[MUSIC] As promised, we're going to enrich the one layer model, with a two layer and if you want the three with four the n-layer model. And as we have seen, we don't really need to do that for the Earth in order to explain the surface temperature of the Earth, because even a one layer model, is a tiny bit too much. So definitely, we went from having a temperature at the surface of the Earth without atmosphere which was too low, with the temperature with one layer which was already a bit too high. So adding a second layer, definitely's going to take us in the wrong direction, so why doing so? Because we want a simple model that explains, not just the temperature of the earth but also the temperature of other planets in the solar system. And actually the temperature of any planets on any system in which there is some atmosphere in which there is energy in and energy out, which is pretty universal. So, the simplest enrichment of the one layer model, is the two layer model. So we imagine that some distance above the first layer, we have a second concentric layer. And, we're still going to use not a lot of imagination the principle of energy in, equal to energy out, and we're going to apply this principle layer by layer. So here there is my artist impression of what is going on at the bottom you can see there is the surface of the earth. Then I have the lower atmosphere which is the first gray horizontal bar, and then the second layer which is called upper atmosphere, which is the second gray horizontal bar. And the reasoning goes as follows, first of all I have energy in coming from the sun, that is the 238 watts per square meter. And if I look at energy out from the whole system which is Earth plus first layer plus second layer, I must get 238 watts per square meter out. So that is the arrow at the far right, 238 out. The energy only escapes in the system from the second layer, therefore for the energy in and energy out balance the upward emission of a second layer, must be equal to the energy in from the sun 238 watts per square meters. And we have said that the radiation is isotropic, therefore by symmetry, the downward emission from the second layer must also be, 238 watts per square meter. So all together the second layer is a meeting 238 times 2, 476 watts per square meter, half of output, half of it downwards. By energy balance then must be applied to each block in my model, I know that it must also be absorbing 476 watts per square meter, that can only get from the upward emission from the first layer. Therefore the first layer also the first layer, emits isotropically so it's going to emit 476 upwards but also, 276 downwards. And now we have finally reached the surface of the Earth, which receives 238 directly from the sun, and an additional 476 from the first layer. So in this two layer model the surface of the Earth, receives altogether 238 + 476 or if you want 238 times 3, which is 714 watts per square meters. And now I can do my energy in equal energy out using my Stefan-Boltzmann law and solving equating this to sigma, t to the fourth. And I obtain a surface temperature of 333 Kelvin, which is 62C definitely, it is too hot. But what the purpose of doing this exercise is to show that I can generalize the one layer model to use not just for the Earth, but if you want for any number of layers which could be appropriate to different planets. And it is not difficult to work out by repeating, you see that every time I add one layer, I multiply the S minus 1, alpha by the number of layers. And then I do my usual Stefan-Boltzmann law and therefore I obtain a function such as this, that gives me the temperature corresponding to different number of layers. So this relationship is displayed in this graph here, in which I have the number of layers and it looks quite extravagant, I'm going up to one under number of layers, and we shall see that for some planets that is not ridiculous. And I have the surface temperature for three possible inputs of energy, 150, 200 and 250 corresponding to the blue, the orange, and the gray line, respectively. The important thing is that adding more layers mean modeling an atmosphere with more and more greenhouse gases, more layers, more greenhouse gases, higher surface temperature. In reality we work backwards, given the surface temperature, we work out the effective number of layers and this can be done for any planet, not just for the Earth. When we do this, we get what is in table one, and this will answer some of the mysteries with which we started our discussion. Here I have a few planets, Mercury and Venus, remember Mercury much closer to the sun than Venus, and Earth and Mars, I have S, S remember is the energy that is received from the sun. I have the abedo, which is 0.1 from mercury and 0.7 from venus. So venus reflects quite a lot, but the surface temperature of venus is much much higher and it is 735. The effective number of layers on Venus is 82 as opposed to Mercury, In the case of Earth, the effective number of layers, not surprisingly, is between zero and one because with one we have already overshot a bit and the explanation of why Mars is not that much colder. Then the Earth is because the effective number of days is 0.22. And you could say well, but you're just working out a number in order to reconcile what you have measured in another way. So it doesn't have a lot of explanatory power. No. Not really. Because we can independently measure the composition of the atmosphere on mercury, on venus and on mars and to check that all of this makes sense. So why should we have an 82? A number like 82 of effective layers on venus? Well, mercury is virtually not. No atmosphere, Therefore an of 0.052 makes perfect sense. On the other hand, the atmosphere of venus is 96.5%. Made up of C. 02 is virtually C. 02 and 3.5% of die atomic nitrogen, Not only, but the surface pressure on venus is fantastic. Is 1300 Pcs, which is 90 times the pressure of the earth. And when you put these things together, then you understand that the effective number of layers of 82 makes sense. So despite the very high Albita, which is 0.7 for venus, it's thick cloud of powerful greenhouse gases raises the surface temperature 550 Calvin degrees above the earth and almost 300 above that of mercury, despite the fact that mercury is so much closer to the sun than venus is. So what we have done is to create a model that explains simply the role played by C. 02 emissions, even in very small quantities to account for changes in temperature of the surface of planets and what is of concerns to us for the surface of the planet Earth. So this is the these are the concepts we're going to use and we're going to build on to continue our development that will be now looking at the persistence of a c. 02 concentration in the atmosphere.