Quantifying Uncertainty in Ice Particle Velocity–Dimension Relationships Using MC3E Observations

Abstract

Ice particle terminal fall velocity (Vt) is fundamental for determining microphysical processes, yet remains extremely challenging to measure. Current theoretical best estimates of Vt are functions of Reynolds number. The Reynolds number is related to the Best number, which is a function of ice particle mass, area ratio (Ar) and maximum dimension (Dmax). These estimates are not conducive for use in most models since model parameterizations often take the form Vt=αDmaxβ, where (α,β) depend on habit and Dmax. A previously developed framework is used to determine surfaces of equally plausible (α,β) coefficients whereby ice particle size/shape distributions are combined with Vt best estimates to determine mass- (VM) or reflectivity-weighted (VZ) velocities that closely match parameterized VM,SD or VZ,SD calculated using the (α,β) coefficients using two approaches. The first uses surfaces of equally plausible (a,b) coefficients describing mass (M)-dimension relationships (i.e., M=aDmaxb) to calculate mass- or reflectivity-weighted velocity from size/shape distributions that are then used to determine (α,β) coefficients. The second investigates how uncertainties in Ar, Dmax, and size distribution N(D) affect VM or VZ. For seven of nine flight legs flown 20/23 May 2011 during MC3E, uncertainty from natural parameter variability – namely the variability in ice particle parameters in similar meteorological conditions – exceeds uncertainties arising from different Ar assumptions or Dmax estimates. The combined uncertainty between Ar, Dmax and N(D) produced smaller variability in (α,β) compared to varying M(D), demonstrating M(D) must be accurately quantified for model fall velocities. Primary sources of uncertainty vary considerably depending on environmental conditions.