Poisson Process Modelling of the Temporal Behavior of Volcanic Eruptions in the East African Rift System

Abstract

The social costs of volcanic eruptions are severe for eruptions of considerable magnitude. Understanding the temporal behavior of volcanic eruptions is thus key to hazard assessments and prevention of future loss of life and damage to property. This project aimed to demonstrate that the temporal behavior of volcanic eruptions in the East African Rift System can be effectively modeled using Poisson processes. The data used for the analysis was from the Smithsonian Institution’s Global Volcanism Program, which is freely available on line. Three models were chosen for analysis: homogeneous Poisson model, log-linear non-homogeneous Poisson model and Weibull power non-homogeneous Poisson model. The assumptions and theory underpinning Poisson processes were presented and the eruption data considered was shown toit into a Poissonian framework. The method of maximum likelihood was used to estimate the parameters of each model. The Akaike Information Criterion was used to select the optimal model. The log-linear non homogeneous Poisson model with intensity function l(t) = exp(ð€€€0:911036781+ 0:009976769t) was found to best t the empirical data with 95% confidence and based on it basic forecasts were issued. It was recommended that governments and disaster management authorities incorporate these findings in their preparedness frameworks as the log-linear model predicts an increasing trend in volcanic activity.