Next Article in Journal
Atmospheric Ozone and Methane in a Changing Climate
Next Article in Special Issue
Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models: COST Action ES0905 Final Report
Previous Article in Journal
Infrared Absorption Spectra, Radiative Efficiencies, and Global Warming Potentials of Newly-Detected Halogenated Compounds: CFC-113a, CFC-112 and HCFC-133a
Previous Article in Special Issue
Performance of Using Cascade Forward Back Propagation Neural Networks for Estimating Rain Parameters with Rain Drop Size Distribution
Atmosphere 2014, 5(3), 484-517; doi:10.3390/atmos5030484
Article

A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation

*  and
Alfred-Wegener-Institut Helmholtz-Zentrum für Polar und Meeresforschung, Bussestraße 24, 27570 Bremerhaven, Germany
* Author to whom correspondence should be addressed.
Received: 14 April 2014 / Revised: 23 June 2014 / Accepted: 3 July 2014 / Published: 24 July 2014
(This article belongs to the Special Issue Cloud and Precipitation)
View Full-Text   |   Download PDF [1537 KB, uploaded 24 July 2014]   |   Browse Figures

Abstract

This paper examines different distribution functions used in a three-moment parameterization scheme with regard to their influence on the implementation and the results of the parameterization scheme. In parameterizations with moment methods, the prognostic variables are interpreted as statistical moments of a drop size distribution, for which a functional form has to be assumed. In cloud microphysics, parameterizations are frequently based on gamma- and log-normal distributions, while for particle-laden flows in engineering, the beta-distribution is sometimes used. In this study, the three-moment schemes with beta-, gamma- and log-normal distributions are tested in a 1D framework for drop sedimentation, and their results are compared with those of a spectral reference model. The gamma-distribution performs best. The results of the parameterization with the beta- and the log-normal distribution have less similarity to the reference solution, particularly with regard to number density and rain rate. Theoretical considerations reveal that (depending on the type of the distribution function) only selected combinations of moments can be predicted together. Among these is the important combination of “number density, liquid water content, radar reflectivity” for all three distributions. Advection or source/sink terms can only be calculated under certain conditions on the moment values (positivity of the Hankel–Hadamard determinant). These are derived from mathematical theory (“moment problem”) and are more restrictive for three-moment than for two-moment schemes.
Keywords: cloud microphysics; drop sedimentation; parameterization; method of moments; Beta distribution; Gamma distribution; Log-Normal distribution; Hankel–Hadamard; moment problem cloud microphysics; drop sedimentation; parameterization; method of moments; Beta distribution; Gamma distribution; Log-Normal distribution; Hankel–Hadamard; moment problem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Export to BibTeX |
EndNote


MDPI and ACS Style

Ziemer, C.; Wacker, U. A Comparative Study of B-, Γ- and Log-Normal Distributions in a Three-Moment Parameterization for Drop Sedimentation. Atmosphere 2014, 5, 484-517.

View more citation formats

Article Metrics

Comments

Citing Articles

[Return to top]
Atmosphere EISSN 2073-4433 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert