Stochastic modelling of streamflow for predicting seasonal flood risk
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.