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

Lecture?04.?Vertical Structure of the Atmosphere; Residence Time

https://oyc.yale.edu/geology-and-geophysics/gg-140/lecture-4

Vertical structure of density and pressure in the atmosphere [00:02:57]

Both density and pressure have a vertical distribution that is close to the exponential function.?So for example, mass density ρ as a function of altitude is given by the density at sea level,.?And the same thing for pressure. Pressure as a function of altitude,?.?

Hs?is the scale height,?the height interval over which the pressure or density decreases by a factor e-1.?A larger value of scale height means that the atmosphere decreases its density more slowly as you go up. You have a deeper atmosphere. A smaller value for scale height means pressure and density decrease more rapidly as you go up. You have a shallower or a thinner--an atmosphere that's not as deep.?When you've gone up one scale height, z is equal to Hs, and you've decreased the pressure by that amount.?Now, e, you may recall-- the mathematical constant e-- is 2.71828,?et cetera. So e-1?is one over that. It's about 0.368 and so on, which we often round off and say, well, that's about one third.

When you go up one scale height, the pressure has dropped to one third of what it was at the bottom of that interval. So mark off three equal parts. Roughly, that's what it's dropped to when you go up one scale height. When you go up another scale height, another-- let me remind you, scale height can be computed from RT/g, and for Earth, that's about 8,400 meters. So when I go up another 8,400 meters and mark off that into three parts, it drops by about another third-- another 2/3 to a value one third of what it was at the bottom of that interval.

And then that just repeats. You see, that gives you a curve that approaches zero but never reaches it. And that's the nature of the atmosphere. The density gets less and less, but it never actually reaches zero because of the nature of this proportional decrease for each scale height that you go up in the atmosphere. So there is no such thing as a top of the atmosphere, where you could find a level where there's atmosphere below and none above. There is no such place. Instead it just--eventually, of course, you're in outer space, but even in outer space, there are a few molecules up there. So that would just be this curve continuing up quite a bit further.?

Vertical structure of temperature in the atmosphere [00:09:59]

Now, while density and pressure have a pretty featureless, smooth decrease with altitude, temperature is very different. So let's talk about the temperature profile in the atmosphere. And again, I'll make a plot of temperature on this axis. And altitude, I'll use z for altitude going up. This axis isn't exactly to scale, but I'll put some numbers on it to help you out.

The temperature of the Earth's atmosphere is very curious. It has a shape like this. The average surface temperature at the surface, 288 Kelvin. Mentioned that. It drops to approximately 200 Kelvin at an altitude of about 10 kilometers. At about 50 kilometers, it comes back to about what it was before--not exactly, but about that--then it decreases again about down to 200 at about 90 kilometers. And then it gets quite warm above that, higher than at the surface of the Earth.

Now, this temperature, though, changes quite a bit between day and night as it gets heated by the Sun and then cools at night. We use the word "diurnal" to indicate a day-to-night fluctuation. There's a bit of a diurnal cycle in temperature. And of course, these temperatures will be changing also with weather patterns, with seasons, and so on.?

Now, this is really important. And the fact that the atmosphere is layered in temperature gives us the basis for classifying these different altitudes. And I'm going to give you the standard classification then. This layer, from the surface of the Earth up to about 10 kilometers, where the temperature decreases with altitude, that's called the troposphere. It's defined in just that way. It's the lowest layer starting at the Earth's surface, and the temperature decreases with altitude. When the temperature turns around and starts increasing again, that's the stratosphere. Then there's the mesosphere. And finally, up here, this is the thermosphere.

Now, these names do have some meaning. They're not just drawn out of a hat. "Tropos" comes from a Greek word meaning "turning." In this case, it implies that that layer of the atmosphere is turning over quite a lot. And we'll see why that is. There's quite a bit of convection turning that air over in the troposphere. So "tropos" or "tropo" does have some meaning.

"Strato" also, the root comes from the word "layers." And here the air does not turn over very much. It lies there more or less in quiet layers. It may be blowing very fast, but you don't have strong, active overturning or convection. Mesosphere, well, it's in the middle somewhere. And then thermosphere is the hottest layer.?We have names also for these boundaries between the different layers. The boundary at the top of the troposphere is the tropopause. And then the stratopause, the mesopause, and there is no top to the thermosphere.

Now, this is an interesting puzzle. Why would the Earth's temperature structure look like that? ?In the stratosphere, it tends to start off cooling it more because of the ozone on top of the stratosphere.?Ozone?absorbs the Sun's UV energy.

