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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.

Hydrological time series are often asymmetric in time, insomuch as rises are more rapid than recessions, as well as having highly skewed marginal distributions. A two-stage transformation is proposed for deseasonalised daily average flow series. Rises are stretched, and recessions are squashed until the series is symmetric over time. An autoregressive moving average (ARMA) model is then fitted to the natural logarithms of this new series The residuals from the ARMA model are represented by Weibull distributions. Seasonal flood risks, as daily average flows, are estimated by simulation. However, floods are often measured as peak flows rather than daily average flows, although both measures are relevant, and the use of growth factors to allow for this is demonstrated. The method is demonstrated with 24 years of daily flows from River Cherwell in the south of England, a 40-years record from the upper reaches of the Thames and 21-years record from the River Coquet in the north-east of England. Seasonal estimates of flood risk are given, and these can be conditioned on catchment wetness at the time of prediction. Comparisons with other methods which allow for time irreversibility are also made. One is ARMA models with exogenous input, in this case rainfall, which will, because of its intermittent nature, impact a natural time irreversibility to the streamflow series. A disadvantage of these models is that they require rainfall data in addition to the streamflow record. A second is the development of a class of shot noise models, which naturally generate highly time irreversibility series. This is the Neyman-Scott model. But, despite its attractive physical interpretation it is inevitably less flexible than the two stage transformation because it has fewer parameters. Although it was found to provide a good fit to daily data it is less convincing for the extremes. Overall the two stage transformation (TST) compared favourably with both models.