Quantifying Uncertainty in Ice Particle Velocity–Dimension Relationships Using MC3E Observations
Abstract Ice particle terminal fall velocity ( V t ) is fundamental for determining microphysical processes, yet remains extremely challenging to measure. Current theoretical best estimates of V t are functions of Reynolds number. The Reynolds number is related to the Best number, which is a function of ice particle mass, area ratio ( A r ), and maximum dimension ( D max ). These estimates are not conducive for use in most models since model parameterizations often take the form , where ( α , β ) depend on habit and D max . A previously developed framework is used to determine surfaces of equally plausible ( α , β ) coefficients whereby ice particle size/shape distributions are combined with V t best estimates to determine mass- ( V M ) or reflectivity-weighted ( V Z ) velocities that closely match parameterized V M ,SD or V Z ,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., ) 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 A r , D max , and size distribution N ( D ) affect V M or V Z . For seven of nine flight legs flown on 20 and 23 May 2011 during the Mesoscale Continental Convective Clouds Experiment (MC3E), uncertainty from natural parameter variability—namely, the variability in ice particle parameters in similar meteorological conditions—exceeds uncertainties arising from different A r assumptions or D max estimates. The combined uncertainty between A r , D max , 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. Significance Statement Ice particle fall velocity is fundamental for numerous processes within clouds, and hence is a critical property that must be accurately represented in weather and climate models. Using aircraft observations of ice particle shapes and sizes obtained in clouds behind midlatitude thunderstorms, this work develops a new framework for estimating ice particle fall velocities and their uncertainty, including quantifying the importance of different uncertainty sources from cloud microphysics measurements. Natural parameter variability contributes the most uncertainty in ice particle fall velocity estimates, although other sources can also be important contributors to uncertainty in certain conditions. Additional work examining ice particle data is needed to further understand how dependent uncertainty in certain ice particle properties are to local environmental conditions.