Tue., Mar. 13 notes

Tuesday, Mar. 13, 2018

Alabama Shakes "Always Alright" (4:19), "Future People" (3:28), "I Ain't the Same" (3:51), "Hang Loose" (2:38), "Mama" (2:46)

The Experiment #2 reports have been graded and were returned in class today. Revised reports (if you choose to do one, a revision of your report is not required) are due in two weeks - by Tuesday, Mar. 27. Please return the original report with your revised report.

The Experiment #1 revised reports have been graded and were returned today.

The Surface Weather Map analyses (you could earn 1S1P or Extra Credit pts) and the Upper Level Charts assignment (you could earn Quiz #2 or Extra Credit pts) have both been graded.

I'm just getting started on the 1S1P Carbon Dioxide reports. It will probably be a week or so before they are graded.

Quiz #2 is Thursday this week. See the Study Guide for more information as well as the times and locations of the reviews.

There are several sets of Expt. #2 and Expt. #3 materials available for checkout. Reports are due by Tue., Mar. 27. If you haven't done an experiment report yet I would suggest you check out some of these materials. If you still have some experiment materials that you checked out earlier in the semester but never got around to doing the experiment, I would encourage you to do the experiment and turn in a report by Mar. 27. It is not safe to assume that you will be allowed to turn in a Scientific Paper or Book in lieu of an experiment. I'm am trying to avoid having a large number of reports turned in on the April 2 due date. We don't have a second Spring Break between now and the end of the semester that will allow me to catch up on grading.

The due date for the 1S1P Assignment #2b (Causes of the seasons or The Equinoxes and Manhattanhenge) reports is Tuesday next week, Mar. 20.

You'll find a two question In-class Optional Assignment embedded in today's notes. If you weren't in class and would like to do the assignment, you'll need to read through the notes below and find the two questions. If you then turn in solutions at the start of class on Wednesday you'll earn at least partial credit.

Filtering effect of the atmosphere on ultraviolet, visible, and infrared light
The plan today is to look at radiative equilibrium (balance between incoming and outgoing electromagnetic radiation) on the earth with an atmosphere that contains greenhouse gases. Before we do that we need to learn about how the atmosphere will affect the incoming sunlight (a mixture of UV, visible, and near IR light) and outgoing far IR light emitted by the earth. We'll draw a filter absorption graph for the earth's atmosphere.

Let's start with something simpler and something we can see, the effects blue, green, and red glass filters have on visible light. We'll be able to be sure we understand what an absorption curve represents.

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. The location of the slot or gap in the absorption curve shifts a little bit to the right with the green and further right with the red filter.

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).

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

2. In our simplified representation oxygen and ozone make the atmosphere pretty nearly completely opaque to UV light (opaque is the opposite of transparent and means that light is blocked or absorbed; light can't pass through an opaque material). We assume that the atmosphere absorbs all incoming UV light, none of it makes it to the ground. This is of course not entirely realistic.

3. Greenhouse gases make the atmosphere a selective absorber of IR light - the air absorbs certain IR wavelengths and transmits others . Wavelengths between 0.7 and 8 or 9 μm are absorbed (by greenhouse gases), radiation centered at 10μm is transmitted by the atmosphere. Wavelengths greater than 10 μm are absorbed (again by greenhouse gases). The atmosphere also emits IR radiation. It is the atmosphere's ability to absorb certain wavelengths of infrared light and emit 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 (and remember 10 um is the wavelength of peak emission for the earth) will pass through the atmosphere. Another transparent region, another window, is found in the visible part of the spectrum.

Back to radiative equilibrium on the earth without an atmosphere

We'll return to our earlier picture of radiative equilibrium

here's the view from space
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've ignored the one arrow of reflected sunlight.

and now radiative equilibrium viewed from the ground
Don't let the fact that there are 4 arrows are being absorbed and emitted in one figure and 2 arrows absorbed and emitted in the other bother you. The important thing is that there are equal amounts being absorbed and emitted in both cases.The reason for only using two arrows in this picture is to keep the picture as simple as possible. It will get complicated enough when we add the atmosphere to the picture.

Here's basically the same picture, this is the one that is in the ClassNotes (p. 70a). There's a little explanation added.

Radiative equilibrium on the earth with an atmosphere - the greenhouse effect
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. Here's a cleaned up version of what we ended up with in class. Energy balance is a little more complex in this case, there are more arrows to sort out.

