Statistics

# There Is No Such Thing As A 1000-Year Flood

Phrases like “100 year rainfalls” or floods or whatever for whatever period of time are awful. They convey an improper idea of uncertainty.

The phrase “X year event” is based on inverting the probability of the event; call that probability p. Thus “X year event” is equal to “1/p year event”, where p is the probability the event happens per year. That means a “100 year event” has a probability of 1%, and so on. A “1000 year event” sounds stupendous, and, to most ears, rarer than a 0.1% chance.

Anyway, these are all wrong. Since all probability is conditional, and the conditions which “generate” the probability are equally or more important than the number p itself, these conditions should be always be stated. There is no such thing as a “100 year flood” because there is no such thing as a flood “having” the probability 0.01. No physical thing “has” a probability.

There are such things as this: “Given the historical evidence, the probability of a flood of a certain size is p”, or, “Given history and our understanding of changed land use, and the information provided by these river flow and meteorological forecasts, the probability of a flood of a certain size is p.”

It’s perfectly correct to make the statements like this: “The last time a flood this size occurred was in 1945.” That statement is not, however, equivalent to (in 2015) “That was a 70 year flood.”

So what are the “right” conditions? There are none—except in one ideal sense. If we could identify true premises (conditions) that allowed us to say, “Given these true premises, the probability of a flood of a certain size is 1.” Anything short of that 100% means we are uncertain, and because we are uncertain, there are many candidates for premises.

One candidate is the raw historical data, the count of floods of this certain size and the number of years in which they happened. These can be fed into a simple probability model. But that count is subject to both uncertainty and effects of changing land use among other things. The conditions that caused the flood in 1945 may or may not be the same as the one that caused the flood in 2015. The ideal conditions we’re looking for are these causes.

Another misuse is to state the supposed rarity of the flood, tacitly using historical counts only as the conditions, to imply that the cause is something like “climate change” or “global warming.” That’s what the media does routinely. But it’s an immediate failure. If we knew the causes, or knew most of the causes, then the probability would be close to 1, and then the flood would not be rare, so there would be no use pointing to its rarity.

Another tactic is to suggest that the “rare” flood that happened now will be less rare in the future because of “global warming” etc. And this might be true. Then again, it might be false. One way to check for its truth would be to identify, here and now, the causes of the flood and prove which of these were due to “global warming” or whatever. And I don’t mean identify in some fast-and-loose sense common in the media. I mean a real scientific investigation which shows the physical forces involved would not have been in the state they were in had it not been for “global warming” or whatever. Vague implications, common in the media, are of zero value.

Those identifications are still weak next to the need of being able to predict, in advance, when the next flood (of the certain size) will occur. If this can’t be done, then there is no evidence we know the causes of the flood. And thus there is no reason to expect that the causes of previous and current floods are any different.

If that’s true, then using the historical counts are fine and so is stating the probabilities based on this history. But then, in the end, all we can say is something like, “Boy, these floods don’t happen often.” That’s saying something, but it isn’t saying much.

The historical premises can also be used for predictions. Given these, we can say things like, “In the next 10 years, the probability of seeing no floods (of a certain size) is p0%, one seeing just one flood is p1%, of seeing two floods is p2% ,…, of seeing ten floods is 10%.”

And, indeed, it is this historical prediction that sets the standard for any claims that we have identified some of the causes of floods. If we can’t beat that history-based prediction, it is almost certainly false we know what we’re talking about.

Categories: Statistics

### 18 replies »

1. John B() says:

As Charlotte once opined:
“Some Pig”

Everyone took it to mean that Wilbur was “one in a billion-trillion”

When in fact the attention should have been on Charlotte and her” cause”

When Charlotte opines:
“Some Flood”

2. Ken says:

As used & implicitly understood by the public at large, a “1000 year flood” reflects an EVENT, a flood. The “flood” is itself a proxy for a confluence of a variety of factors that together rarely occur in such a way to result in a flood.

Again, the vast majority of people “get it” — that words & context can be summarized simply, with the underlying complexities implicitly understood without the need to expend lengthy dialogues to pin down the various nuances.

