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/sci/ - Science & Math

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10410236 No.10410236 [Reply] [Original]

So according to the IPCC the non-feedback climate sensitivity of a doubling of CO2 is about 1-1.2 degrees.
I havent found too many places where this was discussed and shown how the calculations went.

I found one here:
https://scienceofdoom.com/2010/02/19/co2-an-insignificant-trace-gas-part-seven-the-boring-numbers/#comment-136663
It basically uses the following numbers:
Earth radiation at surface = 396 w/m^2
Earth radiation at top of atmosphere (TOA) = 239 W/m^2
Temperature of earth = 288K
And then uses boltzmann:

"Take the solar incoming absorbed energy of 239W/m2 (see The Earth’s Energy Budget – Part One) and comparing the old (only solar) – and new (solar + radiative forcing for doubling CO2 values), we get:

Tnew^4/Told^4 = (239 + 3.7)/239
where Tnew = the temperature we want to determine, Told = 15°C or 288K
We get Tnew = 289.1K or a 1.1°C increase."

My problem with this is that they used the value of the radiation at the TOA and added the forcing of 3.7 W/m^2 to that number.

Instead one should use the value of the radiation at ground level and add the 3.7 to that. Which if done yields a value of 0.67K as climate sensitivity.

If you think about it there is no way the firs equation as the blog puts it can be correct since the radiation at the TOA will never increase to 240.7 W. It will always naturally balance the incoming radiation of the sun in order to keep the earth in a quasi thermal equilibrium. On the other hand the temperature of the surface will increase, that is the whole idea behind this so we can expect for the surface temperature to rise and thus the outgoing radiation at surface level to rise as well.

>> No.10410237

The equilibrium state at TOA can also be written as the radiative balance equation:

I = 0 = (S/4)*(1-a) – eoTs^4
where a is albedo, S is incoming solar radiation, Ts is surface temperature and e is the planet’s effective emissivity.

Note that you can derive the relationship between emissivity and temperature:

(S/4o)*(1-a)*Ts^(-4) = e
and then derive from that
de/dTs = -(S/o)*(1-a)*Ts^(-5)
Filling in for Ts = 289K, a = 0.304 and S = 1362 gives
de/dTs = -(1362/5.670373*10-8)*(1-0.304)*289^(-5) = -0.008269

Now my understanding of emissivity of a greybody is basically how much radiation gets blocked. So we currently have 396 W/m^2 at the surface and 237 at the TOA. This would give an emissivity of (237/396 = 0.5985).
Now doubling the CO2 in the atmosphere would increase this value of 396 again to 399.7 decreasing the emissivity to (237/399.7 = 0.59295)
Giving a change in emissivity of -0.00555.
This change would cause a change in temperature of -0.00555/-0.008269 = 0.67K

So no matter how you slice or dice, I get 0.67K.

It does not make sense to use the blackbody temperature or radiation of a 255K blackbody anywhere in my opinion.

If you do you are just calculating what would happen if you increase a certain emissive substance above the TOA that gives an energy increase of 3.7 W/m^2 at the level of the TOA.
It is nonsensical and it overestimates all climate models with 50% or more.

>> No.10410528

Come on /sci/ this is a genuine question.
Where did I go wrong?

>> No.10411197

>>10410236
hmmm it looks like he's jizzing but I'm not quite sure.

>> No.10411462

>>10410236
One should not use the radiation at ground level because the temperature at the surface is mainly due to convection of heat, not radiative transfer. The radiative balance at the top of the atmosphere determines how much heat there is in the atmosphere. The temperature at ground level is determined by how that heat moves around.