Fri., Oct. 6 notes

Friday Oct. 6, 2006

More problems have been added to Optional Assignment #3. The assignment is now complete and is due at the beginning of class on Monday. You can either print out the assignment or turn in your answers on a separate piece of paper.

There is a new 1S1P assignment. It is complicated, be sure to read the instructions carefully.

We'll get a better understanding of how the atmospheric greenhouse effect works today. Though the greenhouse effect is subtle; if you're not watching for it you'll miss it.

This figures compares the EM radiation emitted by the earth and the sun. First because the sun (surface of the sun) is 20 times hotter than the earth a square meter of the sun's surface emits energy at a rate that is 160,000 times higher than the earth. Lambda max for the sun is 0.5 micrometers, green light. The sun emits more green light than any other kind of light. The sun doesn't appear green because it is also emitting lesser amounts of violet, blue, yellow, orange, and red - together this mix of colors appears white. 44% of the radiation emitted by the sun is visible light, 49% is IR light, and 7% is ultraviolet light.

100% of the light emitted by the earth is invisible IR light. The wavelength of peak emission for the earth is 10 micrometers.

Now we're almost ready to learn about radiative equilibrium. That's just another word for energy balance. Before doing so here's an analogous situation.

Radiative equilibrium is like:
adding water to a leaky bucket

Water is being added to the bucket. No water is being lost so the water level rises.

The water level has reached a hole in the side of the bucket. Water is being lost though not as quickly as water is being added. The water level slowly rises some more.

Now the water is being added and lost at equal rates. The water level won't change. This is a condition of equilibrium.

Instead of adding water to a bucket we will add energy to the earth.

Energy balance on the earth without an atmosphere. The earth (shaded blue) starts out very cold and is not emitting any EM radiation at all. 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 (the slightly warmer earth is now colored green). Eventually it will warm enough that the earth (now shaded brown) will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun. This is radiative equilibrium. The temperature at which this occurs is 0 F (on the earth without any atmosphere). That is called the temperature of radiative equilibrium.

Before we move to the more complex situation of radiative equilibrium on the earth with an atmosphere, we need to learn something about how gases in the atmosphere affect different kinds of light that passes through the atmosphere.

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, the air is transparent to light. The light can pass freely through the atmosphere. 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 a pretty good absorber of UV light The atmosphere is pretty nearly perfectly transparent to VIS light (we can check this out with our eyes, we can see through the air, it is clear). Greenhouse gases make the atmosphere a selective absorber of IR light - it absorbs certain IR wavelengths and transmits others.. 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.

Here's another look at radiative equilibrium on the earth without an atmosphere. Here we're looking at the situation from a vantage point on the ground. In the previous case we were looking at the earth from a point in outer space.

Two units of sunlight arriving at the earth and being absorbed at the ground are balanced by 2 units of IR radiation emitted by the earth. It is the fact that there are equal amounts of energy being absorbed and emitted that tells you this is radiative equilibrium. Balance occurs when the earth's temperature is 0 F.

Now the figure we have all been waiting for, energy balance on the earth with an atmosphere.

1. First there are 2 units (2 arrows) of sunlight energy arriving at the top of the atmosphere. We assume that all of this is transmitted by the atmosphere and gets absorbed at the ground. We'll see how realistic this is next Tuesday.

2. The ground is emitting 1 unit of IR radiation at a wavelength that is transmitted by the atmosphere. Radiation that falls in the atmospheric window region centered at 10 micrometers perhaps.

3. The ground emits an additional 2 units of radiation at slightly different wavelengths that are absorbed by greenhouse gases in the atmosphere. IF it weren't for these greenhouse gases this energy would have gone into space.

At this point you might wonder how can the ground emit 3 units of energy when it is only getting 2 from the sun. The energy balance diagram isn't finished yet, when it is finished we'll see that there isn't a problem.

4. The atmosphere is absorbing two units of IR radiation (radiation that was emitted by the earth). To be in energy balance the atmosphere must also emit 2 units of IR light. ONe is emitted upwards into space, the other downward toward the ground.

Down at the ground now we see that we are now in energy balance. The ground gets 2 units of energy from the sun + 1 unit from the atmosphere. This balances the 3 units that are being emitted by the ground.

Now an important observation. The ground is emitting 3 units. If you look back at the picture of energy balance on the earth without an atmosphere you would see that the ground was only emitting 2 units. The ground in that example had a temperature of 0 F. In this example, the ground must be warmer in order to be able to emit 3 units of radiation. The ground temperature in this case is nearer to 60 F.

In both pictures of radiative equilibrium (with and without the atmosphere) there were 2 units of incoming sunlight. In the case of the earth without an atmosphere the earth emitted 2 units of energy back into space. In case with an atmosphere the ground is warmer and emits 3 units. It can get away with this because some of what it emits is absorbed by the atmosphere. The atmosphere in turn emits radiation and some of this heads back to the ground. This is the greenhouse effect. Greenhouse gases absorb some of the energy emitted by the earth (that would otherwise be lost) and return some that energy back to the ground.