Stochastic Convection Parameterization with Markov Chains in an Intermediate-Complexity GCM

Abstract

Conditional Markov chain (CMC) models have proven to be promising building blocks for stochastic convection parameterizations. In this paper, it is demonstrated how two different CMC models can be used as mass flux closures in convection parameterizations. More specifically, the CMC models provide a stochastic estimate of the convective area fraction that is directly proportional to the cloud-base mass flux. Since, in one of the models, the number of CMCs decreases with increasing resolution, this approach makes convection parameterizations scale aware and introduces stochastic fluctuations that increase with resolution in a realistic way. Both CMC models are implemented in a GCM of intermediate complexity. It is shown that with the CMC models, trained with observational data, it is possible to improve both the subgrid-scale variability and the autocorrelation function of the cloud-base mass flux as well as the distribution of the daily accumulated precipitation in the tropics. Hovmöller diagrams and wavenumber-frequency diagrams of the equatorial precipitation indicate that, in this specific GCM, convectively coupled equatorial waves are more sensitive to the mean cloud-base mass flux than to stochastic fluctuations. A smaller mean mass flux tends to increase the power of the simulated MJO and to diminish equatorial Kelvin waves.

The impact of stochastic physics on tropical rainfall variability in global climate models on daily to weekly time scales

“…Davini et al [] showed that stochastic parameterizations in EC‐Earth improve the simulation of tropical rainfall rate distributions and the Madden‐Julian Oscillation, and Wang et al [] found that the scheme of Plant and Craig [] improves the simulated tropical rainfall rate distribution in the NCAR Community Atmosphere Model as well. Dorrestijn et al [], Goswami et al [], and Peters et al [] showed that variants of the stochastic multicloud model of Khouider et al [] improved aspects of tropical variability simulated in different GCMs, and Frenkel et al [] showed similar results in a single‐column model context. Christensen et al [] also found that stochastic physics greatly reduced excessive El Niño variability in the NCAR Community Atmosphere Model, version 4 (CAM4).…”

“…Such parameterizations have been used in several numerical weather prediction models, including some run operationally, and have been found to improve forecast skill by both increasing the spread of ensemble forecasts and reducing the size of errors of the ensemble mean forecasts [e.g., Buizza et al, 1999;Palmer et al, 2009;Reynolds et al, 2011;Yonehara and M. Ujiie, 2011;Bouttier et al, 2012;Sušelj et al, 2014;Berner et al, 2015;Sanchez et al, 2016]. There are also numerous other promising schemes that have been or are being developed [e.g., Plant and Craig, 2008;Khouider et al, 2010;Bengtsson et al, 2013;Rochetin et al, 2014;Kober et al, 2015;Shutts, 2015;Dorrestijn et al, 2016;Sakradzija et al, 2016;Ollinaho et al, 2017;Peters et al, 2017].…”

Toward a Stochastic Relaxation for the Quasi‐Equilibrium Theory of Cumulus Parameterization: Multicloud Instability, Multiple Equilibria, and Chaotic Dynamics

“…For the sake of simplicity, Khouider et al (2010) neglected interactions between lattice sites by making the transition rates R kl depend exclusively on the large-scale predictors-independent on the realizations of X t outside the underlying site x. This simplification enabled the derivation of a coarse-grained stochastic birth-death process for the CAFs associated with each cloud type, in closed form without any further assumptions, and its successful validation and implementation in a hierarchy of climate models (Bergemann et al, 2017;Deng et al, 2015;Dorrestijn et al, 2016Dorrestijn et al, , 2013Frenkel et al, 2012;Goswami et al, 2017aGoswami et al, , 2017bPeters et al, 2013Peters et al, , 2017.…”

“…The microcells then make random transitions from one state to another according to prescribed probability rules depending on the large-scale state. Various flavors of the SMCM have been successfully implemented and tested in both wave-dynamical models of intermediate complexity and in comprehensive state-of-the-art climate models (Dorrestijn et al, 2016;Frenkel et al, 2012;Goswami et al, 2017a;2017b;Peters et al, 2017).…”

Climate SPHINX: evaluating the impact of resolution and stochastic physics parameterisations in the EC-Earth global climate model

“…There has been significant progress in developing stochastic schemes over the last decade, primarily for use in medium-range and seasonal ensemble forecasts (e.g. Plant and Craig, 2008;Khouider et al, 2010;Bengtsson et al, 2013;Grell and Freitas, 2013;Dorrestijn et al, 2016;Sakradzija et al, 2016;Ollinaho et al, 2016). These schemes introduce an element of randomness into physical parameterisation schemes to account for the impact of uncertain, unresolved processes on the resolved-scale flow (Palmer, 2012).…”