WEBVTT 00:01.000 --> 00:03.870 RONALD SMITH: So now we are into this new section of 00:03.867 --> 00:06.667 the course, oceanography. 00:06.667 --> 00:11.697 And last time I gave an overview of the nature of the 00:11.700 --> 00:15.830 ocean basins, basically the geometry of the basins in 00:15.833 --> 00:18.273 which the water sits. 00:18.267 --> 00:23.527 We connected that to plate tectonics, both to make the 00:23.533 --> 00:28.033 point that those ocean basins are changing through geologic 00:28.033 --> 00:33.633 time, but also to get at this curious issue of how the 00:33.633 --> 00:38.103 oceans are not just kind of a random roughness on the Earth, 00:38.100 --> 00:45.570 but they really represent two basic levels of Earth crust. 00:45.567 --> 00:48.367 The continental crust which sits a bit higher, and the 00:48.367 --> 00:50.327 ocean crust which sits a bit lower. 00:50.333 --> 00:53.703 And that's why there are these vast areas of the ocean that 00:53.700 --> 00:58.100 are at about the same depth below sea level, 00:58.100 --> 01:00.630 these abyssal planes. 01:00.633 --> 01:03.873 It's an oversimplification to say, of course, that the ocean 01:03.867 --> 01:08.897 basins have flat bottoms like a bathtub or something. 01:08.900 --> 01:11.470 But there is a little bit of a tendency that way because they 01:11.467 --> 01:14.667 do have--they do have ocean crust beneath them which 01:14.667 --> 01:18.127 floats at a certain level and gives you the depth of about 5 01:18.133 --> 01:22.833 kilometers in many, many places around the world ocean. 01:22.833 --> 01:25.403 Some places are deeper, some places are shallower, but 01:25.400 --> 01:28.930 there is that reference level from which we work. 01:28.933 --> 01:32.003 Any questions on that? 01:32.000 --> 01:36.170 Then we moved into a discussion of how to measure 01:36.167 --> 01:40.367 salinity and temperature in the oceans, and I talked about 01:40.367 --> 01:42.367 some of the methods to do that. 01:42.367 --> 01:45.467 And I wanted to pursue that just a little bit further, and 01:45.467 --> 01:49.397 then get into some quantitative methods for 01:49.400 --> 01:53.770 estimating how the atmosphere forces various things that go 01:53.767 --> 01:54.497 on in the ocean. 01:54.500 --> 01:58.230 So let me just start here, and I showed you this last time. 01:58.233 --> 02:04.533 This is a typical ocean sounding. 02:04.533 --> 02:09.733 Zero refers to sea level, and then depth is in meters below 02:09.733 --> 02:31.303 that, and this one going down to 4,000 meters. 02:31.300 --> 02:34.870 The temperature is shown here with a distinct cooling as you 02:34.867 --> 02:38.067 go down that starts pretty quickly below the surface. 02:38.067 --> 02:41.867 Maybe in this case, just a couple hundred meters below 02:41.867 --> 02:46.627 the surface you go from a mixed layer to a strong 02:46.633 --> 02:51.733 gradient region called the thermocline, "cline" referring 02:51.733 --> 02:56.573 to change, and "thermo", of course, referring to 02:56.567 --> 02:57.597 temperature. 02:57.600 --> 02:59.730 Then you get down to temperatures below that that 02:59.733 --> 03:04.073 are four, five, six degrees Celsius and colder, and that 03:04.067 --> 03:08.197 fills most of the interior of the ocean basin. 03:08.200 --> 03:11.030 So this point I was emphasizing last time about 03:11.033 --> 03:14.373 how the surface temperature does not represent the deep 03:14.367 --> 03:18.727 ocean temperature is shown nicely here. 03:18.733 --> 03:21.173 Salinity is somewhat similar in that you can have strong 03:21.167 --> 03:24.497 gradients near the air surface, but more uniform 03:24.500 --> 03:26.570 conditions below. 03:26.567 --> 03:30.267 In this case, it's saltier, then gets a bit fresher, than 03:30.267 --> 03:33.097 gets very slowly saltier below. 03:33.100 --> 03:37.030 But always staying in this remarkably narrow range 03:37.033 --> 03:41.603 between 34 and 35 and 1/2 parts per thousand. 03:41.600 --> 03:46.070 Then the dynamical quantity we're interested in is the 03:46.067 --> 03:49.427 seawater density with units that you're familiar with, 03:49.433 --> 03:52.603 kilograms per cubic meter, for example. 03:52.600 --> 03:54.900 And that is a generally a function of 03:54.900 --> 03:56.570 temperature and salinity. 03:56.567 --> 04:00.927 The warmer the water is, the more it expands a little bit 04:00.933 --> 04:04.103 and its density is less. 04:04.100 --> 04:06.930 The colder it is, the more it contracts, 04:06.933 --> 04:09.173 the density is greater. 04:09.167 --> 04:14.467 And salt, when you add salt to water, the salt goes a little 04:14.467 --> 04:18.597 bit into the pores between the water molecules, which 04:18.600 --> 04:19.670 increases the density. 04:19.667 --> 04:23.327 So the greater the salt content the greater is the 04:23.333 --> 04:26.703 density, and the fresher the water is the less 04:26.700 --> 04:28.130 is the water density. 04:28.133 --> 04:32.173 And since density is what gravity acts on, we're 04:32.167 --> 04:33.267 particularly interested in this. 04:33.267 --> 04:36.097 For example, if you wanted to apply the hydrostatic relation 04:36.100 --> 04:41.530 to find out how fast pressure increases with depth, you'd 04:41.533 --> 04:47.173 want to use the density derived from the salinity and 04:47.167 --> 04:49.827 the temperature. 04:49.833 --> 04:54.703 The word pycnocline is used when you're referring to this 04:54.700 --> 04:58.430 gradient region as it applies to density. 04:58.433 --> 05:02.233 So here it's the halocline referring to the salt, there 05:02.233 --> 05:04.773 the thermocline referring to the temperature, and the 05:04.767 --> 05:09.097 pycnocline refers to that combined quantity which is the 05:09.100 --> 05:11.100 density of the water. 05:14.533 --> 05:18.533 These profiles vary from place to place in the world ocean. 05:18.533 --> 05:21.333 For example, the high latitudes where you might have 05:21.333 --> 05:25.003 a lot of precipitation and because it's cold, not very 05:25.000 --> 05:27.600 much evaporation. 05:27.600 --> 05:32.430 The surface waters, notice the salinity scale is reversed on 05:32.433 --> 05:33.933 this diagram. 05:33.933 --> 05:38.803 The water might be a little less saline at the surface 05:38.800 --> 05:41.100 than it is down deep. 05:41.100 --> 05:44.530 Whereas in the tropics, for example, in the belt of 05:44.533 --> 05:48.103 deserts, the descending branch of the Hadley cell, you'd have 05:48.100 --> 05:51.900 a lot of evaporation, but very little precipitation. 