2 00:00:09,555 --> 00:00:13,616 We started with a very simple model of the climate of the Earth and the greenhouse effect. 4 00:00:13,616 --> 00:00:16,117 It was simple enough that we could understand but 5 00:00:16,117 --> 00:00:20,265 now, it's so simple that we have to work on it awhile to make 7 00:00:20,265 --> 00:00:24,040 it realistic enough to make predictions about the real world. 8 00:00:24,040 --> 00:00:30,020 You remember, the layer model relied on light 9 00:00:30,020 --> 00:00:35,730 to carry energy between the ground and this pane of glass that we're calling the atmosphere. 10 00:00:35,730 --> 00:00:42,340 And it worked, making the Earth warmer because the way the light carried 11 00:00:42,340 --> 00:00:47,950 the energy around insisted that the ground should be warmer than the pane of glass. 12 00:00:47,950 --> 00:00:51,542 For the pane of glass, the temperature is sort of anchored at the skin temperature, 13 00:00:51,542 --> 00:00:56,710 the way these arrows work, the ground had to be warmer than that. 14 00:00:58,440 --> 00:01:00,990 Now we sort of enlarge the model by thinking 15 00:01:00,990 --> 00:01:04,330 about how the real atmosphere doesn't absorb all the infrared 16 00:01:04,330 --> 00:01:08,130 light from the ground but it's selective because gases are choosy. 17 00:01:08,130 --> 00:01:12,870 We ended up with this picture where the CO2 is absorbing strongly in 18 00:01:12,870 --> 00:01:17,390 the CO2 bend region and there's another region 19 00:01:17,390 --> 00:01:19,860 called the atmospheric window where nothing much absorbs. 20 00:01:19,860 --> 00:01:22,780 You look down from space, you see some light that's 21 00:01:22,780 --> 00:01:26,000 coming from high up in the cold part of the atmosphere and 22 00:01:26,000 --> 00:01:29,070 other light it's coming from down near the ground. 23 00:01:29,070 --> 00:01:32,250 It's more complicated than layer model. 24 00:01:32,250 --> 00:01:34,570 Well it turns out, that the temperature structure 25 00:01:34,570 --> 00:01:38,690 of the atmosphere, the cold and warm here, is 26 00:01:38,690 --> 00:01:41,110 the same sense as in the layer model 27 00:01:41,110 --> 00:01:43,680 but the physics behind it are very different. 28 00:01:43,680 --> 00:01:46,920 That's because the temperature in the real atmosphere 29 00:01:46,920 --> 00:01:51,370 is set by convection, which is a process whereby 30 00:01:51,370 --> 00:01:56,260 warm gas near the ground rises up and carries its heat up higher 31 00:01:56,260 --> 00:01:59,394 in the atmosphere and then the cold stuff high up falls down. 32 00:01:59,394 --> 00:02:02,790 We're going to talk for quite a while about how this works and 33 00:02:02,790 --> 00:02:05,740 how it sets this temperature contrast between 34 00:02:05,740 --> 00:02:07,771 the upper atmosphere and the lower atmosphere. 35 00:02:07,771 --> 00:02:19,340 In the simple layer model we defined the skin layer as being the topmost layer 37 00:02:19,340 --> 00:02:21,790 and that temperature was always anchored at the skin temperature, 38 00:02:21,790 --> 00:02:24,570 which is only dependent on 39 00:02:24,570 --> 00:02:27,210 the intensity of the sunlight and the albedo of the earth. 40 00:02:27,210 --> 00:02:33,480 Now, for this more complicated model, we can also define a skin altitude 41 00:02:33,480 --> 00:02:39,380 as the average altitude where infrared light leaves from space. 42 00:02:39,380 --> 00:02:41,700 Looking at this figure here, some of the 43 00:02:41,700 --> 00:02:45,296 light is coming from all the way up there, some of it's coming from all the 44 00:02:45,296 --> 00:02:49,210 way down at the ground. The average has got to be in the middle some place. 