It's a surprise to me that it is possible to construct a climate model that is meaningful in the space of a blog post. At least you can if you're interested in atmospheric temperatures. This isn't the case for the oceans, which is interesting for different reasons.
Here it is: T = (S*(1-a)/r^2/4/s)^(1/4)
1 line, easily dumped into your spreadsheet program of choice or calculator. I'll give some sample spreadsheet code at the bottom.
T is the temperature the earth radiates to space with.
S is the solar constant, which is about 1367 Watts per square meter (on a plane face-on to the sun, which our spheroidal earth isn't -- that's why the division by 4)
a is the albedo of the earth -- how much of the sun's energy is bounced straight back to space (now an observable quantity, it's about 0.30)
r is the average earth-sun distance, 1.00 Astronomical Unit
s is the Stefan-Boltzman constant, 5.67*10^(-8)
and ^ means 'to the power of' (x^y key on calculators, this symbol in spreadsheets).
If we plug in this values, we see that T is 255 K (-18 C, 0 F). ... and this matches the observations fairly well. (I've rounded several of the numbers above, and this one -- research the figures yourself and plug them in, and then go looking on your own for reference figures on how much energy the earth radiates to space and its equivalent temperature. This is one of the 'projects' I mentioned)
What happened? Certainly where I live (Washington DC area) seldom gets that cold, and I did say this was a meaningful model. The thing is, the model is meaningful for two reasons, first, that it does match up with the observations fairly well (temperature as radiated to space -- we have satellites circling the earth to check this figure now). Second, the model does not match up to the figure we really want -- the temperatures at the surface.
This tells us that the model is missing something important that affects the surface temperature, but not the temperature the earth shows to space. Whatever it is, its average effect is about 33 K (60 F).
But first, play around with those numbers and see what happens to temperature. In the next part, I'll go in to how to derive this model. Third part will be some looking at analyzing it. There's more here than may meet the eye.
If you're comfortable with naming variables, just paste this formula in to a1 and name the variables S, r, a, s elsewhere. The figures in a1 will be the temperature.
s: 5.67e-8 (cannot change)
if you're less comfortable with your spreadsheet, use this formula in a1:
b4: 5.67e-8 (cannot change)