Spectral estimation of flood risks
A model for estimating seasonal flood risks which uses flow readings which are equally spaced in time is presented in this thesis. The model is referred to as the Spectral Model. This model can be used to estimate the probability of at least 1 exceedance of given critical levels. The model is based on the Rice distribution for peaks of a Gaussian stochastic process, whose parameters are associated with the spectral moments of the process. In the simpler form of the model, peaks are assumed independent. Simulation results obtained using realisation of Gaussian AR(1) processes indicated that the estimates of the risks using Spectral Model are less biased than those obtained from the EV1 and the POT Model, especially for higher critical levels.
A modification which removes the assumption that peaks are independent using the multi-fold integrals of Gupta and Moran is also considered. Gupta's method assumes that the correlation between peaks at any lag are equal to the first autocorrelation. The Monte Carlo simulation of Moran has no such restriction on the autocorrelations but may not converge.
The Model was applied to River Greta, a small catchment in County Durham in the North of England.