Bayesian approach to Spatio-temporally Consistent Simulation of Daily Monsoon Rainfall over India

Simulation of rainfall over a region for long time-sequences can be very useful for planning and policy-making, especially in India where the economy is heavily reliant on monsoon rainfall. However, such simulations should be able to preserve known spatial and temporal characteristics of rainfall over India. General Circulation Models (GCMs) are unable to do so, and various rainfall generators designed by hydrologists using stochastic processes like Gaussian Processes are also difficult to apply over the highly diverse landscape of India. In this paper, we explore a series of Bayesian models based on conditional distributions of latent variables that describe weather conditions at specific locations and over the whole country. During parameter estimation from observed data, we use spatio-temporal smoothing using Markov Random Field so that the parameters learnt are spatially and temporally coherent. Also, we use a nonparametric spatial clustering based on Chinese Restaurant Process to identify homogeneous regions, which are utilized by some of the proposed models to improve spatial correlations of the simulated rainfall. The models are able to simulate daily rainfall across India for years, and can also utilize contextual information for conditional simulation. We use two datasets of different spatial resolutions over India, and focus on the period 2000--2015. We consider metrics to study the spatio-temporal properties of the simulations by the models, and compare them with the observed data to evaluate the strengths and weaknesses of the models.