05:51.900 --> 05:55.430 So the water near the surface would be salty there, but not 05:55.433 --> 05:55.973 at the bottom. 05:55.967 --> 05:59.667 The bottom is more homogeneous. 06:05.433 --> 06:10.033 Let's take a look at the salt itself, and this will connect 06:10.033 --> 06:13.433 a little bit with the lab that you're currently writing up. 06:13.433 --> 06:19.833 So if you take a kilogram of seawater, about 965 grams of 06:19.833 --> 06:28.133 that is water, H2O, and about 34.4 of that is in weight, in 06:28.133 --> 06:30.133 mass, grams, is the salt. 06:32.767 --> 06:35.497 Then if you break up that little salt wedge into its 06:35.500 --> 06:40.900 chemical compositions you get this little pie chart here. 06:40.900 --> 06:43.230 It shows the most abundant ions. 06:43.233 --> 06:46.473 So assuming that this quantity, these chemicals 06:46.467 --> 06:48.967 break apart when they dissolve in the water into their 06:48.967 --> 06:51.427 positive and negative ions. 06:51.433 --> 06:55.573 By far the largest contribution is the chlorine, 06:55.567 --> 07:03.197 18.96 grams of the 34, a little more than half of that 07:03.200 --> 07:05.930 salt mass is due to the chlorine. 07:05.933 --> 07:09.233 And let's look at the other negative ions here. 07:09.233 --> 07:13.403 There's a sulfate radical, SO4, and there's a 07:13.400 --> 07:19.200 bicarbonate, HCO3 with minus signs for the charge. 07:19.200 --> 07:22.500 Then we come to the cat ions, which is what you're studying 07:22.500 --> 07:24.470 in the lab this week. 07:24.467 --> 07:27.997 The dominant ones are sodium, which is by far and away the 07:28.000 --> 07:30.030 most abundant. 07:30.033 --> 07:34.233 But also we have magnesium, calcium, and potassium. 07:34.233 --> 07:37.473 Those are the four things that you have data for in the lab 07:37.467 --> 07:43.127 as you go from fresh water river into the ocean. 07:43.133 --> 07:46.373 So you might want to compare these numbers that I have here 07:46.367 --> 07:54.667 in lecture, the 10.56 grams per kilogram of seawater. 07:54.667 --> 08:03.027 The 1.27 for the magnesium, 0.04 for calcium, and 0.38 for 08:03.033 --> 08:04.503 potassium with the values you had. 08:04.500 --> 08:11.670 But just remember, when we got to Long Island Sound we only 08:11.667 --> 08:15.567 had a salinity of about half that of ocean water. 08:15.567 --> 08:21.297 So you should divide these numbers approximately in half, 08:21.300 --> 08:26.870 or double your numbers before you do the comparisons. 08:26.867 --> 08:29.997 But I think that'd be useful to try to understand how our 08:30.000 --> 08:34.770 measurements agree with the textbook values for what makes 08:34.767 --> 08:36.327 up the salts. 08:36.333 --> 08:39.103 The reason they can make a diagram like this is these 08:39.100 --> 08:42.770 relative proportions are the same everywhere you go in the 08:42.767 --> 08:43.627 world ocean. 08:43.633 --> 08:47.603 Even when the salinity varies a little bit, maybe down to 34 08:47.600 --> 08:50.530 or up to 36. 08:50.533 --> 08:53.973 These all increase in proportion. 08:53.967 --> 08:59.297 So that these relative numbers are quite stable when you go 08:59.300 --> 09:04.400 from place to place in the world ocean. 09:04.400 --> 09:11.130 And of course, our simple theory of this is that this 09:11.133 --> 09:16.403 represents an accumulation over geologic time of small 09:16.400 --> 09:20.130 amounts of these chemicals, these salts, that have come 09:20.133 --> 09:23.633 into the ocean from rivers. 09:23.633 --> 09:27.233 And you're testing that idea in using your lab data. 09:31.967 --> 09:33.227 Any questions there? 09:36.867 --> 09:39.797 Now, you remember in the atmosphere we spent a good 09:39.800 --> 09:43.200 deal of time talking about static stability, that is, we 09:43.200 --> 09:47.230 looked at the role of the atmospheric lapse rate how the 09:47.233 --> 09:51.103 temperature changes in the vertical to whether parcels 09:51.100 --> 09:55.900 can rise and fall easily or not. 09:55.900 --> 09:58.830 Or whether that atmosphere might even be unstable and 09:58.833 --> 10:00.003 break down to convection. 10:00.000 --> 10:03.830 So we defined an unstable lapse rate, a stable lapse 10:03.833 --> 10:07.373 rate, the inversion, which was an example of a very stable 10:07.367 --> 10:08.427 lapse rate. 10:08.433 --> 10:11.703 We're interested in the same kind of analysis in the ocean. 10:11.700 --> 10:14.530 But there's a couple of essential differences. 10:17.233 --> 10:21.073 One is that the ocean density depends not just on 10:21.067 --> 10:24.897 temperature, but on salinity too. 10:24.900 --> 10:27.230 So we'll have to take into account both of those 10:27.233 --> 10:28.033 quantities. 10:28.033 --> 10:31.133 We'll do that simply by computing the density. 10:31.133 --> 10:34.303 We'll base our stability analysis on water density, 10:34.300 --> 10:38.200 rather than on temperature or salinity alone. 10:38.200 --> 10:40.770 The other big difference is that while air is 10:40.767 --> 10:45.027 compressible, so as a parcel lifts in the atmosphere and 10:45.033 --> 10:49.003 moves to lower pressure, it expands does work on its 10:49.000 --> 10:51.170 environment and its temperature changes. 10:51.167 --> 10:55.567 That affect is very, very small in the oceans. 10:55.567 --> 11:00.527 It's not exactly zero, but it is so small that for many 11:00.533 --> 11:05.703 quick calculations we ignore that volume change and that 11:05.700 --> 11:09.930 so-called adiabatic cooling or adiabatic warming as air 11:09.933 --> 11:12.503 parcels rise up and down in the atmosphere. 11:12.500 --> 11:16.000 We ignore that in the ocean. 11:16.000 --> 11:20.800 So because of these two differences, the idea of what 11:20.800 --> 11:25.130 determines stability in the atmosphere and the ocean are 11:25.133 --> 11:28.303 significantly different. 11:28.300 --> 11:31.100 The basic principle is that while temperature and salinity 11:31.100 --> 11:34.930 can either increase or decrease with depth, the 11:34.933 --> 11:40.373 density derived from them must always increase with depth. 11:40.367 --> 11:47.967 We saw that in the earlier diagram here that the 11:47.967 --> 11:51.667 salinity, for example, decreased with depth, then 11:51.667 --> 11:52.897 increased with depth. 11:52.900 --> 11:57.770 But when I computed the density it increased smoothly. 11:57.767 --> 12:03.467 If there was ever a layer where the density got less 12:03.467 --> 12:06.367 with depth, that would be an unstable layer, and it would 12:06.367 --> 12:08.867 immediately cause convection and would mix. 12:11.833 --> 12:14.633 Years ago when I first starting out, I was looking at 12:14.633 --> 12:18.673 some CTD data from a ship and thought I 12:18.667 --> 12:22.627 found an unstable layer. 