Quiz #2 has been graded and was returned in class today
together with a mid term grade summary. You'll find more
information about the grade summary near the end of today's
notes. You'll also find a short 1-question Optional
Assignment stuck onto the end of today's notes.
I hope to have the Experiment #2 reports graded by
Thursday. The revised Expt. #1 reports and the 1S1P
reports on the seasons will follow after that.
The 1S1P Assignment #2b topic reports are due Thursday this
week (Oct. 23). I plan to finalize Assignment #2c today. Light emitted by the earth and sun
Here's a short topic, the light emitted by the earth & sun,
that I stuck onto the end of the Tues. Oct. 14 notes (we didn't
have time last week to cover it in class).
The curve on the left is for the sun. The surface of the
sun has a temperature of 6000 K so we can use Wien's law to
calculate λmax
. It turns out to be 0.5 micrometers, green light. The
sun emits more green light
than any other kind of light but appear green because it is also
emitting lesser amounts of violet, blue, yellow, orange, and red -
together this mix of colors appears white (it's a
cooler white than you would get from a tungsten bulb). 44%
of the radiation emitted by the sun is visible light, Almost
as much, 37%, is near IR light. More about that below.
More than half of the light emitted by the sun (56%,
the UV and IR) is invisible.
100% of the light emitted by the earth (temperature = 300 K) is
invisible far IR light. The wavelength of peak emission for
the earth is 10 micrometers. The light emitted by the earth
is also much weaker
The world in near IR light.
The world would not look the same if we were able to see near
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 near
IR film
The picture at left
was taken using normal film, film that is sensitive to
visible light. The picture at right used near
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
visible light being 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 very
good reflectors of near infrared light. Here are
many
more images taken with infrared film.
Photographs of the ground taken from an air plane using
ordinary film at left (responds to visible light) and near
infrared film at right. Notice how much clearer the river is
in the picture at right. The IR photograph is able to "see
through" the haze. The haze is scattered light.
You may remember from the 1S1P topic on scattering that air
molecules scatter shorter wavelengths in much greater amounts that
longer wavelengths. IR light is not scattered nearly as much
as visible light.
You wouldn't have seen the tree or the river if the photos above
had been taken at night. That is because they photograph
reflected sunlight.
A final example, a thermal
image of a house, was shown in class. These are
photographs of far 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. The reds show you
were energy is being lost (often through window glass). Many
of the roof tops are blue, they are cool. There is probably
a lot of insulation in the attic and little energy is being lost
out the roof.
In a week or so we will be looking at satellite photographs of
clouds. Satellites take pictures of both the visible light
reflected by clouds and also the IR radiation emitted by
clouds.
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
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 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). 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 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 picture that is in
your ClassNotes (p. 70a). It's the same picture with a
little explanation added.
Radiative equlibrium 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 (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). 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. 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). 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
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 end up warmer than ground that is only absorbing 2?
The next picture shows an even better way of analyzing the
situation.
To be in energy balance, the ground in the
picture above at left must emit 2 arrows of radiant
energy. At right the ground must emit 3 arrows.
The amount of energy emitted by an object depends on
temperature (to the 4th power). The Stefan Boltzmann law
tells us that. The ground above at right has to be
warmer in order to emit more radiant energy.
How much incoming sunlight reaches the ground?
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. We will now 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.
This is the only number in the figure you should try to remember.
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 most of the UV (UV makes
up only 7% of sunlight). Roughly half (49%) of sunlight is
IR light and greenhouse gases will absorb some of that.
The remaining 30% of the incoming sunlight is reflected or
scattered back into space (by the ground, clouds, even air
molecules).
average (no
quiz scores dropped): 75.1% + 0.6
= 75.7%
average
(lowest quiz score dropped): 76.9% + 0.6 = 77.5
* because you haven't
completed the experiment or book report
yet (or your report
hasn't been graded yet) an average score was
used to compute your
writing grade
Here's an example of the grade summaries
handed out in class.
The first two items (green)
are your scores on the quizzes.
This is followed by the number of extra credit (EC) points (purple) you've earned so
far. If you've done all the Optional Assignments (an
selected the extra credit points option on the two most recent
assignments) you could have earned up to 1.7 pts so far.
There will be at least 3 pts possible by the end of the
semester. You can also see whether they enter into your
overall grade.
Your writing score (orange)
is next. This is made up of your experiment report grade
(up to 40 pts) and the number of 1S1P pts you've earned so far
(this should be 45 pts by the end of the semester). Many
of you haven't done an experiment or have turned in a report
that hasn't yet been graded. In these cases your grade
summary shows a 0 but the computation of your writing
percentage grade assumes an average score (I think I assumed
33 out of 40). This is just to show you how the writing
grade can help your overall average.
Finally two overall averages are computed:
(i) the first doesn't drop any quiz scores. This is the
score that must be 90.0 or above at the end of the semester in
order to be exempt from the Final Exam.
(ii) the lowest quiz score when computing the 2nd average.
These grade estimates attempt to predict the grade you will
end up with at the end of the semester if you keep on doing as
you have done so far.
If you're happy with your overall
average, you need to keep up the quality of work you have done
so far.
If your score is lower than you'd
like there is still plenty of time for improvement.
Improved scores on the remaining two quizzes can
change
your overall average
dramatically. Also be sure to turn in an experiment
report and earn 45 1S1P pts (the max. no. allowed). The
writing
percentage grade has the same weight
as a quiz and there is no reason it shouldn't be near or even
above 100%.
Finally be sure to check that all of the information on your
grade summary is correct.
A couple of Optional Assignments (to be turned in
before the start of class on Thursday)
Now that we know a little bit more about the fate of
incoming sunlight we'll improve our simplified illustration of
the greenhouse effect somewhat. We'll make it a little
more realistic.
Question 1
In this case we'll assume that 1 of the 2 incoming arrows of
sunlight is absorbed in the atmosphere instead of passing through
the atmosphere and being absorbed at the ground. The ground
is still emitting 3 arrows of IR light. Your job is to
complete the picture. What would you need to add to the
picture to bring everything into energy balance?
Hint: various parts of the picture are isolated
below. Check each to see if they are in energy balance.
Atmosphere
Here's just the middle part of the picture, the
atmosphere.
How many arrows are being absorbed, how many are being
emitted.
Note the two lines marked with * are just "passing
through"
no energy is absorbed or emitted
it's as if they weren't even there
The two "passing through" arrows
have been removed.
Is the atmosphere in energy balance?
Ground
The ground is absorbing 1 arrow
and emitting 3 arrows.
Obviously it's not in energy
balance.
What would you need to add to the picture to bring
it into balance?
Top of the atmosphere
How many arrows are arriving and leaving?
What needs to be added to bring this into balance?
Question #2
This question wasn't mentioned in
class. It's a Hidden Optional
Assignment. Turn answers in to this question and the
question above and you 'll earn double credit.
What would you need to add to this picture
to bring it into energy balance?
