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A correlated stochastic model for the large‐scale advection, condensation and diffusion of water vapour
Author(s) -
Beucler Tom
Publication year - 2016
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2768
Subject(s) - advection , monte carlo method , statistical physics , turbulence , discretization , mechanics , stochastic modelling , condensation , water content , saturation (graph theory) , physics , thermodynamics , mathematics , geology , mathematical analysis , statistics , geotechnical engineering , combinatorics
The statistically steady distribution of water vapour and its characteristics are studied in the framework of the Ornstein–Uhlenbeck (OU) turbulent dispersion model. Particles are advected by a stochastic velocity field with a finite time correlation, and condense as soon as their moisture content exceeds a local saturation value. We discretize the OU model to a finite number of velocity values, and find simple analytical solutions for the bimodal distribution of water vapour and the non‐diffusive moisture flux, which perfectly agree with the corresponding Monte‐Carlo simulations. Furthermore, we show that these simple models produce results that approximate well the OU Monte‐Carlo simulations, suggesting that they could be used as general tools to understand correlated stochastic processes that involve condensation.