  We propose a representation of the Indian summer monsoon rainfall in terms of
a probabilistic model based on a Markov Random Field, consisting of discrete
state variables representing low and high rainfall at grid-scale and daily
rainfall patterns across space and in time. These discrete states are
conditioned on observed daily gridded rainfall data from the period 2000-2007.
The model gives us a set of 10 spatial patterns of daily monsoon rainfall over
India, which are robust over a range of user-chosen parameters as well as
coherent in space and time. Each day in the monsoon season is assigned
precisely one of the spatial patterns, that approximates the spatial
distribution of rainfall on that day. Such approximations are quite accurate
for nearly 95% of the days. Remarkably, these patterns are representative (with
similar accuracy) of the monsoon seasons from 1901 to 2000 as well. Finally, we
compare the proposed model with alternative approaches to extract spatial
patterns of rainfall, using empirical orthogonal functions as well as
clustering algorithms such as K-means and spectral clustering.
