Calibration of the Stochastic Multicloud Model using Bayesian Inference

The Stochastic Multicloud Model (SMCM) was recently developed (Khouider, Biello, and Majda, 2010) to represent the missing variability in global climate models due to unresolved features of organized tropical convection. This research aims at finding a robust calibration methodology for the SMCM to estimate key model parameters from data. We formulate the calibration problem within a Bayesian framework to derive the posterior distribution over the model parameters. The model likelihood function involves the calculation of a large matrix exponential, which we maintain computationally feasible using a parallel Uniformization method. Sampling of the high dimensional posterior distribution is achieved using the Markov Chain Monte Carlo technique. The robustness of the calibration procedure is tested using synthetic data produced by a simple toy climate model. A sensitivity study to the length of the data time series and to the prior distribution is presented, and a sequential learning strategy is also tested.