It would be hard to sort through and try to understand all of this if you weren't in class (difficult enough even if you were in class). So below we will go through it again step by step (which you are free to skip over if you wish). Caution: some of the colors below may be different from those used in class.

1. In this picture we see the 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 wouldn't be too bad of an assumption if sunlight were just visible light. But it is not, sunlight is about half IR light and some of that is going to be absorbed. But we won't worry about that at this point.

The ground is emitting a total of 3 arrows of IR radiation. That might seem like a problem. How can the earth emit 3 arrows when it is absorbing only 2 from the sun. We'll see how this can happen in a second.

2. One of these (the pink or purple arrow above) is emitted by the ground at a wavelength that is not absorbed by greenhouse gases in the atmosphere (probably around 10 micrometers, in the center of the "atmospheric window"). This radiation passes through the atmosphere and goes out into space.

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

4. The atmosphere is absorbing 2 units of radiation. In order to be in radiative equilibrium, the atmosphere must also emit 2 units of radiation. That's shown above. 1 unit of IR radiation is sent upward into space, 1 unit is sent downward to the ground where it is absorbed. This is probably the part of the picture that most students have the most trouble visualizing (it isn't so much that they have trouble understanding that the atmosphere emits radiation but that 1 arrow is emitted upward and another is emitted downward toward the ground). Both arrows leave the atmosphere, one goes out into space and the other goes into the ground.

Now that all the arrows are accounted for, we will check to be sure that every part of this picture is in energy balance.

Checking for energy balance at the ground.

It might help to cover up all but the bottom part of the picture with a blank sheet of paper (that's what I tried to do in the right figure below).

The ground is absorbing 3 units of energy (2 green arrows of sunlight and one blue arrow coming from the atmosphere) and emitting 3 units of energy (one pink and two red arrows). The ground is in energy balance. The earth emits more energy (3 units) than it gets from the sun (2 units). It can do this because it gets energy from the atmosphere.

Checking for energy balance in the atmosphere

The atmosphere is absorbing 2 units of energy (the 2 red arrows coming from the ground) and emitting 2 units of energy (the 2 blue arrows). One goes upward into space. The downward arrow goes all the way to the ground where it gets absorbed (it leaves the atmosphere and gets absorbed by the ground). We don't care where the arrows are coming from or where they are going. We are just interested in the amounts of energy gained and lost by the atmosphere. The atmosphere is in energy balance.

And we should check to be sure equal amounts of energy are arriving and leaving at the top of the atmosphere

2 units of energy arrive at the top of the atmosphere (green) from the sun after traveling through space, 2 units of energy (pink and orange) leave the earth and head back out into space. Energy balance here too.

Did you spot the greenhouse effect?

It's Points 3 & 4 in the figure. The greenhouse effect depends on both absorbing IR radiation and emitting IR radiation. Here's how you might put it into words.

We didn't cover the following section in class today.
The greenhouse effect warms the earth's surface. The global annual average surface temperature is about 60 F on the earth with a greenhouse effect. It would be about 0 F without the greenhouse effect.

Here are a couple other ways of understanding why/how this warming occurs.

The picture at left is the earth without an atmosphere (without a greenhouse effect). At right the earth has an atmosphere, one that contains greenhouse gases.

Here we have removed all but the energy arriving at the ground. At left the ground is getting 2 units of energy (from the sun). At right it is getting three, two from the sun and one from the atmosphere (thanks to the greenhouse effect). Doesn't it seem reasonable that ground that absorbs 3 units of energy will end up warmer than ground that is only absorbing 2?

The next picture shows an even better (but more subtle) way of analyzing the situation.

And again we'll simplify the picture by removing all but the emitted energy.

To be in energy balance, the ground in the picture above at left must emit 2 arrows of radiant energy.

At right the ground has to somehow send 2 units of IR energy back into space. The ground "knows" that some of what it emits will be returned to the ground (some of what the ground emits is absorbed by the atmosphere and sent (emitted) back to the ground because of the greenhouse effect). So the ground emits a "little extra" (3 units) so that 2 units can escape into space.

The amount of energy emitted by an object depends on temperature (to the 4th power). The Stefan-Boltzmann laws tell us that. So to be able to emit 3 units of IR energy the ground has to be warmer than if it only has to emit 2 units of energy.

How much of the sunlight arriving at the top of the atmosphere actually makes it to the ground?

In the simplified explanation of the greenhouse effect last week we assumed that 100% of the sunlight arriving at the top of the earth's atmosphere passed through the atmosphere and got absorbed at the ground. That would be a reasonable assumption if sunlight were just visible light, but it's not. We will get a better idea of what happens to the incoming sunlight.

