the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Technical Note: General Formulation For the Distribution Problem: Prognostic Assumed PDF Approach Based on The Maximum–Entropy Principle and The Liouville Equation
Abstract. A general formulation for the distribution problem is presented, which is applicable to frequency distributions of subgrid-scale variables, 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 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 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 modelling problems, is specifically applied to condensation growth of cloud droplets as a demonstration.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2023-2278', Anonymous Referee #2, 08 Feb 2024
- CC1: 'Reply on RC1', Jun-Ichi Yano, 20 Feb 2024
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RC2: 'Comment on egusphere-2023-2278', Anonymous Referee #1, 13 May 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2278/egusphere-2023-2278-RC2-supplement.pdf
- AC1: 'Reply on RC2', Jun-Ichi Yano, 27 May 2024
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