Interaction between solar radiation and the atmosphere [00:15:50]

So let me lay that out a little more systematically. If you look at the light that comes from the Sun and I plot intensity versus wavelength, it has kind of a bell-shaped curve like this. The Sun emits at all wavelengths--very short, intermediate, very long--but most of its radiation is centered somewhere close to about--well, I'll put some numbers on here in just a minute.

So there's a range here from 0.4 to 0.7 microns that's what we call the visible part of the spectrum. That's the part of the spectrum that the human eye is sensitive to. To the right of that, at longer wavelengths, we call that the infrared part of the spectrum. And we break that further up into the near-infrared, NIR, and then the middle- or the long-wave infrared further out.

And the same thing to the left. At shorter wavelengths, we have the ultraviolet, which I'll abbreviate UV. And the nearest part of that is the NUV, the near ultraviolet. And then you have the middle and the far ultraviolet. Way out here, you have x-rays as part of that spectrum.

So the Sun is radiating like this, and those photons, that radiation, approaches the Earth and hits the atmosphere. What's going to happen? Well, it turns out that the x-rays and the far-ultraviolet are absorbed by the first molecules that they encounter.?

These other wavelengths-- the near ultraviolet, the visible, the near-infrared, the far-infrared-- they are not absorbed at that level. They come streaming on through. So I'll draw another arrow here to indicate what happens to the near UV, NUV. It gets absorbed by the ozone that's in the stratosphere. Ozone is a molecule. You know it's O3. It has three oxygen atoms tied together like that. And that molecular structure happens to be able to absorb near ultraviolet rays. So that provides a heat source which can act here. Everything else-- the visible, the near-infrared, and much of the far-infrared-- come streaming all the way down through and gets absorbed, finally, by the ground, by the Earth's surface itself.

The atmosphere doesn't absorb it at all, but the Earth's surface does. And then, the Earth's surface heats up and passes that heat back to the atmosphere by conduction, and then pretty quickly, by convection as well to heat up the lower part of the atmosphere.

Examples of height scales in the atmosphere [00:20:39]

We don't have a good feeling for distances in the vertical. So I want to supplement the simple diagram by just a few facts.

For example, Mount Washington, which is the highest mountain in New England, is 1,917 meters. That is to say, about two kilometers.?Mount McKinley, sometimes called Denali, is 6,196 meters.?That's the highest mountain in North America, and it's about there. Mount Everest is 8,848 meters.?

So that gives you some sense of vertical scale on this tropopause business.?Some mountains-- in fact, this is not always the same altitude. It varies quite a bit. Sometimes the tropopause could be as low as six kilometers on occasion, in which case, if you were standing even on Mount McKinley, on such a day, you would be standing in the stratosphere. On other days, though, on a typical day, on the top of Mount McKinley, you'd be standing in the upper part of the troposphere.?On Mount Everest, it's going to be a near thing. You're going to be the stratosphere quite often, actually.

Now a few other things. If you fly around a little bit with aircraft,?a light plane, like a Piper or a Cessna, it is?13,000 feet. Now that's feet, so I divide that by three, I get something like four kilometers. That's about as high as one of those little airplanes can get.?

If you've flown recently in a commuter aircraft-- just flying from one city to a close one nearby, you're probably going to be at about 20,000 feet, and what that's going to be, maybe seven kilometers. Remember, aviation today, and always, still uses feet as its distance unit. They don't use the metric system. But then, for the scientist, you've got to quickly convert that to meters, because we think in terms of meters. So there's a constant conflict in terms of how we describe elevation between science and aviation.

If you're flying in a regular airliner, how high are you flying there, it will be?35,000 feet, 37,000 feet, 34,000 feet. So it varies, but let's say 35,000 feet. And you notice, you'll always use feet for that. That's going be about 11 kilometers.?

Most of the time, when you're flying back and forth across this country in a commercial airliner, you are just at the bottom of the stratosphere. You're just up in the stratosphere slightly, but then as soon as you begin to descend down, you're back into the troposphere, and you'll be in the troposphere all the way down to the surface. Questions on that?

Layers in the Ocean [00:25:40]

I'd like to continue this discussion a little bit. You know the ocean is layered, too. If I draw the surface of the ocean here, most of the ocean has a depth of about five kilometers. This is particularly true in the part of the ocean that's called the Abyssal plane. We'll be coming back to it later in the course when we talk about the ocean. There are large parts of the oceans that have a rather flat bottom, and when it is flat like that, usually it's about five kilometers below sea level. And so on this scale, that would be about that depth below. So the oceans typically are about that depth on that kind of a scale.

