Hours of Daylight and Angle of Light

I learned in elementary science class that the reason it’s colder in the winter is that the sunlight is coming in at an angle. We did an experiment with a piece of paper and a lamp that stuck with me.

However, it occurs to me that another reason that it’s colder in the winter is that there are simply fewer hours of daylight. There’s less time to heat up the ground/water/atmosphere, and more time for the heat to radiate out to space. I suppose that you could say that nighttime is just low angle light taken to an extreme.

Which effect dominates? Would a full 12-hour day of lower angle light be warmer than a 9-hour day of full light?

There’s another effect, too. During summer and winter, the earth is farther from the sun than during spring and fall. I’m not sure of the exact numbers, but I do know that the radiation intensity drops with respect to the square of the distance. Of course it’s farther in the summer, too, but fall and spring would probably be a bit cooler if we didn’t travel closer to the sun during those seasons.

Not quite. The Earth is closest to the Sun in January, and furthest in July. Spring and fall are in between. But that’s obviously a smaller effect than the inclination of the axis, given that the Northern Hemisphere is significantly colder in January than it is in July.

As for the OP’s question, you can’t really separate the two effects, since they have the same root cause: Both are a result of the tilt of the Earth’s axis.

The difference in solar intensity caused by the differing distances at perihelion and aphelion is about 7% (more than I expected), sez NASA.

However, they also go on to say that:

Generally not, as you can tell if you visit high latitudes in the summertime. Far above the Arctic Circle, you get 22±hour stretches of daylight at a time. But it’s still much colder there than at the equator where a summer day is only 12 hours long.

If you’re looking at smaller changes in latitude, I suppose the effect of more direct light might slightly outweigh a shorter day, but in general, it’s the sun’s angle that makes the difference.

Anyway, your contrafactual premise is creeping me out, because it’s geometrically unthinkable. You can’t have both shorter days and higher solar altitudes, if you’ve got a rotating spherical planet revolving in a nearly circular tilted orbit about a sun. (See the diagrams in this explanation, for example.) And now you’ve got me trying to figure out what kind of solar system geometry would be necessary so that that could happen, which is a completely pointless speculative exercise. Take yer factual answer and get outta here, kid. :wink:

I mean, of course, that you can’t have shorter days and higher solar altitudes combined for a given terrestrial latitude. For any given latitude, as the days get shorter, the sun gets lower in the sky, and that’s the way it’s gotta be for a rotating sphere.

You’re asking about insolation, the amount of solar radiation to strike a given location on the Earth’s surface over a course of a day.

Both angle and duration of sunshine affect insolation, via a mathematical formula involving sines and integration. Check out the graph near the bottom of the link for some interesting effects:

On the June solstice, as you move from the equator to 30 degrees N, the amount of insolation increases due to the longer days. Then, as you move from +30 to +60, insolation decreases even though the days continue to get longer–because the lower angle of the sun has more effect.

But then, as you move from +60 to +90, insolation increases again. The 24 hours of full daylight at the pole more than compensates for the fact that the Sun never rises more than 23 degrees above the horizon. On June 21, the North Pole gets more insolation than anywhere else on Earth.

It’s colder because of the residual effect of the other 10 months of the year, when the Poles get virtually zero insolation. But they do get a lot at the solstice.

So as you see there is no simple answer as to which cause has more effect.

I take it you’ve never been in the Southern Hemisphere?

As other posts have said, you can’t really disentangle the two effects. However, it’s not too hard to figure out the difference between insolation at noon on the Summer and Winter Solstices at a given latitude; this might give you a better feel for the degree to which it varies. If L is your latitude, then the insolation your get at noon on the Summer Solstice is

I[sub]s[/sub] = I[sub]0[/sub] cos(L - 23.5[sup]o[/sup])

and at the Winter Solstice, it’s

I[sub]w[/sub] = I[sub]0[/sub] cos(L + 23.5[sup]o[/sup])

where I[sub]0[/sub] is some baseline isolation. For someone at the latitude of the OP, this corresponds to the insolation at noon on the Winter Solstice being only about 54% of the insolation at noon on the Summer Solstice. This calculation makes the assumption that the insolation is constant throughout the year, which is not, as noted above, strictly correct; taking this into account brings the noon winter insolation up to 58% of the noon summer insolation.

For comparison, the day length at the Winter Solstice (again, at the latitude of the OP) is about 68% of the day length at the Summer Solstice.

I was in Brazil for a month last summer (their winter, which was quite a lovely temperature). It was awesome.

I was misunderstanding the scale of the picture I was using to describe what I figured would be a small but significant effect of the distance from the sun. Based on the picture I was looking at, I chose my words carefully so that they would apply to both the northern and southern hemispheres.

This is pretty much what I was looking for.

I realize that you can’t have one effect without the other on the surface of a sphere, and that “at an angle” isn’t precise, but I wanted to get a feel for it. It seems like even long summer days at extreme lattitude doesn’t make them really hot.

Nice graphs, Freddy.

You could isolate the angular one by living on a cylindrical planet.

No, with the sun off at (conceptual) infinity, you’ve still got the same day length and same sun-angle at any “latitude”.

Yes - exactly - if the cylinder has a tilt like the earth, it can experience a variety of seasonal changes to the angle of sunlight incidence, without any corresponding change in day length.

There are periods when this can happen. For example given curvature considerations of the earth, Daylight time at the equator and at the equinox will be slightly shorter and the altitude of the sun will be slightly higher compared to a period approaching the summer solstice near the Tropic of Cancer.

In other words, there’s longer daylight during the summer solstice at the Tropic of Cancer than during the equinox at the equator.

Daylight at the equator is always ~12 hrs. It is with increasing latitude that the difference in daylight duration increases and decreases with the seasons.

Good point.