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Precipitation is a large-scale, spatio-temporally heterogeneous phenomenon,with frequent anomalies exhibiting unusually high or low values. We use MarkovRandom Fields (MRFs) to detect spatio-temporally coherent anomalies in griddedannual rainfall data across India from 1901-2005. MRFs are undirected graphicalmodels where each node is associated with a \{location,year\} pair, with edgesconnecting nodes representing adjacent locations or years. Some nodes representobservations of precipitation, while the rest represent unobserved(\emph{latent}) states that can take one of three values: high/low/normal. TheMRF represents a probability distribution over the variables, using \emph{nodepotential} and \emph{edge potential} functions defined on nodes and edges ofthe graph. Optimal values of latent state variables are estimated by maximizingthe posterior probability of the observations, using Gibbs sampling. Edgepotentials enforce spatial and temporal coherence, and node potentialsinfluence threshold for anomalies by affecting the prior probabilities of thestates. The model can be tuned to recover anomalies detected by threshold-basedmethods. The competing influences of spatial and temporal coherence can beadjusted through edge potentials.  We study spatio-temporal properties of rainfall anomalies discovered by thismethod, using suitable measures. We identify nonstationarities in occurrence ofpositive and negative anomalies between the first and second halves of the 20thcentury. We find that between these periods, there has been decrease inrainfall during June-September (JJAS) and an increase during other months.These effects are highlighted prominently in the statistics of anomalies.Properties of anomalies learnt from this approach could present tests ofregional-scale rainfall simulations by climate models and statisticalsimulators.

Detection of Spatiotemporally Coherent Rainfall Anomalies Using Markov Random Fields