Does the Greenhouse Effect Contradict the 2nd Law of Thermodynamics?

Occasionally I hear people claim that the greenhouse effect isn't real because it would contradict the 2nd law of thermodynamics. The idea behind this is that the atmosphere is cooler than the Earth's surface, and the 2nd law of thermodynamics says that the net flow of heat always goes from hot to cold. Therefore, the Earth's atmosphere can't heat the Earth's surface. Therefore, the greenhouse effect can't exist in a universe in which the 2nd law of thermodynamics is operable.

The silliness of this objection can become apparent with a simple analogy. If you walk outside with a thin t-shirt on a cold day (let's say 20°F), you'll quickly feel cold, and the surface of your skin will be significantly colder than normal. If you find a winter coat outside, its temperature will be 20°F. But if you put it on, you will begin to warm. It's not that the coat is generating heat and sending it to your body. It's simply slowing down the rate at which heat leaves your body and allows your body to maintain a warmer temperature. With or without a blanket, the net flow of heat is from the your body (~98.6°F) to the outside (20°F).

In much the same way, the Sun radiates solar energy towards the surface of the Earth, and since the Sun is much hotter than the Earth, the net flow of heat is from hot to cold. Some of that solar energy is absorbed by the Earth and radiated back towards space as IR light. Since space is much colder than the Earth's surface, the net flow of heat is from hot to cold. Greenhouse gases function as a jacket that slows down the rate of heat loss towards space, allowing the surface to maintain a warmer temperature than it otherwise would. That's the short answer to this objection. 

I think there are two reasons why people object to the science on this. The first comes from the way thermodynamics is simply explained. It's often stated that heat flows from hot to cold, and superficially that's true, but with the caveat that the net flow of heat is from hot to cold. That is, all objects with a temperature emit thermal radiation in all directions; this means necessarily that they emit heat the direction of both hotter and colder objects, but the net flow is from hot to cold. The second reason comes from the way the greenhouse effect is simply explained. In short explanations of the greenhouse effect, we're told that greenhouse gases trap heat in the climate system to keep the earth about 33°C warmer than the Earth's effective temperature of -18°C. From this I suspect that people believe that the atmosphere is thought to be a generator of heat which it sends to the surface, rather than functioning like a jacket that slows down the rate of heat loss from the Earth's surface to space. So let's look at this a little more closely.

The Earth's surface is constantly receiving energy from the Sun. If the Earth were just a rock hurling through space far away from any star, it's temperature would be ~2.7 K. But because we're orbiting a star and receiving heat from it, we're much warmer. The Sun is constantly shedding its heat towards us, and so the Earth is constantly receiving heat. However, like the Sun, the Earth is also constantly shedding its heat towards space. If the Earth lacked the ability to shed heat, the Earth's surface would be much hotter than it is. Venus doesn't shed heat very well, and so it's a balmy ~750 K compared to our comparably comfortable ~288 K. However, if the Earth lacked any atmosphere and had no greenhouse effect, the Earth's surface would only be ~255 K. The Earth's surface is colder than Venus and warmer than its effective temperature because 1) we have a greenhouse effect but 2) it's not nearly as strong on Earth as it is on Venus (and because the Earth is a bit farther away from the Sun).

The Earth's actual surface temperature essentially depends on the rate at which it receives heat and sheds heat. If the Sun were to increase its output, the earth's surface would receive heat more rapidly than it loses it; the Earth's temperature must increase, and this increase in temperature causes the Earth's surface to shed heat at a higher rate, and a new equilibrium would be reached at a higher temperature. Likewise, if greenhouse gas concentrations increase, the Earth's surface will not shed heat as well, and the Earth's temperature must increase. As it increases, though, the Earth sheds heat more rapidly until the Earth the rate it sheds heat equals the rate it receives it again. At no point is there a net flow of heat from cold to hot. 

The above chart shows incoming solar radiation at 342 W/m^2, of which 107 W/m^2 is reflected either in the atmosphere or from the surface, leaving 235 W/m^2 to be absorbed by the atmosphere and the surface. The Earth's surface at an equilibrium, stable temperature must therefore shed heat at a rate equal to the 235 W/m^2 it receives. Whenever an imbalance occurs, whether in the rate at which the earth receives or sheds energy, the Earth's temperature must change until the imbalance is closed. This is required by the laws of thermodynamics.

In reality, the greenhouse effect was essentially discovered by Fourier in the 1820s, even though he didn't know about greenhouse gases, because of thermodynamics. Fourier understood that the Earth's surface was much warmer than it should be given its distance from the Sun. Since energy can't be created out of nothing, he reasoned that the cause of this discrepancy had to do with some property of the atmosphere slowing down the rate at which the Earth's surface sheds heat. It wasn't until ~30 years later that experiments by Eunice Foote and John Tyndall discovered how gases like CO2 make the greenhouse effect work.

This is another aspect of climate science about which there is essentially no disagreement among climate scientists. You can find essentially the same explanation, with different examples and emphases, from Roy Spencer, Stefan Rahmstorf at RealClimate and Skeptical Science. Denial of the greenhouse effect is now essentially a denial of observational evidence, since we now can observe the greenhouse effect with IR sensors and satellites. There is absolutely no merit to the claim that the greenhouse effect breaks the laws of thermodynamics; quite to the contrary, it depends on them.