Use of a two-component exponential distribution in partial duration modelling of hydrological droughts in Zimbabwean rivers

Abstract

An investigation of hydrological droughts has been conducted, based on the truncation level approach: each drought event is characterized by its duration and deficit volume. The truncation level is defined to reflect the expected natural water availability and, therefore, is evaluated monthly as a fixed percentile of the monthly flow-duration curve. Thus, the problem of expected zero flow of ephemeral rivers during the dry season is taken care of. The data material consists of daily discharge data from ten Zimbabwean rivers, and both ephemeral and perennial rivers are included in the analysis. The partial duration series approach is used to predict the severity of future droughts, i.e. the T-year events. The two-component exponential distribution is adopted as exceedence distribution for both duration and deficit volume. The parameters of the two-component exponential distribution are estimated using the maximum likelihood method. A method for calculating the T-year event and an approximate expression of the uncertainty of the T-year events have been developed. An observed problem of underestimation of observed deficit volumes is reduced by the introduction of censoring in the partial duration series. A better description of the observed events has been obtained by censoring the duration and deficit volume series. A relationship between optimal censoring and the coefficient of variation of the drought series has been indicated.