There is, however, some deeper parts of the ocean, and they are the so-called ocean trenches, and the deepest one is the Marianas Trench.?And that goes down to about 11 kilometers, more than twice that typical depth. That's the deepest part of the ocean. And that on this scale,?tropopause is about as high as the deepest part of the ocean is deep.

Layers in the Earth’s Interior [00:27:22]

What else can we use to put this in some kind of a context? The Earth itself is layered. If this is Earth. You have the core, which has an inner and outer part. You've got the mantle, and then you've got a thin layer of rocky material at the surface that's called the crust.

And the two numbers I have here, the ocean crust-- when you're over the ocean and then go down to the bottom and find out how deep that rocky crust layer is, it's typically five to ten kilometers. Continental crust, on the other hand. If you went to the center the United States and measured how deep that rocky crust is there, it's deeper. It can be 30 to 50 kilometers deep. And then beneath that, you get into the mantle, and you go down all the way, eventually, to the center of the Earth, the radius of the Earth is 6,370 kilometers.

Systems analysis [00:29:24]

I want to begin now a different subject. And the broad name for what I'm about to do is called Systems analysis. It's used in everything from chemistry to manufacturing to-- the basic systems analysis is a study of a somewhat complicated system that has inputs and outputs. Normally, you're looking at a reservoir containing water,?then you're keeping track of inputs and outputs and trying to understand the processes involved and how those processes control how much you have in the reservoir.

So the experiment that I'll be doing on Friday in class upstairs is a simple little experiment where we use a water tank. We put water in at certain rate, we take water out at a certain rate, and we try to understand the equilibrium states of that simple system. I'm using it in this course as a kind of metaphor for all the different systems that are important in atmosphere ocean dynamics, including the heat budget of the Earth, the CO2?budget of the atmosphere, and so on and so on. Almost everything we think about in the atmosphere and the ocean can be approached using the simple ideas of systems analysis.

Residence Time and the Hydrologic Cycle [00:31:20]

The first concept that I want to introduce in this discussion is the concept of residence time. It's defined as the average time, or the typical time, that a particle--or whatever the substance is--spends in the reservoir. So if I have a tank of something--maybe it's water, maybe it has heat in it, whatever--there are inputs. There's a certain content. And there's output.

The residence time can be defined as the content divided by the flux. Now if this is in steady state--if input equals output--it doesn't matter which number we use for the flux. It could be the input flux or the output flux, but it has units of time as we'll see. And if we know these two things, the content and the flux, we can quickly compute how long a typical molecule, or a typical amount of heat, or whatever, stays in that reservoir.

So let me do some examples, because I think that will make it clearest, if I just quickly do some examples of this. I'm going to start with the hydrologic cycle. So let's imagine that this is the surface of the Earth. There is precipitation falling out of the atmosphere. There is evaporation providing water to the atmosphere, and our system is the atmosphere itself, and we'd like to understand something about the residence time of water vapor in the Earth's atmosphere.

I can take a balloon with an instrument under it, send that up through the atmosphere, measure the humidity at each level, and compute the total amount of water vapor in the atmosphere. We do that all the time. And I'll give you a good round number, a good average number, for how much water vapor is in the atmosphere. But I'm going to give it to you in terms of a liquid equivalent.

If I condensed out all of that water vapor into a layer of liquid, it would be approximately 2.5 centimeters deep. So walk outside today, imagine you've converted all that water vapor into a little liquid layer, it's only going to be that deep. That would be the content. That would be one way to represent how much water vapor is in the atmosphere. Now you could multiply that by the surface of the Earth-surface area of the Earth to get a volume, but I'm going to leave it just as a little layer depth as long as I'm consistent with the units in flux,?

So the other thing I need is the average precipitation. And that is approximately 1 meter per year. So New Haven, Connecticut, gets about 1.5 meters per year of rain. That's quite a lot. Certain desert areas get almost none. There are certain mountain top areas in the tropics where you may get seven or eight or nine meters per year of rainfall. But I'm going to give you this as a typical global average value. What it says is that every year, rainfall is equivalent to about a meter of liquid water depth.

