A Stochastic Characterization of Palmer Drought Severity Index

Abstract

The Palmer Drought Severity Index (PDSI) combines a set of key meteorologic and hydrologic variables to assign a numerical value for drought severity which can be used as a unified drought scale for comparison among different geographical regions. The index values are further put in several drought severity classes with highest class being the severest drought. This class assignment is taken advantage of, to formulate a time varying (non-homogeneous) Markov chain approach for characterizing the underlying drought stochastic process. The approach identifies drought prone geographical regions, persisting drought classes, periods of return to a particular drought class, and yields short term predictions for future droughts. A time homogenous Markov chain is also formulated. The average of the statistics taken over all months from the non-homogeneous Markov chain agrees quite well with that of the time homogeneous chain. Monthly statistics from the non-homogeneous chain also compare very well with the empirical results obtained with the aid of 1152 months of data for the years 1895–1990 belonging to two climatic divisions in Virginia, USA, namely the Tidewater Region the Southwest Mountains Regions. The Tidewater Region is short of water as opposed to the Southwest Mountains Regions which is water rich.