We’ve all heard the terminology. An extreme event happens — a flood or heat wave — and soon after it is characterized as a “1,000-year event” (or it doesn’t have to be 1,000, it could be any number). This week I watched one of the world’s most visible climate scientists, Michael E. Mann, go on national TV and in process show that he had no idea what the concept actually means.

Let’s start by correcting that climate scientist who expressed a popular misconception (about which climate scientists should know better). A 1,000-year flood does * not* refer to a level of flooding that comes around every 1,000 years.

As the U.S. Geological Survey explains:

The term “1,000-year flood” means that, statistically speaking, a flood of that magnitude (or greater) has a 1 in 1,000 chance of occurring in any given year. In terms of probability, the 1,000-year flood has a 0.1% chance of happening in any given year.

Similarly, a 2-year flood has a 50% probability of occurring in any year and a 100-year flood has a 1% chance of occurring in any year. If we are instead talking about two six-sided die, then in the same vernacular rolling snake eyes (2 ones) would be called a 36-roll event. No one talks like that in the dice games I play. No wonder people are confused.

Can you roll snake eyes in two successive rolls? Sure you can. It is certainly rare, especially if you are all by yourself — a 1,296-roll event — but it can happen. Now imagine that you have 30 people in all 50 U.S. states each rolling two dice at the same time, how many snake eyes would you expect across those 1,500 rolls? Now imagine that they roll their dice together every day for a year, or that it is 500 people not 30.

The notion of the 100-year flood can be traced to U.S. flood policy and dates at least to the 1930s and concepts introduced by the father of U.S. flood policy Gilbert White (who I am happy to say was my former University of Colorado colleague). Despite White’s brilliance and influence, the concept is deeply problematic. In 1999, I included the N-year flood as one of my Nine Fallacies of Floods in a paper of that name, and for good reason. Careful readers of that paper will note a few page-proof correction fails in that section!

Here are some problems with the notion of the N-year event:

The N-year event is not a fixed value. It changes over time due both to climate variability and change. Think of it like this, the chances that California will see massive amounts of rainfall are not the same every year — they depend on the state of the climate that year, and things like the phase of ENSO, PDO and many other factors.

The N-year event is typically estimated based on very short climate records — sometime as little as 10 or 30 years. For instance, Texas energy regulators considered only 14 years of data in determining the risks of freezes before the 2021 blackout.

The N-year event is not an independent occurrence in time or space. Climate patterns can make N-year events closely related. So much for the dice analogy!

In fact, there may not actually be such a thing as a N-year event, at least in terms have have any real-time practical meaning. Sure, we can conceptualize the idea, but, for instance, if we find ourselves talking about many N-year floods in a row, it is probably more likely that our understanding of N-year floods is off target as it is that wildly improbable things are going on in the real world (there is a comparison to be made her to risk models in the global financial crisis, but that will await a future post).

Have a read of the U.S. Geological Survey explanation of the concept:

"100-year floods can happen 2 years in a row"Statistical techniques, through a process called frequency analysis, are used to estimate the probability of the occurrence of a given precipitation event. The recurrence interval is based on the probability that the given event will be equaled or exceeded in any given year. For example, assume there is a 1 in 50 chance that 6.60 inches of rain will fall in a certain area in a 24-hour period during any given year. Thus, a rainfall total of 6.60 inches in a consecutive 24-hour period is said to have a 50-year recurrence interval. Likewise, using a frequency analysis (Interagency Advisory Committee on Water Data, 1982) there is a 1 in 100 chance that a streamflow of 15,000 cubic feet per second (ft^3/s) will occur during any year at a certain streamflow-measurement site. Thus, a peak flow of 15,000 ft^3/s at the site is said to have a 100-year recurrence interval. Rainfall recurrence intervals are based on both the magnitude and the duration of a rainfall event, whereas streamflow recurrence intervals are based solely on the magnitude of the annual peak flow.

Ten or more years of data are required to perform a frequency analysis for the determination of recurrence intervals. Of course, the more years of historical data the better—a hydrologist will have more confidence on an analysis of a river with 30 years of record than one based on 10 years of record.

Recurrence intervals for the annual peak streamflow at a given location change if there are significant changes in the flow patterns at that location, possibly caused by an impoundment or diversion of flow. The effects of development (conversion of land from forested or agricultural uses to commercial, residential, or industrial uses) on peak flows is generally much greater for low-recurrence interval floods than for high-recurrence interval floods, such as 25- 50- or 100-year floods. During these larger floods, the soil is saturated and does not have the capacity to absorb additional rainfall. Under these conditions, essentially all of the rain that falls, whether on paved surfaces or on saturated soil, runs off and becomes streamflow.

Simple, right? And this explanation doesn’t even get into climate variability and change, both of which are important for understanding that the N-year flood is not fixed or stationary.

Here is my view on the use of the N-year event in discussions of extreme events.

**Just say no. **

The concept is widely misunderstood and implies a set of assumptions about the climate system that are not reflective of reality. I know the concept is now widely used in so-called event attribution analyses and press releases, and that just adds to the confusion. It is also built into the policy fabric of U.S. flood policy and is used in the insurance industry.

But if a decorated climate scientist doesn’t even understand the concept, then it probably won’t work in public discourse. Let’s talk about extreme events without invoking the N-year event.

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I tried to animate the concept several years ago.

http://polistrasmill.blogspot.com/2012/11/non-random-thoughts-about-random.html

Via email from Tom Wigley (climate scientist) with a request to post here:

"Comment on 1000-yr return period. Roger Pielke makes some interesting points. For scientific background on this issue, including examples of how one can usefully employ the return period concept, see my 2009 paper in Climatic Change, 97(1-2), 67-76, “The effect of changing climate on the frequency of absolute extreme events.” This paper is a low level exposition on extremes, return periods, risk, and related ideas. It was originally written in 1988, but is still (even today, 2023) relevant.

First paragraph:

" In some areas of climate impact analysis, the possible impact of a changing mean climate has been dismissed by some writers either because of a belief that society can adapt to a slowly changing mean and/or because expected rates of future changes lie within or not far outside those experienced in the past. The two standard counter arguments to this optimistic view are: (1) the future will lead to much longer periods of protracted change in one direction, with final conditions well into the no-analogue region; and/or (2) the main impacts will accrue through changes in the frequency of extremes. In the literature on greenhouse effect, lip service is often paid to the effect of changes in the frequency of extremes. But just how will a slowly changing mean affect the frequency of extremes? Quantitative discussions of this subject are rare."