The bottom figure above shows that on average (averaged over the year and over the globe) about half (50%) of the incoming sunlight makes it through the atmosphere and gets absorbed at the ground. This is the only number in the figure you should try to remember.

About 20% of the incoming sunlight is absorbed by gases in the atmosphere. Sunlight is a mixture of mostly visible and near IR light. There are smaller amounts of far IR and UV light. Ozone and oxygen will absorb most of the UV (UV makes up only 7% of sunlight). Roughly half (49%) of sunlight is IR light and greenhouse gases will absorb some of that.

The remaining 30% of the incoming sunlight is reflected or scattered back into space (by the ground, clouds, even air molecules).

Expt. #3 students take note. The object of Expt. #3 is to measure the energy in the sunlight arriving at the ground here in Tucson. About 2 calories of sunlight energy pass through a one square centimeter area every minute at the top of the atmosphere. Since about 50% of that will reach the ground, you should get a value of about 1 calorie/(cm² min).


Here is our simplified version of the greenhouse effect from earlier in the day. This figure is in energy balance	This is a more realistic representation because it allows only half of the incoming sunlight to reach the ground. The other half is absorbed by the atmosphere.

As shown here the figure is incomplete and is not in energy balance.
The atmosphere is absorbing 3 units of energy but not emitting any.
We need to add 3 arrows of emitted energy. The question is what direction
to send them, up or down. This was the first part of an Optional In-class Assignment.

The ground is emitting 3 units of energy and getting 1 from the sun. It needs two additional units to be in energy balance. At the top of the picture we need 1 more unit of outgoing energy.

We send 1 of the 3 units of energy emitted by the atmosphere upward. We send the two remaining units downward. Now all three parts of the figure are in energy balance.

Here's the solution to the problem of bringing the figure into energy balance.

Here's another example to try to balance on your own. This was the 2nd question on the In-class Assignment. You'll find the answer at the end of today's notes

A more realistic picture of energy balance on the earth

The top part of the figure below is our new and improved but still simplified representation of energy balance and the greenhouse effect.

In the top figure you should recognize the incoming sunlight (green), IR emitted by the ground that passes through the atmosphere (violet), IR radiation emitted by the ground that is absorbed by greenhouse gases in the atmosphere (orange) and IR radiation emitted by the atmosphere (blue).

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. That's why we used a simplified version. Once you understand the upper figure, you should be able to find and understand the corresponding parts in the lower figure (I've tried to use the same colors for each of the corresponding parts).

The figure assumes that 100 units of sunlight energy are arriving at the top of the atmosphere. About half of the incoming sunlight (51 units in green, we rounded that down to 50 in an earlier figure) reaches the ground and is absorbed. 19 units of sunlight (we rounded that up to 20 in the earlier figure) are absorbed by gases in the atmosphere. The 30 units of reflected sunlight weren't included in the figure.

The ground emits a total of 117 units of IR light. Only 6 shine through the atmosphere and go into space. The remaining 111 units are absorbed by greenhouse gases.

There were 3 somewhat surprising things to notice in the figure.

(1). How can the ground be emitting more energy (117 units) than it gets from the sun (51 units ) and still be in energy balance?

The answer is that the ground isn't just receiving sunlight energy. It is also getting energy from the atmosphere. That's thanks to the greenhouse effect. Most of the energy emitted by the ground is absorbed by greenhouse gases in the atmosphere. The atmosphere then emits some of this energy downwards. The ground gets back some of what it would otherwise have lost.

If you're really paying attention you would notice that 117 units emitted doesn't balance 96 + 51 = 147 units absorbed. The surface is emitting 117 units but an additional 30 units are being carried from the ground to the atmosphere by conduction, convection, and latent heat (at the far left of the figure). That brings everything into balance (117 + 30 = 147). Note how much smaller the energy transport by conduction, convection, and latent heat are compared to radiant energy transport.

(2). Why are the amounts of energy emitted upward (64 units) and downward (96 units) different?

One reason might be that the lower atmosphere is warmer than the upper atmosphere (warm objects emit more energy than cold objects). But I think a better explanation is that there is more air in the bottom of the atmosphere (the air is denser) than near the top of the atmosphere. It is the air in the atmosphere that is emitting radiation. More air = more emission.

Note that the atmosphere is emitting more energy downward than upward in our simplified version of the greenhouse effect.

