« Flat Tax | Main | Mods to my KTM 950 »

Katrina, New Orleans and the Limits of Knowledge

September 1, 2005 09:39 AM

For New Orleans, Katrina is the storm of the century. Or is it?

It turns out there is no storm of the century in the statistical sense. Looking back, one can see what the biggest storm was over the past. But, in forecasting storms one never knows what the biggest event will be or how probable it is.

The 100 year flood plain that many of you will know of because of home purchases, does not exist. That's right, the 100 year flood plain that represents an attempt to forecast what area will flood from the biggest storm likely to occur in the next century is impossible to calculate. But, it is done all the time and has taken hold as the way to quantify flood risk.

It does not exist because the rain fall time series in a location does not have a mean. How can it not have a mean? It has an average, which is just a calculation looking back at past rain falls and taking the average as the sum of the rain falls divided by the number. But, even though the series has an average (called the sample average) it does not have a mean. It turns out the average is dominated by extreme events; forty percent of the total erosion in a decade is done by a single storm. And, of all the storms we have seen we can never know what the future will hold. Larger ones are probable.

The mean is a parameter of the underlying true probability distribution of rain falls. But, it need not exist and does not exist for rain fall. Why should it? Nature doesn't do means as often as people like to think, given their exposure to averages in every thing they read. In order for there to be a mean the probabilities of large events have to fall off quickly enough for the integral of the size of the event, x, with the probability density of the event, f(x), to converge.

It turns out that it doesn't for rain fall and for a lot of other natural phenomena. In other cases, the mean exists but the variance does not. This is true of hurricanes and tornadoes for example. And the movies.

Why this is so is not so hard to understand. It says that there is a lot out there we haven't seen yet. Nature has more in store for us than we have experienced or can know. Our knowledge is limited and our experience is finite in a world where Nature is open and infinite. A hurricane draws in energy and mass from an area far larger than itself and the Earth's atmosphere is so full of stuff that the hurricane is essentially an open system that is driven far from equilibrium drawing mass from far. It is almost unlimited in what it can pull in if the energy driving it is high enough.

As for the global warming explanations; they reveal the ignorance and political agenda of the proponents. And the flood control "protection" built around our rivers and cities, these end up raising the damage because people build in these areas with the false belief that they are protected.

Adventure Motorcycling
Complex Systems
Endurance Training: Death, Injury, and Risk
Everything
Evolutionary Fitness
Meals
Sports
The Movie Business
Uncertainty

December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007
December 2006
November 2006
October 2006
September 2006
August 2006
July 2006
June 2006
May 2006
April 2006
March 2006
February 2006
January 2006
December 2005
November 2005
October 2005
September 2005
August 2005
July 2005
June 2005
May 2005
April 2005
March 2005

Powered by Movable Type 3.33
Site design by Sekimori

Syndicate this site (XML)