## A Note on the "1000-year" Flood And Our Intuition About Outlier Events

Many media outlets were calling the post-Harvey flooding in East Texas a "1000-year" flood.  Forget for a moment on the craziness of saying this is a 1000-year flood when we have at most about 150 years of weather records for the Houston area.  Consider something else -- that our intuition about outlier events tends to suck.

Let's say the flood affected a quarter of Texas.  This is probably an exaggeration, but it will help the following analysis be conservative.   Based on numbers from Wikipedia, Texas has 268,597 square miles of land area and the whole globe has 57.5 million square miles of land area.  This means that a quarter of Texas is about 1/1000 of the land area of the globe.  Even if this were truly a 1000-year storm, we should see such a storm over a similar area of land every single year on average somewhere in the world.  And if you add in other weather events that I have seen described as "thousand year", including snowfalls, heat waves, cold waves, droughts, etc. then we should be seeing a thousand-year weather event of some sort over a similar area as that affected by Harvey every few months.

### 20 Comments

1. #### dork:

What puzzles me about the reaction to the devastation of cities and livelihoods by the hurricanes this year is the focus on rebuilding.

If I were in charge of handing out any kind of federal aid, I'd make it conditional on resettlement or at least include a clause that prevents recipients of aid from receiving any more for the next ten years.

There's plenty of great land to build on elsewhere.

2. #### craftman:

I have run into so much misunderstanding of floodplain designations. It usually takes one sentence to tell people "a 1,000 year flood means that it has 0.1% chance of occurring in any given year" for them to go "Oh, I guess I don't know what I'm talking about".

I'm sure it was meant to make describing floods a little more colloquial, but a 10-year flood can happen twice in 2 consecutive years and we don't need to go running around with our heads cut off. It's statistics, based on past data, not a well timed recurring event like eclipses or lunar cycles.

3. #### texasjimbo:

I've seen a lot of this type of commentary. A huge % of the US population lives less than 100 feet above sea level. NYC is lower than Houston and fared worse during Sandy than Houston did in Harvey. Not to mention the fact that we aren't going to do away with ports, and the existence of ports requires the existence of large costal cities. A large % of California's population lives in earth quake zones that are over due for a big event. A large portion of population along the Mississippi River lives in an earthquake zoon that is due a big event. Resettlement is simply not an option.
That doesn't mean that building codes can't and shouldn't be changed. Most newer single family houses in Houston fared much better than older ones because they are raised several feet above the ground. And it certainly doesn't mean that the government should be subsidizing insurance for private property. Make the user pay.

4. #### johnmoore:

"Forget for a moment on the craziness of saying this is a 1000-year flood
when we have at most about 150 years of weather records for the Houston
area."

Hydrologists are quite capable of using geological information to determine return intervals such as 1000 years.

5. #### LowcountryJoe:

Warren, you need to immediately purchase some carbon offsets for your blasphemy. Also need to say eight 'HAIL GAIAs' and four 'OUR IPCCs'.

6. #### Bloke in North Dorset:

Indeed. From the 2nd Sept Economist (\$):

"Victor Baker, a palaeohydrologist at the University of Arizona, studies floods far away in time and space (he is particularly renowned for his work on catastrophic torrents in the distant past of Mars). The scars left by the biggest past events provide benchmarks for what might happen again: as Mr Baker puts it, “What has happened, can happen.” In 2013 he and his colleagues analysed 44 ancient inundations of the Upper Colorado River, estimating the floods’ intensity from the volume of sediment and establishing their age using a technique which reveals when quartz in those sediments was last exposed to daylight. Their analysis showed that the river’s “500-year floods” were twice as severe as estimates based on modern records alone implied: what had been considered a once-a-millennium flood turns out to occur more than once a century."

7. #### BobSykes:

For the Gulf coast, Harvey is more or less a 30-year event. Over the last hundred years there a few hurricanes of that power have come ashore. Think of Galveston just down the river, destroyed by a hurricane with thousands killed.

8. #### DirtyJobsGuy:

People actually had a better feel for this 50 years ago. Big storms were well publicized and remembered so someone in the big New England hurricane of 1954 instinctively compared it to the last big hurricane of 1938. Also large protective measures were undertaken by such now reviled organizations such as the Army Corps of Engineers. Here in New England after the 1954 hurricane a large number of dams (both dry lakes for flood storage and new reservoirs) were built and storm surge barriers in the form of movable gates constructed on cities like Providence. Shoreside homes were still largely shacks as no flood insurance or government reimbursement program existed. This lowered the public perception of moderate storms and made them less threatening.

9. #### The_Big_W:

People are really really bad at statistics.

