GG 140: The Atmosphere, the Ocean, and Environmental Change

Lecture 35

 - Review and Overview


The material covered throughout the course is reviewed. Properties of air and water are discussed. Hydrostatic balance is discussed as related to the atmosphere, ocean and solid earth. Geostrophic balance is a force balance between the Coriolis force and the pressure gradient force, and applies to winds in the atmosphere as well as currents in the ocean. Several examples of equilibrium states are reviewed. Heat and mass are transported by fluid motion in the earth system through winds, ocean currents and rivers. Mixing, dilution and concentration is discussed as related to ocean and atmosphere pollutants as well as salinity in the ocean. Finally, symmetry between the northern and southern hemispheres is discussed, focusing on differences in land mass, Coriolis force and the seasons.

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The Atmosphere, the Ocean, and Environmental Change

GG 140 - Lecture 35 - Review and Overview

Chapter 1: Overview of Course Material [00:00:00]

Professor Ron Smith: What have we learned? Well, we’ve learned about the atmosphere and the ocean, and how they work. The physical processes that go on to make the ocean and atmosphere, like we find them on our planet. We’ve also learned a little bit about how they’re changing in time and what processes are causing them to change as well. So in a nutshell, that’s kind of what we’ve learned.

And how did we do it? This may not have been apparent to you, but as I look at the course, we’ve been using three intellectual approaches as we’ve gone through this material. Observation has been one, a very important one. Quantification, trying to get numbers onto everything. Amounts, numbers, and units. And then logic, interpretation, and explanation.

Why are things the way they are? How do things connect? How do physical principles explain this phenomena, but also that phenomena. So observations, quantification, and I guess explanation are the themes, or the approaches, that we’ve used going through the course.

What can we do with this? Well, that’s not so easy maybe. On a kind of a trivial basis, you could use the material of this course to lead you into more advanced courses. If you need—if you want to chat with me about any of that, I’d be more than happy to talk to you about what other courses are offered, especially in G&G, which I know the best. But also EVST, maybe engineering as well has some other courses. So you can–you know this is an introductory course. It’s a survey course, and for many it can serve as a good foundation for doing more advanced courses.

Another thing that you can do with this that I think is fun, I remember when I was a student, I loved to take material I learned in one course and see if I could fit it together with things I was learning in other, seemingly unrelated courses. Find ways in which they connect. A few of you over the course have mentioned to me examples where you’ve seen the material in here kind of match up in a certain way with other courses you are taking, have taken, or maybe you’ll find out this will happen in the future as you take other courses.

But that’s really important because this stuff is not meant to have sharp boundaries around it. It’s not a body of knowledge that’s controlled and fenced off from other disciplines. It’s supposed to be just the opposite. A subject that has a lot of connections, whether it’s economics, or engineering, or biology. I hope you’ll try to find those connections as you go forward.

So I think this course–you can take a course in music appreciation. Or you can take a course in nature appreciation. Maybe this is a course in nature appreciation, where you learn a bit about how to observe and appreciate things that are going on. Now some would take the other side of the argument. Some would say, no, no, if I approach environmental studies from a physical or a quantified point of view, it loses–some of nature loses its appeal to me, its wonder, its beauty, and so on. Now I’ve never found that to be true.

I got into this field because I appreciated what was going on around me in nature. And I’ve found that only deepening as I’ve studied it quantitatively. It’s true that when I see something happening now I can understand, at some level, why it’s happening. But that only leaves another thousand mysteries beyond that of things that I don’t yet understand, but wish that I did. So in a sense this I don’t think will limit your appreciation of what goes on in the out-of-doors. It will just perhaps change a little bit the approach you take to understanding it.

And the last one I have on my list here is that this material, I think, is important because there are some important political and moral questions that face us as individuals and as a society for which you need some scientific knowledge in order to understand what direction we should be going. You know this idea–I’m sure you’ve heard this in other courses but–this idea of a common, something that’s shared by a number of people.

In the old days in New England, it was the town green. Like what’s now New Haven Green, and all these old New England villages, was a common space and people could bring their cows and their sheep to graze there. Now that didn’t last too long, because after a while they were too many sheep and too many cows to–they would overgraze a single common area like that. But the point is, it’s a shared area where everybody benefited from it, but everybody had to take some responsibility for it as well.

Well now, the atmosphere and the ocean are the commons, right? We all derive benefits from it. We all pollute it in some way. And so we have to take responsibility for that. And that’s the basis for these moral and political questions that I alluded to. Having a scientific understanding of that system may help us to make the right choices there.