Those that don’t, those that cannot comprehend conceptual / metaphorical discourse and are compelled to literal semantic interpretation & the resulting nitpicky “hairsplitting,” are exhibiting another issue entirely.

3. John B() says:

Ken

But MOST people DON’T get it

They’re looking at the pig not the spider

When Skeptics said “Look at this winter” – Climate Warriors said “Look at the Skeptic”

When Climate Warriors said “Look at Sandy – Look at Tornado – Look at Drought – Look at Flood”, everybody says ooooh and aaaah, like a Climate Warrior “4th of July” fireworks display.

4. Nate says:

Is the historical method the way we predict local weather today? “In the past when we saw conditions x, y, and z, about half the time it rained”?

5. A recent comment to the “global warming” proponents.
A examination of field animals we find…
Can you explain why a cow produces a flat runny pile of excrement?
Can you explain why a horse produces a dry muffin like excrement?
Can you explain why a deer produces small pellet like excrement?
The person can not explain this..
Conclusion= They don’t know s__t…

6. Semiotic Animal says:

Dr. Briggs,

Is your style of writing on your blog (considering only posts related to statistics and probability) similar to the style in your book?

7. Briggs says:

Semi,

Why? Are you considering in investing in Springer or whoever else publishes it? Or did I make the subject too accessible, too understandable in posts like this?

8. Gary says:

Past performance is not a guarantee of future returns. Only the financial advisory firms say it plainly, and then because they have to. Maybe this can be extended to the media?

9. I remember meeting with the members of the county’s emergency operations, listening to the delivery of the representative of the state’s geology department (DOGAMI). After his presentation–alarm!–I asked, isn’t a 100 year event just as likely today, as it will be next week?

He affirmed the truthfulness of the statement.

So, the most likely event, is a non-tsunami event. Given the unlikelyhood of a 100 year event, or 500 year event, or thousand year event, how much of our resources should be spent to prepare for exceedingly unlikely events, when in the worst case, no amount of preparation will prevent the complete destruction of the area?

No answer. But, DOGAMI still gets its budget re-authorized each session. So, their jobs are safe.
.

10. Ken: Most people think a 1000 year flood occurs once every thousand years. If it occurs again in 5 years, they are confused. It’s not nitpicking. Many people where surprised we could have 2 or 3 100 year blizzards or fires in 10 years time. I don’t see that they understand at all.

This was an interesting discussion on 1000 year floods and 1000 year rainfall. Neither mean what most people think they do:

11. Well, duh

Here in Sunny southern Alberta, for example, we have a 100 year flood roughly every eight to ten years – and that’s been true essentially since records started in about 1895.

12. JohnK says:

In the guise of a simple example, a lovely summary of some of the fundamental critical issues in probability, its uses, and its inherent limitations. The adept student could learn much from a careful examination of your 780 words.

Well done, Matt.

13. Semiotic Animal says:

@Briggs

For several reasons, I find your writing personally difficult to read and the the more posts, academics articles and videos of yours I watch the less inclined I am to want your book, if it is in the same vein of prose and method (hence my question).

14. Mesomeso says:

I happened to listen to a presentation on this by a couple of hydrologists the other night. “Recurrence interval” is the term they use, but the concept is roughly “the average time between floods greater than or equal to a certain size. Obviously this is all contingent on things ranging from land use to climate changes, and the folks using it understand that and discussed it. The government even has tables for this, although I suspect they make some unwarranted assumptions about probability distributions – but then these tables are used when historical data is insufficient to actually measure an average over a decent number of centuries, and hence are obviously suspect.

They showed a nice graph of historical flood levels for one local gauge vs. measured recurrence interval (for intervals < 20 years) and the graph was nicely log-linear. Except there were two big events, with "calculated" (not measured) recurrence intervals that were way off of that trend line. So much for the assumption of simple distribution shapes.

The reason they go to this trouble isn't to please headline writers, but in order to have some sort of rough metric to use in decision making about flood control investments. As an engineer, I can appreciate the need to use data that isn't rigorous, because it is all that is available, and because they didn't make the mistake of assuming that the numbers from the table were very accurate.