Probabilistic Formulation of Spatio-temporal Drought Pattern

Abstract

Meteorological and hydrological drought occurrences along time and space take place randomly and therefore their scientific quantifications are possible by the probabilistic methods. Herein drought occurrences are assumed to have spatial and temporal stationarity with underlying independent generating mechanism. The drought stricken area is considered as composed of mutually exclusive and collectively exhaustive subareas each with different probability of drought occurrence. Two types of spatio-temporal drought formulations are presented. The first is referred to as the regional persistence model and it assumes that if any subarea is stricken by drougth it will remain to stay in this state till the whole area is covered by drought. The second alternative is multi-seasonal model and it is based on the assumption that drought stricken area might recover and have wet period during the course of time. The necessary theoretical probability distribution functions for partially drought stricken areas are derived based on the Bernoulli trials both along time and space axis. The expectation and variance parameters are derived based on the percentage of drought stricken area and the basic wet and dry spell probabilities. Necessary charts for practical purposes are prepared and interpretations are given.