# 100-year floods

According to the National Weather Service:

What is a 100 year flood? A 100 year flood is an event that statistically has a 1% chance of occurring in any given year. A 500 year flood has a .2% chance of occurring and a 1000 year flood has a .1% chance of occurring.

The accompanying map shows a part of Tennessee that in May 2010 had 1000-year levels of flooding.

At first, it seems hard to believe that a 1000-year flood would have just happened to occur last year. But then, this is just a 1000-year flood for that particular place. I don’t really have a sense of the statistics of these events. How many 100-year, 500-year, and 1000-year flood events have been recorded by the Weather Service, and when have they occurred?

## 14 thoughts on “100-year floods”

1. Funny you bring this up. I thought about this a bit when writing the section on hurricanes in my book. Since there is a 1% chance in any year, over a 10-year interval, there is higher-than-intuition-would-suggest chance of getting more than 1 such storms! Using a binomial distribution, the probability of more than 1 events is 9.6% over 10 "trials". So the way we refer these as "100-year storms" is misleading.

2. Longtime lurker here with a question: How do you define "that particular place"? Intuitively if the county next door is having a 1000-year flood, you ought to be at much higher risk of one, assuming your mean elevation isn't 1000 feet higher or something. I imagine there are ways to adjust for spatial proximity and terrain and so forth. But usually in debunking "what are the odds?" questions like this, the strategy is to count all the times something uninteresting happened instead, so you have a sensible comparison. How do you do that with spatial problems? Percentage of the counties in the nation that didn't have a 1000-year flood that year?

3. It would seem almost unlikely/unlucky to get a 1000 year flood just now, if it wasn't for the fact that the underlying process is not stationary (global warming). Extreme precipitation is expected to increase with global warming. So, it is consistent with expectations from process understanding. However, i would guess that the statistical return period estimates are a bit off as well.

It is common to estimate what the 100-year flood level from a distribution fit to the observed record. Usually that is based on a continuous high-quality record which is ~50 years. So, the distribution has to be extrapolated beyond the largest magnitude ever observed. That is obviously very difficult, and must have large uncertainties. It is therefore common that the estimates are wrong. A critical step (i feel) in these return period estimates is to gather all historical evidence of past extreme events even if they have large uncertainties. Then you can atleast check if it is reasonably consistent with the distribution model.

4. We had two 100-year floods at a solar site at Victor Valley Community College (southern Mojave desert) last year, although one was actually due to a fish hatchery that was cleaning out its tanks and forgot to cap the outflow valve over the weekend. Since the sensors on the inflow didn't detect that the water in the hatchery tanks had risen to a sufficient level, it just kept pumping water into the hatchery which in turn flowed right out the other end just uphill from the solar site, which would up over a foot deep in water in August.

So maybe that one doesn't count, since it was a man-made flood. Or should it?

5. A "100-year flood" has a return period of 100 years. Say at some measurement station at some river there have been observations for the last 100 years. Then a 100-year flood is the flood event that led to the largest recorded water level in the observation period.
Several problems occur:
– often you don't have 100 years of recorded data. Then you have to use some method to estimate a distribution based on less than 100 years of data;
– often you want to predict even rarer ("more extreme") flood events. Then you'd need even better data;
– if the geometry of the river has changed (construction, obstruction, vegetation change,…), you have to somehow compensate for that;
– if there is a trend in your data (climate change) you have to somehow take that into account;

Especially because of the latter reason, but also just by chance, two events can occur within one year, that both have a 50 year return period. Or even a 1000 year return period.

Feel free to read more here: http://planetwater.org/2010/05/04/magnitudes-of-e
Otherwise I agree with Aslak.

Kaiser's book I believe is this one: http://www.amazon.com/Numbers-Rule-Your-World-Pro… and I'd recommend to read it!

6. When I worked on estimating extreme precipitation for my MS thesis (ie: 100-year or 1000-year storms), the standard was to make "regional" estimates by pooling the data over a larger area, and assuming all locations in the region followed this same distribution. There are generally issues with spatial and temporal correlation to be considered.
I would guess these N-year flood estimates are doing something similar, possibly modeling the flood distribution as a function of the size of the watershed area, and likely NOT making much or any correction for correlations.

7. Martin: it's called Numbers Rule Your World. Click on my name and you get linked to the book blog. It's a general stats book, not a book about extreme event statistics, but I mentioned the fact that there is almost a 10% chance that you get more than one 100-year storms within 10 years.

Erin: interesting question. I'd imagine that each place have a different water level that maps to a 100-year flood. But I think Andrew's last sentence pretty much answers the question: we don't need to track individual places in this sort of analysis.

8. Claus, you say "Say at some measurement station at some river there have been observations for the last 100 years. Then a 100-year flood is the flood event that led to the largest recorded water level in the observation period." That's not the way a 100-year flood is normally defined, though. In fact, I have never seen it defined that way! The National Weather Service definition, or something very similar, is what hydrologists use. Or at least, that's what I was told when I was on a committee that looked into regulations related to building near creeks.

9. Actually, the idea of the "return period" is mentioned in Gumbel's book,
http://freakonometrics.blog.free.fr/index.php?pos
it is related to geometric (Pascal) distribution: the expected value of N (which is driven by a geometric distribution) is 1/p: for p=1%, then E(N)=100, so if an event has a 1% chance (per year), then the expected time before observing the event is 100 years.
You do not need 100 years of observations, you "simply" need to use EVT to assess rare event probabilities

10. I've never said that 100 years of data are a prerequisite to derive a 100-year flood. I just said, if you had that data, it would be ideal. You can do it with less data, of course, using EVT. Otherwise you could never predict a 1000-year flood, because you will never have 1000 years worth of data. I just wanted to stress that data is really important (like Aslak also did)! You could probably fit some distribution to a 10 year long time-series very well, but I'd be very skeptical about that predicted water level.

For the concept of "return period" or "annuity": It is 1/P(x>X0). F(x) is the distribution fitted to whatever data you have. F(x) = P(x≤X0) , then the return period is 1/(1-F(x)).

11. Here's something regarding the Fukushima Tsunami return levels:

I think this emphasizes the great value old events have when designing infrastructure.

12. What is the relationship between the 100-year flood elevation and flood stage elevation, moderate stage elevation and major stage elevation? Many designs utilize the 100-year elevation as a datum for construction but I see most of the staging information associated with flooding uses the other stage elevations but it seems there should be some relationship. Thanks, Doug