WEBVTT 00:01.433 --> 00:03.833 RONALD SMITH: What have we learned? 00:03.833 --> 00:05.833 Well, we've learned about the atmosphere and the ocean, and 00:05.833 --> 00:07.433 how they work. 00:07.433 --> 00:11.603 The physical processes that go on to make the ocean and 00:11.600 --> 00:15.000 atmosphere, like we find them on our planet. 00:15.000 --> 00:17.670 We've also learned a little bit about how they're changing 00:17.667 --> 00:20.597 in time and what processes are causing them 00:20.600 --> 00:21.700 to change as well. 00:21.700 --> 00:24.930 So in a nutshell, that's kind of what we've learned. 00:24.933 --> 00:26.333 And how did we do it? 00:26.333 --> 00:29.433 This may not have been apparent to you, but as I look 00:29.433 --> 00:33.833 at the course, we've been using three intellectual 00:33.833 --> 00:38.573 approaches as we've gone through this material. 00:38.567 --> 00:43.267 Observation has been one, a very important one. 00:43.267 --> 00:48.427 Quantification, trying to get numbers onto everything. 00:48.433 --> 00:51.273 Amounts, numbers, and units. 00:51.267 --> 00:54.367 And then logic, interpretation, and 00:54.367 --> 00:55.927 explanation. 00:55.933 --> 00:58.833 Why are things the way they are? 00:58.833 --> 01:00.133 How do things connect? 01:00.133 --> 01:03.673 How do physical principles explain this phenomena, but 01:03.667 --> 01:06.327 also that phenomena. 01:06.333 --> 01:09.973 So observations, quantification, and I guess 01:09.967 --> 01:14.427 explanation are the themes, or the approaches, that we've 01:14.433 --> 01:16.533 used going through the course. 01:21.000 --> 01:22.300 What can we do with this? 01:22.300 --> 01:25.630 Well, that's not so easy maybe. 01:25.633 --> 01:30.773 On a kind of a trivial basis, you could use the material of 01:30.767 --> 01:34.127 this course to lead you into more advanced courses. 01:37.433 --> 01:39.003 If you need--if youwant to chat with me about any of 01:39.000 --> 01:41.570 that, I'd be more than happy to talk to you about what 01:41.567 --> 01:45.367 other courses are offered, especially in G&G, which I 01:45.367 --> 01:50.597 know the best. But also EVST, maybe engineering as well has 01:50.600 --> 01:51.870 some other courses. 01:54.000 --> 01:57.030 So you can you know this is an introductory course. 01:57.033 --> 02:02.633 It's a survey course, and for many it can serve as a good 02:02.633 --> 02:06.903 foundation for doing more advanced courses. 02:06.900 --> 02:10.370 Another thing that you can do with this that I think is fun, 02:10.367 --> 02:13.397 I remember when I was a student, I loved to take 02:13.400 --> 02:16.400 material I learned in one course and see if I could fit 02:16.400 --> 02:20.200 it together with things I was learning in other, seemingly 02:20.200 --> 02:22.230 unrelated courses. 02:22.233 --> 02:24.173 Find ways in which they connect. 02:24.167 --> 02:27.967 A few of you over the course have mentioned to me examples 02:27.967 --> 02:32.597 where you've seen the material in here kind of match up in a 02:32.600 --> 02:36.970 certain way with other courses you are taking, have taken, or 02:36.967 --> 02:40.067 maybe you'll find out this will happen in the future as 02:40.067 --> 02:42.227 you take other courses. 02:42.233 --> 02:44.973 But that's really important because this stuff is not 02:44.967 --> 02:48.397 meant to have sharp boundaries around it. 02:48.400 --> 02:55.230 It's not a body of knowledge that's controlled and fenced 02:55.233 --> 02:56.573 off from other disciplines. 02:56.567 --> 02:58.827 It's supposed to be just the opposite. 02:58.833 --> 03:02.673 A subject that has a lot of connections, whether it's 03:02.667 --> 03:07.397 economics, or engineering, or biology. 03:07.400 --> 03:09.070 I hope you'll try to find those 03:09.067 --> 03:12.327 connections as you go forward. 03:15.133 --> 03:21.303 So I think this course you can take a course in music 03:21.300 --> 03:23.370 appreciation. 03:23.367 --> 03:27.327 Or you can take a course in nature appreciation. 03:27.333 --> 03:30.073 Maybe this is a course in nature appreciation, where you 03:30.067 --> 03:32.927 learn a bit about how to observe and appreciate things 03:32.933 --> 03:33.733 that are going on. 03:33.733 --> 03:35.773 Now some would take the other side of the argument. 03:35.767 --> 03:40.067 Some would say, no, no if I approach environmental studies 03:40.067 --> 03:45.427 from a physical or a quantified point of view, it 03:45.433 --> 03:50.773 loses--some of nature loses its appeal to me, its wonder, 03:50.767 --> 03:51.827 its beauty, and so on. 03:51.833 --> 03:54.633 Now I've never found that to be true. 03:54.633 --> 03:59.773 I got into this field because I appreciated what was going 03:59.767 --> 04:01.297 on around me in nature. 04:01.300 --> 04:04.870 And I've found that only deepening as I've studied it 04:04.867 --> 04:05.827 quantitatively. 04:05.833 --> 04:09.303 It's true that when I see something happening now I can 04:09.300 --> 04:12.930 understand, at some level, why it's happening. 04:12.933 --> 04:17.173 But that only leaves another thousand mysteries beyond that 04:17.167 --> 04:18.727 of things that I don't yet understand, 04:18.733 --> 04:19.903 but wish that I did. 04:19.900 --> 04:24.170 So in a sense this I don't think will limit your 04:24.167 --> 04:27.167 appreciation of what goes on in the out-of-doors. 