Error structure of multiparameter radar and surface measurements of rainfall. Part III: specific differential phase

Abstract

Parts I and II of this three part paper dealt with the error structure of differential reflectivity and X-band specific attenuation in rainfall as estimated by radar and surface disdrometers. In this Part III paper we focus on the error structure of the specific differential phase (K_DP, °km⁻¹) measurement in rainfall. This allows us to analyze three estimators of rainfall rate, the first based on the reflectivity factor Z_H, the second based on combining reflectivity and Z_DR, [R(Z_H, Z_DR)], and the third based on K_DP alone, R(K_DP). Simulations are used to model random errors in Z_H, Z_DR and K_DP. Physical variations in the raindrop size distribution (RSD) are modeled by varying the gamma parameters (N₀, D₀, m) over a range typically found in natural rainfall. Thus, our simulations incorporate physical fluctuations onto which random measurement errors have been superimposed. Radar-derived estimates of R(Z_H, Z_DR) and R(K_DP) have been intercompared using data obtained in convective rainfall with the NSSL Cimarron radar and the NCAR/CP-2 radar. As practical application of the analysis presented here, we have determined the range of applicability of the three rainfall rate estimators: R(Z_H), R(Z_H, Z_DR) and R(K_DP). Our simulations show that when the rainfall rate exceeds about 70 mm h^-1, R(K_DP) performs better than R(Z_H, Z_DR). This result is valid over a 1 km propagation path. At intermediate rainfall rates around 20≲R≲70 mm h⁻¹, our simulations show that R(Z_H, Z_DR) gives the least error. However, there are other reasons which make R(K_DP) useful; i.e., (i) its stability with respect to mixed phase precipitation, and (ii) the fact that it is a differential phase measurement and thus insensitive to system gain calibration. This last premise suggests an accurate method of system gain calibration based on the rain medium.