Wednesday Feb. 27, 2013
click here to download today's notes in a more printer friendly format

Keb'Mo' sung "Better Man" before class this afternoon.

After a long delay I am happy to be able to say that the last of the 1S1P Assignment #1 reports (Carbon Dioxide) have been graded.  Several students turned in a third report even though there was a two report limit for this assignment.  I read those reports but didn't record the grades.  Nonetheless you should hang on to your report because you may have an opportunity later in the semester to turn it in for credit.

Now that 1S1P Assignment #1 is in the book Assignment #2 is starting to take shape.  Two topics are available online and I plan to add a third soon.  Reports on the first two topics aren't due until after Spring Break.

The Experiment #1 revised reports were collected today.  Materials for Experiment #3 will be distributed in class on Friday.

We were talking about filters in class on Monday and a student asked whether filtering of sunlight is what causes the sky to appear blue.  The blue color of the sky is caused by scattering of sunlight.  The following series of pictures tries to explain how this works (this discussion also appears at the end of the Mon., Jan. 14 online class notes)

You can find all kinds of things in the sky: air, particulates, clouds, etc.  But first let's imagine there isn't an atmosphere.  No air, clouds, particulates, nothing.


If you went outside and looked at the sun (you shouldn't do that of course) you'd see a bright white sun against a black background.  You'd see the sun because you're looking back in the direction of one of the rays of light coming from the sun. 

If you look away from the sun and toward the sky you wouldn't see anything.  The sky would appear black.  That's because there's nothing to scatter the sunlight.  This is just like when you couldn't see the laser beam as it traveled across the front of the classroom (in the light scattering demonstration early in the semester).  You couldn't see the beam unless something was put into the beam to scatter some of the laser light.

In the next picture we'll add an atmosphere.  Just air molecules, no particles, or clouds.





Air molecules scatter light.  We didn't see this light in the laser demonstration because the laser light scattered by the air was too weak.  But when you're dealing with intense sunlight traveling through a lot more air in the atmosphere you can see the scattered light.

The incoming sunlight is white.  White light is a mixture of all the colors.  Air molecules scatter the shorter wavelengths (violet blue green) more than the longer wavelengths (yellow orange red).  This is depicted above.  Air molecules scatter light in this way because they are very small (much smaller than the wavelength of visible light).

Violet has the shortest wavelength and is scattered the most.  However there isn't as much violet in sunlight as there is blue and green.  There's a lot of green light in sunlight (more than any other color as a matter of fact) but it isn't scattered as readily as blue.  So the end result is that we see blue light coming from the sky.  This is why the sky is blue.  When the air is clean (from of particulates), the sky has a deep blue color.  Here's a little more explanation of why the mixture of violet, blue, and green appears blue.

Next we'll add a cloud to the picture.  As we saw in the laser demonstration, cloud droplets and ice crystals are good scatters of light.  Cloud droplets and ice crystals though are much larger than air molecules.  Because of this they scatter all the colors in equal amounts.




When white light strikes a cloud, white light is scattered and reflected.  This is why clouds are white (with some shades of grey mixed in if the cloud is thick).  When you look up at a cloud you see a white cloud (sunlight being scattered by cloud droplets) surrounded by blue sky (sunlight being scattered by air molecules.

What about particles?  Particulates are much bigger than air molecules and a little bit smaller than cloud droplets.  They scatter light is the same way that cloud droplets and ice crystals do.  The scattered light from particles is white.




What do you see now when you look at the sky?  It depends on how much particulate matter is in the air.  When the air is clean and doesn't contain much particulate matter the sky is a deep blue.  As the concentration of particulates increases you mix in more and more white light.  The color of the sky can change to a whitish blue when the particulate concentration is high.

The world would not look the same if we were able to see IR light instead of visible light.
visible light reflected by the tree
and photographed with normal film
 near IR light reflected by the tree
and photographed using IR film


The picture at left was taken using normal film, film that is sensitive to visible light.  The picture at right used infrared film.  In both pictures we are looking at sunlight that strikes the tree or the ground and is reflected toward the camera where it can be photographed (i.e. these aren't photographs of light emitted by the tree or the ground).  The tree at left is green and relatively dark (it reflects green light but absorbs the other colors of visible light).  The tree at right and the ground are white, almost like they were covered with snow.  The tree and grass on the ground are reflecting infrared light.  Here are many more images taken with infrared film.