04:27.167 --> 04:29.497 It will just perhaps change a little bit the approach you 04:29.500 --> 04:34.770 take to understanding it. 04:34.767 --> 04:37.527 And the last one I have on my list here is that this 04:37.533 --> 04:39.833 material, I think, is important because there are 04:39.833 --> 04:44.703 some important political and moral questions that face us 04:44.700 --> 04:49.600 as individuals and as a society for which you need 04:49.600 --> 04:53.370 some scientific knowledge in order to understand what 04:53.367 --> 04:56.127 direction we should be going. 04:56.133 --> 04:58.303 You know this idea I'm sure you've heard this in other 04:58.300 --> 05:01.670 courses but this idea of a common, something that's 05:01.667 --> 05:04.697 shared by a number of people. 05:04.700 --> 05:08.230 In the old days in New England, it 05:08.233 --> 05:09.703 was the town green. 05:09.700 --> 05:12.370 Like what's now New Haven Green, and all these old New 05:12.367 --> 05:15.497 England villages, was a common space and people could bring 05:15.500 --> 05:19.030 their cows and their sheep to graze there. 05:19.033 --> 05:21.773 Now that didn't last too long, because after a while they 05:21.767 --> 05:26.067 were too many sheep and too many cows to--they would 05:26.067 --> 05:28.427 overgraze a single common area like that. 05:28.433 --> 05:32.873 But the point is, it's a shared area where everybody 05:32.867 --> 05:36.127 benefited from it, but everybody had to take some 05:36.133 --> 05:38.373 responsibility for it as well. 05:38.367 --> 05:41.367 Well now, the atmosphere and the ocean are 05:41.367 --> 05:42.527 the commons, right? 05:42.533 --> 05:44.903 We all derive benefits from it. 05:44.900 --> 05:48.370 We all pollute it in some way. 05:48.367 --> 05:51.497 And so we have to take responsibility for that. 05:51.500 --> 05:55.670 And that's the basis for these moral and political questions 05:55.667 --> 05:57.567 that I alluded to. 05:57.567 --> 06:02.427 Having a scientific understanding of that system 06:02.433 --> 06:05.133 may help us to make the right choices there. 06:05.133 --> 06:09.533 So that's some of the why's and what's we 06:09.533 --> 06:13.003 did during the term. 06:13.000 --> 06:15.900 I want to finish up by spending the next few minutes 06:15.900 --> 06:17.870 talking about some common themes. 06:17.867 --> 06:21.697 And I passed out this sheet of paper which lists some, and 06:21.700 --> 06:25.370 I've--that's up on the server as well. 06:25.367 --> 06:29.927 I tried to scan through, the other night, the things--kind 06:29.933 --> 06:32.903 of the physical principles that we've run across in this 06:32.900 --> 06:34.370 course more than once. 06:38.367 --> 06:40.997 We didn't always state them in the same way sometimes they 06:41.000 --> 06:43.730 were, because they had such a different context. 06:43.733 --> 06:46.133 They almost seem like a different physical principle. 06:46.133 --> 06:48.173 But today I want to spend some time trying 06:48.167 --> 06:49.567 to tie these together. 06:49.567 --> 06:54.497 Because I don't know I want to OK, agreed there's a lot of 06:54.500 --> 06:57.970 individual little facts and figures that you dealt with 06:57.967 --> 06:58.767 throughout the course. 06:58.767 --> 07:00.267 But I've never looked at it that way. 07:00.267 --> 07:04.727 I've always looked at it as kind of a continuum where we 07:04.733 --> 07:07.673 could learn a few physical principles, and use them over 07:07.667 --> 07:11.027 and over again to solve related or maybe even 07:11.033 --> 07:15.733 seemingly unrelated problems during the semester. 07:15.733 --> 07:17.403 And that's what I want to emphasize today. 07:17.400 --> 07:20.330 I don't think I've done a good enough job during the term 07:20.333 --> 07:24.673 emphasizing those common themes, so my last day here is 07:24.667 --> 07:29.467 an attempt to repair my errors for the semester by paying 07:29.467 --> 07:34.427 more attention to these common themes. 07:34.433 --> 07:36.473 The first, which is not even on the list, 07:36.467 --> 07:40.267 would be physical units. 07:40.267 --> 07:43.627 So we talked about units earlier in the course, and 07:43.633 --> 07:46.503 we've had to use them every time we were doing any kind of 07:46.500 --> 07:49.230 a quantitative calculation. 07:49.233 --> 07:52.203 And I hope you've come to appreciate them as much as I 07:52.200 --> 07:56.200 have. Not only did they provide us a common language 07:56.200 --> 08:01.470 when I say the air density in this room is 1.2 and leave it 08:01.467 --> 08:03.627 there, that conveys essentially zero 08:03.633 --> 08:05.803 information to you. 08:05.800 --> 08:08.830 Unless I put the units onto that, kilograms per cubic 08:08.833 --> 08:11.803 meter, it has no meaning. 08:11.800 --> 08:14.970 So the units are really essential in how we talk to 08:14.967 --> 08:16.797 each other and convey information. 08:16.800 --> 08:20.230 They also have this magical property of allowing us to 08:20.233 --> 08:25.503 check our work, to see whether a formula that we're plugging 08:25.500 --> 08:28.400 numbers into, or that we've derived in some way, is 08:28.400 --> 08:32.630 physically consistent, by seeing if the units work out. 08:32.633 --> 08:35.073 So it's really a wonderful set of things. 