Characterizing the Radar Backscatter-Cross-Section Sensitivities of Ice-Phase Hydrometeor Size Distributions via a Simple Scaling of the Clausius–Mossotti Factor

One of the challenges that limit the amount of information that can be inferred from radarmeasurements of ice and mixed-phase precipitating clouds is the variability in ice mass within hydrometeors. The variable amount of ice mass within particles of a given size drives further variability in single-scattering properties that results in uncertainties of forward-modeled remote sensing quantities. Nonspherical ice-phase hydrometeors are often approximated as spheroids to simplify the calculation of single-scattering properties, yet offline calculations remain necessary to quantify these radiative properties as a function of size in discrete increments. In this paper, a simple scaling of the Clausius–Mossotti factor is used that allows for an approximation of the scattering and extinction cross sections for an arbitrary mass–dimensional power-law relationship of a nonspherical particle given a single T-matrix calculation. Using data collected by the University of Wyoming King Air in snow clouds over the Colorado Park Range, the uncertainty in forwardmodeled radar reflectivity to assumptions regarding mass–dimensional relationships is examined. This is accomplished by taking advantage of independently measured condensedmass and particle size distributions to estimate the variability of the prefactor in the mass–dimensional power law. Then, calculating the partial derivative of the radar backscatter cross sections using the scaling relationships, an estimate is made of the statistical uncertainty in forward-modeled radar reflectivity. Uncertainties on the order of 4 dB are found in this term for the dataset considered.