Thursday Mar. 6, 2008

Quiz #2 Study Guide now available.

The Experiment #3 materials were distributed today.  You will have another opportunity to check out materials next Tuesday.
The Experiment #4 materials should also become available next week. 

Note: By the end of next week you should either already have completed an experiment, should be working on an experiment, or should be working on one of the other options (book report, scientific paper report).
We now have most of the tools we will need to begin to study energy balance on the earth.  It will be a balance  between incoming sunlight energy and outgoing energy emitted by the earth.  We will look at the simplest case first, the earth without an atmosphere (or at least an atmosphere without greenhouse gases) found on p. 68 in the photocopied Classnotes.

You might first wonder how, with the sun emitting so much more energy than the earth, it is possible for the earth (with a temperature of around 300 K) to be in energy balance with the sun (6000 K).  The earth is located about 90 million miles from the sun and therefore only absorbs a very small fraction of the energy emitted by the sun.

To understand how energy balance occurs we start, in Step #1, by imagining that the earth starts out very cold and is not emitting any EM radiation at all.  It is absorbing sunlight however so it will begin to warm.

Once the earth starts to warm it will also begin to emit EM radiation, though not as much as it is getting from the sun (the slightly warmer earth in the middle picture is now colored blue).  Because the earth is still gaining more energy than it is losing the earth will warm some more.

Eventually it will warm enough that the earth (now shaded green) will emit the same amount of energy (though not the same wavelength energy) as it absorbs from the sun.  This is radiative equilibrium, energy balance.  The temperature at which this occurs is about 0 F.  That is called the temperature of radiative equilibrium.  You might remember this is the figure for global annual average surface temperature on the earth without the greenhouse effect.
Before we start to look at radiant energy balance on the earth we need to learn about filters.  The atmosphere will filter sunlight as it passes through the atmosphere toward the ground.  The atmosphere will also filter IR radiation emitted by the earth as it trys to travel into space.

We will first look at the effects simple blue, green, and red glass filters have on visible light.  This figure wasn't shown in class.

If you try to shine white light (a mixture of all the colors) through a blue filter, only the blue light passes through.  The filter absorption curve shows 100% absorption at all but a narrow range of wavelengths that correspond to blue light.  Similarly the green and red filters only let through green and red light.

The following figure is a simplified easier to remember representation of the filtering effect of the atmosphere on UV, VIS, and IR light (found on p. 69 in the photocopied notes).  The figure below was redrawn after class for improved clarity.


You can use your own eyes to tell you what the filtering effect of the atmosphere is on visible light.  Air is clear, it is transparent.  The atmosphere transmits visible light.

In our simplified representation oxygen and ozone make the atmosphere a pretty good absorber of UV light.

Greenhouse gases make the atmosphere a selective absorber of IR light - it absorbs certain IR wavelengths and transmits others.  It is the atmosphere's ability to absorb (and also emit) certain wavelengths of infrared light that produces the greenhouse effect and warms the surface of the earth.

Note "The atmospheric window" centered at 10 micrometers.  Light emitted by the earth at this wavelength will pass through the atmosphere.  Another transparent region, another window, is found in the visible part of the spectrum.

You'll find a more realistic picture of the atmospheric absorption curve on p. 70 in the photocopied Classnotes, but the simplified version above will work fine for our needs.
Here's the outer space view of radiative equilibrium on the earth without an atmosphere.  The important thing to note is that the earth is absorbing and emitting the same amount of energy (4 arrows absorbed balanced by 4 arrows emitted).

We will be moving from an outer space vantage point of radiative equilibrium (above) to the earth's surface (below).

Don't let the fact that there are
4 arrows are being absorbed and emitted in the top figure and
2 arrows absorbed and emitted in the bottom figure
bother you

We'll be adding a lot more arrows to the bottom figure
It would get too complicated if we had more than 2 arrows of incoming sunlight.
The next step is to add the atmosphere.
We will study a simplified version of radiative equilibrium just so you can identify and understand the various parts of the picture.  Keep an eye out for the greenhouse effect.  We will look at a more realistic version later. 
Here's the figure that we ended up with in class

It would be hard to sort through all of this if you weren't in class (and maybe even if you were) to see how it developed.  So below we will go through it again step by step (which you are free to skip over if you wish).

The figure shows two rays of incoming sunlight that pass through the atmosphere, reach the ground, and are absorbed.  100% of the incoming sunlight is transmitted by the atmosphere (this is not a very realistic assumption). 

The ground is emitting 3 rays of IR radiation.

One of these is emitted by the ground at a wavelength that is NOT absorbed by greenhouse gases in the atmosphere.  This radiation passes through the atmosphere and goes out into space.

The other 2 units of IR radiation emitted by the ground are absorbed by greenhouse gases is the atmosphere.

The atmosphere is absorbing 2 units of radiation.   In order to be in radiative equilibrium,the atmosphere must also emit 2 units of radiation.  1 unit of IR radiation is sent upward into space, 1 unit is sent downward to the ground where it is absorbed.

The greenhouse effect is found in this absorption and emission of IR radiation by the atmosphere.  We tried to put into words what is illustrated above:

Before we go any further we will check to be sure that every part of this picture is in energy balance.

The ground is absorbing 3 units of energy and emitting 3 units of energy

The atmosphere is absorbing 2 units of energy and emitting 2 units of energy

2 units of energy arrive at the earth from outer space, 2 units of energy leave the earth and head back out into space.
The greenhouse effect makes the earth's surface warmer than it would be otherwise.

