So now I want to do a thought experiment. What if the Earth had no atmosphere? What would its temperature be, in that situation? So, I've constructed here a graph of the input from the Sun. That's 1362 watts per meter squared, at the top of the Earth's atmosphere. This energy gets absorbed unevenly, around the Earth. Half of it is in sunlight, remember, but half of it is in darkness. But this energy is absorbed, and for the Earth to be in thermal equilibrium. In other words, the temperature of the Earth is neither rising or decreasing, and is just reached at a steady state. If the Earth is in thermal equilibrium, then the amount of energy emitted in the infrared part of the spectrum, must equal the incoming solar radiation. And that's what we see here. The incoming solar radiation equals the outgoing terrestrial radiation in order for the Earth to be in thermal equilibrium. Well, it turns out that we can use those equations, the radiation laws, to calculate what the temperature of the Earth would be in this situation. So when we do this, we find that the temperature of the Earth, if it had no atmosphere, would be -18 degree Celsius, globally average temperature. But we know that the Earth has a much higher temperature than that, from the observations. We can calculate what the average temperature on the Earth is, and we find that it has an average temperature of 15 degrees Celsius. So there's a 33 degree Celsius difference between our simple calculation of the Earth without an atmosphere, and the temperature that the Earth actually has. So we can see that the atmosphere is adding 33 degrees of temperature, to the average surface temperature of the Earth. So to reiterate this point once again, there's a 33 degree difference here between an Earth without an atmosphere, and an Earth with an atmosphere. Where does this come from? It's the greenhouse gases in the atmosphere. The water vapor, the carbon dioxide, the methane, and some other trace gases. Why is this important? These greenhouse gases absorb infrared radiation, but they are transparent to the solar radiation. Thus, we see the solar radiation penetrating through the atmosphere to go the ground. It gets absorbed by the ground, and then the temperature of the Earth then results in an emission of infrared radiation. And this infrared radiation is absorbed by the atmosphere. Let me show you this in a little bit more detail. So, here's a schematic of the Earth without an atmosphere. At thermal equilibrium, the amount of incoming solar radiation must equal to the amount of outgoing longwave radiation emitted by the Earth. And you can see because the solar radiation is more intense, I've indicated one beam of radiation here, with more radiation being emitted by the Earth, it's at a lower energy. When we do this calculation as I showed before, we end up with a temperature of -18 degrees Celsius. Now, what happens when we have an atmosphere? Specifically, an atmosphere that contains greenhouse gases. Well, the amount of incoming solar radiation still has to equal the amount of outgoing long wave radiation at the top of the earth's atmosphere. But the story of that longwave radiation, as it goes up through the atmosphere is a very different one. Specifically, we have the solar radiation that travels through the atmosphere because remember these greenhouse gases are transparent to solar radiation. They don't absorb solar radiation. So radiation gets to the ground, where it heats up the ground. And of course, having a temperature, the ground now emits longwave radiation. This longwave radiation now has the potential to be absorbed by the greenhouse gases in the atmosphere. The absorption of this radiation causes this temperature to increase. With this increasing temperature, these gases are now emitting longwave radiation. Some of that radiation goes up, and tries to get out at the top of the atmosphere. The other part of that radiation comes down, back towards the ground, which may reach back down to the ground, and heat up the ground, heat up the lower atmosphere. So, the reason why the Earth's atmosphere with greenhouse gases is warmer, than the Earth with an atmosphere that has no greenhouse gasses is because of this emission of long wave radiation back down to the surface. This is causing that 33 degree C increase in the temperature. So, I want to conclude this lecture with the summary of why the atmosphere so important to Earth. First, without an atmosphere, the Earth would have wide swings in temperature between the day side and the night side. Just look at the Moon or Mars, which have 80 to 100 degrees difference in temperature from one side to the other. 2, without the atmosphere there would be no protection from harmful radiation, such as the x-rays and the ultraviolet light that are stopped by the thermosphere, and the ozone in the middle atmosphere. So life would still develop, but it would be much different, and we wouldn't have the kind of lifeforms that we have now. Third, the atmosphere transfers energy from the tropics to the poles, and so without this, there would be a huge gradient in temperature between the warm tropics, and the much colder polar regions. Fourth, the atmosphere provides winds and precipitation, and this leads to weathering of the rocks, and the erosion of the continents. So the whole part of the rock cycle that depends on the recycling of rocks and minerals, and so forth would not occur. And finally, carbon dioxide and methane in the atmosphere both show strong relationships to the Earth's climate. We see in ice cores from Greenland and Antarctica, the changes in the atmospheric concentration of carbon dioxide and methane. And we see these strongly linked to glacial and interglacial cycles, relatively warm periods, and relatively cool period in the recent past. And we recognize these relationships, we don't know if they're cause and effect or not. But there's certainly a strong indication that there's something going on here between these greenhouse gases and the Earth's temperature.
