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

Abstract

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.

Understanding flood regime changes in Europe: a state-of-the-art assessment

“…For example, hydrometric monitoring networks were often installed in response to recent floods or recent droughts, which causes such extreme periods not appear in the observational data. This can be seen in the UK and Ireland, where the gauging network expanded from the 1970s onwards, a period with drought conditions and particularly few floods which is considered to influence the outcomes of trend analyses performed (Hannaford and Marsh, 2008;Murphy et al, 2013;Prosdocimi et al, 2014). Another factor resulting in similar biases are changing societal priorities and/or financial constraints, which sometimes cause gauges to be closed down (e.g.…”

Detection and attribution of urbanization effect on flood extremes using nonstationary flood‐frequency models

“…To give a representation of the potential for high rainfall in each year and season the 99th percentile of the daily rainfall series for each year and season were used for each catchment. In a national scale study, Prosdocimi et al [2014] had found that the 99th percentile of the annual catchment averaged daily rainfall series was significantly correlated to block maxima values for most catchments in the UK.…”

“…As discussed in Prosdocimi et al [2014] and later in this work, the record length available for annual maxima series (typically around 35 years in the UK) is not large enough to allow for an unequivocal detection and attribution of trends via statistical testing, and the analysis of such block maxima can be highly influenced by anomalies in the data series. Beside block maxima, peaks-over-the threshold series (POT), also known as a Partial Duration Series (PDS), are frequently used to assess the behavior of extreme events [see Madsen et al, 1997;Lang et al, 1999].…”

The impact of seasonal flood peak dependence on annual maxima design quantiles

“…Thus, comparing the annual with the seasonal distributions we encountered the problem of cross-over in the probability plot: the annual distribution must always lie on or above the highest seasonal distribution (Waylen, and Woo 1982, Durrans et al 2003, Baratti et al 2012, Prosdocimi et al 2014. For example, the probability of one peak value being exceeded in an entire year must be higher than the probability of the same value being exceeded in one season.…”