Here's another example, photographs of the ground taken from an air plane using ordinary film at left (responds to visible light) and  infrared  film at right.  Notice how the IR photograph is able to "see through" the  haze.  The haze at left is scattered light.  IR light is not scattered as readily as visible light.

Another example was shown in class, a thermal image of a house.  These are photographs of  infrared light that is being emitted (not reflected light) by a house.  Remember that the amount of energy emitted by an object depends strongly on temperature (temperature to the 4th power in the Stefan-Boltzmann law).  Thus it is possible to see hot spots that emit a lot of energy and appear "bright" and colds spots.  Photographs like these are often used to perform an "energy audit" on a home, i.e. to find spots where energy is being lost.  Once you locate one of these hot spots you can add insulation and reduce the energy loss.  Don't worry too much about the colors.  The photograph is probably taken using just a single wavelength.  The thing that varies is the intensity of the IR light.  Processing of the photograph adds color to make differences in intensity more apparent.  Reds and orange mean more intense emission of IR radiation (warmer temperature) than the blues and greens.  We'll something similar when we look at IR satellite photographs of clouds.

One last point which might not have been mentioned in class:  the pictures of reflected IR light are probably looking at near IR light with a wavelength of 1 μm (light with a wavelength just a little bit longer than visible light).  The photographs of emitted IR light at capturing far IR emissions, light with a wavelength of 10 μm.

We now have most of the tools we will need to begin to study radiant energy balance on the earth.  It will be a balance between incoming sunlight energy and outgoing IR radiation 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).  The sun is bigger, hotter, and emits much more radiant energy than the earth.  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.  The earth only needs to balance the energy is absorbs from 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 5 arrows of incoming sunlight in the first picture are absorbed, 1 of the arrows is being reflected) so it will begin to warm  This is like opening a bank account, the balance will start at zero.  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 arrow of reflected sunlight has 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 (4 arrows) than it is losing (3 arrows) 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 (it's about 0 F for the earth).

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.  Someone might deposit money into your bank account in Euros while you spend dollars.

Before we start to look at radiant energy balance on the earth with an atmosphere we need to learn about how the atmosphere will affect the incoming sunlight and outgoing IR light emitted by the earth.  We'll draw a filter absorption graph for the earth's atmosphere. 

We will first look at the effects simple blue, green, and red glass filters have on visible light.  This is just 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 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 effect the atmosphere has 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 .   Wavelengths between 0.7 and  8 or 9 μm are absorbed, radiation centered at 10μm is transmitted by the atmosphere.  Wavelengths greater than 10 μm are absorbed (again by greenhouse gases).  It is the atmosphere's ability to absorb certain wavelengths of infrared light that produces the greenhouse effect and warms the surface of the earth.  The atmosphere also emits IR radiation.  This is also an important part of the greenhouse effect.

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.

Now back to 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).  The arrow of reflected sunlight doesn't any role at all.



We will be moving from outer space 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 figure above and
2 arrows absorbed and emitted in the bottom figure below
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 the same picture with some more 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 (I added a little information at the bottom of the picture.



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).  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 won't worry about that at this point.
The ground is emitting a total of 3 arrows of IR radiation.  At this point that might seem like a problem.  How can the earth emit 3 arrows when it is absorbing only 2.  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 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, something we didn't have time to do in class.


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).  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



Doesn't it make sense that if the ground is getting back some of the energy it would otherwise lose, the ground will end up being warmer.  That's what the greenhouse effect does, it 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 the greenhouse effect warms the earth.  We didn't cover this material in class but I'll stick it in here anyway just to complete this part of the topic.



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, more subtle, explanation of why the ground is warmer with a greenhouse effect than without.


At left the ground only needs to emit 2 units of energy to be in energy balance, at right the ground must emit 3 units to be in balance.  Remember that the amount of energy emitted by something depends on temperature (the left equation below).

The cold ground in the left picture above must warm in order to be able to emit 3 arrows of  energy needed in the right picture.