10. #### Dan Wendlick:

There's a legend in Vegas about a Cowboy (or soldier, it varies) who wandered into a casino some time in the 50s, put \$5 down on the pass line and proceeded to throw 12 straight sevens, then pulled back his winnings (~\$20k) and promptly crapped out. When asked how his day went, he replied "Not so great, I lost my five bucks."

I've also seen proofs that given the number of people who go to Vegas, this story should actually repeat about once a year, if people were actually willing to press their bets that hard. Two points of this story: people don't understand probability, and are more sensitive to losses than gains. The fact that people benefitted from living in the flood plain for 99 years gets lost in the fact they got wiped out in year 100.

11. #### dfsuther:

Indeed! Some wag once pointed out that "7 out of every 5 people are mathematically illiterate." My experience suggests that the situation is even worse when considering statistics. Indeed, I consider myself lucky to merely recognize my own statistical not-quite-illiteracy.

As always, YMMV; I am not a lawyer, nor do I play one on TV; past results are no guarantee of future results; [insert generic disclaimer here!]

12. #### dfsuther:

Those wise recommendations wouldn't even begin to offset our host's transgressions. He'd need to be somewhere more in the range of "What if we refund the customers' money, shut down the location, fire the local employees and managers, and send the CEO to apologize to his ancestors in person? Would that be enough?" [/sarc for the reading-comprehension-impaired]

13. #### dfsuther:

Things like that do happen sometimes. We know this, in part, because [the smarter] casinos eagerly advertise them... at least the winnings part. The _really_ smart casinos even survive the inevitable regulatory investigation that follows "to ensure that they aren't fraudulently enticing customers to gamble"

14. #### Mike Powers:

What amuses me (in the bitter, cynically sarcastic reading of "amuses") is that this is yet another one of those fucking things where the pro-AGW team flips on their previous position.

Like, remember when the Hansen emails came out and they shit themselves telling us about how "HIDE THE DECLINE" didn't actually mean what it looked like it meant, and that we were supposed to ignore both the plain reading of the words and the surrounding context and *understand* that it was just statistical jargon that we shouldn't really use to draw any conclusions?

And now suddenly "hundred-year storm" means exactly what the words says, that the thing will only ever happen once in a hundred years. The idea that it's jargon for "one-in-a-hundred chance that this thing will happen in this way, at this time, in this place" is ignored; no, it's ONE EVERY HUNDRED YEARS AND WE HAVE HAD THREEEEEE ZOOOOOOOMG

Same deal as how hurricanes mean that Global Warming is totally real, but when there's a massive snowstorm we are told that The Weather Is Not The Climate.

15. #### Mike Powers:

Fun statistics:

Let's say someone is flipping coins. Which of these sequences is most likely to occur:

HHHHHH
HTHTHT
THHTTH

Trick question. All are equally likely!

16. #### cc:

A bunch of us guys were at a party--mostly engineer types. Someone said--looking at me--these hurricanes are worse because of climate change, right? I said what about the 12 year drought of hurricanes? Was that a disproof? shut them up good because they are actually numerate.
It is not actually possible to estimate such an event as Houston from 150 years of data because it is a fat tail distribution problem where we have almost no data on the tails.
How big can floods get? Try floods that pick up boulders the size of large houses and drop them on top of hills:
https://en.wikipedia.org/wiki/Missoula_Floods

17. #### drobviousso:

An "X-year" flood has nothing to do with periodicity of a flood. Due to the kind of shitty math only a governing body could love, a 1000-year flood is a flood that has a 1/1000 chance to happen in a given year, based on the estimated flow rates in an area.

It leads to such absurdities as this statement from wikipedia "In fact, there is approximately a 63.4% chance of one or more 100-year floods occurring in any 100-year period. On the Danube River at Passau, Germany, the actual intervals between 100-year floods during 1501 to 2013 ranged from 37 to 192 years"

18. #### Mark:

The 63% chance of one or more 100-year events occurring in a 100 year interval is the correct result of applying simple probability theory for a binomial distribution. I can't tell if you think it's absurd because you believe it's false, or because it's true and shows how misleading the "100-year flood" terminology is.

19. #### drobviousso:

I think the "x-year" formulation is absurd because what you say is correct and shows how misleading the "100-year flood" terminology is.

20. #### Conqueror of All Foes Cheese:

I teach stats and have to remind myself fairly often not to let my colloquial thoughts crowd out the math. I did shut down a few friends who were hooting about 500 year floods that according to their understanding I must be older than Methuselah since I had lived through 3 500-year floods on the lower Illinois and mid Mississippi Rivers. FWIW I'm 70.