Non-stationarity in annual and seasonal series of peak flow and precipitation in the UK

Abstract

When designing or maintaining an hydraulic structure, an estimate of the frequency and magnitude of extreme events is required. The most common methods to obtain such estimates rely on the assumption of stationarity, i.e. The assumption that the stochastic process under study is not changing. The public perception and worry of a changing climate have led to a wide debate on the validity of this assumption. In this work trends for annual and seasonal maxima in peak river flow and catchment-average daily rainfall are explored. Assuming a two-parameter log-normal distribution, a linear regression model is applied, allowing the mean of the distribution to vary with time. For the river flow data, the linear model is extended to include an additional variable, the 99th percentile of the daily rainfall for a year. From the fitted models, dimensionless magnification factors are estimated and plotted on a map, shedding light on whether or not geographical coherence can be found in the significant changes. The implications of the identified trends from a decisionmaking perspective are then discussed, in particular with regard to the Type I and Type II error probabilities. One striking feature of the estimated trends is that the high variability found in the data leads to very inconclusive test results. Indeed, for most stations it is impossible to make a statement regarding whether or not the current design standards for the 2085 horizon can be considered precautionary. The power of tests on trends is further discussed in the light of statistical power analysis and sample size calculations. Given the observed variability in the data, sample sizes of some hundreds of years would be needed to confirm or negate the current safety margins when using at-site analysis.