A discrete view of the Indian monsoon to identify spatial patterns of rainfall

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 to 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 and 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 and clustering algorithms such as K-means and spectral clustering