derived to form a single layer of IMT. Then, the monotonic relationship between $\mu $ and the specific differential propagation phase shift ( $K_{\text {DP}}$ ) or backscatter differential phase ( $\delta _{\text {CO}}$ ) can aid in determining $\mu $ and a single layer of IMT. Thus, the inverse mapping database from polarimetric observations to the three gamma-type RSD parameters $\mu $ , $N_{\text {T}}$ , and $D_{0}$ can be established. Demonstration studies during a convective rainfall event and a large-scale rainfall event which occurred in northeastern China are carried out to examine the performance of this IMT method compared to a constrained-gamma (C-G) method that uses empirical relations between RSD parameters. The results show that the IMT method has a better performance in the convective case and similar performance in the large-scale continuous rainfall case.