So that’s some of the why’s and what’s we did during the term. I want to finish up by spending the next few minutes talking about some common themes. And I passed out this sheet of paper which lists some, and I’ve–that’s up on the server as well. I tried to scan through, the other night, the things—kind of the physical principles that we’ve run across in this course more than once.

We didn’t always state them in the same way sometimes they were, because they had such a different context, they almost seem like a different physical principle. But today I want to spend some time trying to tie these together. Because I don’t know I want to–OK, agreed there’s a lot of individual little facts and figures that you dealt with throughout the course. But I’ve never looked at it that way. I’ve always looked at it as kind of a continuum where we could learn a few physical principles, and use them over and over again to solve related or maybe even seemingly unrelated problems during the semester. And that’s what I want to emphasize today.

I don’t think I’ve done a good enough job during the term emphasizing those common themes, so my last day here is an attempt to repair my errors for the semester by paying more attention to these common themes.

The first, which is not even on the list, would be physical units. So we talked about units earlier in the course, and we’ve had to use them every time we were doing any kind of a quantitative calculation. And I hope you’ve come to appreciate them as much as I have. Not only did they provide us a common language–when I say the air density in this room is 1.2 and leave it there, that conveys essentially zero information to you. Unless I put the units onto that, kilograms per cubic meter, it has no meaning.

So the units are really essential in how we talk to each other and convey information. They also have this magical property of allowing us to check our work, to see whether a formula that we’re plugging numbers into, or that we’ve derived in some way, is physically consistent, by seeing if the units work out. So it’s really a wonderful set of things. And if you’re not fully up to speed on that by now, I recommend that you work a bit on that, because that will improve everything that you do in this course and in another physical science courses. Having a more of a facile understanding and adeptness of using units will certainly improve all of your work and your thinking.

Chapter 2: Properties of Air and Water [00:09:00]

So let’s go on then to the first one that I do have on this list, the properties of air. And of course, density and how it’s related to other things is important. And we found that air is a perfect gas. P=ρRT. And so we know that we can solve that equation for density if we want. P/RT. And that shows us that density is a function of pressure and temperature. At constant pressure, if you heat up the air it’ll expand and the density will become less. At constant temperature, if you add pressure to it, the air will compress and the density will become greater.

So we had to know that, and that’s so important in all of the things we did. And that gas constant, which appears in the perfect gas law, is different for every gas. Remember that. And that can be found by dividing the universal gas constant by the molecular weight for that particular gas. So the other thing we needed to know is heat capacity. How much heat is stored in a chunk of air at a given temperature? And that’s important for how the winds transport heat, how air cools and warms as it rises and sinks in the atmosphere, we used it over and over again. OK, so any questions on properties of air?

Properties of water. Now the list is longer. Why is the list longer for water than for air? Very simple. Air, in the realm in which we experience it, conditions here on earth, is always a gas. You can compress it to a liquid. I suppose, with enough compression and cooling, you might even reduce it to a solid. But we never see air in anything other than the gaseous state, so all we need are those three little things that I mentioned for air.

But for water, we find it in all three phases on normal conditions on earth. Gas, liquid, and solid, that is to say, ice. So we have to have some information about its density in the gaseous state—in the liquid state.

And for the oceans, we’ve learned they’re dependent on salinity and temperature. We need to know the heat capacity of water. How much heat can be stored in water at a certain temperature?

And then everything else here has to do with phase changes. So at what temperature does it freeze from liquid to solid? And that was actually slightly dependent on salinity. Remember, at full ocean salinity, the freezing point is not zero Celsius, but about -2. It’s not much of a difference, but it makes some difference.

And then there was this definition, or this thing we talked about, of supercooled water, which happens frequently in clouds in the atmosphere, where you cool the temperature down below the freezing point, but yet the water doesn’t freeze until something triggers that freezing. When freezing does occur, heat is either–well, for freezing to occur, you have to remove heat.

The reverse of that, when you melt ice, you have to add heat. That is called the latent heat of freezing, or the latent heat of melting. It’s the same number, either way. And when you’re condensing vapor to form liquid, there’s a big heat required, depending whether you’re condensing or evaporating.

So that’s really important, and then the saturation vapor pressure, this idea that you can keep more water in the liquids—in the vapor state, the hotter it is, is so important for the atmosphere. It explains why clouds form, for example. Rising air, adiabatic cooling, eventually you come to the saturation point and then cloud liquid water begins to form.

So water is a little more complicated, maybe, than air, because it gets in these different phases and we really have to understand how these phase changes occur in order to understand the atmosphere ocean system. Questions on that?

