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

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

Â the climate sensitivity.

Â So if two climate scientists meet in a bar, and

Â they wanna discuss to compare their models, the first thing that they'll

Â compare about the two models is what the climate sensitivities of the models are.

Â The climate sensitivity is defined as the change in temperature from doubling CO2.

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

Â used to mean change in something.

Â And the 2x means doubled CO2.

Â So this is a convenient metric,

Â because of the way that the temperature responds to CO2.

Â Because of the band saturation effect.

Â You remember that a little bit of greenhouse gas goes a long way.

Â But when you put more and more in,

Â the energy consequences of it get less and less.

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

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

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

Â 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

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

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

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

Â by multiplying the climate sensitivity by the number of doublings,

Â which you can calculate here using logarithms.

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

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

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

Â so that would be 1 times the climate sensitivity.

Â [SOUND] So we can calculate what the climate sensitivity

Â to change in the, energy flux should be without any

Â feedbacks just using the Stefan-Boltzmann equation.

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

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

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

Â then the temperature raised to the fourth power.

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

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

Â So if you put that, you run this twice calculate two temperatures and

Â change the forcing by four watts per square meter.

Â You end up calculating that the climate sensitivity of a bare rock with no

Â greenhouse effect and no feedbacks would be about one degree centigrade.

Â So the climate sensitivity for CO2 alone would be about 1 degree centigrade.

Â But then, we've got the water vapor feedback and the ice-albedo feedback,

Â and those together just about double the climate sensitivity of the Earth, so

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

Â 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

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

Â doubling CO2, or to having a higher feedback

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

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

Â because they are formed by process that happen on all different spatial scales.

Â It's very difficult to do a whole

Â atmosphere full of clouds in a realistic way.

Â And this is the main source of uncertainty in the climate models for

Â the future prediction.

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Â