A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications
Abstract
The orientation of falling ice particles directly influences estimates of microphysical and radiative bulk quantities as well as in situ retrievals of size, shape, and mass. However, retrieval efforts and bulk calculations often incorporate very basic orientations or ignore these effects altogether. To address this deficiency, this study develops a general method for projecting bulk distributions of particle shape for arbitrary orientations. The Amoroso distribution provides the most general bulk aspect ratio distribution for gamma-distributed particle axis lengths. The parameters that govern the behavior of this aspect ratio distribution depend on the assumed relationship between mass, maximum dimension, and aspect ratio. Individual spheroidal geometry allows for eccentricity quantities to linearly map onto ellipse analogs, whereas aspect ratio quantities map nonlinearly. For particles viewed from their side, this analytic distinction leads to substantially larger errors in projected aspect ratio than for projected eccentricity. Distribution transformations using these mapping equations and numerical integration of projection kernels show that both truncation of size distributions and changes in Gaussian dispersion can alter the modality and shape of projection distributions. As a result, the projection process can more than triple the relative entropy between the spheroidal and projection distributions for commonly assumed model and orientationmore »
- Authors:
-
- The Pennsylvania State University, University Park, Pennsylvania
- Publication Date:
- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER)
- OSTI Identifier:
- 1489713
- Alternate Identifier(s):
- OSTI ID: 1611950
- Grant/Contract Number:
- SC0012827; SC0013953
- Resource Type:
- Published Article
- Journal Name:
- Journal of the Atmospheric Sciences
- Additional Journal Information:
- Journal Name: Journal of the Atmospheric Sciences Journal Volume: 76 Journal Issue: 1; Journal ID: ISSN 0022-4928
- Publisher:
- American Meteorological Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; meteorology & atmospheric sciences; cloud microphysics; ice crystals; ice particles; aircraft observations; in situ atmospheric observations; model comparison
Citation Formats
Dunnavan, Edwin L., and Jiang, Zhiyuan. A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications. United States: N. p., 2019.
Web. doi:10.1175/JAS-D-18-0177.1.
Dunnavan, Edwin L., & Jiang, Zhiyuan. A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications. United States. https://doi.org/10.1175/JAS-D-18-0177.1
Dunnavan, Edwin L., and Jiang, Zhiyuan. Tue .
"A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications". United States. https://doi.org/10.1175/JAS-D-18-0177.1.
@article{osti_1489713,
title = {A General Method for Estimating Bulk 2D Projections of Ice Particle Shape: Theory and Applications},
author = {Dunnavan, Edwin L. and Jiang, Zhiyuan},
abstractNote = {The orientation of falling ice particles directly influences estimates of microphysical and radiative bulk quantities as well as in situ retrievals of size, shape, and mass. However, retrieval efforts and bulk calculations often incorporate very basic orientations or ignore these effects altogether. To address this deficiency, this study develops a general method for projecting bulk distributions of particle shape for arbitrary orientations. The Amoroso distribution provides the most general bulk aspect ratio distribution for gamma-distributed particle axis lengths. The parameters that govern the behavior of this aspect ratio distribution depend on the assumed relationship between mass, maximum dimension, and aspect ratio. Individual spheroidal geometry allows for eccentricity quantities to linearly map onto ellipse analogs, whereas aspect ratio quantities map nonlinearly. For particles viewed from their side, this analytic distinction leads to substantially larger errors in projected aspect ratio than for projected eccentricity. Distribution transformations using these mapping equations and numerical integration of projection kernels show that both truncation of size distributions and changes in Gaussian dispersion can alter the modality and shape of projection distributions. As a result, the projection process can more than triple the relative entropy between the spheroidal and projection distributions for commonly assumed model and orientation parameters. This shape uncertainty is maximized for distributions of highly eccentric particles and for particles like aggregates that are thought to fall with large canting-angle deviations. Finally as a result, the methods used to report projected aspect ratios and the corresponding values should be questioned.},
doi = {10.1175/JAS-D-18-0177.1},
journal = {Journal of the Atmospheric Sciences},
number = 1,
volume = 76,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 2019},
month = {Tue Jan 01 00:00:00 EST 2019}
}
https://doi.org/10.1175/JAS-D-18-0177.1
Web of Science
Works referenced in this record:
The Spectral Ice Habit Prediction System (SHIPS). Part III: Description of the Ice Particle Model and the Habit-Dependent Aggregation Model
journal, June 2011
- Hashino, Tempei; Tripoli, Gregory J.
