We can summarize the impacts of these feedbacks within the context of this
parameter, this number that climate scientists talk
about a lot called the climate sensitivity.
If two climate scientists meet in a bar,
and they want to discuss and compare their models, the
first thing that they'll compare about the two models
is what the climate sensitivities of the models are.
The climate sensitivity is defined as the change in temperature
from doubling CO2.
It's written with this capital letter, Greek letter delta,
which is often times used to mean a change in something.
And the two x means doubled CO2.
This is a convenient metric, because of the way that
the temperature responds to CO2, because of the band saturation effect.
You remember that a little bit of greenhouse gas
goes a long way, but when you put
more and more in, the, energy consequences of it get less and less.
What actually, how it seems to work pretty well
for CO2, is that any doubling of the CO2 concentration --
here's a doubling, here's a second doubling,
here's a third doubling ---
results in about the same amount of temperature change.
Yyou can see this curve is kind of flattening out.
You should be aware that it takes centuries for the Earth to
fully equillibrate, to really change its temperature, when you change the CO2.
But still, you can kind of use this climate sensitivity to give an order of
magnitude, or a rough impression of what climate change will be.
By multiplying the climate sensitivity by
the number of doublings, which you can calculate here using logarithms.
The logarithm of the ratio of the CO2 at the end of some time,
versus the initial, so that is your change in CO2, divided by the logarithm of two.
If you put in 560 over 280 you
end up with one doubling.
That would be one times the climate sensitivity.
We can calculate what the climate sensitivity to a change in the energy
flux should be without any feedbacks. Just using the Stefan Boltzmann equation.
We have the the total energy flux
here, in watts per square meter. Here is epsilon,
the emissivity, which we've assumed is pretty much equal to one.
Sigma, the Stefan Boltzmann
constant is just a constant.
And then the temperature raised to the fourth power.
By running a model like the mod tran model, where you add more CO2, you
can get that doubling CO2, changes the energy
balance by about four Watts per square meter.
If you run this twice, calculate two temperatures and change the
forcing by four Watts per square meter,
you end up calculating that the climate sensitivity of a bare rock
with no greenhouse effect and no feedbacks would be about one degree centigrade.
The climate sensitivity for CO2 alone would be about one degree centigrade.
But then we've got the water vapor feedback, and the ice albedo feedback.
And those together, just about double the climate sensitivity of the earth.
If they didn't exist it would be much less of a problem.
And then clouds.
Clouds are the biggest uncertainty in climate models.
Different models range from either having not much cloud feedback,
and then they will have a fairly low climate
sensitivity of maybe two degrees C for maybe doubling C02,
or to having a higher feedback from clouds which
results in an overall climate sensitivity that's much higher.
It's really, unfortunate that the clouds are so difficult to model because
They are formed by processes
that happen on all different spatial scales.
It's very difficult to do a whole
atmosphere full of clouds, in a realistic way.
And this
is the main source of uncertainty in the climate models for the future prediction.