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Comment by pjot | Hacker News Reader

And considering weather in the US has been recorded for only about 250 years it’s hard to say what a 500-year storm even looks like.

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A "100 year storm" is a storm with a 1% probability of occurrence within any given year.[1] So a 500-year storm has an 0.2% annual occurrence probability.

Those of us who understand probabilities immediately recognise that even assuming the base-line probabilities are correct, this will occur far more frequently than once in 100 years.[2]

And of course, the probabilities require a known historical distribution, which itself changes over time (climate change being only one of multiple factors). It is possible to make inferences based on the observed rate vs. intensity or magnitude of events. In many cases these follow an inverse-log relation, such that order-of-magnitude greater intensity events occur with an order of magnitude less frequency. Tracking the more-frequent, lower-intensity incidents actually gives a good proxy for how often higher-intensity events will occur.[3]

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Notes:

1. "The 100-Year Flood" <https://www.usgs.gov/special-topics/water-science-school/sci...>

2. A 1% probability event has a 99% probability of not occurring. For a period of time, raise 0.99 to the power of the periods occuring. Over a 100 year period, that's 0.99^100, or a 63.4% chance of no such events occurring. For the probability of k occurrences over n periods you'd apply the binomial distribution: <https://en.wikipedia.org/wiki/Binomial_distribution>.

3. This is a relationship which applies to a whole host of events, and is very frequently observed in general physical phenomena. Asteroid impacts, earthquake intensities, volcanic eruptions, storms, wildfires, terrorist attacks, and the like.

It's plenty, because 30yrs is usually the rule of thumb for enough, and extreme events are more likely to be recorded even in the absence of/before there were regular record intervals.

There are well established probability distributions for these things, so you're really just solving for which published curve and maybe a magnitude multiplier and seeing where your data fits.

Also there's uncertainty baked-in and accounted for at every step of the engineering design process.

Eg. Geotechnical engineers love to calculate 6 digits to 4 decimals then throw in a 400% factor of safety.

>it’s hard to say what a 500-year storm even looks like.

Not to worry, that was taken into account when they came up with the 500-year naming scheme.

Sure it sounds like 500 consecutive years, but it's really a 1 in 500 chance of absolute devastation every year.

How bad was the devastation?

Approximately 5x as bad as the ones where it's only a 1 in 100 chance of striking every year, naturally.

This is like saying that if you've only seen 250 people in your life, it's hard to imagine someone who is at the 99.8th percentile of height.

It is though? You probably wouldn't be aware that hormonal disorders can exist and affect height, so you'd massively underestimate how tall people can actually get.

Now I want to know how those people fit in a distribution. It could still be a continuous function.

Of course it's continuous, but (guessing) it's closer to power-law than normal - the tails are fatter than you'd think, and when you try to estimate variance from a sample you get an underestimate.

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