[WorldMaker]

The problem is not making numerical estimates of low probability events or how such events are modeled: it's completely ignoring the statistical probability distributions of the model. All of the models are extremely "long tail" distributions and just about entirely ignoring the long tail.

We shouldn't be referring to this as a low-probability flood but as a high sigma flood.

ETA: Disclaimer: Day job includes rainfall statistics analysis.

[tedunangst]

I don't know much about the field, but I'm curious. How much are estimates based on normal distributions, and how much does the model consider other distributions?

As you say, I don't think we know much about the tail. More than ten inches of rain may be a once a year phenomenon, but that once a year event might be twenty or fifty inches?

[WorldMaker]

Disclosure: I am not a subject matter expert, I just do the programming they tell me to do. Mistakes/oversights here are likely my own, not my employer's or the software I work on.

The rain gage analysis the software I work on does is largely based on USGS data. [1] Almost all of that data is publicly accessible and you can explore the data down to individual monitoring stations if you wander through the site far enough.

The application I work with is primarily concerned with two bits of analysis from the data in a given station: average peak annual flow and mean daily flow. The distribution used for analysis of both (beyond linear interpolation and best fit line options) is fitting to a Gamma distribution [2], and plotted on a logarithmic scale. (Rainfall is specifically mentioned under applications of that distribution on Wikipedia, so it seems to be the industry standard even outside of the specific application(s) I work on.)

[1] https://waterdata.usgs.gov/nwis/rt [2] https://en.wikipedia.org/wiki/Gamma_distribution

[idlewords]

I am not a math, but I remember that if you can't assume a normal distribution and want to know the shape of the tails, you need a pretty ridiculous number of observations.

[SomewhatLikely]

Pretty much the same errors that were made in the 2008 financial crisis.