Insolation

Today's topic is not "insulation," as in "my apartment doesn't have enough insulation to keep me warm in this frigid weather." Rather, insolation is how much sunlight hits the earth's surface.
Ever since moving up north and noting how low the sun is in the sky and how short are the days during winter, I've wondered about how much actual energy gets dumped onto a unit area on the surface of the earth.

After googling all sorts of permutations on "day integrated solar flux" and similar terms, I stumbled upon the more accurate term of insolation (which, after the fact, I remembered having heard through science bowl). Searching around some more resulted in this factual page, and further searching led me to a NASA page with all sorts of useful information. Based on values from one of NASA's programs, which takes into account most of the important stuff, here is a plot of the solar intensity as a function of the days of the year:

It's no wonder it feels dark and cold here in the winter. A similar plot of the average solar angle shows how the sun is always lower in the sky here, too.

Of course, the plot does not include the extra atmospheric attenuation from the sun coming in at lower angles. (The same thickness of clouds will require sunlight to travel further as a result.) That gives Ann Arbor and the other northern places an even more severe disadvantage.

Incidentally, the MATLAB code to display the months (where the x axis data is stored as days) is:
monthlengths = [0 31 28 31 30 31 30 31 31 30 31 30];
months = {'J' 'F' 'M' 'A' 'M' 'J' 'J' 'A' 'S' 'O' 'N' 'D'};
set(gca,'XTick',cumsum(monthlengths));
set(gca,'XTickLabel',months);
and I created the graphic with the same script I posted about earlier.