Wednesday Mar. 5, 2014

An interesting coincidence lead to today's musical selection.  I heard a portion of a song I liked in an advertisement for a new program on NBC TV the other night.  On the internet I was able to find it was Kelly Sweet's version "In the Air Tonight."  I've also been wanting to play an acapella group for a while and remembered having seen a group singing in one of the cars on the Paris Metro.  The group turned out to be Naturally Seven and they happened also to be singing "In the Air Tonight" and that's what you heard today.

The last two of the 1S1P Assignment #2 reports (Causes of the Seasons and Ultraviolet Light) were collected today.  There's a good chance you won't get those back before Spring Break.

The Experiment #1 revised reports were also collected today.  They are even lower on the grading priority list so don't expect to see them very soon either.

In addition to grading one of the other things I'll be doing over Spring Break is to put everyone's grades into my computer and generating mid term grade summaries.

Quiz #2 is one week from today and the Quiz #2 Study Guide is now available (I forgot to mention that in class).

A warning about the reviews scheduled for next week.  You should come to the reviews having had a serious preliminary look at everything on the Study Guide.  I expect I will find individuals that are completely unfamiliar with material we have been covering for the past 2 weeks or so.  When that happens the review is going to come to an abrupt end for one of us.

Finally a new Optional Assignment was handed out in class today.  The assignment is due next Monday.  As always, you should have the assignment completed before coming to class.

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 ClassNotes.  Radiative equilibrium is really just balance between incoming and outgoing radiant energy. 



You might first wonder how it is possible for the relatively small cool earth (with a temperature of around 300 K) to be in energy balance with the much larger and hotter sun (6000 K).  Every square foot of the sun emits 160,000 times more radiant energy than a square foot of the earth.  And the sun has a lot more square feet of surface area than the earth.

At the top right of the figure above you can see that because the earth is located about 90 million miles from the sun it only absorbs a very small fraction of the total energy emitted by the sun.  The earth only needs to balance the energy it 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).  That is called the temperature of radiative equilibrium (it's about 0 F for the earth, a number you might remember having heard before).

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 the same the earth will be in energy balance.  Someone might deposit money into your bank account in Euros while you spend dollars.

A short demonstration at this point to try to show how light from green, red, and purple laser pointers blends together to produce white light.  The TV camera at the front of the room didn't handle the bright laser light very well.  I'm going to work on the demonstration a little bit more in my office and use my camera to see if I can't photograph the demonstration.  If it works out I'll put the photos online.

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 (a mixture of UV, visible, and IR light) 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 a
filter 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 laser pointers were used to show this.  Light from the red laser point passed through a red filter with little or no attenuation.  But you couldn't shine the green laser light through the red filter.  It was blocked (absorbed by the 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).  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 have 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.



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). 


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.  There's a little bit of UV in sunlight and we know that mostly gets absorbed by the ozone layer.  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).

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 than it gets from the sun.  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).  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.


Did you spot the greenhouse effect?

The 10 am class thought it was Point 4.  The 2 pm class said Point 3.  Actually it's both.  The greenhouse effect depends on both absorbing IR radiation and emitting IR radiation.   Here's how you might put it into words

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 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?

If the ground is getting three arrows of radiant energy it must also be able to emit 3 arrows of energy. 

The Stefan Boltzmann law makes an appearance again.  It is the law that says the amount of energy emitted by an object depends on temperature (to the 4th power).

The cold ground in the left picture below that is only emitting 2 units of energy must warm in order to be able to emit 3 arrows of  energy needed in the right picture.