08:35.067 --> 08:39.097 And if you're not fully up to speed on that by now, I 08:39.100 --> 08:42.270 recommend that you work a bit on that, because that will 08:42.267 --> 08:45.267 improve everything that you do in this course and in another 08:45.267 --> 08:46.997 physical science courses. 08:47.000 --> 08:52.930 Having a more of a facile understanding and a adeptness 08:52.933 --> 08:58.273 of using units will certainly improve all of your work and 08:58.267 --> 09:00.367 your thinking. 09:00.367 --> 09:03.667 So let's go on then to the first one that I do have on 09:03.667 --> 09:06.567 this list, the properties of air. 09:06.567 --> 09:11.327 And of course, density and how it's related to other things 09:11.333 --> 09:12.073 is important. 09:12.067 --> 09:17.167 And we found that air is a perfect gas. 09:17.167 --> 09:19.227 p equals rho r t. 09:19.233 --> 09:22.403 And so we know that we can solve that equation for 09:22.400 --> 09:23.630 density if we want. 09:26.300 --> 09:28.130 p over r t. 09:28.133 --> 09:32.573 And that shows us that density is a function of pressure and 09:32.567 --> 09:34.097 temperature. 09:34.100 --> 09:38.830 At constant pressure, if you heat up the air it'll expand 09:38.833 --> 09:41.203 and the density will become less. 09:41.200 --> 09:44.600 At constant temperature, if you add pressure to it the air 09:44.600 --> 09:46.800 will compress and the density will become greater. 09:46.800 --> 09:50.530 So we had to know that, and that's so important in all of 09:50.533 --> 09:51.403 the things we did. 09:51.400 --> 09:56.030 And that gas constant, which appears in the perfect gas 09:56.033 --> 09:57.873 law, is different for every gas. 09:57.867 --> 09:58.497 Remember that. 09:58.500 --> 10:02.400 And that can be found by dividing the universal gas 10:02.400 --> 10:04.670 constant by the molecular weight for 10:04.667 --> 10:06.097 that particular gas. 10:06.100 --> 10:10.670 So the other thing we needed to know is heat capacity. 10:10.667 --> 10:17.027 How much heat is stored in a chunk of air at a given 10:17.033 --> 10:19.803 temperature? 10:19.800 --> 10:25.530 And that's important for how the winds transport heat, how 10:25.533 --> 10:28.203 air cools and warms as it rises and sinks in the 10:28.200 --> 10:32.330 atmosphere, we used it over and over again. 10:32.333 --> 10:34.773 OK, so any questions on properties of air? 10:37.467 --> 10:38.467 Properties of water. 10:38.467 --> 10:40.397 Now the list is longer. 10:40.400 --> 10:44.470 Why is the list longer for water than for air? 10:44.467 --> 10:45.167 Very simple. 10:45.167 --> 10:50.927 Air, in the realm in which we experience it, conditions here 10:50.933 --> 10:53.873 on earth, is always a gas. 10:53.867 --> 10:56.997 You can compress it to a liquid. 10:57.000 --> 10:59.200 I suppose, with enough compression and cooling, you 10:59.200 --> 11:02.270 might even reduce it to a solid. 11:02.267 --> 11:04.597 But we never see air in anything other than the 11:04.600 --> 11:07.930 gaseous state, so all we need are those three little things 11:07.933 --> 11:10.173 that I mentioned for air. 11:10.167 --> 11:15.467 But for water, we find it in all three phases on normal 11:15.467 --> 11:16.427 conditions on earth. 11:16.433 --> 11:21.633 Gas, liquid, and solid, that is to say, ice. 11:21.633 --> 11:27.103 So we have to have some information about its density 11:27.100 --> 11:28.630 in the gaseous state--in the liquid state. 11:28.633 --> 11:31.233 And for the oceans, we've learned they're dependent on 11:31.233 --> 11:33.573 salinity and temperature. 11:33.567 --> 11:36.867 We need to know the heat capacity of water. 11:36.867 --> 11:40.097 How much heat can be stored in water at a certain 11:40.100 --> 11:41.330 temperature? 11:41.333 --> 11:43.833 And then everything else here has to do with phase changes. 11:43.833 --> 11:49.173 So at what temperature does it freeze from liquid to solid? 11:49.167 --> 11:54.827 And that was actually slightly dependent on salinity. 11:54.833 --> 11:58.273 Remember, at full ocean salinity, the freezing point 11:58.267 --> 12:00.697 is not zero Celsius, but about -2. 12:00.700 --> 12:03.670 It's not much of a difference, but it makes some difference. 12:03.667 --> 12:06.667 And then there was this definition, or this thing we 12:06.667 --> 12:10.067 talked about, of supercooled water, which happens 12:10.067 --> 12:15.597 frequently in clouds in the atmosphere, where you cool the 12:15.600 --> 12:18.000 temperature down below the freezing point, but yet the 12:18.000 --> 12:20.670 water doesn't freeze until something 12:20.667 --> 12:22.927 triggers that freezing. 12:22.933 --> 12:30.803 When freezing does occur, heat is either well, for freezing 12:30.800 --> 12:33.930 to occur, you have to remove heat. 12:33.933 --> 12:36.073 The reverse of that, when you melt ice, 12:36.067 --> 12:37.527 you have to add heat. 12:37.533 --> 12:40.773 That is called the latent heat of freezing, or the latent 12:40.767 --> 12:41.527 heat of melting. 12:41.533 --> 12:44.073 It's the same number, either way. 12:44.067 --> 12:48.627 And when you're condensing vapor to form liquid, there's 12:48.633 --> 12:52.003 a big heat required, depending whether you're condensing or 12:52.000 --> 12:53.800 evaporating. 