The Rain Profiling Algorithm Applied to Polarimetric Weather Radar

Abstract

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 full rain profile along the radar beam is derived from the reflectivity profile. However, to be stable such algorithms require an external constraint. In TRMM, the constraint is the total path attenuation derived from the observation of the ocean surface, which is used as a reference target. In the present algorithm, the external constraint is provided by the differential phase shift ΦDP between H and V polarizations. This is the reason for calling this new algorithm ZPHI. The inverse model on which ZPHI is based is a set of three power law relationships between A and Ze, KDP and A, and R and A, respectively (A, specific attenuation; Ze, 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]1?bZbe. In ZPHI, N*0 (retrieved by the algorithm) is assumed constant along the profile. Nevertheless, because ZPHI authorizes a segmentation of the treatment, it can deal with complex situations where two (or several) types of rain with different N*0 occur along the profile (e.g., as convective and stratiform rain). Also ZPHI includes a correction scheme for the backscattering effects that may affect ΦDP 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 N*0 over two decades, and of the shape parameter ? between 0 and 10), and to operate the rain-rate retrieval with a statistical error similar to that with a ?classic? Z?R relationship (when ?ΦDP is large enough). The algorithm collapses when the relative error in ?ΦDP 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, ZPHI possesses all characteristics required in an operational application: mathematical simplicity, robustness, and stability with respect to the measurement noise. It admits a very short dwell time, compatible with scanning velocities of 15°?20° s?1.