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We propose a representation of the Indian summer monsoon rainfall in terms ofa probabilistic model based on a Markov Random Field, consisting of discretestate variables representing low and high rainfall at grid-scale and dailyrainfall patterns across space and in time. These discrete states areconditioned 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 overIndia, which are robust over a range of user-chosen parameters as well ascoherent in space and time. Each day in the monsoon season is assignedprecisely one of the spatial patterns, that approximates the spatialdistribution of rainfall on that day. Such approximations are quite accuratefor nearly 95% of the days. Remarkably, these patterns are representative (withsimilar accuracy) of the monsoon seasons from 1901 to 2000 as well. Finally, wecompare the proposed model with alternative approaches to extract spatialpatterns of rainfall, using empirical orthogonal functions as well asclustering algorithms such as K-means and spectral clustering.

A Discrete View of the Indian Monsoon to Identify Spatial Patterns of Rainfall