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

Andrew M. DzamboaCooperative Institute for Severe and High Impact Weather and Research Operations, University of Oklahoma, Norman, Oklahoma

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Greg McFarquharaCooperative Institute for Severe and High Impact Weather and Research Operations, University of Oklahoma, Norman, Oklahoma
bSchool of Meteorology, University of Oklahoma, Norman, Oklahoma

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Joseph A. FinloncDepartment of Atmospheric Sciences, University of Washington, Seattle, Washington

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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=αDmaxb) 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 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 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.

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.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andrew Dzambo, dzamboam@ou.edu

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=αDmaxb) 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 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 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.

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.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andrew Dzambo, dzamboam@ou.edu
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