Chapter 3: Physical Balances [00:13:40]

Hydrostatic balance is something we’ve come across over and over again. It’s the idea that when you go up–the way we derived it in an incremental form–is that if you go up in the atmosphere a height, delta z, move up from there to there, the pressure will decrease–keep the minus sign to remind me of that–at a rate that depends on the acceleration of gravity and the density of the fluid. So we use that.

We came across that first in atmospheres, but then it’s true in the oceans as well. But remember, a typical density in the atmosphere, well it’s 1.2 kilograms per cubic meter at sea level. But then it decreases strongly as you go up. So this value will change at different altitudes in the atmosphere. In the ocean, it’s about 1025. It changes a bit around that based on the salinity. Same units, 1000 times greater.

When you get down into the earth–you can go down through the earth’s mantle–this equation continues to be valid, but there the density is more like 2000 or 3000 kilograms per cubic meter. So the pressure increases even faster as you go down.

So the same equation can be used in all three spheres. But just remember, the density can be all over the place. From nearly zero, up in the top of the atmosphere, to this value at the surface, to this value in the ocean, and this value down in the interior of the earth.

We also use that with a barometer. You know, the whole principle of a mercury barometer is the hydrostatic law. That column of mercury rises to a height needed to balance the atmospheric pressure pushing up at its base. And so you see that principle of hydrostatic balance there as well. Questions on hydrostatic?

Geostrophic balance, another kind of important force balance. The idea there is that when objects or fluids move relative to the earth, they have a Coriolis force. And very often in the atmosphere and the ocean, after a few hours, you end up in a state of geostrophic balance, where the pressure gradient force balances that coriolis force. And that gives some very special properties.

It says that the air or the water moves along the isobars rather than across. And the speed of the fluid is proportional to the strength of the pressure gradient. Here’s how we derive that.

We said that the pressure gradient force was the product of the pressure gradient and the volume of some little block of air that we imagined (PGF=PG*V). And then we equate that with the Coriolis force, which was 2 times the mass, which is rho times volume, times the velocity of the object, times the rotation rate of the earth and the sine of the latitude (CF=2ρVUΩsinϕ). So having equated those then and solving for U, and canceling out the volumes, I get pressure gradient over 2 rho U omega sine phi for the geostrophic—the speed of the geostrophic wind. [correction: I get pressure gradient over 2 omega sine phi for the speed of the geostrophic wind (U=PG/2Ωsinϕ).]

And the direction of course depends on the hemisphere, but along the isobars. Applies to both the atmosphere and the ocean. So any questions on that?

Chapter 4: Equilibrium States [00:17:47]

OK, now, this fifth item on the list I’ve handed you is the concept of equilibrium states. And I tried to get that started in the early part of the course by taking you upstairs and doing this tank experiment, where I had a certain qin, and then I had a qout that depended on the depth of the water.

It depended on how much water there was in the tank. And we tried to understand the equilibrium states of this simple system. And in a nutshell, this is the way you do it.

If you make an axis–a plot like this, with rates on this axis, and some measure of the amount of water–in this case, maybe it’s the depth, z, on that axis–you can work out the solution to this equilibrium state graphically. For example, if I’m putting a certain amount of water into this tank per unit, time, that doesn’t depend on how much water I have in the tank. This is just, you know, how much water am I squirting into the tank per unit time? So that is a constant. That’s the rate of inflow.

But the rate of outflow will depend on how much water is in the tank. The deeper the water, the more pressure there is at the bottom pushing water through that valve. And so if I make a plot here of the outflow rate, versus the depth of water in the tank, it’s going to look something like this.

The deeper the water, the faster the water will gush out. And there will be a crossing point where the two are equal. That’s the equilibrium state. Then the depth will remain constant because the rate at which we are putting fluid in balances the rate at which fluid is moving out. That’s what I mean by an equilibrium state. We saw this early in the course.

Now let’s see if some of the ways that we have run across this in the atmosphere are perhaps not appreciated enough. For example, if we’re evaporating water from the surface of the earth and putting water vapor molecules into the atmosphere, when we get enough water in the atmosphere, given the vertical motions that are there from convection, from fronts, and so on, we’re going to eventually build up clouds. And under some circumstances, those clouds will precipitate.

And generally speaking, the amount of water you take out per unit time is going to be related to how much water you have in the atmosphere. Well obviously, if you don’t have any water in the atmosphere, you can’t take any out. And if you’ve completely saturated the atmosphere with water, you’re going to be raining a lot out.

So there is some curve like this, where, again, rate would be on this axis. This might be the water vapor content of the atmosphere. The rate at which we’re putting it in might depend a little bit on water vapor content. But the rate at which we’re taking water out will certainly depend on the water vapor content. And there will be a crossover point.

