What's the cost of misusing a flood frequency plot?

An approach to managing flood risk usually begins with the estimation of the frequency of flood flows (flood estimation). If it’s known that a specific flow causes flooding, it’s useful to assess, on average, how often that flow will occur and therefore how often flooding can be expected. Likewise it’s useful to assess, for a given extreme flow, the water depth and the extent of the area that is likely to be inundated.

Why is it important to assess flood frequency?

Estimating these flood characteristics is vital in deciding which flood risk management measures may be most effective in a given scenario, especially in relation to designing structures like flood defences. The choice of method for estimating flood frequency, and thus the accuracy of the resulting estimation, can have a major impact on the success of a flood defence.

If the flood estimation is incorrect, the flood management scheme may not provide the standard of protection for which it was designed. Similarly it may be over-designed at great cost and in some cases it may not be necessary at all.

How do we estimate an extreme flood flow?

Flood estimation methods are numerous and often complex, but they generally involve analysing historical extreme flow events. For example, a flood hydrologist may analyse the annual maximum peak flows of a river gauge and fit a statistical model to extrapolate to extreme events above those recorded. Similarly, a rainfall runoff model may be developed to simulate thousands of years of data from which an annual maximum series can be extracted.

When analysing previous extreme flows, it’s important to compare the results of the model with the observed data. The most common way of doing this is to use an extreme value plot, often called a frequency curve plot. Broadly speaking the plot has flow magnitude on the y axis and probability of exceedance on the x axis. The observed flows and the modelled are then plotted for comparison. This means that a probability has to be attributed to the observed flows in order to plot them.

Yet we’re attempting to assess a model that provides flow probabilities. The key limitation, therefore, is that a broad estimate of the flow frequencies (or probabilities) has to be made in order to compare the modelled flow to the observed flow. The plot compares one model of frequency against another; not a particularly sound approach.

An example of concern

As part of a project team involved in a proposal to build a flood storage scheme and associated walls and embankments along a river, I reviewed the hydrological report and found a discrepancy in the flood estimation method.

The proposal was planned with a suggested cost of over £17 million. The hydrological report relating to the scheme undertook flow estimation at a river gauge in the area at risk. The authors used the extreme value plot to determine whether or not the model being used provided results that were suitably similar to the past data. The plot suggested that it wasn’t. However, the authors attributed the mismatch to the inadequacy of the frequencies attributed to the observed flows by the extreme value plot method. The model was accepted despite the plot results.

I assessed the discrepancy and found that the proposed flow frequency model had only a 1-in-10,000 chance of reproducing the observed data in a randomised simulation - either the flows were wrong or the model was wrong.

On further inspection it seemed it was a bit of both; there was a lack of confidence in the relationship between water level and flow at the gauge, which means even if the frequencies attributed to given flows were reasonable, it would not give confident estimates of the associated water levels and therefore could under or overestimate the risk of flooding, reducing the effectiveness of any defence walls and embankment.

Through the misuse of a single flood estimation evaluation tool, a huge sum of money would have been misspent. After my investigation, the flood management scheme was withdrawn and flood management plans are under review.

It’s vital to reduce such flood estimation problems as it could lead to underestimation of flood scheme requirements - which can put lives at risk through unexpected flooding and incur high costs of recovery - or overestimation which could lead to over design or building of a scheme that isn’t needed at all, at needless expense.

A different method for flood model evaluation

This experience led me to write a paper with a suggested plot to compare the observed data with the modelled data, without the need to estimate frequencies for the observed flows. I called it the extreme rank plot (ER plot) and the paper was published in the Journal of Hydrology Research.

Flood frequency model analysis using the proposed ER method (left) compared to the standard Extreme Value method (right).

The ER plot, rather than plotting flows against probability, plots flows against flow ranks and can be considered non-parametric. Furthermore the ranks are attributed to the modelled flows by the simulation of thousands of flow samples, the same sample size as the observed. This means that the flow frequency model being assessed is compared to the observed flows without bias and with the sampling error considered inherently within the plot.

At JBA, the use of this method can better validate our hydrological extreme models and improve our choice of these models for the catastrophe modelling we undertake, helping us to better understand flood risk across the world.

You can read the full paper hereIf you’re interested in learning more about our work in flood risk management, including our flood maps, catastrophe modelling or bespoke consultancy, please get in touch.

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