Variational Bayes Inference for Stochastic Convection Parametrizations

In recent years, the stochastic multicloud model (SMCM) framework, which uses a microscopic lattice system to mimic the interactions and lifecycle of various tropical cloud types, has been used to successfully represent the subgrid variability in climate models (Khouider, 2010). The SMCM uses a set of sensitive timescale parameters to modulate the transition probabilities between different cloud type states. The timescales are typically learned from radar data using a Bayesian inference algorithm. The complexity of the SMCM means that the associated likelihood function is not known in closed form, and a Markov Chain Monte Carlo (MCMC) sampling approach is used during the learning process (De La Chevrotiere, 2014). However, the MCMC method is slow to converge and leads to prohibitively expensive computations, which severely occludes the use of sufficiently long timeseries, spanning multiple phases of intraseasonal oscillation systems, such as the MJO. A developing alternative, derived from machine learning, uses variational inference (VI), to find an optimal proposal distribution among a judiciously chosen subspace of finite dimension. VI has been shown to significantly speed up Bayesian inference traditionally reliant on brute force sampling, such as MCMC. VI has become a rapidly emergent field among other machine learning methods, boasting a wide array of different techniques (Blei, 2017). Here, a black box variational inference approach is comprehensively tested for time series parameters, using new adaptive learning rates for noisy gradients and variance reduction techniques. Preliminary VI results are compared to MCMC performance on synthetic cloud data to demonstrate its effectiveness and usefulness in the context of the SMCM.