Technical note : General formulation for the distribution problem - prognostic assumed probability density function (PDF) approach based on the maximum-entropy principle and the Liouville equation
Yano, Jun Ichi ; Larson, Vincent E. and Phillips, Vaughan T.J. LU
(2025)
In Atmospheric Chemistry and Physics
25(16).
p.9357-9386
- Abstract
A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables and hydrometeor size distributions, as well as to probability distributions characterizing data uncertainties. The general formulation is presented based upon two well-known basic principles: the maximum-entropy principle and the Liouville equation. The maximum-entropy principle defines the most likely general distribution form if necessary constraints are specified. This paper proposes to specify these constraints as the output variables to be used in a host model. Once a general distribution form is defined, the problem of the temporal evolution of the distribution reduces to that of predicting a... (More)
A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables and hydrometeor size distributions, as well as to probability distributions characterizing data uncertainties. The general formulation is presented based upon two well-known basic principles: the maximum-entropy principle and the Liouville equation. The maximum-entropy principle defines the most likely general distribution form if necessary constraints are specified. This paper proposes to specify these constraints as the output variables to be used in a host model. Once a general distribution form is defined, the problem of the temporal evolution of the distribution reduces to that of predicting a small number of parameters characterizing it. This paper derives prognostic equations for these parameters from the Liouville equation. The developed formulation, which is applicable to a wide range of atmospheric modeling problems, is specifically applied to the condensation growth of cloud droplets as a demonstration.
(Less)
- author
- Yano, Jun Ichi
; Larson, Vincent E.
and Phillips, Vaughan T.J.
LU
- organization
- publishing date
- 2025-08
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Atmospheric Chemistry and Physics
- volume
- 25
- issue
- 16
- pages
- 30 pages
- publisher
- Copernicus GmbH
- external identifiers
-
- scopus:105014760641
- ISSN
- 1680-7316
- DOI
- 10.5194/acp-25-9357-2025
- language
- English
- LU publication?
- yes
- id
- db3135de-0e84-4365-85e3-dd01561ed196
- date added to LUP
- 2025-10-20 13:57:35
- date last changed
- 2025-10-20 13:58:23
@article{db3135de-0e84-4365-85e3-dd01561ed196,
abstract = {{<p>A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables and hydrometeor size distributions, as well as to probability distributions characterizing data uncertainties. The general formulation is presented based upon two well-known basic principles: the maximum-entropy principle and the Liouville equation. The maximum-entropy principle defines the most likely general distribution form if necessary constraints are specified. This paper proposes to specify these constraints as the output variables to be used in a host model. Once a general distribution form is defined, the problem of the temporal evolution of the distribution reduces to that of predicting a small number of parameters characterizing it. This paper derives prognostic equations for these parameters from the Liouville equation. The developed formulation, which is applicable to a wide range of atmospheric modeling problems, is specifically applied to the condensation growth of cloud droplets as a demonstration.</p>}},
author = {{Yano, Jun Ichi and Larson, Vincent E. and Phillips, Vaughan T.J.}},
issn = {{1680-7316}},
language = {{eng}},
number = {{16}},
pages = {{9357--9386}},
publisher = {{Copernicus GmbH}},
series = {{Atmospheric Chemistry and Physics}},
title = {{Technical note : General formulation for the distribution problem - prognostic assumed probability density function (PDF) approach based on the maximum-entropy principle and the Liouville equation}},
url = {{http://dx.doi.org/10.5194/acp-25-9357-2025}},
doi = {{10.5194/acp-25-9357-2025}},
volume = {{25}},
year = {{2025}},
}