Application of Gamma Autoregressive Model to Analysis of Dry Periods

Abstract

In water resources projects the determination of the dry period characteristics of rivers is important especially in arid and semiarid regions. Classical run and range analyses are based mainly on the use of the first-order autoregressive model, AR(1). However, some other models with gamma type marginal distribution have recently been developed. Unlike the classical approaches, these models do not require variable transformation. In this study, the gamma autoregressive (GAR) model is used to determine the statistical run and range parameter values of the annual flow series. The model is applied to the 10 Turkish rivers that have longest records and largest drainage basins. The GAR(1) model results are compared with those of the classical first-order autoregressive model. The statistical run and range parameter values of the generated series based on the GAR(1) model are practically the same as those of the AR(1) model when bias adjustments are made to the AR(1) model, whereas the AR(1) model gives unsatisfactory results without the bias adjustments.