12:22.633 --> 12:25.273 Went running up to the chief scientist to show him this 12:25.267 --> 12:28.697 remarkable discovery, and he quickly pointed out where I'd 12:28.700 --> 12:30.930 made a mistake in my calculations. 12:30.933 --> 12:34.873 So once again, the ocean was found to be stable. 12:34.867 --> 12:37.397 It's been proven many, many times. 12:37.400 --> 12:40.270 The point is, you could have an unstable layer, but it 12:40.267 --> 12:44.127 would exist only minutes because immediately convection 12:44.133 --> 12:48.003 would begin, that layer would mix, and you might produce a 12:48.000 --> 12:51.400 layer of constant density from that mixing, but you would be 12:51.400 --> 12:55.630 unlikely to sustain any layer that is unstable. 12:55.633 --> 12:57.903 So you should always expect to find this kind of 12:57.900 --> 13:01.070 relationship, and if you don't, you've either made a 13:01.067 --> 13:04.327 wonderful discovery, or somewhat more likely you've 13:04.333 --> 13:08.503 screwed up your calculations when you compute a density 13:08.500 --> 13:12.330 from temperature and salinity. 13:12.333 --> 13:15.233 So it's a very important principle. 13:15.233 --> 13:19.233 Probably almost universally true in the atmosphere--in the 13:19.233 --> 13:21.473 oceans, sorry. 13:21.467 --> 13:24.867 So yeah, so there it is. 13:24.867 --> 13:31.827 Now, this diagram is nice because it combines together 13:31.833 --> 13:37.833 hundreds of CTD and Nansen bottle data sets from three of 13:37.833 --> 13:41.303 the major world ocean basins the Pacific Ocean, the Indian 13:41.300 --> 13:43.430 Ocean, and the Atlantic Ocean. 13:43.433 --> 13:46.103 What I like even better about this diagram is that it's 13:46.100 --> 13:47.170 superimposed. 13:47.167 --> 13:53.197 These balloons of data are superimposed on a diagram that 13:53.200 --> 13:56.170 has lines of constant density on it. 13:56.167 --> 13:59.697 Let me walk you through those lines first. So on this axis 13:59.700 --> 14:03.430 is the salinity in parts per thousand that we're used to 14:03.433 --> 14:05.733 working with, PPT. 14:05.733 --> 14:09.573 On this axis is temperature in degrees Celsius. 14:09.567 --> 14:14.427 And then these lines are lines of constant seawater density. 14:17.033 --> 14:20.833 And by the way, so what is this unit here? 14:20.833 --> 14:27.833 This unit is the density of seawater with the 1 and the 0 14:27.833 --> 14:29.733 dropped off. 14:29.733 --> 14:35.973 So you would read this as 1,028.5 14:35.967 --> 14:41.697 kilograms per cubic meter. 14:41.700 --> 14:44.930 And since it only changes in those last couple of digits, 14:44.933 --> 14:49.473 we don't want to keep writing that 10 in front of all of 14:49.467 --> 14:50.827 those values. 14:50.833 --> 14:54.373 But you can see that the density is greater down here, 14:54.367 --> 14:57.427 29, 28.5, and 28. 14:57.433 --> 15:04.833 And that corresponds to salty water and low temperatures. 15:04.833 --> 15:10.603 And the seawater density is less up here, 25, 24.4--24.5, 15:10.600 --> 15:15.900 and 24 for high temperatures and low salinity. 15:15.900 --> 15:18.830 So that's as we thought it would be. 15:18.833 --> 15:20.073 Are there any questions on that? 15:23.100 --> 15:24.930 There's a couple of other things I'd like you to notice 15:24.933 --> 15:27.433 about this diagram. 15:27.433 --> 15:31.203 Up in the warmer temperature region, up near the top of the 15:31.200 --> 15:38.600 diagram, because of the way these lines are tilted, the 15:38.600 --> 15:43.100 density is most sensitive to temperature changes. 15:43.100 --> 15:46.200 Whereas down in the colder regions where the lines are 15:46.200 --> 15:49.570 tilted more like this, the density is more sensitive to 15:49.567 --> 15:52.967 salinity changes. 15:52.967 --> 15:57.867 So when you're talking to a tropical oceanographer, and we 15:57.867 --> 16:02.527 have one in our department, Professor Fedorov. He is 16:02.533 --> 16:04.903 usually most interested in talking to you about the 16:04.900 --> 16:08.870 temperature profiles in the ocean. 16:08.867 --> 16:10.667 Of course, he hasn't forgotten that salinity 16:10.667 --> 16:11.927 plays a role in this. 16:11.933 --> 16:15.673 But in the tropical in the warm parts of the ocean, the 16:15.667 --> 16:20.197 temperature is the primary control on the density. 16:20.200 --> 16:24.500 If you're talking to an Arctic oceanographer, and we have one 16:24.500 --> 16:28.330 of those in our department, Mary-Louise Timmermans. 16:28.333 --> 16:31.103 She's usually most interested in understanding the salinity 16:31.100 --> 16:34.830 field because the salinity field hacking down here, as 16:34.833 --> 16:40.833 you can see, is more in control of the density field 16:40.833 --> 16:43.633 in the colder regions of the ocean. 16:43.633 --> 16:46.333 So I don't want to exaggerate that too far. 16:46.333 --> 16:51.033 Both are always playing a role, but in warm areas it's 16:51.033 --> 16:54.703 mostly the temperature, in cold areas it's mostly the 16:54.700 --> 16:58.700 salinity that's controlling the density. 16:58.700 --> 17:02.100 Any questions on this diagram? 17:02.100 --> 17:06.070 So let's look at these big kind of balloons. 17:06.067 --> 17:14.427 The Pacific Ocean is generally a little fresher, and maybe 17:14.433 --> 17:18.333 even a little bit warmer than the Atlantic Ocean. 17:21.600 --> 17:23.970 There is a little part down here which is common to both 17:23.967 --> 17:26.367 oceans, they come together down there, called the 17:26.367 --> 17:27.927 Antarctic Bottom Water. 17:27.933 --> 17:30.673 We're going to be talking about that probably next time. 17:30.667 --> 17:34.497 It's a mass of water that's produced near Antarctica. 17:34.500 --> 17:37.770 It flows Northward along the bottom of the ocean, and we 17:37.767 --> 17:40.327 find it in both the Atlantic and the Pacific. 17:40.333 --> 17:41.633 So there's a common element. 17:41.633 --> 17:44.773 But other than that, there is a general systematic 17:44.767 --> 17:49.367 difference between the Pacific and the Atlantic Ocean. 17:49.367 --> 17:52.267 And that, of course, has to do with atmospheric controls, 17:52.267 --> 17:53.767 which I'm just about to get to. 17:56.833 --> 17:59.673 If you do a cross-section, this happens to be a 17:59.667 --> 18:03.327 North-South cross-section through the Atlantic Ocean 18:03.333 --> 18:05.233 from high latitudes to low. 18:05.233 --> 18:06.533 Perhaps you can't read in the back, but 18:06.533 --> 18:08.633 the Equator is there. 