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.