45 00:02:49,210 --> 00:02:52,660 You could sort of just count up the energy from the 46 00:02:52,660 --> 00:02:56,480 different frequencies and ask where did you come from, and 47 00:02:56,480 --> 00:03:01,560 calculate, or figure out, visualize the, the skin altitude 48 00:03:01,560 --> 00:03:04,850 which would be an average altitude where energy leaves to space. 49 00:03:06,360 --> 00:03:14,450 Another way to do it would be to use the Stefan-Boltzmann equation to calculate 51 00:03:14,450 --> 00:03:19,750 what temperature of a black body would it take to have just as much radiation 52 00:03:19,750 --> 00:03:25,820 as the sum of this dim stuff from the cold upper atmosphere 53 00:03:25,820 --> 00:03:30,040 in the CO2 bend region and this bright stuff from the warm ground. 54 00:03:30,040 --> 00:03:32,070 We can calculate, 55 00:03:32,070 --> 00:03:35,330 from the infrared model, that we just looked at, 56 00:03:35,330 --> 00:03:40,360 the total energy leaving the system to space. 57 00:03:40,360 --> 00:03:42,330 And then we could say what temperature would a 58 00:03:42,330 --> 00:03:44,720 black body have to be to give us that energy. 59 00:03:44,720 --> 00:03:48,900 That's essentially taking this equation and solving for the temperature. 60 00:03:48,900 --> 00:03:52,060 And that can give us a kind of a skin temperature and we could figure 61 00:03:52,060 --> 00:03:54,350 out what altitude 62 00:03:54,350 --> 00:03:57,080 in the atmosphere has that temperature, and that 63 00:03:57,080 --> 00:03:59,400 could be sort of a skin altitude. 64 00:03:59,400 --> 00:04:01,650 So it seems like a stretch maybe to you 65 00:04:01,650 --> 00:04:04,760 to try to take this very simple skin layer concept 66 00:04:04,760 --> 00:04:07,010 and apply it to this case where everything is kind of fuzzier 67 00:04:07,010 --> 00:04:09,750 but it's useful, and I'll show you why. 68 00:04:11,190 --> 00:04:17,880 Here is a graph of temperature in the atmospehre as a function of altitude. 69 00:04:17,880 --> 00:04:23,050 And there's a slope, it cools down as you go higher up in the atmosphere. 70 00:04:23,050 --> 00:04:26,650 Change in temperature with respect to height, this 71 00:04:26,650 --> 00:04:30,880 slope is called by atmospheric scientists, the lapse rate. 72 00:04:30,880 --> 00:04:34,470 It's kind of a ugly and not particularly descriptive term 73 00:04:34,470 --> 00:04:37,370 but its pretty entrenched and so going to stick with it. 74 00:04:38,530 --> 00:04:44,800 Imagine that we had a planet 75 00:04:44,800 --> 00:04:48,200 in energy equilibrium, so that it was balancing its energy budgets, 76 00:04:48,200 --> 00:04:53,220 like the kitchen sink when everything was in balance, and this point right 77 00:04:53,220 --> 00:04:56,840 here is the skin temperature at the 78 00:04:56,840 --> 00:05:00,890 skin altitude that we calculate using these methods. 79 00:05:00,890 --> 00:05:04,600 Now, we're going to add some more CO2 to that atmosphere. 80 00:05:04,600 --> 00:05:08,119 We're going to have more of this stuff that's fairly dim because 81 00:05:08,119 --> 00:05:13,440 it's coming from a cold atmosphere, this absorption band is going to get fatter. 82 00:05:13,440 --> 00:05:17,470 And in general, that's going to raise the 83 00:05:17,470 --> 00:05:22,160 average altitude where the energy is leaving from space. 84 00:05:22,160 --> 00:05:27,120 If this was the average altitude before, this is what the 85 00:05:27,120 --> 00:05:33,140 skin altitude would look like after adding more greenhouse gas. 86 00:05:33,140 --> 00:05:35,650 And the temperature at that higher altitude is 87 00:05:35,650 --> 00:05:38,900 colder than the temperature was at this altitude because 88 00:05:38,900 --> 00:05:45,200 that temperature profile in the atmosphere is following this slope, the lapse rate, 89 00:05:45,200 --> 00:05:49,760 which I'm going to tell you in the next couple of lessons where this comes from. 90 00:05:49,760 --> 00:05:51,350 Today I'm telling you why we care. 91 00:05:53,130 --> 00:05:58,540 By adding more CO2, we've made the skin altitude higher 92 00:05:58,540 --> 00:06:04,100 but the temperature is colder up there. And we already know from the layer 93 00:06:04,100 --> 00:06:06,670 model that the temperature of the skin always has 94 00:06:06,670 --> 00:06:09,920 to be just balanced by the sun and the albedo. 