[Stoch] Preprint "A stochastic model for the transition to stong convection" by Stechmann and Neelin

[Sam Stechmann]

Hi All

Below are a link and the abstract for a paper by me and David Neelin, "A 
stochastic model for the transition to stong convection," which was 
recently accepted to JAS.

Best

Sam Stechmann

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A stochastic model for the transition to stong convection
by Stechmann and Neelin
to appear in JAS

Preprint:

https://www.math.wisc.edu/~stech/publications/StechmannNeelin2011.pdf

Abstract:

A simple stochastic model is designed and analyzed in order to further 
understand the transition to strong convection. The transition has been 
characterized recently in observational data by an array of statistical 
measures, including (i) a sharp transition in mean precipitation, and a 
peak in precipitation variance, at a critical value of column water vapor 
(CWV), (ii) approximate power-law in the probability density of 
precipitation event size, (iii) exponential tails in the probability 
density of CWV values, when conditioned on either precipitating or 
non-precipitating locations, and (iv) long and short autocorrelation times 
of CWV and precipitation, respectively, with approximately exponential and 
power-law decays in their autocorrelation functions, respectively. The 
stochastic model presented here captures these four statistical features 
in time series of CWV and precipitation at a single location. In addition, 
analytic solutions are given for the exponential tails in (iii), which 
directly relates the tails to model parameters. The model parameterization 
includes three stochastic components: a stochastic trigger turns the 
convection on and off (a two-state Markov jump process), and stochastic 
closures represent variability in precipitation and in external forcing 
(Gaussian white noise). This stochastic external forcing is seen to be 
crucial for obtaining extreme precipitation events with high CWV and long 
lifetimes, as it can occasionally compensate the heavy precipitation and 
encourage more of it. This stochastic model can also be seen as a 
simplified stochastic convective parameterization, and it demonstrates 
simple ways to turn a deterministic parameterization - the trigger and/or 
closure - into a stochastic one.