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The advection–condensation model and water‐vapour probability density functions
Author(s) -
Sukhatme Jai,
Young William R.
Publication year - 2011
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.869
Subject(s) - humidity , water vapor , probability density function , advection , relative humidity , sink (geography) , atmospheric sciences , saturation (graph theory) , meteorology , environmental science , mechanics , mathematics , thermodynamics , physics , statistics , geography , cartography , combinatorics
The statistically steady humidity distribution resulting from an interaction of advection, modelled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modelled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep‐tropical southern boundary of the domain and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker–Planck equation delivers a simple expression for the resulting probability density function ( PDF ) of the water‐vapour field and also the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDF s of specific and relative humidity are broad and non‐Gaussian. The domain‐averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDF s derived from the ERA interim dataset. Copyright © 2011 Royal Meteorological Society