(3). The ground is receiving more energy from the atmosphere (96 units) than it gets from the sun (51 units)!

Doesn't that seem surprising? I think the main reason for this is that the sun just shines for part of the day (half the day on average over the course of a year). We receive energy from the atmosphere 24 hours per day, 365 days per year.

We didn't cover this section and the one after it in class.
A common misconception about the cause of global warming.

Many people know that sunlight contains UV light and that the ozone layer absorbs much of this dangerous type of high energy radiation. People also know that release of chemicals such as CFCs are destroying stratospheric ozone and letting some of this UV light reach the ground. That is all correct.

But then they conclude that it is this additional UV energy reaching the ground that is causing the globe to warm. This is not correct. There isn't enough additional UV light to cause significant warming. The additional UV light will cause cataracts and skin cancer and those kinds of problems but not global warming.

If all 7% of the UV light in sunlight were to reach the ground it probably would cause some warming. But it probably wouldn't matter because some of the shortest wavelength and most energetic forms of UV light would probably kill us and most other forms of life on earth. We wouldn't be around long enough to have to worry about climate change. Ultraviolet Light is the subject of one of the new 1S1P Report topics.

Enhancement of the greenhouse effect and global warming

Here's the real cause of global warming and the reason for concern (this is also the last time you'll see these energy balance pictures)

The figure (p. 72b in the photocopied Class Notes) on the left shows energy balance on the earth without an atmosphere (or with an atmosphere that doesn't contain greenhouse gases). The ground achieves energy balance by emitting only 2 units of energy to balance out what it is getting from the sun. The ground wouldn't need to be very warm to do this, only 0 F.

If you add an atmosphere and greenhouse gases, the atmosphere will begin to absorb some of the outgoing IR radiation. The atmosphere will also begin to emit IR radiation, upward into space and downward toward the ground. After a period of adjustment you end up with a new energy balance. The ground is warmer and is now emitting 3 units of energy even though it is only getting 2 units from the sun. It can do this because it gets a unit of energy from the atmosphere. This is what I refer to as the beneficial greenhouse effect. It makes the earth more habitable by raising the average surface temperature to 60 F.

In the right figure the concentration of greenhouse gases has increased even more (due to human activities). The earth might find a new energy balance. In this case the ground would be warmer and could be emitting 4 units of energy, but still only getting 2 units from the sun. With more greenhouse gases, the atmosphere is now able to absorb 3 units of the IR emitted by the ground. The atmosphere sends 2 back to the ground and 1 up into space. A new balance is achieved but the earth's surface is warmer. How much warmer? That's the big question. An even bigger question is what effects that warming will have.

Don't worry about all the details in this figure, just notice the trend. As greenhouse gas concentrations increase, the earth warms.

The effects of clouds on daytime high and nighttime low temperatures

This is a topic that I often "beat to death." I want to keep it as short and simple as I can this semester.

Here are some pretty typical high and low temperatures for this time of year in Tucson. Notice the effects that clouds have: they generally lower the daytime high temperature (it doesn't get quite as hot on a cloudy day as it would on a clear day) and raise the nighttime low temperature (it doesn't get quite as cold on a cloudy night as it would on a clear night).

Sunlight is what warms the earth during the day. Sunlight is mostly visible and near-IR light. Clouds are good reflectors of visible and near IR light (clouds appear white). A smaller fraction of the incoming sunlight will reach the ground on a cloudy and it won't get as warm.

The situation is different at night. The sun is no longer in the picture. The ground cools by emitting far-IR light. Without an atmosphere at all this IR energy would travel out to space and the ground would cool very quickly and get very cold. Greenhouse gases absorb some of this IR light emitted by the ground and re emit a portion of it back to the ground.

It turns out that clouds are good absorbers of far-IR light too (they absorb some of the wavelengths that greenhouse gases do not). I've colored the cloud layer grey in the right picture above. If our eyes were sensitive to far IR instead of visible clouds would appear gray or black. I've also added some orange to the gray cloud because clouds also emit far IR light. Some of this emitted IR light is downward to the ground and reduces the rate at which the ground cools. It doesn't get as cold on a cloudy night as it would on a clear night.

Here's the answer to the 2nd question on the In-class Optional Assignment.

The atmosphere is absorbing two units of energy so it needs to also emit 2 units. We'll send 1 upward and 1 downward.

At the top of the picture we now have equal amounts of incoming and outgoing energy. Down at the ground the 1 unit being emitted is balanced by 1 unit of absorbed energy.