Wednesday, Mar. 2, 2016

Janis Joplin "Kozmic Blues" (4:23), "Little Girl Blue" (3:51)

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. 

Radiative equilibrium on the earth without an atmosphere
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 and 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 as much energy as a square foot on the earth.  At the top right of the figure, however, you can see that because the earth is located about 90 million miles from the sun and only absorbs a very tiny 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 it doesn'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 the earth will warm enough that it (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).

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.

Filtering effect of the atmosphere on ultraviolet, visible, and infrared light
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 near  IR light) and outgoing far 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 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).  The figure was redrawn after class.





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).  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 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 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).  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 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?



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.



This is as far as we got in class today.  We'll cover the information that follows at the start of class on Friday.
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 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. 

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.