- Journal of the Atmospheric Sciences, Vol. 68, Issue 6
The Modified Gamma Size Distribution Applied to Inhomogeneous and Nonspherical Particles: Key Relationships and Conversions
journal, July 2011
- Petty, Grant W.; Huang, Wei
- Journal of the Atmospheric Sciences, Vol. 68, Issue 7
The Spectral Ice Habit Prediction System (SHIPS). Part II: Simulation of Nucleation and Depositional Growth of Polycrystals
journal, October 2008
- Hashino, Tempei; Tripoli, Gregory J.
- Journal of the Atmospheric Sciences, Vol. 65, Issue 10
Improved Measurements of the Ice Water Content in Cirrus Using a Total-Water Probe
journal, April 1995
- Brown, Philip R. A.; Francis, Peter N.
- Journal of Atmospheric and Oceanic Technology, Vol. 12, Issue 2
A Theory of Snow-Crystal Habit and Growth
journal, April 1954
- Marshall, J. S.; Langleben, M. P.
- Journal of Meteorology, Vol. 11, Issue 2
Inferring Fall Attitudes of Pristine Dendritic Crystals from Polarimetric Radar Data
journal, January 2005
- Matrosov, Sergey Y.; Reinking, Roger F.; Djalalova, Irina V.
- Journal of the Atmospheric Sciences, Vol. 62, Issue 1
Improvement in Determination of Ice Water Content from Two-Dimensional Particle Imagery. Part I: Image-to-Mass Relationships
journal, September 2006
- Baker, Brad; Lawson, R. Paul
- Journal of Applied Meteorology and Climatology, Vol. 45, Issue 9
A New Double-Moment Microphysics Parameterization for Application in Cloud and Climate Models. Part I: Description
journal, June 2005
- Morrison, H.; Curry, J. A.; Khvorostyanov, V. I.
- Journal of the Atmospheric Sciences, Vol. 62, Issue 6
Parameterization of Cloud Microphysics Based on the Prediction of Bulk Ice Particle Properties. Part I: Scheme Description and Idealized Tests
journal, January 2015
- Morrison, Hugh; Milbrandt, Jason A.
- Journal of the Atmospheric Sciences, Vol. 72, Issue 1
Observations and Parameterizations of Particle Size Distributions in Deep Tropical Cirrus and Stratiform Precipitating Clouds: Results from In Situ Observations in TRMM Field Campaigns
journal, December 2002
- Heymsfield, Andrew J.; Bansemer, Aaron; Field, Paul R.
- Journal of the Atmospheric Sciences, Vol. 59, Issue 24
Radar Scattering from Ice Aggregates Using the Horizontally Aligned Oblate Spheroid Approximation
journal, March 2012
- Hogan, Robin J.; Tian, Lin; Brown, Philip R. A.
- Journal of Applied Meteorology and Climatology, Vol. 51, Issue 3
The Shape and Riming Properties of Ice Crystals in Natural Clouds
journal, January 1969
- Ono, A.
- Journal of the Atmospheric Sciences, Vol. 26, Issue 1
Growth of ice particle mass and projected area during riming
journal, January 2017
- Erfani, Ehsan; Mitchell, David L.
- Atmospheric Chemistry and Physics, Vol. 17, Issue 2
A Multimoment Bulk Microphysics Parameterization. Part I: Analysis of the Role of the Spectral Shape Parameter
journal, September 2005
- Milbrandt, J. A.; Yau, M. K.
