The entry in my risk blog that has attracted the greatest number of hits is the one that I wrote about the UK floods in July. So, I thought I would go with the flow, so to speak, and say a little more on the subject. I'm just reading Statistics of Extremes by Emil Gumbel, one of the pioneers of flood risk analysis. There, amongst all the complicated mathematics, are some simple observations about the probability of flooding.

Risk of flooding is usually expressed as a chance of flooding each year or as a flood return period, which amount to the same thing. For example, a 0.5% chance of flooding each year is the same as a flood return period of 200 years: (0.5% = 1/200). But the problem is that, as soon as we put a number on it, it looks like we know what we're talking about. The numbers help to create an illusion of certainty. Whereas, with flood risk, we are most certainly speaking about uncertainty.

When I say uncertainty here, I'm not referring to errors. Oh yes, there are possible errors, for sure. The experts' predictions can be based on incomplete data, they can rely on inadequate forecasting models, or they can be influenced by political bias. However, even if the predictions were free from all these sources of error, we would still not know when the next flood is coming! There is a natural uncertainty... a randomness, which we find difficult to grasp.

Let's say we have a reliable prediction of a 200-year flood. This means that, in the very long term, the flood will happen on average every 200 years. But it doesn't mean that, if we had a flood last year, it won't happen again for another 199 years. There is still a (small) chance that it will flood again this year. Think of tossing a coin. The chance of a head is 50%, which corresponds to a head return period of 2 tosses. Every time you toss the coin, the chance of a head is 50%, even if it was heads last time, or the last 20 times. It's the same with floods. The probability of a flood is the same every year!

NOAA's Flood Calculator

When it comes to flood defences, it is not so much the chance of flooding each year that is important but the chance of flooding during the lifetime of the flood defences. Let's say we want a 90% probability that the flood defences will never be over-topped during a design lifetime of 50 years. The formula in Statistics of Extremes tells us that, in order to meet these expectations, the flood return period would have to be 475 years!

Cartoon created for Cool Risk by Michael Mittag

And you don't have to do the calculation yourself. I found that the US National Oceanic and Atmospheric Administration (NOAA) provides an online calculator that does it for you. Or you can use the Cool Risk handy flood risk calculator. If we stay with a 200-year flood, which is typically considered as a low risk, then there is a 22% probability that the defences will be over-topped at least once in 50 years.

What do we make of this 22% probability? It's not a comfortably low risk. We could imagine 9 towns with similar flood risks and similar flood defences. In 50 years, 2 of these towns will suffer a flood.

The long and the short of it is that flood risk analysis is a very complicated process. And understanding the results of the analysis is not easy either! We should not be lulled into a sense of false security by impressive-sounding flood return periods of 200 years or higher. There can still be a significant risk of flooding in the much shorter term.

My blog, 'Risk of Flooding', in July

Cool Risk flood risk calculator

NOAA's flood risk calculator

For Gumbel's Statistics of Extremes, see my Bibliography