We started with a very simple model of the climate of the Earth and the greenhouse effect.
It was simple enough that we could understand but
now, it's so simple that we have to work on it awhile to make
it realistic enough to make predictions about the real world.
You remember, the layer model relied on light
to carry energy between the ground and this pane of glass that we're calling the atmosphere.
And it worked, making the Earth warmer because the way the light carried
the energy around insisted that the ground should be warmer than the pane of glass.
For the pane of glass, the temperature is sort of anchored at the skin temperature,
the way these arrows work, the ground had to be warmer than that.
Now we sort of enlarge the model by thinking
about how the real atmosphere doesn't absorb all the infrared
light from the ground but it's selective because gases are choosy.
We ended up with this picture where the CO2 is absorbing strongly in
the CO2 bend region and there's another region
called the atmospheric window where nothing much absorbs.
You look down from space, you see some light that's
coming from high up in the cold part of the atmosphere and
other light it's coming from down near the ground.
It's more complicated than layer model.
Well it turns out, that the temperature structure
of the atmosphere, the cold and warm here, is
the same sense as in the layer model
but the physics behind it are very different.
That's because the temperature in the real atmosphere
is set by convection, which is a process whereby
warm gas near the ground rises up and carries its heat up higher
in the atmosphere and then the cold stuff high up falls down.
We're going to talk for quite a while about how this works and
how it sets this temperature contrast between
the upper atmosphere and the lower atmosphere.
In the simple layer model we defined the skin layer as being the topmost layer
and that temperature was always anchored at the skin temperature,
which is only dependent on
the intensity of the sunlight and the albedo of the earth.
Now, for this more complicated model, we can also define a skin altitude
as the average altitude where infrared light leaves from space.
Looking at this figure here, some of the
light is coming from all the way up there, some of it's coming from all the
way down at the ground. The average has got to be in the middle some place.
You could sort of just count up the energy from the
different frequencies and ask where did you come from, and
calculate, or figure out, visualize the, the skin altitude
which would be an average altitude where energy leaves to space.
Another way to do it would be to use the Stefan-Boltzmann equation to calculate
what temperature of a black body would it take to have just as much radiation
as the sum of this dim stuff from the cold upper atmosphere
in the CO2 bend region and this bright stuff from the warm ground.
We can calculate,
from the infrared model, that we just looked at,
the total energy leaving the system to space.
And then we could say what temperature would a
black body have to be to give us that energy.
That's essentially taking this equation and solving for the temperature.
And that can give us a kind of a skin temperature and we could figure
out what altitude
in the atmosphere has that temperature, and that
could be sort of a skin altitude.
So it seems like a stretch maybe to you
to try to take this very simple skin layer concept
and apply it to this case where everything is kind of fuzzier
but it's useful, and I'll show you why.
Here is a graph of temperature in the atmospehre as a function of altitude.
And there's a slope, it cools down as you go higher up in the atmosphere.
Change in temperature with respect to height, this
slope is called by atmospheric scientists, the lapse rate.
It's kind of a ugly and not particularly descriptive term
but its pretty entrenched and so going to stick with it.
Imagine that we had a planet
in energy equilibrium, so that it was balancing its energy budgets,
like the kitchen sink when everything was in balance, and this point right
here is the skin temperature at the
skin altitude that we calculate using these methods.
Now, we're going to add some more CO2 to that atmosphere.
We're going to have more of this stuff that's fairly dim because
it's coming from a cold atmosphere, this absorption band is going to get fatter.
And in general, that's going to raise the
average altitude where the energy is leaving from space.
If this was the average altitude before, this is what the
skin altitude would look like after adding more greenhouse gas.
And the temperature at that higher altitude is
colder than the temperature was at this altitude because
that temperature profile in the atmosphere is following this slope, the lapse rate,
which I'm going to tell you in the next couple of lessons where this comes from.
Today I'm telling you why we care.
By adding more CO2, we've made the skin altitude higher
but the temperature is colder up there. And we already know from the layer
model that the temperature of the skin always has
to be just balanced by the sun and the albedo.
So by adding the greenhouse gas we've knocked the
energy balance of the planet out of equilibrium.
And so what happens is now there's more energy coming in than is going out,
it's kind of like water accumulating in
our kitchen sink, it makes the planet warmer.
And assuming that the
profile of temperature with altitude follows the same lapse rate as before,
you will get this sort of a change and this much warming at the ground.
It's really the temperature difference between the
skin and the ground that drives the greenhouse effect.
You can imagine a case where if the lapse rate was
determined by the physics of convection that we will
talk about in the next lessons, to just be zero,
so no temperature change with altitude, then you could
add CO2 and make the skin altitude higher,
but it would not affect the temperature at the skin altitude,
so you wouldn't have to warm up anymore.
If the lapse rate were zero like this there would be no greenhouse effect.
You could put as much greenhouse gas as you want
in there and it wouldn't change the temperature of the ground.
Whereas, if the lapse rate is fairly gradual like
these red pair of curves, you get that much warming at the ground.
If it's a really, really strong function
of altitude like the yellow curves,
you get a much bigger temperature change at the ground
for the same amount of greenhouse gas.
The way this works geometrically, you could say
that the change in temperature at the ground, is equal to
the change in the height and then this gets
back to our factor label kind of thing now.
You can cancel the h's and just get t's on both sides and see that it works out.
This change in temperature with h, that is our lapse rate again.
And so you can see that the strength
of the greenhouse effect is directly proportional to
the strength of that temperature gradient, the lapse rate.
To understand the greenhouse effect, how strong it is and how
it will respond to changes in CO2, to make a climate model
realistic in other words, we have to understand
what's controlling this lapse rate in the atmosphere.