Friday Oct. 7, 2011
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I got distracted and started the music a little late.  There was time for only on Domingo DeGrazia song ("Tres Ninas")

The Upper Level Charts Optional Assignment has been graded and was returned in class.  Everyone that did the assignment received 0.5 pts of extra credit.  If you missed 3 pts or less you also earned a Green Card.

You'll find a link on the class home page that shows you how to estimate your grade in this class.  I will try to hand out grade summaries after Quiz #2 and once we have all the 1S1P Assignment #1 papers graded.

In class on Wednesday we learned about the laws that govern the amount and kind of EM radiation emitted by an object.  We looked at the light produced by an ordinary tungsten bulb as an example.

Now we will compare the light emitted by the sun and the earth.



The curve on the left is for the sun.  We first used Wien's law and a temperature of 6000 K to calculate λmax and got 0.5 micrometers.  This is green light; the sun emits more green light than any other kind of light.  The sun doesn't appear green because it is also emitting lesser amounts of violet, blue, yellow, orange, and red - together this mix of colors appears white.  44% of the radiation emitted by the sun is visible light,  49% is IR light (37% near IR + 12% far IR), and 7% is ultraviolet light.  More than half of the light emitted by the sun is invisible.

100% of the light emitted by the earth (temperature = 300 K) is invisible IR light.  The wavelength of peak emission for the earth is 10 micrometers. 

Because the sun (surface of the sun) is 20 times hotter than the earth the sun's surface emits energy at a much higher rate than the earth.  Note the vertical scale on the earth curve is different than on the sun graph.  If both the earth and sun were plotted with the same vertical scale, the earth curve would be too small to be seen.

On Wednesday we also 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 class 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.  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 disposed of properly (at a hazardous materials collection site or perhaps at 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 (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 (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 on Friday):



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. 



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.