12:53.800 --> 12:56.670 So that's really important, and then the saturation vapor 12:56.667 --> 13:02.027 pressure, this idea that you can keep more water in the 13:02.033 --> 13:07.173 liquids--in the vapor state, the hotter it is, is so 13:07.167 --> 13:08.267 important for the atmosphere. 13:08.267 --> 13:10.627 It explains why clouds form, for example. 13:10.633 --> 13:15.173 Rising air, adiabatic cooling, eventually you come to the 13:15.167 --> 13:17.567 saturation point and then cloud liquid 13:17.567 --> 13:19.327 water begins to form. 13:19.333 --> 13:24.973 So water is a little more complicated, maybe, than air, 13:24.967 --> 13:27.867 because it gets in these different phases and we really 13:27.867 --> 13:31.367 have to understand how these phase changes occur in order 13:31.367 --> 13:34.767 to understand the atmosphere ocean system. 13:34.767 --> 13:36.027 Questions on that? 13:40.433 --> 13:42.933 Hydrostatic balance is something we've come across 13:42.933 --> 13:43.973 over and over again. 13:43.967 --> 13:49.567 It's the idea that when you go up the way we derived it in an 13:49.567 --> 13:58.967 incremental form is that if you go up in the atmosphere a 13:58.967 --> 14:04.327 height, delta z, move up from there to there, the pressure 14:04.333 --> 14:08.533 will decrease keep the minus sign to remind me of that at a 14:08.533 --> 14:11.903 rate that depends on the acceleration of gravity and 14:11.900 --> 14:15.200 the density of the fluid. 14:15.200 --> 14:16.430 So we use that. 14:16.433 --> 14:20.333 We came across that first in atmospheres, but then it's 14:20.333 --> 14:21.803 true in the oceans as well. 14:21.800 --> 14:26.830 But remember, a typical density in the atmosphere, 14:26.833 --> 14:32.373 well it's 1.2 kilograms per cubic meter at sea level. 14:32.367 --> 14:35.497 But then it decreases strongly as you go up. 14:35.500 --> 14:39.570 So this value will change at different altitudes in the 14:39.567 --> 14:40.367 atmosphere. 14:40.367 --> 14:44.297 In the ocean, it's about 1025. 14:44.300 --> 14:48.130 It changes a bit around that based on the salinity. 14:48.133 --> 14:50.733 Same units, 1000 times greater. 14:50.733 --> 14:53.003 When you get down into the earth-- 14:53.000 --> 14:55.270 you can go down through the earth's mantle-- 14:55.267 --> 14:59.367 this equation continues to be valid, but there the density 14:59.367 --> 15:05.227 is more like 2000 or 3000 kilograms per cubic meter. 15:05.233 --> 15:09.773 So the pressure increases even faster as you go down. 15:09.767 --> 15:13.727 So the same equation can be used in all three spheres. 15:13.733 --> 15:16.703 But just remember, the density can be all over the place. 15:16.700 --> 15:21.770 From nearly zero, up in the top of the atmosphere, to this 15:21.767 --> 15:25.067 value at the surface, to this value in the ocean, and this 15:25.067 --> 15:29.727 value down in the interior of the earth. 15:29.733 --> 15:32.273 We also use that with a barometer. 15:32.267 --> 15:35.427 You know, the whole principle of a mercury barometer is the 15:35.433 --> 15:36.573 hydrostatic law. 15:36.567 --> 15:41.727 That column of mercury rises to a height needed to balance 15:41.733 --> 15:45.173 the atmospheric pressure pushing up at its base. 15:45.167 --> 15:48.397 And so you see that principle of hydrostatic 15:48.400 --> 15:50.570 balance there as well. 15:50.567 --> 15:51.797 Questions on hydrostatic? 15:55.000 --> 15:57.830 Geostrophic balance, another kind of 15:57.833 --> 16:00.103 important force balance. 16:00.100 --> 16:05.330 The idea there is that when objects or fluids move 16:05.333 --> 16:09.573 relative to the earth, they have a Coriolis force. 16:09.567 --> 16:14.097 And very often in the atmosphere and the ocean, 16:14.100 --> 16:17.470 after a few hours, you end up in a state of geostrophic 16:17.467 --> 16:21.927 balance, where the pressure gradient force balances that 16:21.933 --> 16:22.673 coriolis force. 16:22.667 --> 16:25.227 And that gives some very special properties. 16:25.233 --> 16:28.973 It says that the air or the water moves along the isobars 16:28.967 --> 16:30.727 rather than across. 16:30.733 --> 16:36.733 And the speed of the fluid is proportional to the strength 16:36.733 --> 16:38.403 of the pressure gradient. 16:38.400 --> 16:39.470 Here's how we derive that. 16:39.467 --> 16:46.067 We said that the pressure gradient force was the product 16:46.067 --> 16:49.867 of the pressure gradient and the volume of some little 16:49.867 --> 16:52.597 block of air that we imagined. 16:52.600 --> 16:56.230 And then we equate that with the Coriolis force, which was 16:56.233 --> 17:03.833 2 times the mass, which is rho times volume, times the 17:03.833 --> 17:07.933 velocity of the object, times the rotation rate of the earth 17:07.933 --> 17:10.303 and the sine of the latitude. 17:10.300 --> 17:14.270 So having equated those then and solving for U, and 17:14.267 --> 17:19.897 canceling out the volumes, I get pressure gradient over 2 17:19.900 --> 17:27.130 rho U omega sine phi for the geostrophic--the speed of the 17:27.133 --> 17:29.833 geostrophic wind. 17:29.833 --> 17:35.503 And the direction of course depends on the hemisphere, but 17:35.500 --> 17:38.530 along the isobars. 17:38.533 --> 17:41.473 Applies to both the atmosphere and the ocean. 