UNCERTAINTY IN FLOOD RISK ANALYSIS

This thesis is concerned with four aspects of flood risk analysis. The use of Bayesian estimation theory is central in all four aspects.; The first aspect concerns the parameter estimation for probability distributions used for flood data. It will be shown that a Bayesian approach gives better estimates than the usually preferred method of maximum likelihood. Lindley's approximation technique greatly simplifies the computation of all Bayes estimates.; The second aspect concerns the estimation of the probability that a flood will be exceeded in a future period. Then the uncertainty in the parameters of the probability distribution must be taken into account. This is done by using the predictive distribution as distinct from the descriptive distribution.; Next the customary assumption of stochastic independence for annual flood peak series is waived. A calculation of the Hurst statistic for about fifty annual flood series from all over Canada indicates that long term serial correlation is present in many rivers. This is shown to increase the uncertainty of the sample statistics and leads to a substantial upward assessment of the flood risk. A simple but efficient technique of modelling series with a high Hurst statistic is described.; The fourth aspect of flood risk analysis is an attempt at reducing the uncertainty in the estimation of the probability of exceedence of extreme floods. Taking the Red River at Emerson as a case study, a physically-based stochastic flood simulation model is developed using soil moisture, snowfall, snowmelt, and rainfall as input. The predictive distribution of flood peaks obtained from this model shows less uncertainty than the predictive distribution based only on the recorded flood peaks. This is not necessarily the whole answer. Updating the predictive distribution with historic or regional information using the simulation model is still possible, but has not been attempted in this thesis.; The research described in the thesis shows that parameter uncertainty appears to be more important than the question of plotting positions, parameter estimation by one method or another, or the choice between 2-parameter and 3-parameter probability models.