So the amount of water vapor in the atmosphere is going to be sustained at a–roughly at a level where these two things can balance with time. And that’s the way we think about water vapor in the atmosphere.

Let’s do another one. Heat in the climate system. So the sun’s radiation is warming the earth. If it had—if it was ice cold, or if it were colder than ice, if it were absolute zero Kelvin, it would not be radiating to space. But it’s not. It’s at some temperature, so its radiating to space as well, in relationship to its temperature.

So if I make this plot again, the rate will be the energy from the sun absorbed on the earth. That’s going to be independent of the temperature of the planet. But the rate at which I’m radiating to space is going to be strongly dependent on the temperature of the planet.

Remember, it goes like T4. The Stefan-Boltzmann law says that this goes like temperature to the fourth power. So there’s some crossover point. And that’s where we are most of the time with the earth. We’re at an equilibrium state set by seeking out this balance between inflow and outflow.

I’ll do two more and then we’ll–I don’t want to beat this too much to death but it is so important. If I had a–what’s next–if I had a mountain glacier, snow falling on this glacier, it’s going to be flowing under gravity. So the rate at which I’m adding snow to the top of this is independent about how much ice and snow I have on the mountain. That’s just an atmospheric thing, so the input is just constant. And this will be a measure. Let’s call this the thickness of the glacier.

Thickness of the glacier. If it’s really thin, it’s not going to flow, and there’s not going to be any ice leaving the system. That is to say, running down the mountainside. But as it gets thicker, now gravity is going to be pulling that ice down away from this region. And that will be a loss that will increase with ice thickness.

The system will seek out an equilibrium where the snow falls. You’ve reached a balance. The amount of ice sliding down the mountain is just equal every year to how much snow has fallen. So you’ve reached a steady-state system for the glacier. Now these glaciers are not always in that steady state, but this is one of the possibilities we should always investigate, to see whether that system is in steady state.

And the last one I had here was the ozone layer, where you remember far above the earth there is this ozone layer. You make ozone from oxygen. You photosynthesize it and recombine it differently to make ozone. So the rate at which you are making ozone, for our intents and purposes is pretty much fixed, because you’re not going to change that very much.

But the rate at which are destroying ozone is going to be proportional to how much ozone you have. I showed you that chemical reaction, also. The more ozone you have, the more chances that you’ll dissociate an ozone, combine them in such a way that removes ozone from the system. So once again, you’ve got curves generally like this. The input’s relatively independent of how much ozone you have. The loss rate is proportional to how much ozone you have. So there’s going to be a crossing point, and that’s going to be a steady-state solution.

Again, I’m not claiming that the earth’s ozone layer is in steady state, but that’s one possibility that we’d want to look at. And then if it’s not, we’d want to understand why there are temporal changes going on. Why has that system not yet reached its steady state? Questions there?

Chapter 5: Static Stability [00:26:01]

So this idea of lapse rate and static stability, we ran across for the ocean and the atmosphere. And for the atmosphere, we did it this way. We plotted temperature versus height. And we put reference lines on there, which we call capital gamma (Γ)_. The dry adiabatic lapse rate was about negative 9.8 degrees Celsius per kilometer.

And we ran our reasoning about whether an atmosphere would be stable, just stay there in layers, or whether it would turn over and begin to come back based on this kind of an argument. This is for the atmosphere.

For the ocean, we get a little differently. We plot in density versus height or depth. And we looked at various possibilities. Our reference line there was really a line of constant density. If the density increased as you went up, that would be unstable. If the density increased as you went down, that would be stable. Why do we do the two differently?

Well, the answer is clear. For atmospheres we’re dealing with a compressible substance. Gas is very compressible. And so we had to work out this adiabatic lapse rate, and do the argument this way. For water, it’s incompressible and it has the other components. It’s got salinity in it as well.

Remember density is a function of temperature and salinity in the ocean. So the fact that it’s incompressible and the fact that salinity is involved makes us do the argument a little bit differently. But the question we’re asking is the same. Is that column of fluid going to stay stagnant in layers, or is it going to turn over and mix? And that’s important in both spheres, the atmosphere and the ocean.

Chapter 6: Transport of Heat and Mass [00:28:18]

Transport of heat by fluid motion.

So we’ve come across this several times, but the idea is if you have a pipe, let’s say with fluid passing through it, the volumetric flow rate is a product of the velocity and the area. Now it doesn’t have to be confined in a pipe. In the atmosphere or the ocean it’s not confined in a pipe. But still it’s the area and the velocity that gives you the volumetric flow rate.