18:08.633 --> 18:12.703 10 degrees North, 20, on up to 60 degrees North, and on down 18:12.700 --> 18:17.870 to minus 70 degrees latitude, 70 South. 18:17.867 --> 18:22.927 Here's a depth scale going from 0 down to 6 kilometers. 18:22.933 --> 18:26.633 And then the horizontal scale is what I indicated. 18:26.633 --> 18:29.573 And contoured here is temperature. 18:29.567 --> 18:34.727 Temperature actually gets a little bit below 0 here. 18:34.733 --> 18:36.003 Minus 0.2. 18:39.000 --> 18:43.670 But by the time you're up in here it's 1.2 degrees, 2.4. 18:43.667 --> 18:46.197 And then you've got some strong gradients near the top, 18:46.200 --> 18:50.070 well that's the thermocline, and then near the surface of 18:50.067 --> 18:54.167 the ocean in the mid-latitudes and low latitudes, you have 18:54.167 --> 18:59.627 this little lens of warm water floating on the surface. 18:59.633 --> 19:05.173 Many of you I expect have been swimming in a fresh water lake 19:05.167 --> 19:06.397 in early summer. 19:08.633 --> 19:14.833 You may have noticed that as you swim out, the water's 19:14.833 --> 19:17.673 pretty comfortable in terms of this temperature, but when you 19:17.667 --> 19:20.867 stop swimming and let your legs dangle down a bit, 19:20.867 --> 19:23.997 suddenly it's a lot colder down there. 19:24.000 --> 19:27.100 What's happening is that that fresh water that's warm is a 19:27.100 --> 19:29.630 little bit less dense than the cold water. 19:29.633 --> 19:32.903 So it floats in a little layer on top. 19:32.900 --> 19:35.200 Well that's exactly what's going on here. 19:35.200 --> 19:39.170 There's salinity involved, but mostly it's a temperature 19:39.167 --> 19:43.367 control, and you've got a warm layer of water kind of 19:43.367 --> 19:50.927 floating in a broad, deep, cold layer of ocean. 19:50.933 --> 19:54.003 And you'll find this as you go North to South in all of the 19:54.000 --> 19:57.530 world's oceans, you'll find this thermocline that 19:57.533 --> 20:00.973 separates this warm sphere from the deep cold sphere. 20:00.967 --> 20:03.927 That's kind of a common element in both the Atlantic, 20:03.933 --> 20:06.303 the Pacific, and the Indian ocean. 20:06.300 --> 20:08.400 So we'll talk more about that later on. 20:08.400 --> 20:11.370 Any questions on what this diagram shows? 20:11.367 --> 20:14.927 By the way, this blue water here, that's that Antarctic 20:14.933 --> 20:17.773 Bottom Water that I was talking about. 20:17.767 --> 20:18.997 I'll come back to that. 20:23.800 --> 20:26.030 Are there any other simple analogies to this? 20:26.033 --> 20:30.333 Well, I would point you to the Great Salt Lake as kind of an 20:30.333 --> 20:32.373 analogy to the world ocean. 20:32.367 --> 20:35.897 The Great Salt Lake unlike most lakes 20:35.900 --> 20:39.030 doesn't have an outflow. 20:39.033 --> 20:42.703 When water flows into the Great Salt Lake in Utah, it 20:42.700 --> 20:45.270 doesn't spend a few weeks there and then flow in some 20:45.267 --> 20:46.567 river into the ocean. 20:46.567 --> 20:47.297 No. 20:47.300 --> 20:51.300 It basically stays there until it evaporates. 20:51.300 --> 20:54.630 This is a no outflow lake. 20:54.633 --> 20:59.973 And for that reason, you get the same kind of concentration 20:59.967 --> 21:05.627 of salts, the same process, as you do in the ocean. 21:05.633 --> 21:10.703 So it's a little mini ocean, if you like, in the sense that 21:10.700 --> 21:13.030 it has to evaporate its water, get rid of it, and therefore, 21:13.033 --> 21:15.033 it concentrates the salts. 21:15.033 --> 21:18.473 Now, in this case, it concentrates the salts even 21:18.467 --> 21:19.967 much more than the ocean does. 21:19.967 --> 21:21.967 The salinity is three to five times 21:21.967 --> 21:24.127 saltier than in the ocean. 21:24.133 --> 21:27.433 Has anybody swum in the Great Salt Lake? 21:27.433 --> 21:29.773 Dip your body in it? 21:29.767 --> 21:30.867 But you've heard about it, right? 21:30.867 --> 21:35.097 The remarkable thing is how high you float. 21:35.100 --> 21:37.700 You're sitting there, and maybe from here on up you're 21:37.700 --> 21:40.000 out of the water. 21:40.000 --> 21:40.500 Why? 21:40.500 --> 21:46.770 Because the water is salty, and therefore more dense. 21:46.767 --> 21:50.167 Following Archimedes rule, the denser the water is, the more 21:50.167 --> 21:53.267 mass you're displacing, the more the buoyancy force, the 21:53.267 --> 21:54.067 higher you float. 21:54.067 --> 21:58.997 So this is a good thing to think about when you're trying 21:59.000 --> 22:01.500 to understand basically how oceans work. 22:01.500 --> 22:03.730 It's kind of a little mini ocean. 22:08.467 --> 22:12.897 Now, the subject I was going to get into today, and I will 22:12.900 --> 22:15.570 get into it is atmospheric forcing of the ocean. 22:15.567 --> 22:21.327 For the most part, any motions you have in the ocean, in 22:21.333 --> 22:23.833 fact, almost everything that goes on in the ocean, is 22:23.833 --> 22:31.173 driven from above by either sunlight hitting the ocean, or 22:31.167 --> 22:34.327 some other interaction with the Earth's atmosphere. 22:34.333 --> 22:36.433 Now is there any forcing from below at all? 22:36.433 --> 22:40.473 Well there is a little bit of geothermal heat coming out of 22:40.467 --> 22:42.397 the bottom of the ocean basins, but 22:42.400 --> 22:44.870 that's quite small. 22:44.867 --> 22:48.797 So except for that, it's pretty much the oceans are 22:48.800 --> 22:51.870 driven by the atmosphere from above. 22:51.867 --> 22:53.797 These three things are how that happens. 22:56.600 --> 23:01.130 You can add or remove heat at the top of the ocean, either 23:01.133 --> 23:04.233 by radiation, the Sun's radiation, or long-wave 23:04.233 --> 23:07.173 radiation emitted from the ocean surface. 23:07.167 --> 23:09.527 Or by contact with the atmosphere. 23:09.533 --> 23:13.873 if you have cold air, that'll suck heat out of the ocean. 23:13.867 --> 23:19.127 If you have warm air that'll conduct heat into the ocean. 23:19.133 --> 23:23.903 Or you can add fresh water by precipitation, or remove fresh 23:23.900 --> 23:28.030 water by evaporation, leaving the salt behind. 23:28.033 --> 23:32.933 These two things will change the salinity of the surface, 23:32.933 --> 23:34.233 and therefore, the density. 23:34.233 --> 23:36.303 And this one will change the temperature and, therefore, 23:36.300 --> 23:36.970 the density. 23:36.967 --> 23:38.997 Or you've got the wind stress. 