  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 the 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 vast and 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 propose a large number of 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.