95 00:06:09,920 --> 00:06:14,270 So by adding the greenhouse gas we've knocked the 96 00:06:14,270 --> 00:06:18,020 energy balance of the planet out of equilibrium. 97 00:06:18,020 --> 00:06:22,470 And so what happens is now there's more energy coming in than is going out, 98 00:06:22,470 --> 00:06:24,330 it's kind of like water accumulating in 99 00:06:24,330 --> 00:06:27,270 our kitchen sink, it makes the planet warmer. 100 00:06:27,270 --> 00:06:29,520 And assuming that the 101 00:06:30,950 --> 00:06:36,550 profile of temperature with altitude follows the same lapse rate as before, 102 00:06:36,550 --> 00:06:41,320 you will get this sort of a change and this much warming at the ground. 103 00:06:42,570 --> 00:06:44,850 It's really the temperature difference between the 104 00:06:44,850 --> 00:06:51,030 skin and the ground that drives the greenhouse effect. 105 00:06:51,030 --> 00:06:56,140 You can imagine a case where if the lapse rate was 106 00:06:56,140 --> 00:06:59,280 determined by the physics of convection that we will 107 00:06:59,280 --> 00:07:02,430 talk about in the next lessons, to just be zero, 108 00:07:02,430 --> 00:07:06,080 so no temperature change with altitude, then you could 109 00:07:06,080 --> 00:07:10,420 add CO2 and make the skin altitude higher, 110 00:07:10,420 --> 00:07:13,632 but it would not affect the temperature at the skin altitude, 111 00:07:13,632 --> 00:07:17,010 so you wouldn't have to warm up anymore. 112 00:07:17,010 --> 00:07:22,360 If the lapse rate were zero like this there would be no greenhouse effect. 114 00:07:22,360 --> 00:07:24,160 You could put as much greenhouse gas as you want 115 00:07:24,160 --> 00:07:26,930 in there and it wouldn't change the temperature of the ground. 116 00:07:28,332 --> 00:07:32,840 Whereas, if the lapse rate is fairly gradual like 117 00:07:32,840 --> 00:07:36,960 these red pair of curves, you get that much warming at the ground. 118 00:07:36,960 --> 00:07:39,070 If it's a really, really strong function 119 00:07:39,070 --> 00:07:41,250 of altitude like the yellow curves, 120 00:07:41,250 --> 00:07:43,340 you get a much bigger temperature change at the ground 121 00:07:43,340 --> 00:07:45,900 for the same amount of greenhouse gas. 122 00:07:45,900 --> 00:07:50,450 The way this works geometrically, you could say 123 00:07:50,450 --> 00:07:53,980 that the change in temperature at the ground, is equal to 124 00:07:53,980 --> 00:07:57,040 the change in the height and then this gets 125 00:07:57,040 --> 00:07:59,950 back to our factor label kind of thing now. 126 00:07:59,950 --> 00:08:03,990 You can cancel the h's and just get t's on both sides and see that it works out. 127 00:08:03,990 --> 00:08:08,400 This change in temperature with h, that is our lapse rate again. 128 00:08:08,400 --> 00:08:11,188 And so you can see that the strength 129 00:08:11,188 --> 00:08:14,878 of the greenhouse effect is directly proportional to 130 00:08:14,878 --> 00:08:19,571 the strength of that temperature gradient, the lapse rate. 131 00:08:19,571 --> 00:08:23,243 To understand the greenhouse effect, how strong it is and how 132 00:08:23,243 --> 00:08:27,459 it will respond to changes in CO2, to make a climate model 134 00:08:27,459 --> 00:08:30,247 realistic in other words, we have to understand 135 00:08:30,247 --> 00:08:33,542 what's controlling this lapse rate in the atmosphere.