17:41.467 --> 17:43.827 So any questions on that? 17:47.267 --> 17:51.227 OK, now, this fifth item on the list I've handed you is 17:51.233 --> 17:55.033 the concept of equilibrium states. 17:55.033 --> 17:59.333 And I tried to get that started in the early part of 17:59.333 --> 18:04.073 the course by taking you upstairs and doing this tank 18:04.067 --> 18:08.727 experiment, where I had a certain q in, and then I had a 18:08.733 --> 18:15.233 q out that depended on the depth of the water. 18:15.233 --> 18:19.103 It depended on how much water there was in the tank. 18:19.100 --> 18:21.830 And we tried to understand the equilibrium states of this 18:21.833 --> 18:22.933 simple system. 18:22.933 --> 18:25.303 And in a nutshell, this is the way you do it. 18:25.300 --> 18:34.300 If you make an axis--a plot like this, with rates on this 18:34.300 --> 18:40.100 axis, and some measure of the amount of water in this case, 18:40.100 --> 18:45.600 maybe it's the depth, z, on that axis you can work out the 18:45.600 --> 18:48.730 solution to this equilibrium state graphically. 18:48.733 --> 18:52.733 For example, if I'm putting a certain amount of water into 18:52.733 --> 18:58.003 this tank per unit, time, that doesn't depend on how much 18:58.000 --> 18:59.530 water I have in the tank. 18:59.533 --> 19:02.173 This is just, you know, how much water am I squirting into 19:02.167 --> 19:03.497 the tank per unit time? 19:03.500 --> 19:05.500 So that is a constant. 19:05.500 --> 19:06.770 That's the rate of inflow. 19:10.167 --> 19:13.227 But the rate of outflow will depend on how much 19:13.233 --> 19:14.603 water is in the tank. 19:14.600 --> 19:18.430 The deeper the water, the more pressure there is at the 19:18.433 --> 19:22.573 bottom pushing water through that valve. 19:22.567 --> 19:25.867 And so if I make a plot here of the outflow rate, versus 19:25.867 --> 19:28.627 the depth of water in the tank, it's going to look 19:28.633 --> 19:31.403 something like this. 19:31.400 --> 19:33.630 The deeper the water, the faster the 19:33.633 --> 19:35.203 water will gush out. 19:35.200 --> 19:40.830 And there will be a crossing point where the two are equal. 19:40.833 --> 19:42.533 That's the equilibrium state. 19:42.533 --> 19:45.333 Then the depth will remain constant because the rate at 19:45.333 --> 19:48.533 which we are putting fluid in balances the rate at which 19:48.533 --> 19:50.933 fluid is moving out. 19:50.933 --> 19:52.533 That's what I mean by an equilibrium state. 19:52.533 --> 19:54.873 We saw this early in the course. 19:54.867 --> 19:59.197 Now let's see if some of the ways that we have run across 19:59.200 --> 20:01.000 this in the atmosphere are perhaps 20:01.000 --> 20:04.100 not appreciated enough. 20:04.100 --> 20:08.830 For example, if we're evaporating water from the 20:08.833 --> 20:12.273 surface of the earth and putting water vapor molecules 20:12.267 --> 20:16.867 into the atmosphere, when we get enough water in the 20:16.867 --> 20:20.327 atmosphere, given the vertical motions that are there from 20:20.333 --> 20:24.673 convection, from fronts, and so on, we're going to 20:24.667 --> 20:27.267 eventually build up clouds. 20:27.267 --> 20:32.867 And under some circumstances, those clouds will precipitate. 20:32.867 --> 20:37.227 And generally speaking, the amount of water you take out 20:37.233 --> 20:40.233 per unit time is going to be related to how much water you 20:40.233 --> 20:41.473 have in the atmosphere. 20:41.467 --> 20:43.267 Well obviously, if you don't have any water in the 20:43.267 --> 20:46.227 atmosphere, you can't take any out. 20:46.233 --> 20:49.833 And if you've completely saturated the atmosphere with 20:49.833 --> 20:51.933 water, you're going to be raining a lot out. 20:51.933 --> 20:58.073 So there is some curve like this, where, again, rate would 20:58.067 --> 20:59.767 be on this axis. 20:59.767 --> 21:07.197 This might be the water vapor content of the atmosphere. 21:07.200 --> 21:11.030 The rate at which we're putting it in might depend a 21:11.033 --> 21:14.333 little bit on water vapor content. 21:14.333 --> 21:18.073 But the rate at which we're taking water out will 21:18.067 --> 21:23.227 certainly depend on the water vapor content. 21:23.233 --> 21:25.803 And there will be a crossover point. 21:25.800 --> 21:27.870 So the amount of water vapor in the atmosphere is going to 21:27.867 --> 21:33.667 be sustained roughly at a level where these two things 21:33.667 --> 21:36.367 can balance with time. 21:36.367 --> 21:39.067 And that's the way we think about water vapor in the 21:39.067 --> 21:40.327 atmosphere. 21:42.967 --> 21:43.997 Let's do another one. 21:44.000 --> 21:46.330 Heat in the climate system. 21:46.333 --> 21:52.473 So the sun's radiation is warming the earth. 21:52.467 --> 21:56.567 If it had--if it was ice cold, or if it were colder than ice, 21:56.567 --> 21:59.467 if it were absolute zero Kelvin, it would not be 21:59.467 --> 22:01.367 radiating to space. 22:01.367 --> 22:02.427 But it's not. 22:02.433 --> 22:05.703 It's at some temperature, so its radiating to space as 22:05.700 --> 22:07.770 well, in relationship to its temperature. 22:07.767 --> 22:13.967 So if I make this plot again, the rate will be the energy 22:13.967 --> 22:17.327 from the sun absorbed on the earth. 