Bayesian Inference for the Stochastic Multicloud Model

The state-of-the-art cumulus parametrizations used in global climate models (GCM) are based on the quasi-equilibrium theory, which amounts to assuming a large separation of scales between convective processes and the grid-scale eddies. However, deep convection in the tropics is organized into a hierarchy of scales ranging from the convective cell of roughly one to ten kilometres to mesoscale cloud clusters of hundreds of kilometres to synoptic and planetary scale wave disturbances comprising the Madden-Julian oscillation (MJO) and a spectrum of convectively coupled waves (CCWs). In fact, the failure of GCMs to capture well the tropical variability associated with the MJO and CCWs is often associated with the poor performance of the underlying cumulus parameterizations.

Recently, Khouider et al. (2010, Comm. Math. Sci., 8, 187-216) developed a stochastic multicloud model (SMC) to represent the missing variability in global climate models due to unresolved features of organized tropical convection. In the SMC, convective elements are viewed as Markov processes with state transition probabilities that are dependent on the large scale environmental variables, like the convective available potential energy (CAPE) and middle troposphere moisture content. The functional dependence of the transition probabilities upon those exogenous factors are deduced from physical intuition based on recent satellite observations, and are successfully tested a posteriori, for different ranges of the parameters involved, in the simple setting of one-column and slab equatorial circulation models (Khouider et al., 2010, Comm. Math. Sci., 8, 187-216, and Frenkel et al., 2011, J. Atmos. Sci. (in press)). We propose here an information theoretic approach to the model, using a Bayesian reasoning to infer those unobservable parameters from simulated and in situ data, using namely cloud cover fractions and large scale variables from the Giga LES simulations (Khairoutdinov et al., 2009, J. Adv. Model. Earth Syst., 1, 15) and the DYNAMO field campaign (http://www.eol.ucar.edu/projects/dynamo/), respectively. The posterior distributions are approximated using Monte Carlo Markov Chain (MCMC) simulation technique, which enables simulation from a distribution by embedding it as a limiting distribution of a Markov chain and simulating from the chain until it approaches equilibrium.

We present some preliminary diagnostic tests of our posterior simulator using true data generated from the one-column SMC, for different prior assumptions. We perform numerical posterior predictive checks to show that inferences from the model are consistent with data, and discuss the problem of sensitivity to the prior distribution. This is a work in progress, part of M. De La Chevrotière's PhD thesis.