Plus ça change, plus ce n’est pas la même chose

The more things change, the more they stay the same

Duncan Faulkner, Head of Hydrology, shares his thoughts on independent and identically distributed variables in flood risk management.

Analysing the past

Recent events, not least in British politics, have shown us that we don’t know the future – as if we needed reminding.

This is the reason why, in flood risk management, decisions about investments, such as flood alleviation schemes, are nearly always based on analysis of information from the past. We assume that past hydrological conditions will be a reasonable guide to what will happen in the future, usually with the addition of some “adjustment” to allow for the possible impacts of climate change.

More specifically, in analysing flood and rainfall frequency statistics, we tend to assume that the values we are analysing, such as annual maximum flows over the period of record of a gauging station, are independent and identically distributed. Statisticians abbreviate this mouthful to IID. However, is it a good assumption? If annual maximum flows are identically distributed, there is the same chance of a given flood flow occurring nowadays as there was a few decades ago. This is hard to believe given the frequency of severe flooding in some parts of the UK over the past 10-15 years.

Nowhere to IID

There are more advanced methods of analysis that break free from the assumption that the data are identically distributed. The field of non-stationary flood frequency analysis is a fertile ground for research, with new research papers being published almost every week. Up to now, though, these methods have rarely found their way out into the wilds of UK consulting hydrology.

JBA Consulting has been applying non-stationary frequency analysis for rivers in southern and north-western England. Several of these rivers have seen strongly significant upward trends in flood flows over a period of several decades. These trends can be accounted for by allowing some of the parameters of the fitted flood frequency distribution to vary with time, or with some physical quantity such as seasonal rainfall. The strongest trends appear to be on catchments with large volumes of water storage available, whether this is in lakes or below ground in aquifers.


The graph below shows some example results for the River Leven, which is the outflow from Windermere in the English Lake District. The lines show estimates of flood flows for various return periods. For more extreme floods, the non-stationary estimates increase strikingly over the period of record. The estimated occurrence probability of floods on Windermere like that, following Storm Desmond in 2015, doubles in comparison with the results of a stationary analysis.

An implication is that design floods for the Leven could be underestimated by up to 23% if conventional methods of flood frequency analysis are applied.

We cannot assume that these trends will continue into the future. However, if the change in flood probability is modelling using information from a physical variable, rather than being related to time, then it would be possible to incorporate climate change scenarios to help understand future flood risk.

The Environment Agency has recently commissioned JBA Consulting to explore non-stationary flood frequency analysis at 33 locations across north-west England. The results will help inform the appraisal and design of flood protection schemes.

Want to know more?

Contact Duncan Faulkner for more information on this topic or visit our flood and water management web pages.

JBA Flood risk variables graph

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