Detection of spatiotemporally coherent rainfall anomalies using Markov Random Fields

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 spatio-temporally coherent anomalies in gridded annual rainfall data across India from 1901-2005. 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 (\emph{latent}) states that can take one of three values: high/low/normal. The MRF represents a probability distribution over the variables, using \emph{node potential} and \emph{edge potential} functions defined on nodes and edges of the graph. Optimal values of latent state variables are estimated by maximizing the posterior probability of the observations, using Gibbs sampling. Edge potentials enforce spatial and temporal coherence, and node potentials influence threshold for anomalies by affecting the prior probabilities of the states. The model can be tuned to recover anomalies detected by threshold-based methods. The competing influences of spatial and temporal coherence can be adjusted through edge potentials. We study spatio-temporal properties of rainfall anomalies discovered by this method, using suitable measures. We identify nonstationarities in occurrence of positive and negative anomalies between the first and second halves of the 20th century. We find that between these periods, there has been decrease in rainfall 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 of regional-scale rainfall simulations by climate models and statistical simulators.

[1]  Edward R. Cook,et al.  Asian Monsoon Failure and Megadrought During the Last Millennium , 2010, Science.

[2]  J. Dracup,et al.  Drought monitoring , 1991 .

[3]  P. Xavier,et al.  Increasing Trend of Extreme Rain Events Over India in a Warming Environment , 2006, Science.

[4]  Christopher S. McMahan,et al.  Sampling Strategies for Fast Updating of Gaussian Markov Random Fields , 2017, The American statistician.

[5]  Aditi Sharma,et al.  Spatial Data Mining for Drought Monitoring: An Approach Using temporal NDVI and Rainfall Relationship , 2006 .

[6]  Persi Diaconis,et al.  The Markov chain Monte Carlo revolution , 2008 .

[7]  Shashi Shekhar,et al.  Spatiotemporal Data Mining: A Computational Perspective , 2015, ISPRS Int. J. Geo Inf..

[8]  Hongxiang Yan,et al.  A regional Bayesian hierarchical model for flood frequency analysis , 2015, Stochastic Environmental Research and Risk Assessment.

[9]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[10]  Hans-Peter Kriegel,et al.  OPTICS: ordering points to identify the clustering structure , 1999, SIGMOD '99.

[11]  V. Singh,et al.  Uncertainty and variability in bivariate modeling of hydrological droughts , 2016, Stochastic Environmental Research and Risk Assessment.

[12]  H. Rue.  Fast sampling of Gaussian Markov random fields , 2000 .

[13]  M. Katzfuss,et al.  A General Framework for Vecchia Approximations of Gaussian Processes , 2017, 1708.06302.

[14]  Ashish Sharma,et al.  Global assessment of flood and storm extremes with increased temperatures , 2017, Scientific Reports.

[15]  Julien Stoehr,et al.  A review on statistical inference methods for discrete Markov random fields , 2017, 1704.03331.

[16]  C. Santos,et al.  Analysis of precipitation time series using the wavelet transform , 2005, Sociedade & Natureza.

[17]  O. N. Dhar,et al.  Hydrometeorological Aspects of Floods in India , 2003 .

[18]  Radford M. Neal.  Probabilistic Inference Using Markov Chain Monte Carlo Methods , 2011 .

[19]  Gemma Narisma,et al.  Abrupt changes in rainfall during the twentieth century , 2007 .

[20]  D. S. Pai,et al.  On the observed variability of monsoon droughts over India , 2013 .

[21]  P. Shi,et al.  Analysis of dry/wet conditions using the standardized precipitation index and its potential usefulness for drought/flood monitoring in Hunan Province, China , 2013, Stochastic Environmental Research and Risk Assessment.

[22]  Keith D. C. Stoodley,et al.  Time Series Analysis: Theory and Practice I , 1982 .

[23]  Sudipto Banerjee,et al.  Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets , 2014, Journal of the American Statistical Association.

[24]  M. Rouault,et al.  Intensity and spatial extent of droughts in southern Africa , 2005 .

[25]  VARUN CHANDOLA,et al.  Anomaly detection: A survey , 2009, CSUR.

[26]  Slava Kisilevich,et al.  Spatio-temporal clustering , 2010, Data Mining and Knowledge Discovery Handbook.

[27]  B. Carlin,et al.  Accelerating Computation in Markov Random Field Models for Spatial Data via Structured MCMC , 2003 .

[28]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[29]  Xiaodong Liu,et al.  A hybrid segmentation method for multivariate time series based on the dynamic factor model , 2017, Stochastic Environmental Research and Risk Assessment.

[30]  A. Ganguly,et al.  Lack of uniform trends but increasing spatial variability in observed Indian rainfall extremes , 2012 .

[31]  Mathieu Vrac,et al.  Clustering of Maxima: Spatial Dependencies among Heavy Rainfall in France , 2013 .

[32]  Qiang Fu,et al.  Drought Detection of the Last Century: An MRF-based Approach , 2012, SDM.

[33]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .

[34]  A. Gelfand,et al.  Handbook of spatial statistics , 2010 .