22:17.333 --> 22:19.003 That's going to be independent of the 22:19.000 --> 22:22.130 temperature of the planet. 22:22.133 --> 22:25.903 But the rate at which I'm radiating to space is going to 22:25.900 --> 22:29.630 be strongly dependent on the temperature of the planet. 22:29.633 --> 22:31.873 Remember, it goes like t to the fourth. 22:31.867 --> 22:35.697 The Stefan-Boltzmann law says that this goes like 22:35.700 --> 22:37.330 temperature to the fourth power. 22:37.333 --> 22:39.573 So there's some crossover point. 22:39.567 --> 22:41.867 And that's where we are most of the time with the earth. 22:41.867 --> 22:47.267 We're at an equilibrium state set by seeking out this 22:47.267 --> 22:50.697 balance between inflow and outflow. 22:53.467 --> 22:56.367 I'll do two more and then we'll I don't want to beat 22:56.367 --> 22:59.697 this too much to death but it is so important. 23:02.600 --> 23:08.270 If I had a what's next if I had a mountain glacier, snow 23:08.267 --> 23:14.927 falling on this glacier, it's going to be 23:14.933 --> 23:16.173 flowing under gravity. 23:19.633 --> 23:24.673 So the rate at which I'm adding snow to the top of this 23:24.667 --> 23:27.397 is independent about how much ice and snow 23:27.400 --> 23:28.170 I have on the mountain. 23:28.167 --> 23:30.167 That's just an atmospheric thing, so the 23:30.167 --> 23:32.067 input is just constant. 23:32.067 --> 23:33.167 And this will be a measure. 23:33.167 --> 23:36.897 Let's call this the thickness of the glacier. 23:36.900 --> 23:40.370 Thickness of the glacier. 23:40.367 --> 23:43.167 If it's really thin, it's not going to flow, and there's not 23:43.167 --> 23:44.997 going to be any ice leaving the system. 23:45.000 --> 23:48.270 That is to say, running down the mountainside. 23:48.267 --> 23:52.397 But as it gets thicker, now gravity is going to be pulling 23:52.400 --> 23:55.730 that ice down away from this region. 23:55.733 --> 23:58.303 And that will be a loss that will 23:58.300 --> 24:01.170 increase with ice thickness. 24:01.167 --> 24:03.767 The system will seek out an equilibrium 24:03.767 --> 24:05.967 where the snow falls. 24:05.967 --> 24:06.967 You've reached a balance. 24:06.967 --> 24:09.867 The amount of ice sliding down the mountain is just equal 24:09.867 --> 24:12.627 every year to how much snow has fallen. 24:12.633 --> 24:13.973 So you've reached a steady-state 24:13.967 --> 24:15.597 system for the glacier. 24:15.600 --> 24:18.000 Now these glaciers are not always in that steady state, 24:18.000 --> 24:20.630 but this is one of the possibilities we should always 24:20.633 --> 24:23.473 investigate, to see whether that system 24:23.467 --> 24:26.927 is in steady state. 24:26.933 --> 24:29.673 And the last one I had here was the ozone layer, where you 24:29.667 --> 24:34.067 remember far above the earth there is this ozone layer. 24:39.233 --> 24:40.903 You make ozone from oxygen. 24:43.633 --> 24:47.873 You photosynthesize it and recombine it differently to 24:47.867 --> 24:49.267 make ozone. 24:49.267 --> 24:52.467 So the rate at which you are making ozone, for our intents 24:52.467 --> 24:54.627 and purposes is pretty much fixed, because you're not 24:54.633 --> 24:57.633 going to change that very much. 24:57.633 --> 25:01.733 But the rate at which are destroying ozone is going to 25:01.733 --> 25:05.533 be proportional to how much ozone you have. I showed you 25:05.533 --> 25:07.433 that chemical reaction, also. 25:07.433 --> 25:10.273 The more ozone you have, the more chances that you'll 25:10.267 --> 25:13.097 dissociate an ozone, combine them in such a way that 25:13.100 --> 25:14.830 removes ozone from the system. 25:14.833 --> 25:18.733 So once again, you've got curves generally like this. 25:18.733 --> 25:22.033 The input's relatively independent of how much ozone 25:22.033 --> 25:27.173 you have. The loss rate is proportional to how much ozone 25:27.167 --> 25:30.227 you have. So there's going to be a crossing point, and 25:30.233 --> 25:32.103 that's going to be a steady-state solution. 25:32.100 --> 25:35.730 Again, I'm not claiming that the earth's ozone layer is in 25:35.733 --> 25:38.003 steady state, but that's one possibility that we'd 25:38.000 --> 25:39.270 want to look at. 25:39.267 --> 25:42.167 And then if it's not, we'd want to understand why there 25:42.167 --> 25:43.997 are temporal changes going on. 25:44.000 --> 25:50.630 Why has that system not yet reached its steady state? 25:50.633 --> 25:51.873 Questions there? 26:01.867 --> 26:06.497 So this idea of lapse rate and static stability, we ran 26:06.500 --> 26:09.700 across for the ocean and the atmosphere. 26:09.700 --> 26:14.130 And for the atmosphere, we did it this way. 26:14.133 --> 26:18.533 We plotted temperature versus height. 26:18.533 --> 26:21.973 And we put reference lines on there, which we 26:21.967 --> 26:24.367 call capital gamma. 26:24.367 --> 26:31.327 The dry adiabatic lapse rate was about negative 9.8 degrees 26:31.333 --> 26:32.973 Celsius per kilometer. 26:32.967 --> 26:37.497 And we ran our reasoning about whether an atmosphere would be 26:37.500 --> 26:41.530 stable, just stay there in layers, or whether it would 26:41.533 --> 26:44.303 turn over and begin to come back based on 26:44.300 --> 26:45.300 this kind of an argument. 