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Houston is experiencing its third ‘500-year’ flood in 3 years

washingtonpost.com

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Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#41

Post by pesfandiar »

bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

I understand your argument, but you can't compare floods to the birthday problem. Unlike randomly-sampled people's birthdays, floods in US cities are not independent random variables.

For instance, chances of 500-year floods in two Texas cities is not 1 out of 500*500 in a year. If they're geographically similar and physically close, it should be closer to 1 out of 500.

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#42

Post by acomjean »

pixl97 wrote: post #33
TallGuyShort wrote: post #7

Earlier quoted context omitted.

>> Of course, the "once in 500 years flood" may also be an inaccurate probability as well I suspect that's it. Of course I may be falling into the same birthday paradox here, but a similar thing happened when it flooded where I lived now. The x in "x-year Flood" kept increasing (I'm inclinced to blame that on sensationalizing news for ratings), but people kept comparing it to the 3 or 4 similar floods that happened i…

>. It would seem the probably has gone up due to climate change That probably has a small reason to do with the increase, but your next line highlights the issue. > or that we're noticing the floods more now because there's more damage to be caused to more things that have been built up No, not exactly. The more stuff you build, the faster water runs off. Unincorporated land has a pretty high water slowing capability…

There is one additional thing to note. Soil has a certain sponge like quality to absorb water. So a runoff curve number was created to "predict runoff or infiltration"

The tables on the wiki pages shows "curve numbers" for different types of soils. These numbers are based on experimental data which is then used to model runoff. (Or used to be. Its been 20 years since I've done runoff modeling, so maybe things have changed)

https://en.wikipedia.org/wiki/Runoff_curve_number

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#43

Post by hexane360 »

bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

Birthday paradox relies on non-independent events. I'd assume floods should be relatively independent between different cities, meaning that the number of 500-year flood events in the U.S. would follow a binomial distribution (https://en.wikipedia.org/wiki/Binomial_distribution).

p = 1/500 years = 0.002

For 100 cities, the probability of at least one city having a 500-year flood is 18.14%.

For a 3-year run:

p = (1/500)^3 = 8e-9

For 100 cities, the probability is 8e-7 of at least one success. For 1000 cities, the probability is still only 8e-6.

Wolfram alpha helps in calculating PDFs and CDFs: http://www.wolframalpha.com/input/?i=binomial+distribution+n...

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#44

Post by [deleted] »

walshemj wrote: post #20
bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

its the gamblers fallacy black 17 has not come up for ages so its more likely to come up - looks like the journalist does not understand probability

[deleted]

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#46

Post by empath75 »

waqf wrote: post #8
bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

Good point, but the chance of a given city having a 500-year flood in three given successive years is only (0.002)³ = 8 × 10⁻⁹. So even if we allowed for 100 U.S. cities, 10 different natural disasters and 10 different three-year periods we're still talking about a probability of less than 0.01%.

And it's not like Houston is the only city having 100 year+ floods regularly.

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#47

Post by cc439 »

idlewords wrote: post #17

A similar thing has happened on the Mississippi river, which has had '500 year floods' in at least 2011, 2009, 2008, 1993 and 1927. I may be missing a few. Assigning probabilities to rare events is meaningless unless you a) have data over a much longer time period than the recurrence time and b) the mechanism causing flooding is not changing. Neither of these holds in the case of Mississippi flooding, for which we on…

"Assigning probabilities to rare events is meaningless unless you a) have data over a much longer time period than the recurrence time"

This is probably the most important factor nationwide in the US. There simply aren't written records of the weather in the vast majority of land in North America which cover the past 500 years. I wouldn't even be surprised if more than half the land in NA didn't have meaningful data over 200 years old.

"b) the mechanism causing flooding is not changing."

This is probably the biggest factor in Houston's extraordinary reoccurence of "500 year" floods. While Harvey's level of rainfall is truly unprecedented in all of American history, the other floods can easily be blamed on the fact that the rapid growth of Houston's sprawl has turned a gargantuan amount of land area into a concrete swimming pool. Like other posters have mentions, undeveloped land is very effective at slowing and absorbing water but a gutter is nothing but an aqueous superhighway. Flooding isn't just caused by the total volume of rainfall, it's caused by the speed with which that volume reaches natural outflows (rivers, creeks, estuaries, etc).

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#48

Post by T-hawk »

bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

> it's actually quite likely that at least one of them could have a pretty high probability of experiencing one in 500 chance of something each year.

This is the key point here, and it's called the fallacy of multiple endpoints. If there are 500 observable cities, then somewhere among them should occur a "500-year event" every year. It's just that nobody ever notices the big bulk of the population that hasn't yet had any 500-year event in its recorded history.

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#49

Post by kurthr »

bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

But storms aren't people with randomly distributed cities to flood so you don't get the combinatorial effect. It's not like there are a fixed number of 500 year storms every 3 years that have to flood a uniformly distributed list of cities. The floods are supposedly independent (even if our estimates of likelihood are bad) so there's no binomial coeeficient.

The simple calculation is P=1-(1-1/500^3)^N and the probability is less than 1:10000 assuming independence and even given 6000 cities of a million people (the entire world population is in a similar city).

If it was birthday like (every possible 500 year storm for 3 years is in a room choosing out of 100 random million person cities), the probablility would be reasonable. You can use a Poisson distribution to estimate the 3 person birthday problem. P=1-exp(-3choose100/500^2)=48%

Re: Houston is experiencing its third ‘500-year’ flood in 3 years

#50

Post by fjfiggiguffuf »

curiouscats wrote: post #11
bkohlmann wrote: post #2

While the article obliquely makes reference to this, I wonder if this is somewhat similar to the "birthday" problem in statistics. Any given person has ~1 in 365 chance of being born on a particular day. Yet, if you have 30 people in a room, there is a greater than 50 percent chance that at least one PAIR has the same birthday. Given the hundreds of cities (thousands?) in the US that may be affected by a flood, it's…

A 500 year flood event is very likely new data that tells us our prediction it was a 1 in 500 year event was wrong. http://engineering.curiouscatblog.net/2008/07/13/500-year-floods/ It is of course possible, it was actually a once in 500 year event. I just believe it is much more likely our previous conclusion was faulty. Our prediction of 500 year floods is not very good, we rely on way less than 500 years of data.…

yea its almost like the underlying model is... warming?
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