What does it mean to talk about a “1 in 600 year drought”?

Patrick Atwater writes:

Curious to your thoughts on a bit of a statistical and philosophical quandary. We often make statements like this drought was a 1 in 400 year event but what do we really mean when we say that?
In California for example there was an oft repeated line that the recent historic drought was a 1 in 600 year event though we only have a well instrumented hydrologic record of approximately 100 years. Beyond that it’s mostly tree ring studies.
I suppose this is a subset of the larger issue of quantifying rare but impactful events like hurricane, flood, terrorist attacks or other natural and man-made disasters. Generally hard to to infer conclusively from a single observation (in this case the recent droughts in South Africa and California).
The general practice is to utilize the historical instrumented record to construct a probability distribution and see where the current observation lies on that. So what we’re really saying with the 1 in 400 years line then is that this is a 1 in 400 year event assuming the future will continue to look like the past hundred years.
But with climate change there’s good reason not to believe that! So I’m curious if you have any ideas about ways to incorporate priors about future hydrology utilizing climate modeling into these sorts of headline statements about the likelihood of the current drought. And then thinking ideally would communicate through transparent tools like what Bret Victor advocates for so the assumptions are clear ( http://worrydream.com/ClimateChange/ ).
For context we emailed a bit a few years back about applied data science questions [see here and here] and I’ve been leading a small data team automating the integration of urban customer water use data in California and contextual information. You can see the resulting dataset ( http://bit.ly/scuba_metadata ) and analytics ( https://demo.californiadatacollaborative.com/smc/ ) if you’re curious.

My reply:

Get Gerd Gigerenzer on the line.

You’ve got a great question here!

When it comes to communication of probability and uncertainty, I’m only aware of work that assumes that the probabilities are known, or at least that they are constant. Here you’re talking about the real-world scenario in which the probabilities are changing—indeed, the change in these probabilities is a key issue in any real-world use of these numbers.

The point of saying that we’re in a hundred-year drought is not to say: Hey, we happened to see something unexpected this year! No, the point is that the probabilities have changed; that a former “hundred-year drought” is now happening every 20 years or whatever.

I have no answers here. I’m posting because it’s an important topic.

And, yes, I’m sure there are researchers in the judgment and decision making field who have worked on this. Please share relevant ideas and references in the comments. Thank you.

P.S. Hey, I just noticed the name thing: a hydrologist named Atwater! Cool.

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