Date of Award

1991

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Civil and Environmental Engineering

First Advisor

James F. Cruise

Abstract

Two alternative formulations of the exact extreme value stochastic flood model are presented in explaining the behaviour of observed flood series resulting from mixed climatological processes. As a marginal distribution for flood exceedances, a more flexible Weibull distribution is introduced in the place of the traditional exponential distribution. The asymptotic predictive performances of both the exponential and Weibull model formulations are evaluated in terms of relative bias (BIAS) and relative root mean square error (RMSE) of quantile estimation. The model with Weibull marginal performs well over the exponential for population conditions shown to exist in most of the observed flood series of Louisiana. In identifying a robust estimator for the Weibull distribution, the predictive performances of the principle of maximum entropy (POME) and probability weighted moments (PWM) are evaluated. On the basis of BIAS and RMSE of quantile estimation, the POME emerges as the most robust Weibull estimator for a wide range of population conditions. The compound model formulations for both exponential and Weibull marginals are discussed as against the respective simple model formulations in analyzing mixed flood populations. For a wide variation of the means of mixed populations, the predictive performances of both the simple and compound formulations of the exponential model are evaluated in terms of BIAS and RMSE of quantile estimation. Similarly, for a wide variation of the coefficient of variance of mixed populations, the performances of both formulations of the Weibull model are evaluated. The compound formulations of both the exponential and Weibull models demonstrate superior performances over the respective simple formulations if statistically distinct sub-populations are present in the mixed populations. The descriptive properties of those selected formulations of the exact extreme value stochastic flood model are tested for on the observed flood series in Louisiana. The flood series are hydroclimatically separated and tested for the assumption of identical distribution. The flood series are also tested for the Poisson assumption in ensuring the mutual independency. The validity of the exponential and Weibull distributions as marginals for flood exceedances are examined.

Pages

214

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