23:39.000 --> 23:42.330 You've got the wind blowing over the ocean surface 23:42.333 --> 23:45.433 transferring some momentum to the ocean, and getting the 23:45.433 --> 23:47.803 ocean moving in that way. 23:47.800 --> 23:52.030 So we're going to need to understand each of these three 23:52.033 --> 23:57.373 mechanisms. For example, here is our best estimate of the 23:57.367 --> 24:00.127 heat flux in and out of the ocean. 24:03.767 --> 24:08.467 Basically, where you get, for example, cold water and warm 24:08.467 --> 24:12.327 air, the heat is going into the ocean, and that's shown as 24:12.333 --> 24:15.103 positive on this diagram. 24:15.100 --> 24:18.830 Where heat is coming out you've got the blue or the red 24:18.833 --> 24:20.933 color shown as negative. 24:20.933 --> 24:22.773 But it varies from place to place. 24:22.767 --> 24:24.967 It depends on the air temperature. 24:24.967 --> 24:27.997 It depends on how much sunlight is being received. 24:28.000 --> 24:31.200 It depends on the water temperature, whether heat is 24:31.200 --> 24:34.400 going into the ocean or whether heat is coming out. 24:34.400 --> 24:35.270 We'll talk about this 24:35.267 --> 24:38.097 quantitatively in just a moment. 24:38.100 --> 24:42.470 Then the other one is E minus P or P minus E. This one is 24:42.467 --> 24:44.427 evaporation minus precipitation. 24:44.433 --> 24:47.273 The sign is derived in that way. 24:47.267 --> 24:53.767 So whenever water is evaporating, you get a yellow 24:53.767 --> 24:57.297 signature here, and the units on this are in 24:57.300 --> 24:58.370 millimeters per day. 24:58.367 --> 25:03.567 How much water is being peeled off and evaporated in terms of 25:03.567 --> 25:05.767 a layer depth per day. 25:05.767 --> 25:08.997 Whereas in the blue, and you notice it coincides with the 25:09.000 --> 25:13.830 ITCZ, for example, where you have heavy precipitation, 25:13.833 --> 25:16.673 precipitation exceeds evaporation. 25:16.667 --> 25:20.727 So the sign of this quantity of negative shows up as blue. 25:20.733 --> 25:24.033 Then you get up into mid-latitudes again where it's 25:24.033 --> 25:26.903 colder, there's less evaporation, but you have the 25:26.900 --> 25:29.070 frontal storms, and once again, you're getting an 25:29.067 --> 25:32.367 excess of precipitation over evaporation. 25:32.367 --> 25:37.467 So this is driving motions in the ocean as well. 25:37.467 --> 25:42.067 Then the final one is the winds over the ocean, which 25:42.067 --> 25:43.327 change a bit with the season. 25:43.333 --> 25:45.833 There's January, there's July. 25:45.833 --> 25:48.073 But generally you've got Westerlies in the 25:48.067 --> 25:49.867 mid-latitudes and Easterlies in the low 25:49.867 --> 25:52.097 latitudes in both seasons. 25:52.100 --> 25:57.200 And that is generating motions in the ocean itself. 25:57.200 --> 26:02.070 So that is where we'll end the pictures today. 26:02.067 --> 26:05.967 And I want to get into quantifying these things. 26:24.500 --> 26:28.570 So here I've repeated those three ways in which the 26:28.567 --> 26:30.997 atmosphere forces the ocean. 26:31.000 --> 26:34.130 Adding or removing heat, precipitation and/or 26:34.133 --> 26:38.133 evaporation, and the wind stress. 26:38.133 --> 26:41.003 Now, I want to make a further distinction from this. 26:41.000 --> 26:43.100 I've got a little--I've drawn a little cartoon down here. 26:43.100 --> 26:46.530 Here's the cloud that's precipitating, adding fresh 26:46.533 --> 26:48.803 water to the surface of the ocean. 26:48.800 --> 26:51.670 There's some evaporation, that's this one. 26:51.667 --> 26:54.267 Here's some heat being added or removed, either by 26:54.267 --> 26:58.367 radiation or by the effect of the atmosphere itself. 26:58.367 --> 27:01.997 And here's the wind stress I'm going to use Greek letter Tau 27:02.000 --> 27:02.870 to represent that. 27:02.867 --> 27:05.597 But I've indicated that there's a layer which feels 27:05.600 --> 27:11.130 these inputs directly, and that's called the depth of 27:11.133 --> 27:16.333 that capital D. That will vary from time to time and place to 27:16.333 --> 27:20.233 place, but typically that's a very small fraction of the 27:20.233 --> 27:21.873 ocean depth. 27:21.867 --> 27:28.797 When I do examples, I often set D equal to 100 meters. 27:28.800 --> 27:32.200 Roughly only the first few tens or couple of hundred 27:32.200 --> 27:35.870 meters feels these inputs directly. 27:35.867 --> 27:39.167 The rest of the world ocean will feel them, but it'll be 27:39.167 --> 27:41.267 an indirect influence. 27:41.267 --> 27:43.867 Something coming not directly from the atmospheric input, 27:43.867 --> 27:47.997 but something then coming out of this other layer that feels 27:48.000 --> 27:50.130 a direct influence. 27:50.133 --> 27:53.203 So be aware that I'm making this distinction for all three 27:53.200 --> 27:56.670 of these categories of forcing. 27:56.667 --> 28:00.327 My first job is to figure out what does it do to this layer 28:00.333 --> 28:03.833 that feels the influence directly. 28:03.833 --> 28:05.533 The first one will be adding heat. 28:08.600 --> 28:12.630 And you remember that if you add a certain amount of heat 28:12.633 --> 28:18.833 to a mass, M, with a heat capacity C sub P, it's 28:18.833 --> 28:22.903 temperature will change by delta T. We've had that 28:22.900 --> 28:24.370 formula before. 28:24.367 --> 28:30.967 If I write that in a per unit area basis, I'll divide the Q 28:30.967 --> 28:35.197 by A, and the mass by A, and I'll leave 28:35.200 --> 28:37.470 everything else the same. 28:37.467 --> 28:41.367 I've just divided both sides through by the area that I'm 28:41.367 --> 28:44.597 considering, which in oceanography we don't usually 28:44.600 --> 28:45.700 even consider that area. 28:45.700 --> 28:51.770 We just do these calculations on a per unit area basis. 28:51.767 --> 28:57.867 The mass per unit area, if you think of a piece of the ocean, 28:57.867 --> 29:04.267 a little cylinder of area A, its total mass is going to be 29:04.267 --> 29:10.867 its volume times the density of the water. 29:10.867 --> 29:15.367 And the volume is going to be the product of A and D where D 29:15.367 --> 29:19.227 is the depth of that cylinder. 29:19.233 --> 29:24.933 So the mass per unit area here, which divides out the A 29:24.933 --> 29:31.933 is going to be the product of rho D, the water density times 29:31.933 --> 29:35.103 the depth of the layer that I'm considering. 29:35.100 --> 29:39.770 So then let me just take that and plug it into this formula. 