So because these are both depths, I can use them directly to compute the residence time. Their units are?incompatible at the moment. So let me keep it in centimeters. 2.5 centimeters. I'll convert this to centimeters. That will be 100 centimeters in a meter. And so that's going to be 0.025-- oh this is centimeters per year. I've got to keep the time unit in there. The centimeters will cancel. The year will come up top. And the units on my residence time will be years. 0.25 years, you can quickly convert that to nine days. Typical residence time for water vapor in the Earth's atmosphere is nine days. Typically a molecule evaporates from the surface, knocks around up there for about nine days, then gets rained out and spends the time then back on the Earth's surface or in a lake or in the ocean, something like that.?

Now let me do the same argument for water in the ocean. So label that argument water in the atmosphere. And now this will be water in the ocean. So here's the ocean, five kilometers deep. It's the same two processes, by the way. But now the precipitation is a gain and the evaporation is a loss. So that's backwards from what we had before. But we're talking about a different reservoir now. Precipitation adds water vapor, evaporation removes it.

This is going to be really easy. Because we were using equivalent liquid depths over here to do the calculation, we're all set to do this one. The flux-- so the content is going to be the 5 kilometer depth of the ocean. So that's going to be 5,000 meters. And the flux is going to be this precipitation, or evaporation, because I'm going to assume they're in balance.?So the flux is going to be 1 meter per year. And even I can do that math. That gives me 5,000 years for the residence time of a water molecule in the ocean.?

So imagine that you're a water vapor molecule. You've just spent 5,000 years in the ocean. You work your way up near the surface, and then one wonderful, bright sunny day you evaporate. And suddenly you're free. You're a water vapor molecule roaming around in the atmosphere. Nine days later, you're back in the ocean for another 5,000 years. That's the way your life goes if you are a water vapor molecule on planet Earth.

So a big difference. What's the real root? Note the flux is the same. It's the reservoir size that makes a difference in those two calculations.

Let me do oxygen in the atmosphere.?So the source of oxygen in the atmosphere will be photosynthesis. Green plants taking in CO2, building their structures, their biomass, putting off oxygen into the atmosphere. It's going to be 1015?tonnes.?That's a metric ton. A metric ton?is defined as a thousand kilograms. A metric ton is a thousand kilograms.?The flux we can estimate in a number of ways. For one thing, we could put an enclosure over a forest or over a farmer's field and measure how fast oxygen is being released by the green plants.

Respiration is how you lose oxygen. And that's happening right now. Every time I breathe in, I'm breathing in some oxygen, and I'm not breathing that much out. So I'm actually losing oxygen from the atmosphere every time I breathe. Every time a tree rots, you're taking oxygen out of the atmosphere and putting it back into this degrading biomass. And these things are roughly in balance. So I can use either number here. And the flux is approximately 105?tonnes per year.

So the residence time is very easy to compute. It's going to be 1015?over 105. That's going to be 1010?years. That is about 10 billion years. So residence time for oxygen in the atmosphere, very long.

These are rough estimates. That is almost the age of the Earth. In fact, that's longer than the age of the Earth. So that's kind of a crazy answer in a sense. So you can't. You can't have a residence time longer than the reservoir has even been there.?The point though is, these are rough estimates. But oxygen has a very long residence time. Once you get it into the atmosphere it's going to stay there for a very, very long time. But don't take that number too literally. It's done with some crude estimates.

I want to do at least one more here which is really important for global warming. And that is carbon dioxide in the atmosphere. Now again, the arrows are about the same, they're just reversed. So photosynthesis takes CO2?out, and respiration, and oxidation you could say as well, puts it back into the atmosphere.

The content of CO2?in the atmosphere-- again this is a calculation we'll be able to do for ourselves next week. But for now, I'll just give you the answer. It's about 2.3x109?tonnes. And the flux-- the rate at which it's going back and forth between the surface of the Earth and the atmosphere-- is about 1.6x108?tonnes per year.?So the resonance time then is going to be 2,300x106?over 160x106?tonnes and tonnes per year. So I've just shifted decimal places to line them up. So I can do that to the 106. And 2,300 divided by 160 is 15. So by this calculation, the resonance time is about 15 years.

Now this is also a questionable number. Because it turns out that some of this is reversible. In other words, what goes out during winter returns the next summer. So what we've derived here is a low value for the residence time that is largely driven by these seasonal, and therefore reversible, fluxes.

If you averaged over a year, where certain processes cancel out, you could get a much larger number for residence time. We're going to come back to this because it's a key issue with regard to global warming and the buildup of CO2--anthropogenic CO2--in the Earth's atmosphere.