Effects of Raindrop-Size Distribution Variation within the Radar Scattering Volume on Radar Observables

Dual linear polarization weather radars measure as primary observables the mean power P sub(H) and P sub(V) , corresponding to returns at horizontal and vertical polarizations, respectively. Differential reflectivity Z sub(D) sub(R) is defined as the ratio between these two measurements. Under the assumption of an exponential drop-size distribution, characterized by the two parameters N sub(0) and D sub(0) , it has been shown that Z sub(D) sub(R) may be used to estimate the median volume diameter D sub(0) , following which the parameter N sub(0) and, therefore, other drop-size distribution-dependent quantities, may be determined from the horizontal reflectivity Z sub(H) . In this paper the effects of reflectivity gradients, due to the variation of the drop-size distribution within the radar scattering volume, on the radar observables (Z sub(H) , Z sub(D) sub(R) ) and derived rainfall rates are examined for radar observations with a stationary antenna. The bias of the estimates, their standard errors, and the optimum receiver response are computed for power law and logarithmic receivers. Finally, for the special case of the square law receiver, the contrasting effects due to either similar or opposing signs of the gradients of the parameters N sub(0) and D sub(0) are evaluated.