[MUSIC] So we started with a very simple model of the climate of the Earth and the greenhouse effect that was simple enough that we could understand. But not so simple that we have to work on it a while to make it realistic enough to make predictions about the real world. So you remember the layer model relied on light to carry energy between the ground and this pane of glass that we're calling the atmosphere. And it worked, making the Earth warmer because the way the light carried the energy around insisted that the ground should be warmer than the pane of glass. The pane of glass, the temperature is sort of anchored at the skin temperature and then the way these arrows work, the ground had to be warmer than that. Now we sort of enlarge the model by thinking about how the real atmosphere doesn't absorb all the infrared light from the ground, but it's selective because gases are choosy. And so we ended up with this picture where the CO2 is absorbing strongly in the CO2 bend region and there's another region called the atmospheric window, where nothing much absorbs. So, you look down from space. You see some light that's coming from high up in the cold part of the atmosphere and other light that's coming from down near the ground. So, it's more complicated than layer model. Well, it turns out that the temperature structure of the atmosphere. The cold and warm here is the same sense as in the layer model, but the physics behind it are very different. And that's because the temperature in the real atmosphere is set by convection. Which is a process whereby warm gas near the ground rises up and carries its heat up higher in the atmosphere and then the cold stuff high up falls down. So we're gonna talk for quite a while about how this works and how it sets this temperature contrast between the upper atmosphere and the lower atmosphere. And so in the simple layer model we defined the skin layer as being the topmost layer. And that temperature was always anchored at the skin temperature which is only dependent on the intensity of the sunlight and the albedo of the Earth. Then, now for this more complicated model we can also define a skin altitude as the average altitude where infrared light leaves from space. So looking at this figure here, some of the light is coming from all the way up there. Some of it's coming from all the way down at the ground. The average has got to be in the middle someplace. You could sort of, just count up the energy from the different frequencies and ask, where did you come from? And calculate or figure out, visualize a skin altitude which would be an average altitude where energy leaves to space. Another way to do it would be to use the Stefan-Boltzmann equation. To calculate what temperature of a black body would it take to have just as much radiation as the sum of this dim stuff from the cold upper atmosphere in the CO2 bend region. And this bright stuff from the warm ground. So, we can calculate from the infrared model that we just looked at the total energy leaving the system to space. And then we could say, what temperature would a black body have to be to give us that energy? So that's essentially taking this equation and solving for the temperature. And that can give us kind of a skin temperature, and we could figure out what temperature, what altitude in the atmosphere has that temperature and that could be sort of a skin altitude. So it seems like a stretch maybe to you to try to take this very simple skin layer concept and apply it to this case where everything is kind of fuzzier, but it's useful and I'll show you why. Here is a graph of temperature in the atmosphere as a function of altitude and there's a slope, it cools down as you go higher up in the atmosphere. Change in temperature with respect to height, this slope is called by atmospheric scientists, the lapse rate. It's kind of an ugly and not particularly descriptive term but it's pretty entrenched and so gonna stick with it. So imagine that we had a planet that was in energy equilibrium so that it was balancing its energy budgets, like the kitchen sink, when everything was in balance. And this point right here was the skin temperature at the skin altitude that we calculate using these methods. Now we're gonna add some more CO2 to that atmosphere. So we're gonna have more of this stuff that's fairly dim cuz it's coming from the cold atmosphere. This absorption band is gonna get fatter. And in general, that's going to raise the average altitude where the energy is leaving from space. So, if this was the average altitude before, this is what the skin altitude would look like after adding more greenhouse gas. And the temperature at that higher altitude is colder than the temperature was at this altitude because the temperature profile in the atmosphere is following this slope, the lapse rate. Which I'm gonna tell you in the next couple of lessons where this comes from. Today I'm telling you why we care. So by adding more CO2, we've made the skin altitude higher but the temperature is colder up there. And we already know from the layer model that the temperature of the skin always has to be just balanced by the sun and the albedo. So by adding the greenhouse gas, we've knocked the energy balance of the planet out of equilibrium, and so what happens is, now there's more energy coming in than is going out. So it's kinda like water accumulating in our kitchen sink. It makes the planet warmer, and assuming that the profile of temperature with altitude follows the same lapse rate as before, you will get this sort of a change and this much warming at the ground. So it's really the temperature difference between the skin and the ground that drives the greenhouse effect. You could imagine a case where if the lapse rate was determined by the physics of convection that we will talk about in the next lessons to just be zero, so no temperature change with altitude. Then you could add CO2 and make the skin altitude higher. But it would not affect the temperature at the skin altitude so you wouldn't have to warm up anymore. So if the lapse rate were zero like this, there would be no greenhouse effect. You could put as much greenhouse gas as you want in there and it wouldn't change the temperature of the ground. Whereas if the lapse rate is fairly gradual like this red pair of curves, you get that much warming at the ground. If it's a really, really strong function of altitude like the yellow curves, you get a much bigger temperature change at the ground for the same amount of green house gas. So the way this works sort of geometrically, you could say that the change in temperature at the ground is equal to the change in the height, and then this sort of gets back to our sort of factor label kind of thing. Now you can cancel the hs and just get Ts on both sides and see that it works out. This change in temperature with h, that is our lapse rate again. And so you can see that the strength of the greenhouse effect is directly proportional to the strength of that temperature gradient, the lapse rate. So to understand the greenhouse effect, how strong it is, and how it will respond to changes in CO2 to make a climate model that's realistic in other words. We have to understand what is controlling this lapse rate in the atmosphere. [MUSIC]