29:39.767 --> 29:46.397 I get Q over A that's the heat being added per unit area. 29:46.400 --> 29:52.370 Plugging this and I get rho D CP delta T, and solving that 29:52.367 --> 30:00.597 for delta T, I get Q over A over rho D C sub P. And I 30:00.600 --> 30:03.030 think we've seen that formula before, but 30:03.033 --> 30:05.773 there we have it again. 30:05.767 --> 30:08.827 This will tell you how much the temperature of the surface 30:08.833 --> 30:12.073 layer of the ocean changes when you put in a certain 30:12.067 --> 30:14.027 amount of heat per unit area. 30:14.033 --> 30:17.503 And it depends on the density of the seawater, the depth of 30:17.500 --> 30:21.600 the layer over which you're distributing that heat, and 30:21.600 --> 30:25.030 the heat capacity of water. 30:25.033 --> 30:35.703 So a quick example of that I'm going to take a solar flux of 30:35.700 --> 30:39.130 1,000 watts per square meter. 30:39.133 --> 30:41.973 Let's say we have sunlight hitting the surface of the 30:41.967 --> 30:44.197 ocean with that kind of intensity. 30:46.900 --> 31:00.670 That persists for one day, which is 86,400 seconds. 31:00.667 --> 31:02.497 So let's say that persists for one day. 31:05.633 --> 31:11.733 And that heat is distributed over a depth of 1,000 meters. 31:11.733 --> 31:14.803 How much will the temperature of the surface ocean 31:14.800 --> 31:16.270 change in that case? 31:16.267 --> 31:19.027 Let's just put the numbers into the formula that I'm just 31:19.033 --> 31:21.133 extending this formula over. 31:21.133 --> 31:24.973 So to get the heat, I need to multiply 31:24.967 --> 31:27.027 remember this is watts. 31:27.033 --> 31:29.973 That's a rate of putting in heat. 31:29.967 --> 31:32.327 A watt is a Joule per second. 31:32.333 --> 31:38.073 So I need to multiply the time by the watts to get Joules per 31:38.067 --> 31:41.727 square meter, which is what Q over A means, that's Joules 31:41.733 --> 31:42.673 per square meter. 31:42.667 --> 31:49.997 So that's going to be 8.64 times 10 to the seventh Joules 31:50.000 --> 31:52.930 per square meter up top that's just the product 31:52.933 --> 31:54.273 of those two numbers. 31:54.267 --> 32:01.667 And then down below I'm going to put in a estimate for 32:01.667 --> 32:08.497 seawater density, a depth of 100 meters, and the heat 32:08.500 --> 32:15.070 capacity for water which is about 4,200 units of Joules 32:15.067 --> 32:18.967 per kilogram per degree. 32:18.967 --> 32:22.227 That's C sub P, you work that out, and you might want to 32:22.233 --> 32:27.033 check me, but I got 0.2 degrees Celsius. 32:27.033 --> 32:32.673 So the warming turned out to be pretty small because that 32:32.667 --> 32:37.527 heat got distributed over a pretty great depth, and the 32:37.533 --> 32:39.273 mass of that water is large, and its 32:39.267 --> 32:40.967 heat capacity is large. 32:40.967 --> 32:46.027 So although I put in almost 10 to the eighth Joules for every 32:46.033 --> 32:49.573 square meter, the rise in temperature was pretty small. 32:49.567 --> 32:49.927 Yeah. 32:49.933 --> 32:53.873 STUDENT: Is that supposed to be 1000 meters? 32:53.867 --> 32:57.367 PROFESSOR: That's supposed to be I made the 32:57.367 --> 33:00.167 mistake here, 100 meters, sorry. 33:00.167 --> 33:01.897 Thanks for pointing that out. 33:01.900 --> 33:03.170 100 meters, yeah. 33:03.167 --> 33:05.127 That'd be too deep. 33:05.133 --> 33:08.673 Very rarely does the ocean mix down to 1,000 meters, as you 33:08.667 --> 33:09.527 saw in the diagram. 33:09.533 --> 33:13.073 By the time you get down to 1,000 meters you've got a lot 33:13.067 --> 33:15.367 of gradients and things like that, so it doesn't usually 33:15.367 --> 33:17.227 mix that deep. 33:17.233 --> 33:20.303 So you can apply this to a wide variety of circumstances, 33:20.300 --> 33:23.100 depending how you alter the input numbers. 33:23.100 --> 33:26.030 The heat could come from the Sun like I've done, it could 33:26.033 --> 33:29.003 be a loss of heat by radiating to space. 33:29.000 --> 33:32.530 It could be a heat transport from the atmosphere in or out 33:32.533 --> 33:35.433 of the ocean, depending where remember the diagram I showed 33:35.433 --> 33:37.773 you some parts of the world is positive, 33:37.767 --> 33:38.897 some parts it's negative. 33:38.900 --> 33:41.870 So this number's going to depend on where you are, the 33:41.867 --> 33:44.267 season of the year, and so on. 33:47.800 --> 33:51.600 Now, the next one will be number two. 33:54.633 --> 33:57.673 This is a little trickier. 33:57.667 --> 34:04.527 Let me define the salinity as the mass of the salt over the 34:04.533 --> 34:08.433 mass of the water in any particular sample that you 34:08.433 --> 34:13.733 have. I'm going to be looking at change, so I'm going to 34:13.733 --> 34:19.603 define salinity at time 1 as being the mass of salt at time 34:19.600 --> 34:21.930 1 over the mass of water at time 1. 34:21.933 --> 34:26.173 And salinity at time 2 as being MS2 over MW2. 34:30.800 --> 34:33.530 But I'm not going to consider cases where I'm adding and 34:33.533 --> 34:36.773 removing salt. 34:36.767 --> 34:39.027 That doesn't happen very often in the ocean. 34:39.033 --> 34:42.173 Instead I'm going to consider cases where I add and remove 34:42.167 --> 34:43.667 fresh water. 34:43.667 --> 34:49.467 Either it rains, so I'm adding fresh water, or it evaporates. 34:49.467 --> 34:52.597 When it evaporates it leaves all the salt behind, so you 34:52.600 --> 34:56.800 can say that I'm subtracting fresh water. 34:56.800 --> 35:00.400 So I'm going to assume that in the changes I'm about to 35:00.400 --> 35:06.400 describe that MS1 is equal to MS2. 35:06.400 --> 35:09.430 So I'm not changing the mass of salt in the sample, but I'm 35:09.433 --> 35:11.373 going to change the mass of salt water. 35:14.433 --> 35:19.033 I'm going to define the change in salinity as being S2 minus 35:19.033 --> 35:24.733 S1, and just using these formulas that'll be MS over M 35:24.733 --> 35:30.073 water 2 minus MS over M water 1. 35:30.067 --> 35:33.127 And notice I've dropped the subscript now on the MS 35:33.133 --> 35:35.173 because I'm going to assume that the mass of 35:35.167 --> 35:36.527 salt doesn't change. 35:41.300 --> 35:45.530 With just a little bit of manipulation I can rewrite 35:45.533 --> 35:56.273 this as MS over M salt water 1, M water 1 over M water 2 35:56.267 --> 36:01.027 minus M Salt over M water 1. 36:01.033 --> 36:04.303 What I've done is just multiply and divide the first 36:04.300 --> 36:08.130 term by M water 1. 36:08.133 --> 36:09.633 You see it there and there. 36:09.633 --> 36:12.333 I've just multiplied and divided by the same number. 