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Title: Analytical Solutions for Precipitation Size Distributions at Steady State

Abstract

Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of precipitating mass through size bins in a “cascade” yields a characteristic gamma distribution with a Marshall–Palmer exponential tail with respect to particle diameter. For rain, the principle parameters controlling size distribution shape are cloud droplet liquid water path and cloud updraft speed. Stronger updrafts lead to greater concentrations of large precipitating drops and a peak in the size distribution. Finally, the solutions provide a means for relating size distributions measured in the air or on the ground to cloud bulk microphysical and dynamic properties.

Authors:
 [1]
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  1. Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah
Publication Date:
Research Org.:
Univ. of Utah, Salt Lake City, UT (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1504304
Alternate Identifier(s):
OSTI ID: 1612468
Grant/Contract Number:  
SC0016282
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: 4; Journal ID: ISSN 0022-4928
Publisher:
American Meteorological Society
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Meteorology & Atmospheric Sciences; Cloud microphysics; Drop size distribution; Freezing precipitation

Citation Formats

Garrett, Timothy J. Analytical Solutions for Precipitation Size Distributions at Steady State. United States: N. p., 2019. Web. doi:10.1175/JAS-D-18-0309.1.
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Garrett, Timothy J. Analytical Solutions for Precipitation Size Distributions at Steady State. United States. https://doi.org/10.1175/JAS-D-18-0309.1
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Garrett, Timothy J. Mon . "Analytical Solutions for Precipitation Size Distributions at Steady State". United States. https://doi.org/10.1175/JAS-D-18-0309.1.
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@article{osti_1504304,
title = {Analytical Solutions for Precipitation Size Distributions at Steady State},
author = {Garrett, Timothy J.},
abstractNote = {Analytical solutions are derived for the steady-state size distributions of precipitating rain and snow particles assuming growth via collection of suspended cloud particles. Application of the Liouville equation to the transfer of precipitating mass through size bins in a “cascade” yields a characteristic gamma distribution with a Marshall–Palmer exponential tail with respect to particle diameter. For rain, the principle parameters controlling size distribution shape are cloud droplet liquid water path and cloud updraft speed. Stronger updrafts lead to greater concentrations of large precipitating drops and a peak in the size distribution. Finally, the solutions provide a means for relating size distributions measured in the air or on the ground to cloud bulk microphysical and dynamic properties.},
doi = {10.1175/JAS-D-18-0309.1},
journal = {Journal of the Atmospheric Sciences},
number = 4,
volume = 76,
place = {United States},
year = {Mon Apr 01 00:00:00 EDT 2019},
month = {Mon Apr 01 00:00:00 EDT 2019}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1175/JAS-D-18-0309.1
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Cited by: 9 works
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Works referenced in this record:

The Sensitivity of Microwave Remote Sensing Observations of Precipitation to Ice Particle Size Distributions
journal, March 2001

Temporal Evolution of Drop Spectra to Collisional Equilibrium in Steady and Pulsating Rain
journal, January 1987

Natural Variations in the Analytical Form of the Raindrop Size Distribution
journal, October 1983

Snow Size Spectra and Radar Reflectivity
journal, March 1970

Size Distribution of Raindrops Generated by their Breakup and Coalescence
journal, April 1971

Ensemble mean density and its connection to other microphysical properties of falling snow as observed in Southern Finland
journal, January 2016

  • Tiira, Jussi; Moisseev, Dmitri N.; von Lerber, Annakaisa
  • Atmospheric Measurement Techniques, Vol. 9, Issue 9
  • DOI: 10.5194/amt-9-4825-2016

On the Effects of Moisture on the Brunt-Väisälä Frequency
journal, October 1982

Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence
journal, November 1993

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
  • DOI: 10.1175/JAS-D-14-0065.1

High-Speed Optical Disdrometer for Rainfall Microphysical Observations
journal, February 2016

  • Testik, F. Y.; Rahman, M. K.
  • Journal of Atmospheric and Oceanic Technology, Vol. 33, Issue 2
  • DOI: 10.1175/JTECH-D-15-0098.1

Convective initiation uncertainties without trigger or stochasticity: probabilistic description by the Liouville equation and Bayes' theorem
journal, April 2017

  • Yano, Jun‐Ichi; Ouchtar, Eïda
  • Quarterly Journal of the Royal Meteorological Society, Vol. 143, Issue 705
  • DOI: 10.1002/qj.3064

The Distribution with size of Aggregate Snowflakes
journal, October 1958

The Distribution of Raindrops with size
journal, August 1948

Evolution of Snow-Size Spectra in Cyclonic Storms. Part II: Deviations from the Exponential Form
journal, August 1991

First in situ observations of binary raindrop collisions
journal, January 2017

  • Testik, F. Y.; Rahman, M. K.
  • Geophysical Research Letters, Vol. 44, Issue 2
  • DOI: 10.1002/2017GL072516

Observed influence of riming, temperature, and turbulence on the fallspeed of solid precipitation
journal, September 2014

  • Garrett, Timothy J.; Yuter, Sandra E.
  • Geophysical Research Letters, Vol. 41, Issue 18
  • DOI: 10.1002/2014GL061016

Do all raindrops fall at terminal speed?
journal, January 2009

  • Montero-Martínez, Guillermo; Kostinski, Alexander B.; Shaw, Raymond A.
  • Geophysical Research Letters, Vol. 36, Issue 11
  • DOI: 10.1029/2008GL037111

Statistical Theory on the Functional Form of Cloud Particle Size Distributions
journal, August 2018

Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft
journal, May 1976

Use of Mass- and Area-Dimensional Power Laws for Determining Precipitation Particle Terminal Velocities
journal, June 1996

Modes of growth in dynamic systems
journal, April 2012

  • Garrett, Timothy J.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue 2145
  • DOI: 10.1098/rspa.2012.0039

Evolution of Raindrop Spectra. Part I: Solution to the Stochastic Collection/Breakup Equation Using the Method of Moments
journal, November 1988

Single-drop fragmentation determines size distribution of raindrops
journal, July 2009

  • Villermaux, Emmanuel; Bossa, Benjamin
  • Nature Physics, Vol. 5, Issue 9
  • DOI: 10.1038/nphys1340

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
  • DOI: 10.1029/JC079i015p02185

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
  • DOI: 10.1175/JAS-D-14-0011.1

Size Distributions of Hydrometeors: Analysis with the Maximum Entropy Principle
journal, January 2016

  • Yano, Jun-Ichi; Heymsfield, Andrew J.; Phillips, Vaughan T. J.
  • Journal of the Atmospheric Sciences, Vol. 73, Issue 1
  • DOI: 10.1175/JAS-D-15-0097.1
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