Detection of spatiotemporally coherent rainfall anomalies using Markov Random Fields

Abstract

Precipitation is a large-scale, spatio-temporally heterogeneous phenomenon, with frequent anomalies exhibiting unusually high or low values. We use Markov Random Fields (MRFs) to detect anomalies in gridded annual rainfall data across India from 1901 to 2005, such that these anomalies are spatio-temporally coherent, but permitting flexibility in size and spatial and temporal extent. MRFs are undirected graphical models where each node is associated with a {location, year} pair, with edges connecting nodes representing adjacent locations or years. Some nodes represent observations of precipitation, while the rest represent unobserved (latent) states that can take one of three values: high/low/normal. The MRF represents a probability distribution over the variables, using potential functions defined on edges of the graph. In our model, these functions enforce spatial and temporal coherence of the latent variables. Optimal values of latent state variables are estimated by maximizing their posterior probability using Gibbs sampling, conditioned on the observations. From these latent states we can identify spatio-temporally extended rainfall anomalies, both positive and negative. We study various properties of rainfall anomalies discovered by this method, such as spatio-temporal size and intensity. Identification of such rainfall anomalies can help in monitoring and studying floods and droughts in India. Properties of anomalies derived from this approach could be used to test climate models and statistical simulators.