- Journal of the Atmospheric Sciences, Vol. 62, Issue 9
Explicit Forecasts of Winter Precipitation Using an Improved Bulk Microphysics Scheme. Part II: Implementation of a New Snow Parameterization
journal, December 2008
- Thompson, Gregory; Field, Paul R.; Rasmussen, Roy M.
- Monthly Weather Review, Vol. 136, Issue 12
Polarimetric Signatures above the Melting Layer in Winter Storms: An Observational and Modeling Study
journal, March 2013
- Andrić, Jelena; Kumjian, Matthew R.; Zrnić, Dušan S.
- Journal of Applied Meteorology and Climatology, Vol. 52, Issue 3
On the Impacts of Different Definitions of Maximum Dimension for Nonspherical Particles Recorded by 2D Imaging Probes
journal, May 2016
- Wu, Wei; McFarquhar, Greg M.
- Journal of Atmospheric and Oceanic Technology, Vol. 33, Issue 5
The Dimension of Ice Crystals in Natural Clouds
journal, September 1970
- Auer, August H.; Veal, Donald L.
- Journal of the Atmospheric Sciences, Vol. 27, Issue 6
The Theoretical Basis for the Parameterization of Ice Crystal Habits: Growth by Vapor Deposition
journal, May 1994
- Chen, Jen-Ping; Lamb, Dennis
- Journal of the Atmospheric Sciences, Vol. 51, Issue 9
Study of Planar Ice Crystal Orientations in Ice Clouds from Scanning Polarization Lidar Observations
journal, May 2005
- Noel, Vincent; Sassen, Kenneth
- Journal of Applied Meteorology, Vol. 44, Issue 5
Predicting Ice Shape Evolution in a Bulk Microphysics Model
journal, June 2017
- Jensen, Anders A.; Harrington, Jerry Y.; Morrison, Hugh
- Journal of the Atmospheric Sciences, Vol. 74, Issue 6
A Double-Moment Multiple-Phase Four-Class Bulk Ice Scheme. Part I: Description
journal, January 1994
- Schoenberg Ferrier, Brad
- Journal of the Atmospheric Sciences, Vol. 51, Issue 2
A General Equation for the Terminal Fall Speed of Solid Hydrometeors
journal, August 1989
- Böhm, Hannes P.
- Journal of the Atmospheric Sciences, Vol. 46, Issue 15
The behaviour of freely falling cylinders and cones in a viscous fluid
journal, August 1965
- Jayaweera, K. O. L. F.; Mason, B. J.
- Journal of Fluid Mechanics, Vol. 22, Issue 04
A Model Predicting the Evolution of Ice Particle Size Spectra and Radiative Properties of Cirrus Clouds. Part II: Dependence of Absorption and Extinction on Ice Crystal Morphology
journal, March 1994
- Mitchell, David L.; Arnott, W. Patrick
- Journal of the Atmospheric Sciences, Vol. 51, Issue 6
Ice particle habits in stratiform clouds
journal, October 2000
- Korolev, A.; Isaac, G. A.; Hallett, J.
- Quarterly Journal of the Royal Meteorological Society, Vol. 126, Issue 569
Statistical Theory on the Functional Form of Cloud Particle Size Distributions
journal, August 2018
- Wu, Wei; McFarquhar, Greg M.
- Journal of the Atmospheric Sciences, Vol. 75, Issue 8
Use of Mass- and Area-Dimensional Power Laws for Determining Precipitation Particle Terminal Velocities
journal, June 1996
- Mitchell, David L.