36:12.333 --> 36:18.903 But now this can be rewritten as the salinity at time 1 36:18.900 --> 36:30.000 times the bracket M water 1, M water 2 minus 1. 36:30.000 --> 36:36.000 So the change in salinity is related to the salinity you 36:36.000 --> 36:40.200 started with, plus the ratio of the fresh water you started 36:40.200 --> 36:43.900 with to the fresh water you ended with. 36:43.900 --> 36:48.500 That's an M sub W sub 1, and an M sub W sub 2, the fresh 36:48.500 --> 36:51.070 water that you have. 36:51.067 --> 36:55.067 Now I'm going to try to motivate this a little bit 36:55.067 --> 36:55.897 geometrically. 36:55.900 --> 37:01.770 Imagine I've got a column of seawater, perhaps some little 37:01.767 --> 37:04.897 section of the surface layer of the ocean I just sliced out 37:04.900 --> 37:07.800 with a cookie cutter. 37:07.800 --> 37:12.370 And then I add a layer on top of it. 37:12.367 --> 37:15.127 It'll be capital D in its depth, and then I'm going to 37:15.133 --> 37:21.633 put a little thin layer on top of it with depth little d. 37:21.633 --> 37:25.503 Or alternatively, I could strip off, I could evaporate, 37:25.500 --> 37:28.730 a layer of depth little d. 37:28.733 --> 37:32.573 That would make the seawater saltier. 37:32.567 --> 37:37.227 With that geometric interpretation, I can write 37:37.233 --> 37:46.073 the ratio in my formula MW1 over MW2 as being capital D 37:46.067 --> 37:50.667 over capital D plus little d. 37:50.667 --> 37:54.997 In other words, I'm just adding water, and that's going 37:55.000 --> 38:00.430 to change the mass ratio before and after. 38:00.433 --> 38:06.803 That allows me to rewrite this formula finally to can you see 38:06.800 --> 38:08.230 it if I do it here? 38:08.233 --> 38:12.403 So I'm going to take this formula, divide through by the 38:12.400 --> 38:14.900 S1 and use little added formula. 38:14.900 --> 38:24.630 So delta S over S1 can be written finally as big D over 38:24.633 --> 38:30.203 D plus little d minus 1, which can be simplified to little d 38:30.200 --> 38:33.100 over big D plus little d. 38:33.100 --> 38:36.470 That's the formula we're going to use. 38:41.867 --> 38:46.427 If that seems confusing in any way, all I've done is 38:46.433 --> 38:52.173 conserved salt, but change the amount of fresh water, and 38:52.167 --> 38:53.667 therefore the salinity changes. 38:53.667 --> 39:01.427 So if I add a layer of fresh water of depth D with a minus 39:01.433 --> 39:06.233 sign there, that's going to make the water less salty. 39:06.233 --> 39:08.173 The minus sign reminds us of that. 39:08.167 --> 39:12.697 If D is positive, if I've added fresh water, the ocean 39:12.700 --> 39:13.800 gets less salty. 39:13.800 --> 39:17.530 If I subtract by evaporating, then D would be negative. 39:17.533 --> 39:20.103 Negative times a negative is positive, and the salinity 39:20.100 --> 39:22.230 would increase. 39:22.233 --> 39:24.073 So that's the way you'd use this formula. 39:24.067 --> 39:25.727 Let's do an extreme example to be sure 39:25.733 --> 39:28.503 this formula's correct. 39:28.500 --> 39:34.800 Let's say that I doubled the depth. 39:34.800 --> 39:38.300 I put a whole thick layer of fresh water on there equal to 39:38.300 --> 39:41.800 what I had originally of seawater. 39:41.800 --> 39:49.100 Well then it would be minus capital D over capital D plus 39:49.100 --> 39:56.400 capital D. That quantity is going to be minus 1/2. 39:56.400 --> 39:59.770 That means the salinity's going to drop in half of what 39:59.767 --> 40:03.097 it was before because I've added an equal 40:03.100 --> 40:04.130 amount of fresh water. 40:04.133 --> 40:07.533 So that salt now had to mix into twice the 40:07.533 --> 40:08.573 amount of fresh water. 40:08.567 --> 40:12.197 That's going to drop the salinity exactly in half. 40:12.200 --> 40:13.630 Now this would be an extreme example. 40:13.633 --> 40:15.903 Usually in the ocean we're just talking about adding some 40:15.900 --> 40:17.670 small fraction. 40:17.667 --> 40:22.997 So let me do a little more realistic example of this. 40:39.967 --> 40:56.127 My example would be adding 1 meter of fresh water to 100 40:56.133 --> 40:57.433 meters of ocean water. 41:05.033 --> 41:06.833 How much will the salinity change? 41:06.833 --> 41:22.533 So delta S over S1 is going to be minus 1 over 100 plus 1. 41:22.533 --> 41:27.573 So that is approximately minus 0.01. 41:27.567 --> 41:31.627 This is approximately 35 parts per thousand let's say, the 41:31.633 --> 41:33.473 original salinity. 41:33.467 --> 41:38.927 So delta S is going to be 1/100th of that. 41:38.933 --> 41:45.103 It's going to be 0.35 parts per thousand, which means the 41:45.100 --> 41:50.770 new S, the new salinity, I'll call it here S2, is going to 41:50.767 --> 42:01.867 be 34.65 parts per thousand. 42:01.867 --> 42:06.527 I started with 35 parts per thousand, 100 meter column, 42:06.533 --> 42:12.833 added 1 meter of fresh water on top, mixed it all in, the 42:12.833 --> 42:17.373 salinity drops by 0.35 parts per thousand, which takes me 42:17.367 --> 42:21.097 from 35 to 36.65. 42:21.100 --> 42:23.330 That would be a typical situation. 42:23.333 --> 42:26.403 And that's a big difference, considering that the full 42:26.400 --> 42:29.870 range of ocean salinity is only from about 42:29.867 --> 42:32.927 34 to 35 and 1/2. 42:32.933 --> 42:35.573 That's a big difference in ocean salinity. 42:35.567 --> 42:39.227 And that'll cause circulations to begin, because the seawater 42:39.233 --> 42:41.973 density will have changed. 42:41.967 --> 42:45.197 Any questions on that? 42:45.200 --> 42:47.570 STUDENT: Is that only for the surface? 42:47.567 --> 42:48.167 PROFESSOR: Pardon me? 42:48.167 --> 42:49.227 STUDENT: Is that only for the surface? 42:49.233 --> 42:49.773 PROFESSOR: Yeah I don't 42:49.767 --> 42:50.827 imagine well that's right. 42:50.833 --> 42:53.433 So that would affect this top 100 meters. 42:53.433 --> 42:57.573 Then what happens later on to the rest of the ocean, that 42:57.567 --> 42:58.827 would remain to be seen. 42:58.833 --> 43:03.033 If, for example, in this case, I made it less dense, because 43:03.033 --> 43:05.673 I made it less saline, that water would probably remain 43:05.667 --> 43:07.297 floating there. 43:07.300 --> 43:10.970 If I had made it more dense, it might find itself so dense 43:10.967 --> 43:13.627 that it would then fall to the bottom of the ocean. 43:13.633 --> 43:15.403 But that's a separate calculation. 43:15.400 --> 43:17.100 Here I'm just trying to understand what happens to the 43:17.100 --> 43:19.970 surface water when you change its salinity. 