Tuesday, August 31, 2010

Would New Orleans levees hold for a second Katrina?

Christian Science Monitor article "Would New Orleans levees hold for a second Katrina?" (August 29th, 2010) offers only a partial discussion of the costs and distribution of destructive floods.
The Corps says the reinforcements are built to provide a defense against a 100-year storm surge, which means protection against flooding that in any given year, may have a 1 percent chance of taking place. For a peak storm surge, such as one that may occur once every 500 years, the system is designed to allow overtopping, where a storm sends waves over the top of the wall.
Mr. Barry says the levees should be constructed to withstand a 1,000-year flood, adding that Holland enjoys a 10,000-year protection standa
The article should have, but did not, recognize and discuss the nature of the flood distribution that a levee system has to protect against. Specifically, we can imagine that a number of floods or hurricanes occur in New Orleans every year. Each flood's destructive power is drawn from some distribution.  (Note that our general point will hold for any exponential distribution, which includes the normal, gamma, Weibull, binomial, Poisson, and more). What we need to be concerned about is not the distribution itself, but the distribution of the maximum for a given year.

To illustrate our point, we can imagine hurricane density distributed as a normal with mean 5 and standard error .6.  Each year ten floods are sampled from this distribution.   This maximum will be distributed as a Type-I Gumbel Distribution.  These two are depicted graphically below--a single flood's distribution in blue, and the maximum of that season in red (click to enlarge).
The important thing to note is how the distribution of the maximum positively skews the probability distribution we're considering to a long-right-tailed maximum flood, and that this is the distribution we need to consider when making optimal flood insurance decisions.

In this light, the article's discussion of 100, 1,000, and 10,000-year floods should be interpreted--as costs of protection rise, the benefits of protection become dramatically smaller.

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