This one stirred up many interesting and varied arguments at lunch, even spilling over to email throughout the day:
How much of the variation in earths’ temperature across the seasons is accounted for in terms of (1) the changing daylight hours (resulting in either shorter or longer exposure times) vs (2) changing altitude of the sun (resulting in more or less incident flux)? Does your answer depend on where you live? More importantly, how do you know and why do you believe?
As usual, guesses, intuition, wild speculation, careful theory, contrived experiments, and natural data are welcome.
** My bigger point in bringing this up was more to these questions: What does it mean to explain the seasons? How do we want students to approach and attempt to make sense of the seasons? **
Teach. Brian. Teach. 
Damn! I wanna teach at your school!
It’s gotta be more angle than duration (and you can’t mean the *earth’s* temperature, right? Gotta be local temperatures-earth’s average temp must be pretty constant across the seasons). My evidence would be that the sun shining on me feels much, much warmer at noon in July than it does either (1) at noon in January, or (2) in the evening in July.
So speaks a Minnesotan. More exposure to our January sun ain’t gonna help much.
Great question. Sorry I wasn’t there to hear the scientists hashing this out.
Yes, I do mean local temperature. And, you’re intuition about angle being dominant factor is aligned with most others’ intuitions as well. Most of the hashing involves figuring out exactly how much each contributes, with at least one thinking that it might not be possible to disentangle the two mechanisms.
Well the theoretical model would be integral calculus, right? Do I accumulate more energy by increasing the limits of integration, or by increasing the integrand? Defining “amount of contribution” is the tricky bit, I guess (that, and the integral is probably really ugly-but we have tools for that!)
What makes the measure really tricky, I suppose, is that the contribution of each is going to depend on the present value of each. A small increase in sun angle will matter differently at different times of year, likewise a small increase in exposure time. And they are not likely to be proportional to each other.
Which brings us back to observing what a lovely question this is and how wonderful it must be to have you as a colleague.