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

Lecture 35.?Review and Overview

https://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-35

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. 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.?

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.

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.?

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.

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.?

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=2ρVUΩsin?). So having equated those then and solving for U, and canceling out the volumes, I get pressure gradient over 2 omega sine phi for the speed of the geostrophic wind (U=PG/2Ωsin?).

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.?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.

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 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.

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.

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.

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.

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.?

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.

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.?