Characterizing the severity of hydrologic droughts

Abstract

Planning and management studies of water resources systems generally take into account the temporal and spatial variability of hydrological processes such as streamflows, particularly periods of extreme floods and droughts. This dissertation concerns with research on multiyear droughts that may occur in a given river system. One may obtain some relevant information about droughts from the observed streamflows of the river basin under consideration, however it has been shown in literature that the information one may obtain from the observed records is quite limited and uncertain because of the typical short sample sizes that are generally available. The main objective of this research is to characterize the severity of multiyear drought events at one or more sites in a river basin. In particular, mathematical models are developed to determine the return period and risk of extreme droughts. Also simulation experiments are conducted to verify the results obtained from the models. A deficit occurs where the yearly streamflow is smaller than a certain threshold water demand, otherwise surplus occurs. A drought of a given length l occurs where a consecutive number of deficits persists over the time period l. The sequence of surplus and deficit has been modeled by a discrete autoregressive or discrete autoregressive moving average processes. The single year deficit and the drought amount over the length l have been fitted using the beta distribution function. The drought occurrence probability in a given time period (risk) has been determined assuming that the first occurrence probability of drought is geometric. Furthermore, approximate expressions for determining the return period of drought have been developed. The results obtained from the referred models have been compared and verified using simulation experiments based on annual streamflow data of the Poudre, Colorado, and Niger rivers. It is concluded that the models developed are quite reasonable and provide fairly good estimates of drought properties. In addition, the referred models have been extended to characterize regional droughts and it is concluded that the proposed models give fairly good estimates of drought properties on a regional context. Lastly, tree ring indices have been utilized to reconstruct streamflows. A multivariate multiple linear regression model (MREXTN) including an autoregressive term and the random (noise) component was developed in such a way that streamflow variances, autocorrelations, and cross-correlations are properly taken into account. In addition, a procedure was developed that enables one selecting a single reconstructed flow sequence at each site from the multiple sequences that may arise because of using the noise term. The proposed model was tested against competing models using simulation experiments. It is concluded that model MREXTN compares favorably versus alternative models. Furthermore, the model was applied to reconstruct flows at the Colorado River system. It has been shown that the reconstructed flows provide useful information that enables one to analyze drought properties more accurately than using historical records alone.