The rain profiling algorithm applied to polarimetric weather radar

The algorithm developed in this paper for ground-based polarimetric radars is derived from those used for the spaceborne rain radar of TRMM (Tropical Rainfall Measurement Mission)-the so-called rain profiling algorithms. The characteristic of this type of algorithm is to be nonlocal, that is, the fu ll rain profile along the radar beam is derived from the reflectivity profi le. However, to be stable such algorithms require an external constraint. I n TRMM. the constraint is the total path attenuation derived from the obser vation of the ocean surface, which is used as a reference target. In the pr esent algorithm, the external constraint is provided by the differential ph ase shift Phi(DP) between H and V polarizations. This is the reason for cal ling this new algorithm ZPHI. The inverse model on which ZPHI is based is a set of three power law relati onships between A and Z(r), K-DP and A, and R and A. respectively (A, speci fic attenuation: Z(r), equivalent reflectivity; R, rainfall rate). Each of these relationships is parameterized by a "normalized" intercept parameter N-0*: of the drop size distribution (DSD) such as A = a[N-0*](t-b)Z(e)(b). In ZPHI, N-0* (retrieved by the algorithm) is assumed constant along the pr ofile. Nevertheless, because ZPHI authorizes a segmentation of the treatmen t, it can deal with complex situations where two (or several) types of rain with different NX occur along the profile (e.g.. as convective and stratif orm rain). Also ZPHI includes a correction scheme for the backscattering ef fects that may affect Phi(DP) at X and C bands. A series of simulations demonstrate the capability of ZPHI to adjust to the variability of the physical characteristics of the rain (variability of Nr ; over two decades, and of the shape parameter mu, between 0 and 10). and t o operate the rain-rare retrieval with a statistical error similar to that with a "classic" Z-R relationship (when Delta Phi(DP) is large enough). The algorithm collapses when the relative error in Delta Phi(DP) approaches 58 %, which may correspond to an average rain rate of 1.58 mm h(-1) at C band (1 mm h(-1) at X band) along an integration path of 50 km. In conclusion. Z PHI possesses all characteristics required in an operational application: m athematical simplicity, robustness, and stability with respect to the measu rement noise. It admits a very short dwell time, compatible with scanning v elocities of 15 degrees-20 degrees s(-1).