Estimation of seasonal flood risk using a two‐stage transformation

Abstract

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 deseasonalized 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 a double mixture of Weibull and exponential distributions. The method is demonstrated with 24 years of daily flows from the River Cherwell in the south of England, and a 40‐year record from the upper reaches of the Thames. Seasonal estimates of flood risk are given, and these can be conditioned on catchment wetness at the time of prediction.