- Journal of the Atmospheric Sciences, Vol. 53, Issue 12
Principles and applications of dual-polarization weather radar. Part I: Description of the polarimetric radar variables
journal, November 2013
- Kumjian, Matthew
- Journal of Operational Meteorology, Vol. 1, Issue 19
Triple-Moment Modal Parameterization for the Adaptive Growth Habit of Pristine Ice Crystals
journal, May 2016
- Chen, Jen-Ping; Tsai, Tzu-Chin
- Journal of the Atmospheric Sciences, Vol. 73, Issue 5
Processing of Ice Cloud In Situ Data Collected by Bulk Water, Scattering, and Imaging Probes: Fundamentals, Uncertainties, and Efforts toward Consistency
journal, January 2017
- McFarquhar, Greg M.; Baumgardner, Darrel; Bansemer, Aaron
- Meteorological Monographs, Vol. 58
Fall speeds and masses of solid precipitation particles
journal, May 1974
- Locatelli, John D.; Hobbs, Peter V.
- Journal of Geophysical Research, Vol. 79, Issue 15
The Characterization of Ice Hydrometeor Gamma Size Distributions as Volumes in N 0 – λ – μ Phase Space: Implications for Microphysical Process Modeling
journal, February 2015
- McFarquhar, Greg M.; Hsieh, Tsung-Lin; Freer, Matt
- Journal of the Atmospheric Sciences, Vol. 72, Issue 2
The Growth of Atmospheric Ice Crystals: A Summary of Findings in Vertical Supercooled Cloud Tunnel Studies
journal, June 1999
- Fukuta, Norihiko; Takahashi, Tsuneya
- Journal of the Atmospheric Sciences, Vol. 56, Issue 12
A Statistical and Physical Description of Hydrometeor Distributions in Colorado Snowstorms Using a Video Disdrometer
journal, May 2007
- Brandes, Edward A.; Ikeda, Kyoko; Zhang, Guifu
- Journal of Applied Meteorology and Climatology, Vol. 46, Issue 5
Polarization and Brewster angle properties of light pillars
journal, January 1987
- Sassen, Kenneth
- Journal of the Optical Society of America A, Vol. 4, Issue 3
Orientations and aspect ratios of falling snow
journal, June 2015
- Garrett, Timothy J.; Yuter, Sandra E.; Fallgatter, Cale
- Geophysical Research Letters, Vol. 42, Issue 11
A Method for Adaptive Habit Prediction in Bulk Microphysical Models. Part II: Parcel Model Corroboration
journal, February 2013
- Harrington, Jerry Y.; Sulia, Kara; Morrison, Hugh
- Journal of the Atmospheric Sciences, Vol. 70, Issue 2
A Comprehensive Habit Diagram for Atmospheric Ice Crystals: Confirmation from the Laboratory, AIRS II, and Other Field Studies
journal, September 2009
- Bailey, Matthew P.; Hallett, John
- Journal of the Atmospheric Sciences, Vol. 66, Issue 9
New RAMS cloud microphysics parameterization part I: the single-moment scheme
journal, September 1995
- Walko, R. L.; Cotton, W. R.; Meyers, M. P.
- Atmospheric Research, Vol. 38, Issue 1-4
What Can We Conclude about the Real Aspect Ratios of Ice Particle Aggregates from Two-Dimensional Images?
journal, March 2017
- Jiang, Zhiyuan; Oue, Mariko; Verlinde, Johannes
- Journal of Applied Meteorology and Climatology, Vol. 56, Issue 3
Roundness and Aspect Ratio of Particles in Ice Clouds
journal, August 2003
- Korolev, Alexei; Isaac, George
- Journal of the Atmospheric Sciences, Vol. 60, Issue 15
Improvement in Determination of Ice Water Content from Two-Dimensional Particle Imagery. Part II: Applications to Collected Data
journal, September 2006
- Lawson, R. Paul; Baker, Brad A.
- Journal of Applied Meteorology and Climatology, Vol. 45, Issue 9
Air Flow and Particle Trajectories around Aircraft Fuselages. Part III: Extensions to Particles of Arbitrary Shape
journal, December 1985
- King, W. D.
- Journal of Atmospheric and Oceanic Technology, Vol. 2, Issue 4
A laboratory investigation into the aggregation efficiency of small ice crystals
journal, January 2012
- Connolly, P. J.; Emersic, C.; Field, P. R.
