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Size Distributions of Hydrometeors: Analysis with the Maximum Entropy Principle

Yano, Jun-Ichi; Heymsfield, Andrew J. and Phillips, Vaughan LU (2016) In Journal of Atmospheric Sciences 73(1). p.95-108
Abstract
This paper proposes that the maximum entropy principle can be used for determining the drop size distribution of hydrometeors. The maximum entropy principle can be applied to any physical systems with many degrees of freedom in order to determine a distribution of a variable when the following are known: 1) the restriction variable that leads to a homogeneous distribution without constraint and 2) a set of integrals weighted by the distribution, such as mean and variance, that constrain the system. The principle simply seeks a distribution that gives the maximum possible number of partitions among all the possible states. A continuous limit can be taken by assuming a constant bin size for the restriction variable.This paper suggests that... (More)
This paper proposes that the maximum entropy principle can be used for determining the drop size distribution of hydrometeors. The maximum entropy principle can be applied to any physical systems with many degrees of freedom in order to determine a distribution of a variable when the following are known: 1) the restriction variable that leads to a homogeneous distribution without constraint and 2) a set of integrals weighted by the distribution, such as mean and variance, that constrain the system. The principle simply seeks a distribution that gives the maximum possible number of partitions among all the possible states. A continuous limit can be taken by assuming a constant bin size for the restriction variable.This paper suggests that the drop mass is the most likely restriction variable, and the laws of conservation of total bulk mass and of total vertical drop mass flux are two of the most likely physical constraints to a hydrometeor drop size distribution. Under this consideration, the distribution is most likely constrained by the total bulk mass when an ensemble of drops under the coalescence-breakup process is confined inside a closed box. Alternatively, for an artificial rain produced from the top of a high ceiling under a constant mass flux of water fall, the total drop mass flux is the most likely constraint to the drop size distribution. Preliminary analysis of already-published data is not inconsistent with the above hypotheses, although the results are rather inconclusive. Data in the large drop size limit are required in order to reach a more definite conclusion. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Physical Meteorology and Climatology, Cloud microphysics
in
Journal of Atmospheric Sciences
volume
73
issue
1
pages
95 - 108
publisher
Amer Meteorological Soc
external identifiers
  • wos:000367397700001
  • scopus:84957705315
ISSN
1520-0469
DOI
10.1175/JAS-D-15-0097.1
language
English
LU publication?
yes
id
1552d9fd-320b-4aaa-ae03-d51661048610 (old id 8539922)
date added to LUP
2016-01-26 11:51:56
date last changed
2017-01-01 03:07:27
@article{1552d9fd-320b-4aaa-ae03-d51661048610,
  abstract     = {This paper proposes that the maximum entropy principle can be used for determining the drop size distribution of hydrometeors. The maximum entropy principle can be applied to any physical systems with many degrees of freedom in order to determine a distribution of a variable when the following are known: 1) the restriction variable that leads to a homogeneous distribution without constraint and 2) a set of integrals weighted by the distribution, such as mean and variance, that constrain the system. The principle simply seeks a distribution that gives the maximum possible number of partitions among all the possible states. A continuous limit can be taken by assuming a constant bin size for the restriction variable.This paper suggests that the drop mass is the most likely restriction variable, and the laws of conservation of total bulk mass and of total vertical drop mass flux are two of the most likely physical constraints to a hydrometeor drop size distribution. Under this consideration, the distribution is most likely constrained by the total bulk mass when an ensemble of drops under the coalescence-breakup process is confined inside a closed box. Alternatively, for an artificial rain produced from the top of a high ceiling under a constant mass flux of water fall, the total drop mass flux is the most likely constraint to the drop size distribution. Preliminary analysis of already-published data is not inconsistent with the above hypotheses, although the results are rather inconclusive. Data in the large drop size limit are required in order to reach a more definite conclusion.},
  author       = {Yano, Jun-Ichi and Heymsfield, Andrew J. and Phillips, Vaughan},
  issn         = {1520-0469},
  keyword      = {Physical Meteorology and Climatology,Cloud microphysics},
  language     = {eng},
  number       = {1},
  pages        = {95--108},
  publisher    = {Amer Meteorological Soc},
  series       = {Journal of Atmospheric Sciences},
  title        = {Size Distributions of Hydrometeors: Analysis with the Maximum Entropy Principle},
  url          = {http://dx.doi.org/10.1175/JAS-D-15-0097.1},
  volume       = {73},
  year         = {2016},
}