Tue., Feb. 28 notes

Tuesday Feb. 28, 2006

Here are answers to questions on a special assignment given to some of the students in the MWF class. This is offered as a way of reviewing some of the recent material we have covered.

1S1P Assignment #2 and Optional Assignment #3 are both due on Thursday, Mar. 2.

The Quiz #2 Study Guide is now available (Quiz #2 is Thursday next week, Mar. 9).

Distribution of the Experiment #3 materials should begin in class on Thursday.

As long as you are reading through these class notes, you might as well give this surprise optional assignment a try.

Energy balance on the earth without an atmosphere. The earth starts out very cold and is not emitting any EM radiation. It is absorbing sunlight however so it will warm. Once the earth starts to warm it will begin to emit EM radiation, though not as much as it is getting from the sun. Eventually it will warm enough that the earth will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun. This is radiative equilibrium (a balance between the amounts of incoming and outgoing radiant energy). The temperature at which this occurs is 0 F (on the earth without any atmosphere)

Our next step will be to add the earth's atmosphere and see how that affects energy balance. Before doing that however we need to learn about how the atmosphere affects incoming sunlight (UV, VIS, and IR radiation) and IR radiation emitted by the earth.

This is a slightly simplified representation of the filtering effect of the atmosphere on UV, VIS, and IR light (found on p. 69 in the photocopied notes, a more realistic version is reproduced on p. 70). 0% absorption means the atmosphere behaves like a window made of clear glass that is transparent to light. The light can pass freely through the window. 100% absorption on the other hand means the atmosphere is opaque to light, it blocks the light by absorbing it.

In our simplified representation oxygen and ozone make the atmosphere pretty much a perfect absorber of UV light and perfectly transparent to VIS light. Greenhouse gases make the atmosphere a selective absorber of IR light. Note "the atmospheric window" centered at 10 micrometers. Light emitted by the earth at this wavelength will pass through the atmosphere. IR light emitted by the earth at slightly different wavelengths will be absorbed by greenhouse gases. It is this ability of H₂0, CO₂, etc to selectively absorb certain wavelengths of IR light that is responsible for the greenhouse effect.

Now we can get back to radiative equilibrium

This is a slightly different view of radiative equilibrium on the earth without an atmosphere. We're looking at things from a vantage point on the ground instead of from outer space. Don't let the fact that only two incoming arrows of energy are balancing two arrows of outgoing energy (the example at the start of class used 4 arrows). The important thing is that equal amounts of energy are being absorbed and emitted.

Now we'll see how adding an atmosphere can take us from the relatively simple energy balance diagram above (on p. 70a in the photocopied notes) to the more complex situation on p. 70b in the photocopied notes. This explanation is more detailed and hopefully clearer than the discussion in class.

Energy balance without an atmosphere is depicted above at left. We will add an atmosphere to this picture. That is done in the figure at right. We know that the atmosphere selectively absorbs IR light, so we will let one of the arrows of IR emitted by the ground pass through the atmosphere. The other arrow however will be absorbed by greenhouse gases and isn't able to pass through the atmosphere.

Because the atmosphere is absorbing energy it must also emit energy to be in energy balance. The atmosphere emits IR radiation upward into space and downward toward the ground. This is shown in the figure above at left. Note that the ground is now absorbing more energy (2 arrows of sunlight plus the additional energy from the atmosphere) than it is emitting (2 arrows). The ground will begin to warm.

As the ground warms it will begin to emit more IR radiation. We eventually end up with a new equilibrium shown above at right. The ground is warmer (60 F) and is emitting 3 arrows of IR energy. Let's have a careful look at all the numbered points in this figure:

(1) There are two arrows of incoming sunlight. We assume that all of this sunlight is transmitted through the atmosphere and is absorbed by the ground. We will examine how reasonable this is later.
(2) One arrow of IR radiation is emitted by the ground at a wavelength (10 micrometers) that is transmitted by the atmosphere (it passes through the atmosphere into space)
(3) Two arrows of IR energy emitted by the ground at slightly different wavelengths are absorbed by greenhouse gases in the atmosphere.
(4) Two arrows of IR energy are emitted by the atmosphere. One arrow goes upward and into space, the second goes downward to the ground where it is absorbed.