26:45.300 --> 26:46.570 This is for the atmosphere. 26:49.400 --> 26:52.870 For the ocean, we get a little differently. 26:52.867 --> 26:57.697 We plot in density versus height or depth. 26:57.700 --> 27:00.970 And we looked at various possibilities. 27:00.967 --> 27:02.727 Our reference line there was really a 27:02.733 --> 27:05.833 line of constant density. 27:05.833 --> 27:08.673 If the density increased as you went up, 27:08.667 --> 27:10.567 that would be unstable. 27:10.567 --> 27:12.527 If the density increased as you went down, 27:12.533 --> 27:14.733 that would be stable. 27:14.733 --> 27:17.403 Why do we do the two differently? 27:17.400 --> 27:21.000 Well, the answer is clear. 27:21.000 --> 27:25.200 For atmospheres we're dealing with a compressible substance. 27:25.200 --> 27:27.130 Gas is very compressible. 27:27.133 --> 27:31.703 And so we had to work out this adiabatic lapse rate, and do 27:31.700 --> 27:32.900 the argument this way. 27:32.900 --> 27:37.370 For water, it's incompressible and it has the other 27:37.367 --> 27:37.597 components. 27:37.600 --> 27:40.900 It's got salinity in it as well. 27:40.900 --> 27:42.930 Remember density is a function of temperature and 27:42.933 --> 27:45.173 salinity in the ocean. 27:45.167 --> 27:47.497 So the fact that it's incompressible and the fact 27:47.500 --> 27:49.930 that salinity is involved makes us do the argument a 27:49.933 --> 27:51.173 little bit differently. 27:51.167 --> 27:54.367 But the question we're asking is the same. 27:54.367 --> 27:57.667 Is that column of fluid going to stay stagnant in layers, or 27:57.667 --> 27:59.967 is it going to turn over and mix? 27:59.967 --> 28:05.127 And that's important in both spheres, the 28:05.133 --> 28:07.533 atmosphere and the ocean. 28:15.300 --> 28:18.830 Transport of heat by fluid motion. 28:18.833 --> 28:21.773 So we've come across this several times, but the idea is 28:21.767 --> 28:28.167 if you have a pipe, let's say with fluid passing through it, 28:28.167 --> 28:34.797 the volumetric flow rate is a product of the 28:34.800 --> 28:37.800 velocity and the area. 28:37.800 --> 28:40.070 Now it doesn't have to be confined in a pipe. 28:40.067 --> 28:42.827 In the atmosphere or the ocean it's not confined in a pipe. 28:42.833 --> 28:46.033 But still it's the area and the velocity that gives you 28:46.033 --> 28:47.403 the volumetric flow rate. 28:47.400 --> 28:52.700 The mass flow rate would be rho U a. 28:58.167 --> 29:03.097 The heat that you're pushing through the pipe, well we got 29:03.100 --> 29:06.030 the mass flow rate, and we know that the amount of heat 29:06.033 --> 29:12.433 stored per unit mass is C p T. So this is heat capacity times 29:12.433 --> 29:19.133 temperature times rho U A. If that's water and you want know 29:19.133 --> 29:22.233 how much salt is being transported, well it's the 29:22.233 --> 29:28.333 salinity times rho U A. 29:28.333 --> 29:34.203 If it's some other pollutant, like in the air, maybe it's 29:34.200 --> 29:38.470 nitrous oxide, well then that would be the concentration of 29:38.467 --> 29:45.227 no2 times rho U A, if that is a ratio by mass. 29:45.233 --> 29:49.133 Be careful, be sure that's a ratio by mass if you're going 29:49.133 --> 29:50.733 to use it that way. 29:50.733 --> 29:55.073 So anyway, this is a common theme we ran across in the 29:55.067 --> 29:57.567 atmosphere and the ocean. 29:57.567 --> 30:01.267 And this is related to the next one on the list, which is 30:01.267 --> 30:10.067 the general idea of concentration, where if you 30:10.067 --> 30:14.167 put a substance and mix it into a background fluid, we're 30:14.167 --> 30:17.567 very interested in the concentration, which is how 30:17.567 --> 30:21.497 much did you put in, compared to how much 30:21.500 --> 30:23.900 you've mixed it into. 30:23.900 --> 30:27.970 So for example, when I write down, when I say this co2 in 30:27.967 --> 30:30.697 brackets, I'm referring to the 30:30.700 --> 30:34.200 concentration of carbon dioxide. 30:34.200 --> 30:42.300 And that could be either the mass of co2 over the mass of 30:42.300 --> 30:47.400 air, or it could be the molecules, the number of 30:47.400 --> 30:52.430 molecules of co2 versus the number of molecules of air. 30:58.533 --> 31:00.703 So remember which one you're dealing with. 31:00.700 --> 31:04.430 Neither of these ratios has units but you do have to 31:04.433 --> 31:10.603 remember whether it's a mass ratio or a molecular ratio. 31:10.600 --> 31:16.230 This one is usually called "by volume." And this one we would 31:16.233 --> 31:22.073 say that's a ratio "by mass." Taking into account by mass. 31:22.067 --> 31:25.197 So you have to know how much you put in, and into what 31:25.200 --> 31:29.470 volume have you mixed it, and the longer you wait for it to 31:29.467 --> 31:34.167 mix into a larger and larger volume, you have diluted it. 31:34.167 --> 31:37.297 The same amount of material added, but mixed into a larger 31:37.300 --> 31:40.400 and larger amount, the concentration will drop 31:40.400 --> 31:44.230 because you're diluting it into a larger background. 31:47.833 --> 31:53.733 And that brings us to the last one, which is this a question 31:53.733 --> 31:57.733 that's always fascinated me about the degree of symmetry 31:57.733 --> 32:01.173 between the northern and southern hemisphere. 