- Atmospheric Chemistry and Physics, Vol. 12, Issue 4
The 2D-S (Stereo) Probe: Design and Preliminary Tests of a New Airborne, High-Speed, High-Resolution Particle Imaging Probe
journal, November 2006
- Lawson, R. Paul; O’Connor, Darren; Zmarzly, Patrick
- Journal of Atmospheric and Oceanic Technology, Vol. 23, Issue 11
The Capacitance of Pristine Ice Crystals and Aggregate Snowflakes
journal, January 2008
- Westbrook, Christopher David; Hogan, Robin J.; Illingworth, Anthony J.
- Journal of the Atmospheric Sciences, Vol. 65, Issue 1
A Method for Adaptive Habit Prediction in Bulk Microphysical Models. Part I: Theoretical Development
journal, February 2013
- Harrington, Jerry Y.; Sulia, Kara; Morrison, Hugh
- Journal of the Atmospheric Sciences, Vol. 70, Issue 2
Use of observed ice crystal sizes and shapes to calculate mean-scattering properties and multispectral radiances: CEPEX April 4, 1993, case study
journal, December 1999
- McFarquhar, Greg M.; Heymsfield, Andrew J.; Macke, Andreas
- Journal of Geophysical Research: Atmospheres, Vol. 104, Issue D24
Single-Scattering Properties of Aggregates of Bullet Rosettes in Cirrus
journal, June 2007
- Um, Junshik; McFarquhar, Greg M.
- Journal of Applied Meteorology and Climatology, Vol. 46, Issue 6
The Spectral Ice Habit Prediction System (SHIPS). Part I: Model Description and Simulation of the Vapor Deposition Process
journal, July 2007
- Hashino, T.; Tripoli, G. J.
- Journal of the Atmospheric Sciences, Vol. 64, Issue 7
In Situ Observations of the Microphysical Properties of Wave, Cirrus, and Anvil Clouds. Part II: Cirrus Clouds
journal, December 2006
- Lawson, R. Paul; Baker, Brad; Pilson, Bryan
- Journal of the Atmospheric Sciences, Vol. 63, Issue 12
Ricerche intorno alla curva dei redditi
journal, December 1925
- Amoroso, Luigi
- Annali di Matematica Pura ed Applicata, Series 4, Vol. 2, Issue 1
Orientation Model for Particles in Turbulence
journal, June 1995
- Klett, James D.
- Journal of the Atmospheric Sciences, Vol. 52, Issue 12
Free-Fall Behavior of Planar Snow Crystals, Conical Graupel and Small Hail
journal, January 1971
- List, Roland; Schemenauer, Robert S.
- Journal of the Atmospheric Sciences, Vol. 28, Issue 1
An overview of microphysical properties of Arctic clouds observed in May and July 1998 during FIRE ACE
journal, July 2001
- Lawson, R. Paul; Baker, Brad A.; Schmitt, Carl G.
- Journal of Geophysical Research: Atmospheres, Vol. 106, Issue D14
Polarimetric Radar Observation Operator for a Cloud Model with Spectral Microphysics
journal, April 2011
- Ryzhkov, A.; Pinsky, M.; Pokrovsky, A.
- Journal of Applied Meteorology and Climatology, Vol. 50, Issue 4
Air Flow and Particle Trajectories around Aircraft Fuselages. IV: Orientation of Ice Crystals
journal, September 1986
- King, W. D.
- Journal of Atmospheric and Oceanic Technology, Vol. 3, Issue 3
Orientation statistics and settling velocity of ellipsoids in decaying turbulence
journal, June 2014
- Siewert, C.; Kunnen, R. P. J.; Meinke, M.
- Atmospheric Research, Vol. 142
Total Surface Area Estimates for Individual Ice Particles and Particle Populations
journal, April 2005
- Schmitt, C. G.; Heymsfield, A. J.
- Journal of Applied Meteorology, Vol. 44, Issue 4