Energy balance with (right) and without (left) the greenhouse effect.  At left the ground is emitting 2 units of energy, at right the ground is emitting 3 units.  Remember that the amount of energy emitted by something depends on temperature.  Warm ground will emit more energy than colder ground.

Here's another explanation.  At left the ground is getting 2 units of energy.  At right it is getting three, the extra one is coming from the atmosphere.  Doesn't it make sense that ground that absorbs 3 units of energy will be warmer than ground that is only absorbing 2.
Next we will look at how realistic our simplifying assumptions are

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.

About 20% of the incoming sunlight is absorbed by gases in the atmosphere.  Sunlight is a mixture of UV, VIS, and IR light.  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 (IR light accounts for about half of the light in sunlight).

The remaining 30% of the incoming sunlight is reflected back into space (by the ground, clouds, even air molecules).
Now we will look at our simplified version of radiative equilibrium and a more realistic picture of the earth's energy budget.

 The lower part of the figure is pretty complicated.  It would be difficult to start with this figure and find the greenhouse effect in it.  However if you understand the upper figure, you should be able to find and understand the corresponding part in the lower figure.

In the top figure you should recognize the incoming sunlight (green), IR emitted by the ground that passes through the atmosphere (pink), IR radiation emitted by the ground that is absorbed by greenhouse gases in the atmosphere (orange) and IR radiation emitted by the atmosphere (dark blue).  Using the colors you can find each of these parts of the energy budget in the bottom figure.  Notice that conduction, convection, and latent heat energy transport are needed to bring the overall energy budget into balance.  Click here to see a more detailed check to be sure everything is in energy balance.

We took a short detour at this point to look at Archimedes law (see pps 53a & 53b in the photocopied Classnotes) and to see a colorful demonstration.

A gallon of water weighs about 8 pounds, that's pretty heavy.  If you jump into a pool with a gallon bottle of water, the bottle becomes weightless.  Archimedes law explains why this is so.

Archimedes law says that an object immersed in a fluid (gas or liquid) will experience an upward bouyant force equal to the weight of the fluid displaced. 

The gallon water bottle will displace 1 gallon of pool water.  The 8 pound weight (gravity) will be balanced by an 8 pound upward bouyant force.

If you filled the bottle with air (which has practically zero weight), the bottle will float.  The 8 pound upward bouyant force is still there because the bottle still displaces a gallon of pool water.  But the downward force (weight of the air) is gone.

If you fill the bottle with sand, the bottle will now weigh about 12 pounds.  That's more than the 8 pound upward bouyant force, so the bottle will sink.

Basically its a question of how the density of the material in the bottle compares to the density of the water outside.  Objects denser than water will sink, objects less dense than water will float.

This can be applied to the atmosphere

Warm low density air rises, cold high density air sinks.

You can also apply this to people

Many people can fill their lungs with air and make themselves float, or they can empty their lungs and make themselves sink.

People must have a density that is about the same as water.

In at least one way, people are like cans of Pepsi and Diet Pepsi.

A can of regular Pepsi was placed in a beaker of water.  The can sank. 

Both cans are made of aluminum which has a density almost three times higher than water.  The drink itself is largely water.  The regular Pepsi also has a lot of sugar or corn syrup, the diet Pepsi doesn't.  The water+corn syrup mixture has a density greater than plain water.  Both cans contain a little air (or perhaps carbon dioxide gas).  This is much less dense than water.

The average density of the can of regular Pepsi (water&sugar + aluminum + air) ends up being slightly greater than the density of water.  The average density of the can of diet Pepsi (water + aluminum + air) is slightly less than the density of water.
Now one last topic, the effects of clouds on nighttime low and daytime high temperatures.  You'll find this discussed on pps 72a and 72b in the Classnotes.  The discussion below is slightly different from the one in class.

Here's the simplified picture of radiative equilibrium (something you're probably getting pretty tired of seeing)
The two pictures below show what happens at night when you remove the two green rays of incoming sunlight.

The picture on the left shows a clear night.  The ground is losing 3 arrows of energy and getting one back from the atmosphere.  That's a net loss of 2 arrows.  The ground cools rapidly and gets cold during the night.

A cloudy night is shown at right.  Notice the effect of the clouds.  Clouds are good absorbers of IR radiation.  If we could see IR light, clouds would appear black, very from what we are used to.  Now none of the IR radiation emitted by the ground passes through the atmosphere into space.  It is all absorbed either by greenhouse gases or by the clouds.  Because the clouds and atmosphere are now absorbing 3 units of radiation they must emit 3 units: 1 goes upward into space, the other 2 downward to the ground.  There is now a net loss at the ground of only 1 arrow. 

The ground won't cool as quickly and won't get as cold on a cloudy night as it does on a clear night.

The next two figures compare clear and cloudy days.

Clouds are good reflectors of visible light.  The effect of this is to reduce the amount of sunlight energy reaching the ground in the right picture.  With less sunlight being absorbed at the ground, the ground doesn't need to get as warm to be in energy balance.

It is generally cooler during the day on a cloudy day than on a clear day.

Clouds raise the nighttime minimum temperature and lower the daytime maximum temperature. 

Typical daytime highs and nighttime lows in Tucson for this time of year.  Note how the clouds reduce the daily range of temperature.

Thanks for taking some time to read through the online notes - Have a nice remainder of the weekend