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We can summarize the impacts of these feedbacks within the context of this,

this parameter, this number that climate scientists talk about a lot called

the climate sensitivity.

So if two climate scientists meet in a bar, and

they wanna discuss to 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.

So it's written with Greek letter Delta which is oftentimes

used to mean change in something.

And the 2x means doubled CO2.

So 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.

So what actually, how it seems to work pretty well for C02 is that any doubling

of the C02 concentration, so here's a doubling, here's a second doubling,

here's a third doubling results in about the same amount of temperature change,

and so you can see this curve is is kind of flattening out.

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You should be aware that it takes centuries for the Earth

to fully equilibrate, to really change its temperature when you change the CO2.

But still, you can kind of use this climate sensitivity to

give a rough impression of what climate change will be [SOUND]

by multiplying the climate sensitivity by the number of doublings,

which you can calculate here using logarithms.

A logarithm of, the ratio of the CO2 at the end of some time versus the initial.

So the change in CO2 divided by the logarithm of 2.

So if you put in 560 over 280 you end up with 1 doubling,

so that would be 1 times the climate sensitivity.

[SOUND] So we can calculate what the climate sensitivity

to change in the, energy flux should be without any

feedbacks just using the Stefan-Boltzmann equation.

So we have the total energy flux here, and watts per square meter is epsilon,

the emissivity which we assumed is pretty much equal to 1 sigma,

the Stefan-Boltzmann constant, which is the constant, and

then the temperature raised to the fourth power.

So by running a model like the modtran mode,l where you add more CO2, you can get

that doubling CO2 changes the energy balance by about 4 watts per square meter.

So if you put that, 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.

So the climate sensitivity for CO2 alone would be about 1 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, so

if they didn't exist, it would be much less of a problem.

And then, clouds are the biggest uncertainty in climate models.

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Different models range from either having not much cloud feedback, and

then they will have a fairly low climate sensitivity on maybe 2 degrees C for

doubling CO2, or to having a higher feedback

from clouds which results in an overall climate sensitivity that's much higher.

So it's really unfortunate that the clouds are so difficult to model,

because they are formed by process 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.

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