Tuesday Oct. 11, 2011
click here to download a copy of today's notes in a more printer friendly format

A couple of songs from Playing for Change.  The first was Don't Worry (worry a little bit but not too much about this week's quiz) and just about the best version of Stand By Me that you'll ever hear.

In addition to the usual Study Guide and the reviews there are a couple of new items or events to help you prepare for this week's quiz.  First, in reponse to a student question, there's a list of pages from the ClassNotes that cover Quiz #2 material.  Also the class Preceptor, Nicole Venn, is planning to conduct Open Study Hours from 6-7 pm at the Main Library Tuesday evening (you can contact her by email [nvenn@email.arizona.edu] or just meet on the ground floor of the library near the elevators at 6 pm if you're interested).

Last week we learned that ordinary tungsten bulbs (incandescent bulbs) produce a lot of wasted energy.  This is because they emit a lot of invisible infrared light that doesn't light up a room (it will warm up a room but there are better ways of doing that).  The light that they do produce is a warm white color (tungsten bulbs emit lots of orange, red, and yellow light and not much blue, green or violet). 

Energy efficient compact fluorescent lamps (CFLs) are being touted as an ecological alternative to tungsten bulbs because they use substantially less electricity, don't emit a  lot of wasted infrared light, and also last longer.  CFLs come with different color temperature ratings.


The bulb with the hottest temperature rating (5500 K ) in the figure above is meant to mimic or simulate sunlight.  The temperature of the sun is 6000 K and lambda max is 0.5 micrometers.  The spectrum of the 5500 K bulb is similar.

The tungsten bulb (3000 K) and the CFLs with temperature ratings of 3500 K and 2700 K produce a warmer white. 

Three CFLs with the temperature ratings above were set up in class so that you could see the difference between warm and cool white light.  Personally I find the 2700 K bulb "too warm," it makes a room seem gloomy and depressing (a student once said the light resembles Tucson at night).   The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital corridor.  My cats and I prefer the 3500 K bulb in the middle.

The figure below is from an article on compact fluorescent lamps in Wikipedia for those of you that weren't in class and didn't see the bulb display..  You can see a clear difference between the cool white bulb on the left in the figure below and the warm white light produced by a tungsten bulb (2nd from the left) and 2 CFCs with low temperature ratings (the 2 bulbs at right).



There is one downside to these energy efficient CFLs.  The bulbs shouldn't just be discarded in your ordinary household trash because they contain mercury.  They should be taken to a hazardous materials collection site or perhaps back to the store where they were purchased.

It probably won't be long before LED bulbs begin to replace tungsten and CFL bulbs.  At the present time the LED bulbs are pretty expensive.

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.  This will ultimately lead us to an explanation of the atmospheric greenhouse effect. 

We will first look at the simplest kind of situation, the earth without an atmosphere (or at least an atmosphere without greenhouse gases).  The next figure is on p. 68 in the photocopied Classnotes.  Radiative equilibrium is really just balance between incoming and outgoing radiant energy.



You might first wonder how it is possible for the earth (with a temperature of around 300 K) to be in energy balance with the sun (6000 K).  At the top right of the figure you can see that because the earth is located about 90 million miles from the sun and it only absorbs a very small fraction of the total 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 (0 K) and is not emitting any EM radiation at all.  It is absorbing sunlight however (4 of the 6 arrows of incoming sunlight in the first picture are absorbed, 2 of the 6 are being reflected) so it will begin to warm  This is like opening a bank account, the balance will be zero at first.  But then you start making deposits and the balance starts to grow.

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).  Only the four arrows of incoming sunlight that are absorbed are shown in the middle figure.  The two arrows of reflected sunlight have been left off because they don't really play a role in energy balance.  Reflected sunlight is like a check that bounces.  It really doesn't affect your bank account balance.  The earth is emitting 3 arrows of IR light (in red).  Because the earth is still gaining more energy than it is losing the earth will warm some more.  Once you find money in your bank account you start to spend it.  But as long as deposits are greater than the withdrawals the balance will grow.

Eventually it will warm enough that the earth (now shaded brown & blue) will emit the same amount of energy as it absorbs from the sun.  This is radiative equilibrium, energy balance (4 arrows of absorbed energy are balanced by 4 arrows of emitted energy).  The temperature at which this occurs is about 0 F.  That is called the temperature of radiative equilibrium. 

Note that it is the amounts of energy not the kinds of energy that are important.  Emitted radiation may have a different wavelength than the absorbed energy.  That doesn't matter.  As long as the amounts are energy the earth will be in energy balance.

Before we start to look at radiant energy balance on the earth with an atmosphere 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 is just to be able to interpret a filter absorption curve or graph.




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 with the green and red filters.

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 was redrawn after class.



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 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.

Greenhouse gases make the atmosphere a selective absorber of IR light - the air 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 (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.

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 us.

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 (figure above) to the earth's surface (the next two figures 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.  The important thing is that there are equal amounts being absorbed and emitted in both cases.




Here's the same picture with some information added (p. 70a in the photocopied ClassNotes).  This represents energy balance on the earth without an atmosphere.

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.



It would be hard to sort through and try to understand all of this if you weren't in class (probably even more difficult 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).  This is a more detailed version than was done in class.  Caution: some of the colors below are 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 don't worry about that at this point.
The ground is emitting a total of 3 arrows of IR radiation.


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).  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 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.

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 (2 green arrows of sunlight and one bluish arrow coming from the atmosphere) and emitting 3 units of energy (one pink and two red arrows).  So the ground is in energy balance.

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).  The atmosphere is in energy balance.