43:23.900 --> 43:27.330 Now we turn to the third type of forcing, 43:27.333 --> 43:28.603 which is wind stress. 43:40.367 --> 43:43.527 This is perhaps not quite as obvious as the others. 43:43.533 --> 43:45.933 I don't think I've greatly surprised you by either of 43:45.933 --> 43:47.003 these calculations here. 43:47.000 --> 43:50.170 It's pretty much common sense. 43:50.167 --> 43:53.567 But what happens when the wind blows over the ocean? 43:53.567 --> 43:58.467 When the wind blows over the ocean it 43:58.467 --> 44:01.497 produces a wind stress. 44:01.500 --> 44:03.870 Frictionally, just like when you move your hand across the 44:03.867 --> 44:07.127 table pushing down, there's a stress being 44:07.133 --> 44:08.103 applied on that table. 44:08.100 --> 44:11.030 That table starts to move sometimes in the direction 44:11.033 --> 44:13.103 that you're pushing. 44:13.100 --> 44:14.500 And that's my question. 44:14.500 --> 44:17.270 If I put the wind in that direction, from left to right 44:17.267 --> 44:23.897 in this diagram, does the ocean water begin to move in 44:23.900 --> 44:26.800 the same direction? 44:26.800 --> 44:31.670 Well, you're probably on your guard because you know that 44:31.667 --> 44:35.927 the Coriolis force exists so that some things are not quite 44:35.933 --> 44:39.533 as obvious cause and effect-wise when you have the 44:39.533 --> 44:40.573 Coriolis force. 44:40.567 --> 44:42.567 In fact, here's what happens. 44:42.567 --> 44:46.567 So I'm going to draw a plan view here now, North, South, 44:46.567 --> 44:50.467 East and West. I'm going to imagine I've got a Westerly 44:50.467 --> 44:55.467 wind, that is a wind from West to East. So the wind is 44:55.467 --> 44:57.597 blowing in that direction. 44:57.600 --> 45:00.100 The wind stress will also be in that same direction. 45:03.067 --> 45:06.527 I'd like to prove to you, in the remaining three or four 45:06.533 --> 45:12.103 minutes, that when I push the water in that direction it 45:12.100 --> 45:13.870 goes to the right. 45:13.867 --> 45:15.667 It doesn't go in the direction I'm pushing. 45:18.433 --> 45:22.533 This will involve a new kind of force balance called the 45:22.533 --> 45:24.603 Ekman force balance. 45:31.100 --> 45:35.170 It has something in common with geostrophic force 45:35.167 --> 45:37.197 balance, but it's also quite different. 45:39.967 --> 45:44.627 So let's say that I start to put this wind stress, it's 45:44.633 --> 45:47.003 going to--in the first few minutes it is going to do the 45:47.000 --> 45:47.530 obvious thing. 45:47.533 --> 45:50.273 It's going to start the water moving towards East. But then 45:50.267 --> 45:55.367 as soon as it gets moving, if feels the Coriolis force and 45:55.367 --> 45:57.627 it will begin to bend. 45:57.633 --> 46:05.573 After a few hours, I will argue now, that the flow will 46:05.567 --> 46:10.367 be towards the South that'll be the Ekman flow. 46:10.367 --> 46:13.897 To the right angles of that will be the Coriolis force 46:13.900 --> 46:16.630 acting on that Ekman flow. 46:16.633 --> 46:18.803 And that's going to be equal and opposite to the wind 46:18.800 --> 46:20.030 stress itself. 46:22.100 --> 46:27.570 And so when you push on the water on a rotating Earth with 46:27.567 --> 46:30.627 the frictional stress from the wind, instead of moving in the 46:30.633 --> 46:33.073 direction you push, it moves at right angles. 46:33.067 --> 46:38.697 To the right in the Northern Hemisphere, to the south--I'm 46:38.700 --> 46:40.530 sorry, to the left in the Southern Hemisphere. 46:45.233 --> 46:47.703 We could do a calculation. 46:47.700 --> 46:52.000 I probably don't have time to finish this today, but I can 46:52.000 --> 46:54.900 do a calculation of how fast that water will move. 47:00.333 --> 47:08.473 If I have, again, a column of depth D, it has a mass given 47:08.467 --> 47:15.897 by AD rho across the area, the height of the column, and the 47:15.900 --> 47:18.230 density of seawater. 47:18.233 --> 47:23.133 If it begins to move you'll have a Coriolis force given by 47:23.133 --> 47:30.133 2, the mass, the speed, the rotation rate of the Earth, 47:30.133 --> 47:32.833 and the sign of the latitude. 47:32.833 --> 47:37.033 That's going to have to balance the wind stress. 47:37.033 --> 47:40.003 There's a nice empirical formula for wind stress that 47:40.000 --> 47:42.770 I'll give you. 47:42.767 --> 47:45.627 I won't derive it, it's just an observational quantity. 47:45.633 --> 47:47.973 I've written there empirical, which means it's an 47:47.967 --> 47:51.927 experimentally-derived formula. 47:51.933 --> 47:56.903 It's given by constant 0.003 times the density of the air 47:56.900 --> 47:59.670 blowing over the water's surface times 47:59.667 --> 48:00.967 the wind speed squared. 48:07.167 --> 48:09.627 And this has units of Newtons per square meter. 48:19.800 --> 48:26.230 So now, let me just equate those two things following the 48:26.233 --> 48:29.733 prescription for the Ekman layer force balance. 48:32.867 --> 48:35.897 I'm going to say when you've got a well established balance 48:35.900 --> 48:44.070 of this sort, then the Coriolis force which is 2, let 48:44.067 --> 48:52.967 me substitute this in for MD rho then comes U omega sin 48:52.967 --> 49:04.067 phi, must be equal to Taw acting on that same area A. 49:04.067 --> 49:07.267 Since that's a force per unit area, I need to multiply it by 49:07.267 --> 49:09.827 a surface area to get a Newton. 49:09.833 --> 49:11.933 So I got Newtons and Newtons on both sides. 49:11.933 --> 49:16.133 And then solving this for the speed of the flow in the Ekman 49:16.133 --> 49:28.703 layer, I can cancel the A's, and I have Taw over 2D rho 49:28.700 --> 49:34.670 omega sign phi, sign of the latitude. 49:34.667 --> 49:39.067 That is the box formula for this part of how the 49:39.067 --> 49:42.367 atmosphere drives the ocean. 49:42.367 --> 49:47.197 If I know the wind speed I can compute Taw. 49:47.200 --> 49:50.370 If I know Taw, the depth of the layer that's being 49:50.367 --> 49:54.067 influenced directly, the density of seawater, the 49:54.067 --> 49:56.527 rotation rate of the earth, and the latitude, I can 49:56.533 --> 50:01.833 compute how fast this water moves off to the right under 50:01.833 --> 50:04.773 the influence of the wind stress. 50:04.767 --> 50:06.197 So we're out of time today. 50:06.200 --> 50:07.670 This needs a lot more discussion. 50:07.667 --> 50:10.797 But you've got a problem you're working on for the 50:10.800 --> 50:13.830 problem sets where you need to use that formula, I believe. 50:13.833 --> 50:18.233 And I will talk more about the physics of this on Friday.