The mass flow rate would be rho U a(mass flow rate=ρUA). The heat that you’re pushing through the pipe, well we got the mass flow rate, and we know that the amount of heat stored per unit mass is Cp T. So this is heat capacity times temperature times rho U A (heat transport=CpTρUA). If that’s water and you want know how much salt is being transported, well it’s the salinity times rho U A (salt transport=SρUA).

If it’s some other pollutant, like in the air, maybe it’s nitrous oxide, well then that would be the concentration of NO2 times rho U A (NO2 transport=[NO2]ρUA), if that is a ratio by mass. Be careful, be sure that’s a ratio by mass if you’re going to use it that way. So anyway, this is a common theme we ran across in the atmosphere and the ocean.

Chapter 7: Mixing, Dilution and Concentration [00:29:57]

And this is related to the next one on the list, which is the general idea of concentration, where if you put a substance and mix it into a background fluid, we’re very interested in the concentration, which is how much did you put in, compared to how much you’ve mixed it into. So for example, when I write down, when I say this CO2 in brackets, I’m referring to the concentration of carbon dioxide.

And that could be either the mass of CO2 over the mass of air, or it could be the molecules, the number of molecules of CO2 versus the number of molecules of air. So remember which one you’re dealing with. Neither of these ratios has units but you do have to remember whether it’s a mass ratio or a molecular ratio. This one is usually called “by volume.” And this one we would say that’s a ratio “by mass.” Taking into account by mass.

So you have to know how much you put in, and into what volume have you mixed it, and the longer you wait for it to mix into a larger and larger volume, you have diluted it. The same amount of material added, but mixed into a larger and larger amount, the concentration will drop because you’re diluting it into a larger background.

Chapter 8: Symmetry between the Hemispheres [00:31:47]

And that brings us to the last one, which is this question that’s always fascinated me about the degree of symmetry between the northern and southern hemisphere. So here we have our planet, our home planet and it spins in that direction. And to what extent are the northern and southern hemispheres similar or different? Is there some kind of symmetry between the northern and southern hemispheres? So I’ll end up with a brief discussion of this.

So we know that the seasons are reversed between the two hemispheres. And that has to do with the tilt of the earth, right? So if the sun’s over there, at this moment the northern hemisphere is tilted towards–well not at this moment. At this moment, in December, it’s like that, right? At this moment, the northern hemisphere is tilted away from the sun, southern hemisphere towards. So it’s southern hemisphere summer, and then six months later, when the earth is going around to the other side of the sun, it’s like this. And the northern hemisphere has its summer. So there’s an opposite sense of the timing of the seasons between the two hemispheres.

What about the Coriolis force and storms? Well that’s the opposite in the two hemispheres, too. But for a different reason. It has nothing to do with the tilt of the earth. It has to do with the spin of the earth. The fact that it appears to spin this way in the northern hemisphere, but the opposite direction in the southern hemisphere.

So that cyclones move counterclockwise in the northern hemisphere, but clockwise in the southern hemisphere. And that applies to the atmosphere and the ocean. Coriolis force is reverse between the two. Therefore, things just spin differently in the two hemispheres.

Now, are there any other aspects of symmetry? Well, one thing that’s different between the two hemispheres is the amount of land. If you look at that one, there’s a fairly large fraction of land. I want to get this base out of the way, so I’ll do it this way. If you look at it that way, there’s much less land. And as we know, land and ocean have different heat storage capabilities.

The ocean can store heat powerfully, because not only does it have a high specific heat capacity, Cp, but also, when you heat, put heat at the top of the ocean, it mixes it in, because it’s a fluid. So you may have to mix heat. Heat can be stored easily in the first hundred meters or so of the ocean, and that’s an enormous mass. Where when I had heat to a continent, it only goes in about that much. Or maybe over a season, between winter and summer, it will go in about that much. As compared to 100 meters for the ocean.

So the heat storage capacity is very different between land and sea, and the northern hemisphere has much more land than the southern hemisphere. So there’s going to be that asymmetry between the two.

And there’s also a little different configuration, I want to remind you, near the poles. When it comes to this question of Arctic sea ice, for example. The Arctic Ocean is a little–it’s an ocean surrounded by land, whereas in the southern hemisphere, it’s land surrounded by ocean, right? So this interaction between the ocean and the land is quite different at the high latitudes in the two hemispheres.

For example, Antarctic bottom water, which is water formed near the Antarctic coast, the densest water in the sea drops down to the bottom and flows northward. There’s no equivalent to that in the northern hemisphere, because that geometry is different. So these are fundamental ideas and I think I’ll leave it there, and thank you and good luck on the final exam.

[end of transcript]

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