Thursday, September 25, 2014

To What Extent Does Minutes of Sunlight Explain Temperature?

The list of stupid things I wonder about grows longer still. As I evolved in my complaining about Sacramento's summer weather, I started thinking about to what degree you can predict the daily temperature from the minutes of sunlight. Obviously the relationship can't be 1:1 because the solstices are not the coldest or hottest days on average. But it turns out, for American cities that don't have marine climates, minutes of sunlight accounts for over 70% of the variation in average daily temperatures. You might say, "Of course! What else did you think explained hot summers and cold winters, seasonal volcanism?" It's that I didn't expect the relationship to be so clear, and to be obscured by other climactic factors.

Below please note sunlight-temperature scatter plots for Phoenix, Sacramento, San Diego, and Philadelphia. Initially I expected Sacramento and Phoenix to be similar, and San Diego and Philadelphia (Philadelphia because of humidity and cloud cover). I also didn't expect too tight of a correlation. Temperature data is from 1980-2012.

This was a surprise. Cloud cover and humidity per se don't make a difference, but being downwind from a massive heat sink does. And when you break the temperature cycle in half, and do a separate linear goodness of fit for both decreasing and increasing temperature, the R^2 goes up past 0.9! (Again, for the non-marine cities.)

I even adjusted Sacramento for the differing angle of the sunlight (i.e. a minute of sunlight in January is different than in May, because the sun is lower, and the same power is therefore spread over a greater area; that is to say, watts per square meter is lower in winter than summer.) After all, every place on Earth gets the same minutes of daylight per year, but obviously the higher the latitude, the greater the departure from directly-overhead sunlight, and therefore the less power being delivered, and obviously for this reason higher latitudes are colder. But it turns out that adjusting for incident intensity comes out in the wash, within the same dataset - adjusting for different sun intensity only increased the goodness of fit by about 0.02. There is an obvious difference in the pointiness of winter (Sac and PHX are pointier than Philly, i.e. they start warming after the solstice more rapidly than Philly); this might be explained by difference in cloud cover.

One take home: if you want to identify marine-influenced climates, you could write a program that calculates the R^2 for any city, given latitude (so you can calculate minutes of sunlight each day) and daily average temperature data. The worse the fit, the more there's a massive heat sink nearby screwing up your prediction, i.e. the more marine-influenced is the climate you're looking at.

ADDED LATER: This very nice related NOAA map I found at the Map Porn subreddit. Purpler = sooner (December), green-yellow = later (February).

Temperature data is from average daily temperature archive, University of Dayton.

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