|Ivars Peterson's MathTrek|
February 21, 2000
In 1998, researchers at Arizona State University in Tempe reported that daily oceanic rainfall shows a weekly precipitation cycle across a stretch of water to the lee of the coastal metropolitan area in the eastern United States. This extreme western part of the North Atlantic Ocean receives significantly more of its precipitation on weekends, they observed. Similar weekly cycles are evident in the concentrations of two pollutants--ozone and carbon monoxide--and in the incidence of tropical cyclones.
In 1994, an atmospheric scientist noted that daily satellite measurements suggest that, in the Northern Hemisphere, the temperature in the lower troposphere peaks on Wednesdays. However, there appeared to be no significant effect in the Southern Hemisphere.
Earlier studies had hinted at similar weekday-versus-weekend variations in temperature, rainfall, and pollutant concentration, though many of those findings proved controversial.
Statistics is a tricky business, however. Statistician Kevin J. Coakley of the National Institute of Standards and Technology in Boulder, Colo., has analyzed temperature data collected at the San Francisco International Airport from 1949 to 1994. For each week, he determined the day of the week on which the weekly maximum temperature occurs.
Coakley discovered a surprising effect. He found that the warmest day of the week is more likely to fall on the first (or last) day of the week than on a day in the middle of the week. But, this conclusion did not depend on which day is designated as the first day of the week!
In other words, if Coakley chose Sunday as the first day of the week, then Saturdays and Sundays tended to be the warmest days of the weeks. However, if he arbitrarily chose Thursday as his starting point, Wednesdays and Thursdays would emerge as the balmiest.
In the February Bulletin of the American Meteorological Society, Coakley argues that this statistical quirk arises because daily temperatures dont vary randomly. They generally tend to rise or fall steadily over periods that are longer in duration than one week. In effect, day-to-day temperatures are positively correlated. If it is warmer than average today, it is likely to be warmer than average tomorrow, Coakley notes.
So, if the temperature happens to rise steadily for a while, then in any block of 7 days that you pick, the last day would be the warmest, whether the block began on a Sunday or a Thursday. Similarly, if the temperature drops steadily, the warmest day of any 7-day block would be the first day.
In the light of Coakley's analysis, researchers may have to reevaluate their findings of significant weekday-versus-weekend effects and similar weekly weather trends.
Copyright 2000 by Ivars Peterson
Cerveny, R.S., and R.C. Balling Jr. 1998. Weekly cycles of air pollutants, precipitation and tropical cyclones in the coastal NW Atlantic region. Nature 394(Aug. 6):561.
Cleveland, W.S., et al. 1974. Sunday and workday variations in photochemical air pollutants in New Jersey and New York. Science 186(Dec. 13):1037.
Coakley, K.J. 2000. The warmest day of any week tends to occur on the first or last day of that week. Bulletin of the American Meteorological Society 81(February):273. (Available at http://ams.allenpress.com/amsonline/?request=get-abstract&issn=1520-0477&volume=081&issue=02&page=0273.)
Cohen, P. 1998. Rain, rain, go away. . . . New Scientist (Aug. 8):22.
Gordon, A.H. 1994. Weekdays warmer than weekends? Nature 367(Jan. 27):325.
Seife, C. 1999. Lies, damned lies. . . . New Scientist (Sept. 25):22.
Kevin Coakley has a Web page at http://www.itl.nist.gov/div898/bios/coakley.html.
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