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




The greenhouse effect involves the absorption and emission of IR radiation by the atmosphere.  Here's how you might put it into words (something I didn't do in class):


The greenhouse effect warms the surface of the earth.  The average annual surface temperature ends up being about 60 F rather than 0 F.
Here are a couple other ways of understanding why the greenhouse effect warms the earth. 



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.  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 be warmer than ground that is only absorbing 2?

Here's another explanation of why the ground is warmer with a greenhouse effect than without.


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.  The ground in the right picture must be warmer to be able to emit 3 arrows of energy rather than 2 arrows.  It is able to emit 3 arrows of energy even though it only gets 2 arrows of sunlight because it is able to get a 3rd arrow of energy from the atmosphere.

Here's a short question about energy balance to test your understanding.


The atmosphere is absorbing 1 unit of incoming sunlight energy and 1 unit of IR energy coming from the ground.  You basically need to add some arrows to the picture and bring everything into energy balance.  A good place to start is to ask how many arrows the atmosphere must emit.  Then check for energy balance at the ground and for balance between energy arriving at the earth and energy leaving the earth and going out to space. 


The atmosphere is absorbing two arrows and must emit 2 arrows to be in energy balance.  Send one of these down to the ground.  That will balance the 1 arrow of IR being emitted by the ground.  Draw the 2nd arrow pointing upward and going into space.  Now we have 1 arrow arriving at the top of the atmosphere from the sun and 1 arrow leaving the atmosphere and going back out into space.

In our simplified explanation of the greenhouse effect we assumed that 100% of the sunlight arriving at the earth passed through the atmosphere and got absorbed at the ground. We will now look at how realistic that assumption is.

The bottom figure above shows that on average (over the year and over the globe) only about 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 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 (Roughly half of sunlight is IR light).

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

Student performing Experiment #3 will be measuring the amount of sunlight energy arriving at the ground.  About 2 calories pass through a square centimeter per minute at the top of the atmosphere.  Since about half of this arrives at the ground on average, students should expect to get an answer of about 1 calorie/cm2 min.  I didn't show the figure below in class.


Next we will look at our simplified version of radiative equilibrium and a more realistic picture of the earth's energy budget.


In the top figure (the simplified representation of energy balance) you should recognize the incoming sunlight (green), IR emitted by the ground that passes through the atmosphere (pink or purple), 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). 

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 simplied version.  Once you understand the upper figure, you should be able to find and understand the corresponding parts in the lower figure (especially since I've tried to use the same colors for each of the corresponding parts).

Some of the incoming sunlight (51 units in green) reaches the ground and is absorbed.  19 units of sunlight 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.  The atmosphere in turn emits energy upward into space (64 units) and downward toward the ground (96 units).  Why are the amounts different?  One reason might be that the lower atmosphere is warmer than the upper atmosphere (warm objects emit more energy than cold objects).  Part of the explanation is probably also that there is more air in the bottom of the atmosphere (the air is denser) than near the top of the atmosphere. 

Notice that conduction, convection, and latent heat energy transport (the 7 and 23 units on the left side of the figure) are needed to bring the overall energy budget into balance. The amount of energy transported by conduction, convection, and latent heat is small compared to what is transported in the form of EM radiation.

A couple more things to notice in the bottom figure (that I might not have mentioned in class)
(i)  The ground is actually receiving more energy from the atmosphere (96 units) than it gets from the sun (51 units)!  Part of the reason for this is that the sun just shines for part of the day.  We receive energy from the atmosphere 24 hours per day.

(ii)  The ground emits more energy (117 units) than it gets from the sun (51 units).  It is able to achieve energy balance because it also gets energy from the atmosphere (96 units). 

Here's another test your understanding style question.  It's a simplified but slightly more realistic version of energy balance on the earth.

In this case 1 of the 2 incoming arrows of sunlight is absorbed in the atmosphere instead of at the ground.  The ground is still emitting 3 arrows of IR light.  Your task is to bring the picture into energy balance.  Again start with the atmosphere.  How many units does it need to emit.  Then look at what is needed to bring energy balance to the ground (which is now emitting 3 arrows and only getting 1 from the sun).  Look also at the numbers of units of energy arriving at the top of the atmosphere and leaving the atmosphere.


The atmosphere needs to emit 3 arrows of IR light.  1 goes upward and into space, the other two go downward and get absorbed by the ground.

Next we used our simplified representation of the greenhouse effect to understand the effects of clouds on daytime high and nighttime low temperatures.  The following can be found on pps. 72a & 72b in the ClassNotes (I've rearranged things slightly to make it clearer)


Here's the simplified picture of radiative equilibrium again (you're probably getting pretty tired of seeing this).  You should be able to say something about every arrow in the picture.  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 infrared radiation.  If we could see IR light, clouds would appear black, very different from what we are used to (because clouds also emit IR light, if we could see IR light the clouds might also glow).  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.  That makes for nice early morning bicycle rides this time of the year.

The next two figures compare clear and cloudy days.



Clouds are good reflectors of visible light (we see visible light and clouds appear white).  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.  Here are some typical daytime high and nighttime low temperature values on clear and cloudy days for this time of the year. 



This is as far as we got in class on Tuesday.  I've stuck a little more material onto today's notes just to finish this topic.  It isn't something to worry about for this week's quiz.

We'll use our simplified representation of radiative equilibrium to understand enhancement of the greenhouse effect and global warming.




The figure (p. 72c 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.

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 downard 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.

In the right figure the concentration of greenhouse gases has increased even more (due to human activities).  The earth would find a new energy balance.  In this case the ground would be warmer and would 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.

The next figure shows a common misconception about the cause of global warming.



Many people know that sunlight contains UV light and that the ozone 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. 

They then 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 much UV light in sunlight in the first place and the small amount of additional UV light reaching the ground won't be enough to cause global warming.  It will cause cataracts and skin cancer and those kinds of problems but not global warming.