Drought Analysis Based on a Marked Cluster Poisson Model

Abstract

This paper presents an operational definition of drought events based on an “excess over threshold” approach applied on rainfall series and develops a stochastic model for describing droughts defined in that way. The model consists of a Poisson cluster process to represent drought occurrence and a marked process composed of three series of random variables (duration, deficit, and maximum intensity) to describe drought severity; it is theoretically justified, and adequate procedures to check its validity are suggested and applied on five Spanish rainfall series. Useful parameters for the design and planning of water resource systems, together with their confidence intervals, are estimated from the model. Abstract This paper presents an operational definition of drought events based on an “excess over threshold” approach applied on rainfall series and develops a stochastic model for describing droughts defined in that way. The model consists of a Poisson cluster process to represent drought occurrence and a marked process composed of three series of random variables (duration, deficit, and maximum intensity) to describe drought severity; it is theoretically justified, and adequate procedures to check its validity are suggested and applied on five Spanish rainfall series. Useful parameters for the design and planning of water resource systems, together with their confidence intervals, are estimated from the model.