32:01.167 --> 32:08.397 So here we have our planet, our home planet and it spins 32:08.400 --> 32:10.270 in that direction. 32:10.267 --> 32:14.827 And to what extent are the northern and southern 32:14.833 --> 32:17.073 hemispheres similar or different? 32:17.067 --> 32:20.127 Is there some kind of symmetry between the northern and 32:20.133 --> 32:20.633 southern hemispheres? 32:20.633 --> 32:23.873 So I'll end up with a brief discussion of this. 32:23.867 --> 32:29.967 So we know that the seasons are reversed between the two 32:29.967 --> 32:30.797 hemispheres. 32:30.800 --> 32:33.770 And that has to do with the tilt of the earth, right? 32:33.767 --> 32:38.097 So if the sun's over there, at this moment the northern 32:38.100 --> 32:42.330 hemisphere is tilted towards well not at this moment. 32:42.333 --> 32:46.473 At this moment, in December, it's like that, right? 32:46.467 --> 32:50.197 At this moment, the northern hemisphere is tilted away from 32:50.200 --> 32:51.870 the sun, southern hemisphere towards. 32:51.867 --> 32:55.267 So it's southern hemisphere it's summer, and then six 32:55.267 --> 32:57.297 months later, when the earth is going around to the other 32:57.300 --> 33:00.770 side of the sun, it's like this. 33:00.767 --> 33:03.797 And the northern hemisphere has its summer. 33:03.800 --> 33:08.470 So there's an opposite sense of the timing of the seasons 33:08.467 --> 33:10.267 between the two hemispheres. 33:10.267 --> 33:13.027 What about the Coriolis force and storms? 33:13.033 --> 33:16.603 Well that's the opposite in the two hemispheres, too. 33:16.600 --> 33:18.230 But for a different reason. 33:18.233 --> 33:19.903 It has nothing to do with the tilt of the earth. 33:19.900 --> 33:22.500 It has to do with the spin of the earth. 33:22.500 --> 33:25.200 The fact that it appears to spin this way in the northern 33:25.200 --> 33:28.770 hemisphere, but the opposite direction in the southern 33:28.767 --> 33:29.867 hemisphere. 33:29.867 --> 33:34.767 So that cyclones move counterclockwise in the 33:34.767 --> 33:37.797 northern hemisphere, but clockwise in the southern 33:37.800 --> 33:38.570 hemisphere. 33:38.567 --> 33:42.567 And that applies to the atmosphere and the ocean. 33:42.567 --> 33:45.067 Coreolis force is reverse between the two. 33:45.067 --> 33:52.697 Therefore, things just spin differently in the two 33:52.700 --> 33:54.830 hemispheres. 33:54.833 --> 34:00.203 Now, are there any other aspects of symmetry? 34:00.200 --> 34:04.000 Well, one thing that's different between the two 34:04.000 --> 34:07.770 hemispheres is the amount of land. 34:07.767 --> 34:10.727 If you look at that one, there's a fairly large 34:10.733 --> 34:12.003 fraction of land. 34:14.200 --> 34:15.830 I want to get this base out of the way, so 34:15.833 --> 34:17.633 I'll do it this way. 34:17.633 --> 34:22.873 If you look at it that way, there's much less land. 34:22.867 --> 34:27.467 And as we know, land and ocean have different heat storage 34:27.467 --> 34:29.927 capabilities. 34:29.933 --> 34:33.933 The ocean can store heat powerfully, because not only 34:33.933 --> 34:40.203 does it have a high specific heat capacity, C p, but also, 34:40.200 --> 34:44.400 when you heat, put heat at the top of the ocean, it mixes it 34:44.400 --> 34:46.330 in, because it's a fluid. 34:46.333 --> 34:48.333 So you may have to mix heat. 34:48.333 --> 34:52.033 Heat can be stored easily in the first hundred meters or so 34:52.033 --> 34:54.473 of the ocean, and that's an enormous mass. 34:54.467 --> 34:59.767 Where when I had heat to a continent, it only goes in 34:59.767 --> 35:01.327 about that much. 35:01.333 --> 35:04.933 Or maybe over a season, between winter and summer, it 35:04.933 --> 35:08.303 will go in about that much. 35:08.300 --> 35:12.230 As compared to 100 meters for the ocean. 35:12.233 --> 35:16.303 So the heat storage capacity is very different between land 35:16.300 --> 35:19.770 and sea, and the northern hemisphere has much more land 35:19.767 --> 35:20.927 than the southern hemisphere. 35:20.933 --> 35:28.833 So there's going to be that asymmetry between the two. 35:28.833 --> 35:31.233 And there's also a little different configuration, I 35:31.233 --> 35:34.133 want to remind you, near the poles. 35:34.133 --> 35:36.573 When it comes to this question of Arctic 35:36.567 --> 35:38.197 sea ice, for example. 35:38.200 --> 35:43.930 The Arctic Ocean is a little it's an ocean surrounded by 35:43.933 --> 35:51.203 land, whereas in the southern hemisphere, it's land 35:51.200 --> 35:53.470 surrounded by ocean, right? 35:53.467 --> 35:56.197 So this interaction between the ocean and the land is 35:56.200 --> 35:59.270 quite different at the high latitudes in the two 35:59.267 --> 36:00.427 hemispheres. 36:00.433 --> 36:04.833 For example, Antarctic bottom water, which is water formed 36:04.833 --> 36:09.433 near the Antarctic coast, the densest water in the sea drops 36:09.433 --> 36:11.303 down to the bottom and flows northward. 36:11.300 --> 36:14.630 There's no equivalent to that in the northern hemisphere, 36:14.633 --> 36:18.133 because that geometry is different. 36:18.133 --> 36:23.373 So these are fundamental ideas and I think I'll leave it 36:23.367 --> 36:26.027 there, and thank you and good luck on the final exam.