Thursday, February 11, 2010

The Big Snow: Fooled by Variance

No need to visit the gym this week, even if it were possible. I've had plenty of exercise shoveling more snow than I have ever seen at one time in my entire life. More than 4 feet of snow fell in the Baltimore region in just 5 days. As someone who grew up in Albany, New York, and attended schools in Rochester, New York and Madison, Wisconsin, a heavy snowstorm is not a novel event for me. I do not panic the moment flakes start swirling in the air, as many Baltimore-area drivers do. I often question the judgment of school officials, who close the entire system down when an inch or two of the white powder appears. But, 4 feet is an impressive amount of snow by almost any standard. I would not be able to drive anywhere even if I wanted to. Forward motion of my automobile is not physically possible under these conditions.

As snowfall totals go, this event has shattered records. That has kept the media and government people busy tabulating and interpreting numbers. The tabulations are of interest, but the interpretations are mostly silly. Nassim Taleb's wrote a brilliant book on investing titled Fooled by Randomness
. With apologies to Taleb, I've titled this post "Fooled by Variance," which is a condition afflicting a great many of the public statements about the storm.

Variance is a measure of the typical deviation of a measurement from its average value. The usual definition is that it is the range encompassing 95% of the measured values. For example, if we use our rulers to measure human stature instead of snow depth, we would find that the average height of an adult male in the United States is 69 inches. Of course, finding males taller or shorter than 69 inches is common. However, 95% of adult males have a height within 6 inches of the average-between 63 and 75 inches. That range is the variance. However, extreme cases outside of the variance still occur-male heights as short as 30 inches, and as tall as 100 inches have been measured.

In the past week media reports about the storm have referred to it as "a once in a lifetime event," "unprecedented," and "a hundred-year storm." In other words, the storm intensity was far outside the expected variance. But is that claim true? In the 16 years that I've lived in the Baltimore area, this is the third time that I've been snowed-in for an entire week. The week of January 7, 1996 delivered a similar one-two punch with 22.5 inches falling on January 7 and 8, followed by another storm a few days later with more than an additional foot. The blizzard of February 15-18, 2003, with 28.2 inches, remains the record holder for a single storm event. We will never know if the February 5-6, 2010 storm would have topped that number, because the observer, at the official airport weather station, did not follow the proper procedure in recording snowfall measurements.

The established procedure, for determining snow accumulation, is to wipe the snowboard clean every six hours, and then total all of the six-hour measurements. If you wait until the storm ends to measure snow depth, the number will be smaller because the snow will compact under its own weight. If you total more frequent measurements-say every hour-the number will be higher because of reduced compacting. Of course, there is nothing magical about totaling six-hour measurements. It is just an agreed upon protocol to insure that the snowfall amounts were measured under the same conditions, so that a comparison makes sense. But, it also shows that these numbers, and the "records" based on them, are to a certain degree arbitrary.

The 1996, 2003, and 2010 events were all massive paralyzing storms that in each case shut down the city for an entire week. There is not much difference between these three events, which would suggest that the natural occurrence of these kinds of storms is more frequent than "once in a hundred years" or even "once in a lifetime." Not that we would have anyway of knowing the actual intensity of a "hundred-year storm." Snowfall record keeping in Baltimore began in 1883-127 years ago-so we are many centuries away from having enough data to analyze for "hundred-year" or even "once-in-a-lifetime" events.

So should Baltimore be more prepared for large snow events? An article in the Baltimore Sun reports on the amusement of the northern cities. They brag that their streets are clear and their businesses and schools open. But, I lived for five years in one of the snowiest cities in the United States-Rochester, New York-with an average annual snowfall of 92 inches-about 7.5 feet. Actually, 4 feet of snow in 5 days would shutdown Rochester too. The high annual snowfall in Rochester results from lake effect flurries that blanket the city with light snow almost everyday during the winter. My freshman year at the University of Rochester it snowed for 60 consecutive days. It never snowed enough at one time to close the school, but over the course of the entire winter it resulted in an impressive snowfall total. Lake effect flurries mean that snow removal is an ongoing activity during the winter in Rochester. It is not an "event" like it is in Baltimore.

Apparently Rochester has a high average annual snowfall but not much variance. In contrast, Baltimore has a much smaller average annual snowfall-only 18 inches-but a large variance. It is rare, but it does happen that in Baltimore a single storm will dump more than an average annual snowfall. In Rochester it is nearly impossible for a single storm to deliver more than the average annual snowfall. Which means that it makes no sense to have the snow removal capability of Rochester. It would be an under utilized resource, and still not save us in extreme weather events, when the real problem is where to put all the snow that is plowed.

Although, if the climate changes, and monster snowstorms become frequent, then investing in more snow removal equipment would make sense. But a single storm event does not define a climate-a fact that commentators at Fox News are oblivious to. These global warming deniers were quick to claim that the storm "proved" that climate change theories are wrong. It is scary enough when science is politicized. After all, the laws of nature are oblivious to party affiliations. But the inane reasoning of Fox News is laugh out loud funny, a point made in a hilarious spoof on the Daily Show on how to misinterpret data. What is not funny is that Fox News commentators have such a high-profile platform to promote ignorance.

So what can we conclude about this event? The scientific answer is not much. Annual snowfall totals have a great deal of variance, especially in cities such as Baltimore where the annual average is a small number. In those cases, annual snowfall totals will not even form a normal distribution about a mean, because snow accumulations have no upper limit, but a lower limit of zero that cannot be breached. That means that the "average" annual snowfall isn't all that meaningful a number. It is the variance that we should be concerned about.

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