The Experiment #2 reports should be graded by Thursday. I
plan to bring a very limited number of sets of Expt. #4 materials
to class on Thursday as well. Expt. #4 should only be
undertaken by the most patient of individuals. Finally a
couple of new 1S1P topics should appear online by Thursday.
Reports won't be due until the Thursday Mar. 26.
One of my goals over Spring Break is to finish grading everything
that has been turned in recently, enter all the data into one of
my computers, and prepare midterm grade summaries to hand out upon
your return from the break.
Now onto the material at hand. 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 last
Thursday's class notes.
We looked at a couple of curves like these in class last
week. Note the wavelength scale on the bottom of the
figure. The interval from 0.4 to 0.7 micrometers is visible
light. The sun is 20 times hotter than the earth; every
square foot of the sun will emit 160,000 times as much radiant
energy as a square foot on the earth. The type (wavelength)
of light is very different.
The curve on the right is for the earth. Note the peak on
the vertical axis is only 0.05 compared to 15,000 on the curve at
left. Obviously the light emitted by the earth is much
weaker than the sun. 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 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. Almost
half of the light emitted by the sun (37% + 12% = 49%) is
invisible IR light. Only 7% of sunlight is UV light and most
of that gets absorbed by the ozone layer in the stratosphere.
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 are
photographs of reflected sunlight.
This is a picture of the far IR light
that is emitted by a house (source
of this image). You'd see this during
the day or night, sunlight doesn't need to be present.
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.
This photograph has been color coded. 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 poorly insulating windows). 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.
Later in the semester we will 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.
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 (something I meant to do in
class but forgot)
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). A couple of Optional
Assignments (turned in at the end of class)
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?
No clearly not. It's just absorbing energy (3
arrows worth). It's not emitting any of its
own. It needs to be emitting 3 arrows of its
own. You just need to decide whether to send
them up or down.
Ground
The ground is absorbing 1 arrow
and emitting 3 arrows.
Obviously it's not in energy
balance.
The ground needs to more arrows of incoming
(absorbed) energy.
Top of the atmosphere
The number of arrows arriving and leaving aren't
equal. We need one more arrow of energy leaving the
earth and going back out into space.
Here is the solution
The atmosphere must emit 3 arrows of energy, they're shown in
blue. One of them goes up and out into space, the other two
go down to and are absorbed by the ground. Now every part of
the picture is in energy balance.
Question #2
Once again you need to add some arrows (no more than two) and
bring the picture into energy balance.
Examine the picture carefully. The
atmosphere is absorbing two arrows but not emitting
energy. The ground is emitting 1 arrow but not emitting
any. One arrow is arriving at the top of the atmosphere
from the sun but not energy is going back out into space.
The solution is shown below.
Add two arrows. Send one upward
and the other downward to the ground.
