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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?!