Modeling of stationary and non-stationary hydrologic processes

Abstract

This dissertation touches on several aspects related to modeling of stationary and non-stationary hydrologic processes. New methods for regional frequency analysis of extreme events are developed, under the concept of the population index flood (PIF). In this method population quantities are used for estimating the index flood, instead of using the sample mean as is done in traditional index flood methods. PIF models are developed for commonly used distributions in hydrology, and procedures for estimating the standard error of at-site quantile estimators are also developed. Extensive simulation experiments are used to test the proposed methods and procedures based on the PIF models. In addition, a Pareto model is developed utilizing only the largest sample order statistics for parameter estimation based on maximum likelihood, and exact formulas for the mean-squared-error of quantile estimators are also derived. Furthermore, shifting mean models are developed for modeling processes that exhibit a type of non-stationarity in the mean, that is represented by sudden shifting patterns. The shifting mean models are formulated under both univariate and multivariate frameworks, and with and without autoregressive AR(1) persistence. Procedures for param eter estimation are explained in detail. The multivariate model is formulated as a contemporaneous shifting mean model and it is further mixed with contemporaneous ARMA models. That is, the multivariate model is capable of modeling mixed systems, where only part of the sites exhibit sudden shifting patterns and the others sites can be represented by a CARMA(p,g) model. The proposed shifting mean models are capable of preserving key statistical characteristics, and in addition the lag zero spatial correlation in the multivariate models. Numerous examples are presented throughout the dissertation for illustrating the different procedures.