Tuesday, December 27, 2005

As December Goes . . .

After yesterday's official high of 48, temperatures are closer to seasonable levels for late December in the Washington DC metro area, mainly in the mid 40s under partly cloudy skies. Winds have been brisk at times, but well below yesterday's levels. Across the country, there is virtually no precipitation east of the Rockies, except for the Dakotas.

Tonight and Tomorrow

Tonight's lows will range from the mid to upper 30s. Tomorrow will see increasing cloudiness and highs around 54.

. . . So Goes January?

Someone suggested in the previous comments that this weather is so boring it should have a web site called "LowercaseWeather.com". The one thing that is constant about weather is that it will always change. Since things are a little slow now, I had the chance to do some homework.

Following on to Matt's earlier discussion, I looked at the historical relationship between December and January weather in Washington. The chart on the left is a plot of each year's December average temperature (x-axis) vs. the following January's average (y-axis). As you can see, there is a lot of scatter to the data. The solid sloping line is a regression line, which minimizes the collective distance to all of the plotted points. The algebraic equation for that line is shown in the upper part of the graph, along with R². R is known as the correlation coefficient. It is a measure of how well two sets of data are correlated (in this case, December and January temperatures). The value of R can vary all the way from -1 (perfect, but opposite, correlation) to +1 (directly correlated). A value of 0 indicates the relationship is completely random. In this case, the value of R is 0.4, since R² is 0.16. This shows that the quantities are related, but not very strongly. Without getting too technical about it, R² represents the amount of variability of one set of data (January temperature) which is "explained" by the variability in the other set of data (December temperature). In this case, a little over 16% of the variance is explained---not random, but not terribly strong, either.

In the case of snowfall, all bets are off. The chart on the right shows a plot of total snowfall for December vs. January (trace amounts were considered 0). Notice how the points are much more random than in the temperature chart. In fact, the R² value is much less than 0.01; about ¼ of 1% of the variability of January snowfall is explained by the December amount. This is shown by the regression line being almost completely flat. What relationship does exist is actually negative, indicated by the negative coefficient of x in the regression equation. So, there is a non-zero probability that January snowfall will be low when December's is high, but the statistical reliability of that connection is extremely low.

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