When Estimating Is Dangerous

Photo: xlibber

A recent article in The New York Times offers a worrying application of street-fighting reasoning methods. The article describes the deterioration of the Lake Isabella Dam in California. This dam, the article reports, is one of 4,400 considered “susceptible to failure” (out of the 85,000 dams in the country). I’ll pass over lightly the statement early in the article that the repair costs would be “billions of dollars,” and note only that this figure seems like a massive underestimate. (My last blog entry looked at an analogous estimate for health-care costs.)

Instead, another point has me more worried: the claim by the Army Corps of Engineers and local government officials that “the odds of … a disaster are extremely small, and that they have taken interim steps to reduce the risk, like preparing evacuation plans…” When I read that the dam was built on an active fault, I worry that the odds are not extremely small. It reminds me of similar odds claims for the safety of the space shuttle; whereas in reality there have been two disasters (Columbia and Challenger) in roughly 100 flights.

Returning to the dam: It lies upstream from two towns, Lake Isabella and Bakersfield. After an earthquake-related failure, “Bakersfield would still have about seven hours before a wall of water made its way down the canyon.” But how long would the town of Lake Isabella have?

The physics of a wall of water moving down the valley is complex. However, a rough shortcut is available with proportional reasoning — a form of skillful laziness where we piggyback on work already done. Here, the work already done is the estimate of 7 hours for the water to reach Bakersfield.

Bakersfield is 40 miles down the valley. Lake Isabella is only 1 mile away. Thus, the distance from the dam to Lake Isabella is 1/40th of the distance from the dam to Bakersfield. As a result, the time for the water from the failed dam to reach Lake Isabella is probably 1/40th of the time for it to reach Bakersfield:

Time to Lake Isabella = 7 hours to Bakersfield/40 miles to Bakersfield

That is only 10 minutes. How will “preparing evacuation plans” save the residents of Lake Isabella?!


Patrick

It won't save the people of Lake Isabella, in fact it probably won't even help the people of Bakersfield, it is however meant to save many other things. Save money, save face, save tax hikes, save political careers. Coming from a upbringing filled with lawyers when someone says "interim steps to reduce the risk" and the odds of … a disaster are extremely small", suddenly many questions and just about as many concerns come to mind - none of which are comforted by the fact that these statements are being made by the government and or military.

jonathan

There are about 3k people in Lake Isabella. They all choose to live near the risk; the lake and the tourism makes jobs. You can't have everything.

Really Now?

Obviously everyone chooses to live there. Cliche: Think of the kids.

Dale Sheldon-Hess

Two comments:

One, I'd be more worried about loss of life from this damn than from any nuclear plants in the area in the event of an earthquake.

Two, the engineering design parameters of the shuttle aimed for/estimated a one per 75 flights failure rate; the actual failure rate has been one in 65. Which is a bit short of the mark, but not statistically divergent from it. The shuttle wasn't designed to be "safe", it was designed to be "safe enough" while achieving other goals. New frontiers are like that.

Rich

If I recall correctly from one of Feynman's bios which covered the Challenger commission, there was a huge difference between the safety rates quoted by NASA management and those quoted by engineers for the space shuttle.

Management had numbers like rates like 1/10000 or 1/100000 implying you could launch a shuttle everyday for decades before you saw a failure. While that quoted by engineers was in the 1/100 -1/300 range depending on which system in particular you were looking at.

Mark Spaur

Lake Isabella will probably have less than 10 minutes to evacuate since the speed of the water slows over time and distance due to friction with the earth and other things in its path. The water will be traveling faster than the average used in the approximation when it hits Lake Isabella.

sam

I demand the government lower the maximum speed of water.

Rick Matz

As complexity increases, the Black Swans don't merely multiply; they flock.

Marko Horvat

I live in Bakersfield. I can see the mouth of the canyon from my neighborhood. Lake Isabella would be fine, it's on the other side of the dam.
I te dam breaks, the water would flow away from Isabella, towards Bakersfield. The flooding would be bad, but loss of life would probably be minimal due to the fact that there would be hours to evacuate, the property danger, though, would be immense

RJ

I believe the population of Hopkinton, IA had about 10 minutes to evacuate before the Delhi Dam failed last year. There were no casualties.

Mike B

Whenever people talk about risks being small etc what is actually going on is a dance. The public can't deal with the fact that there are certain risks that come with living in a modern civilization. The deal is that you no longer have to worry about getting eaten or starving or dying of a simple infection, but occasionally a town will get flooded or slightly irradiated. The correct response isn't to call out the safety police and try to apply bubble wrap to the world, but it to simply live with risks that are too expensive to mitigate. Sometimes people just need to deal with the fact that "stuff" happens. If you don't want to deal with Earthquakes and their aftermath, don't live in a systemically active area like California. If you do choose to live there don't bitch and moan about how the dam built at Government expense that supplies water to your arid community is unsafe because of the earthquakes that affect said waterless community.

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Casey

See Nassim Taleb's note (#142) on our ability to understand small probabilities - I would not trust the Army Corps of Engineers.

http://www.fooledbyrandomness.com/notebook.htm

Thomas

The study is 7 hours until part of Bakersfield has 1 ft of water. The other part that's higher gets no water.

It doesn't come in a huge wave that washes everything away in front of it, like in some disaster movie.

10 minutes is a silly and inaccurate estimate. Have you considered looking at a map or at the study?

The first factor, is if it's the main dam, or the auxiliary dam that fails.

The main dam is on the other side of a ridge from the town of Lake Isabella. A quick look at a topographical map shows that either no water hits the town, or it at least takes much, much longer since it has to go down around the ridge-line before coming back to the town.

The auxiliary dam is right next to the town. Probably going to release less water, though. Looks close enough that an evacuation siren on the dam during a failure or anticipated failure will be heard in town.

The key figure here is how much warning will the residents have vs. how long will it take them to get to higher ground. Since higher ground is closer than the damn to the town, for an effective evacuation plan, you just need to make sure everyone can laterally to higher ground faster than the water arrives at a dangerous level.

At that point in the analysis, "preparing evacuation plans" to help things go faster and people get to high ground faster makes a LOT more sense than your proportional reasoning.

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This assumes that the dam fails all at once, with zero warning: the earthquake happens, and one second later the entire dam has fallen down. I don't believe that scenario is exactly typical.

PaulS

"How will “preparing evacuation plans” save the residents of Lake Isabella?!"

Not sure from the comments that it's the right town, but: easy! Upon the slightest threat of rain, the authorities order an evacuation, and if need be enforce it at police gunpoint. Not unlike the now routine practice of issuing "tornado" warnings on pure pixel noise, and nothing ever even comes close to touching the ground and very possibly nothing ever even existed. Eventually folks in town become sick and tired of the expense and of not being permitted to have a life, so they move away. Problem solved.

robyn ann goldstein

Simply put- it won't ever be not dangerous) in that instance. I would rather be certain so as to avoid the problem to the limit of what's humanly possible. How can one be certain. Try a real specific thought experiment and you will know for certain of what, when and how at least in that instance. Then you too will be in the strong position of knowing that that problem can be avoided, it is just a matter of the political will, the economic clout and inner strength to do something about it i.e., in effect, of taking personal responsibility for one's real fate. There are many instances wherein the same reasoning applies. This is just one. And this is not so say that estimating should be avoided. Curiously, the same reasoning applies in the case of Omar and the real side of the aisle of life or death that one wishes to be on.

Robyn Ann Goldstein

p.s. I'll take a bit of immortality any time. We humans are so often, so short- sighted when it comes to seeing the hand-writing on the wall.