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

Abstract

One of the challenges that limit the amount of information that can be inferred from radar measurements 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 forward-modeled radar reflectivity to assumptions regarding mass–dimensional relationships is examined. This is accomplished by taking advantage of independently measured condensed mass 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.

Using snowflake surface-area-to-volume ratio to model and interpret snowfall triple-frequency radar signatures

“…Previous studies have shown, however, that the uncertainty in modeled snowfall radar reflectivity factors Z e due to the parameterization of m f (D) is significant. Hammonds et al (2014) found uncertainties in Z e related to m f (D) on the order of 4 dB at X, Ku, Ka, and W band, for example. To evaluate the impact of the parameterization of snowflake mass on the modeled snowfall triplefrequency radar signatures in this study, DWRs for collections of N cl = 1, 27, 125 randomly distributed ice spheres inside the snowflake bounding volume (corresponding to normalized surface-area-to-volume ratios of ξ = 1, 3, 5) were also derived after uniformly increasing and decreasing the density values ρ f (D) obtained from the H04 densitydiameter relationship, and thus the snowflake masses m f (D) given by Eqs.…”

A variational technique to estimate snowfall rate from coincident radar, snowflake, and fall-speed observations

“…S y represents not only random instrument noise but also the impact of uncertainties in forward-model assumptions on simulated measurements, F (x). We use an S y standard deviation value of 2 dBZ for this study for the diagonal matrix elements based upon Hammonds et al (2014), who quantified the uncertainty in forward-modeled radar reflectivity due to assumptions such as mass-dimensional relationships at Kaband frequency. The optimal-estimation approach weights the magnitude of the error covariances to determine the relative impact of both a priori guesses and observations on the final retrieval estimates.…”

A statistical comparison of cirrus particle size distributions measured using the 2-D stereo probe during the TC<sup>4</sup>, SPARTICUS, and MACPEX flight campaigns with historical cirrus datasets

“…For instance, effective radar reflectivity is computed by integrating over particle maximum dimension intervals, using a set of particle maximum dimension/backscatter power laws that were fit piecewise from T-matrix computations of backscatter cross section to particle maximum dimension (Matrosov, 2007;Matrosov et al, 2012;Hammonds et al, 2014) as follows:…”