Return periods and the likelihood of kayaking in my living room.

Once I was told: only if you can successfully explain something to your grandmother it means that you master its understanding. I think this is a very easy way to discover your own lack of knowledge.

Not long ago I tried to explain the concept of return periods in engineering to a friend. In principle this is something straightforward; we define it as the average time-span in which an event of a certain magnitude is exceeded. This is a very useful resource in engineering. For example, let’s say we want to design a piece of river-hydraulic infrastructure. This is meant to work under a certain design criteria. However, extreme events (e.g. high river flow) can threaten its integrity or its performance.

In order to achieve an optimal design (reliable and cost-effective), the common procedure would be: first, do a risk analysis and define which probability of failure are you willing to assume. Then gather data on the threat variable x, by studying long time series you can define what is the recurrence period for each magnitude. This value, T relates to the probability of exceeding a certain event by time unit, like: P(X≥x) = 1/T. Thus, we have it! Matching the total probability of failure with the assumed risk will give the magnitude of the design event.

A simple concept. Until questions come.

It happens that I live under sea level. This can be accomplished by: becoming a fish, building a very complex submarine structure, or moving to Delft, The Netherlands. I chose the last option for obvious reasons, the food here is slightly better than in the submarine.

The Netherlands is a very particular place, and a must-to-see for any hydraulic engineer.

Flood prone areas in The Netherlands,  original source in [1].
Dutch people have been fighting against flooding for centuries. Roughly 30% of habitable land is directly under sea level and 60% of the country’s surface is flood prone. After a series of storm surges of catastrophic impact (in the post-WWII), the Dutch government planned a massive infrastructure development for flood protection. Today, the country resists the rising sea with a series of diked rings and some very impressive pieces of engineering mega-structures (e.g.

A recurrent topic with friends and visitors is; how safe is it to live here? Nothing has happened in a few generations, but how safe is the flood protection system? Well, rainfall-driven flooding is relatively common in some places. But a breach in the dike system and a total sea intrusion (in Delft) is very, very unlikely.

How unlikely? Delft is located in the area known as the Randstad. This is the most populated territory of The Netherlands since it comprises the cities of Amsterdam, The Hague, Rotterdam and partially Utrecht. During the flood defence planning, for political and technical reasons, they selected a period of return of T=10,000 years for this area. Then, the probability that during a 4 years PhD project you suffer such an undesirable event (kayaking in my living room) can be modelled with a Poisson distribution: P(suffer at least 1) = 1 – Ps(k=0, n=4, p=1/T) = 0.00039992 or a 0.039% probability, in theory. I would say very low.

But then someone asked; how do you calculate a 10,000 return period event? Well, observing data. Which data? And here is where things get complicated. It is not until 40-70 years back from now when systematic monitoring data started to be widely compiled. For most variables of interest in hydrology (e.g. rainfall, river flow), you shouldn’t expect to have longer continuous series than that. Still, return periods for critical infrastructure tend to be in the 1000 -10,000 years order of magnitude. So how do you do that?

The estimation of the period of return is usually done by fitting a probabilistic model. The time series used can still suffer of many additional issues as non-stationarity in time, censored data etc. There are a lot of techniques and literature addressing those problems. But the question is still in the air… How can you extract enough statistically sounded information for a 10,000 year return period with only 40 years of information?

This constitutes a few scientific fields by itself but here are some possibilities:

  1. Reconstruction of past events through simulators (e.g. modelling extreme flooding).
  2. Compilation of non-systematic data. Continuous monitoring time series are 40-70 years long, however extra information is available on singular events. This is especially the case in floods in Western Europe where chronological city records can be traced back to 1000 AD or more.
  3. Study of geomorphological sedimentary strata and physical marks of past extreme events. This is known as Paleohydrology.

All this information does not produce exact reliable values but it can be used as bounding regions for refining large return period estimates. With the use of alternative data we are capable of stretching our short time series and refining extreme event predictions. This is quite critical since, as you have seen all our design depends directly on this estimate.

If you want to know more about the Dutch sea defence system, [1] is a good summary. And if you want to read more about the use of non-systematic data in return period estimates, [2] has a few good examples.

I hope you learned something new, as I did after trying to explain this simple concept.

by Antonio Moreno Rodenas, TUDelft.

[1] Slomp, R. 2012. Flood Risk and Water Management in the Netherlands. Rijkswaterstaat, Waterdienst. uuid:7d27240f-1169-4536-b204-fc821345669b

[2] Benito, G., Lang, M., Barriendos, M., Llasat, M. C., Francés, F., Ouarda, T., … & Bobée, B. (2004). Use of systematic, palaeoflood and historical data for the improvement of flood risk estimation. Review of scientific methods. Natural Hazards31(3), 623-643.

Return periods and the likelihood of kayaking in my living room.