The greenhouse effect is this ability of the atmosphere to absorb some of the IR energy emitted by the ground and then return some of that energy to the ground. The ground is warm and is emitting more energy (3 arrows) than it gets from the sun (2 arrows). It can get away with this because it gets 1 arrow of energy back from the atmosphere.

You can check for energy balance at several positions in the figure above. First at the ground: 2 arrows of sunlight + 1 arrow of IR from the atmosphere are begin absorbed. This is balanced by three arrows of IR being emitted by the ground. In the atmosphere 2 arrows of IR emitted by the ground are being absorbed. This is balanced by the 2 arrows of IR radiation emitted by the atmosphere. Finally from a position above the atmosphere. The energy arriving, 2 arrows of sunlight is balanced by 2 arrows leaving (one from the ground and one from the atmosphere)

In our simplified version of the greenhouse effect we assumed that 100% of the sunlight arriving at the top of the atmosphere passes through the atmosphere and gets absorbed by the ground. The bottom figure above shows that in reality only about 50% of the incoming sunlight gets absorbed at the ground (168 units our of the total 342 units).

About 20% is absorbed by gases in the atmosphere (67 units out of the total 342 units). Sunlight is a mixture of UV, VIS, and IR. Ozone and oxygen will absorb a lot of the UV (though there isn't much UV in sunlight) and greenhouse gases will absorb some of the IR radiation in sunlight (there's a lot more IR in sunlight than UV).

The remaining 30% of sunlight is reflected by the ground, by clouds, and even by air molecules themselves.

The simple figure at the top of p. 72 in the photocopied notes was meant to show you how the greenhouse effect works.

Now for a more realistic and more complete depiction of energy balance on the earth.This is the busy figure at the bottom of p. 72 is more complete and more realistic. Now because you know something about what happens to sunlight arriving at the earth and passing through the atmosphere and because you know about what can happen to IR radiation emitted by the earth, you should be able to identify each of the various parts of the figure and should be able to check for energy balance.

We'll start with the atmosphere

Energy being added to the atmosphere is shown in the figure above. Moving from left to right, 24 units are transported from the ground to the atmosphere by conduction and convection. 78 units are transported by latent heat. 350 units of IR radiation emitted by the ground are absorbed by the atmosphere. 67 units of sunlight are absorbed from the atmosphere. That is a total of 519 units of energy.

The figure below shows the atmosphere emitting 195 units of energy upward into space and 324 units of energy downward toward the ground. That is a total of 519 units which means the atmosphere is in energy balance.

Why is there more downward energy emitted by the atmosphere than upward energy? One explanation would be that the upper atmosphere is colder than the lower atmosphere. Warm objects emit more energy than cold objects.

Now the situation at the ground

Conduction and convection transport 24 units of energy away from the ground, latent heat transport another 78 units (3 times as much as conduction and convection). The ground emits 350 + 40 units of IR radiation. That is a grand total of 492 units.

In the figure below 168 units of sunlight energy and 324 units of IR energy emitted by the atmosphere are absorbed by the ground. The total, 492 units, balances what is lost by the ground. Note that the ground gets about two times as much energy from the atmosphere (324 units) as it gets from the sun (168 units).

Now from a vantage point above the earth's atmosphere

There are 67 + 168 units of sunlight energy arriving at the earth (see figure above).

This is balanced by 40 (emitted by the ground) + 195 units of energy (emitted by the atmosphere) leaving the earth. So we are in energy balance there also.

One additional comment about this figure.
The ground loses a total of 492 units of energy (24+78+350+40). 390 units (350+40) of this is IR radiation. IR radiation accounts for about 80% of the total amount of energy transported away from the ground.

Now we'll go back to our simplified version of energy balance on the earth with an atmosphere and use it to understand how clouds affect daytime and nighttime temperatures.

In the bottom figure the incoming sunlight has been removed from the energy balance diagram. The ground is emitting 3 units of energy and getting 1 back from the atmosphere. That is a net loss of 2 units. The ground will cool fairly rapidly during the night.

A layer of clouds has been added. In the top figure the clouds reduce the net loss of energy at the ground. The ground cools more slowly and doesn't get as cold during the night.

The bottom figure above is a daytime figure (the sunlight is back). The clouds will reflect some of the incoming sunlight and reduce the daytime high temperatures.

Typical daytime highs and nighttime lows in Tucson for late February. Note how the clouds reduce the daily range of temperature.