Thursday Oct. 7, 2010
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Music today featured two songs from Bob Dylan ("Like a Rolling Stone" and "Stuck Inside of Mobile with the Memphis Blues Again")

The Bonus 1S1P Assignment that was turned in on Tuesday has been graded and was returned in class today (click here to see a drawing of the completed surface weather map analysis).

The Upper Level Charts Optional Assignment was collected today.  I'll return these papers next Tuesday.  If you weren't able to finish the assignment in time to turn it in today you can have until next Tuesday.

The Quiz #2 Study Guide is now online.  Quiz #2 is Thursday, Oct. 14.  There will be reviews Monday, Tuesday and Wednesday afternoon next week.  See the Study Guide for times and locations.

The Experiment #2 reports and the Expt. #1 revised reports are due next Tuesday, Oct. 12.  Try to return your materials Friday or Monday (in my office) so that you can pick up the Supplementary Information sheet.

An In-class Optional Assignment was handed out today.  If you download the assignment and turn in your answers at the beginning of class next Tuesday you can receive at least partial credit (maybe even full credit).

We began class with a short demonstration of Stefan Boltzmann and Wien's Laws in action.  These are the two equations that allow you to calculate the amount and kind of electromagnetic radiation emitted by an object.

An ordinary 200 W tungsten bulb connected to a dimmer switch was used (see p. 66 in the photocopied ClassNotes).  We'll be seeing the EM radiation emitted by the bulb filament.



The graph at the bottom of p. 66 has been split up into 3 parts and redrawn for improved clarity.



We start with the bulb turned off (Setting 0).  The filament will be at room temperature which we will assume is around 300 K (remember that is a reasonable and easy to remember value for the average temperature of the earth's surface).  The bulb will be emitting radiation, it's shown on the top graph above.  The radiation is very weak so we can't feel it.  The wavelength of peak emission is 10 micrometers which is long wavelength, far IR, radiation that we aren't able to see. 

Next we use the dimmer switch to just barely turn the bulb on (the temperature of the filament is now about 900 K).  The bulb wasn't very bright at all and had an orange color.  This is curve 1, the middle figure.  Note the far left end of the emission curve has moved left of the 0.7 micrometer mark - into the visible portion of the spectrum.  That is what you are able to see, just the small fraction of the radiation emitted by the bulb that is visible light (but just long wavelength red and orange light).  Most of the radiation emitted by the bulb is to the right of the 0.7 micrometer mark and is invisible IR radiation (it is strong enough now that you could feel it if you put your hand next to the bulb).

Finally we turn on the bulb completely (it was a 200 Watt bulb so it got pretty bright).  The filament temperature is now about 3000K.  The bulb is emitting a lot more visible light, all the colors, though not all in equal amounts.  The mixture of the colors produces a "warm white" light.  It is warm because it is a mixture that contains a lot more red, orange, and yellow than blue, green, and violet light.  It is interesting that most of the radiation emitted by the bulb is still in the IR portion of the spectrum (lambda max is 1 micrometer).  This is invisible light.  A tungsten bulb like this is not especially efficient, at least not as a source of visible light.

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.  The 5500 K bulb is "too cool" and creates a stark sterile atmosphere like you might see in a hospital.  I prefer the 3500 K bulb in the middle.

This 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).

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.  We will look at the simplest case first, the earth without an atmosphere (or at least an atmosphere without greenhouse gases) found on p. 68 in the photocopied Classnotes.


You might first wonder how, with the sun emitting so much more energy than the earth, 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 the earth is located about 90 million miles from the sun and therefore 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 (0K) and is not emitting any EM radiation at all.  It is absorbing sunlight (4 of the 6 arrows of incoming sunlight in the first picture are absorbed, 2 of the 6 are being reflected) however so it will begin to warm  This is like opening a bank account, the balance will be 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).  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.  The earth is emitting 3 arrows of IR light (in red).  Once you find money in your bank account you start to spend it.  Because the earth is still gaining more energy than it is losing the earth will warm some more.  Reflected sunlight is like a check that bounces.  It really doesn't affect your bank account balance.

Eventually it will warm enough that the earth (now shaded green) will emit the same amount of energy (though not the same wavelength 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. 

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 become familiar with filter absorption graphs.



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.  Similarly the green and red filters only let through green and red light.

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 .  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 and something I didn't mention in class.  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 (figure 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.

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 something close to what we ended up with in class




It would be hard to sort through all of this if you weren't in class (and maybe even if you were) to see how it developed.  So below we will go through it again step by step (which you are free to skip over if you wish.  This is a little more detailed version than was done in class.  Caution: some of the colors below are different from used in class.
1.   The figure shows 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 it is about half IR light and some of that is going to be absorbed.
The ground is emitting 3 rays of IR radiation.

2.   One of these (pink 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.  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 visualizing.

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)

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)

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 outer space, 2 units of energy (pink and orange) leave the earth and head back out into space.


The greenhouse effect is found in the absorption and emission of IR radiation by the atmosphere.  Here's how you might put it into words (close to but perhaps not exactly the same wording as in class):


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.  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 this is true.




Energy balance without an atmosphere (left) and with an atmosphere that contains greenhouse gases (right) the greenhouse effect.  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.


Here's another explanation (not mentioned in class).  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.  Doesn't it seem reasonable that ground that absorbs 3 units of energy will be warmer than ground that is only absorbing 2?

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. Next we will 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.

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 that is about 1 calorie/cm2 min.

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), 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).  Using the colors you can find each of these parts of the energy budget in the bottom figure.  Notice that conduction, convection, and latent heat energy transport 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.

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.

Two or three things to note in the bottom (not mentioned in class on Thursday)
(i)  First the ground receives 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 gets lots of energy from the atmosphere. 

(iii)  The atmosphere emits 64 units upward and 96 units downward.  This might be explained by the lower atmosphere being warmer than higher up in the atmosphere.  Part of the explanation is also that there is more air in the bottom of the atmosphere than near the top of the atmosphere.