Restoring The Equilibrium

Guest Post by Willis Eschenbach

In this post, I will both provide additional data for, and also correct an error and a claim in, my post entitled Where Is The Top Of The Atmosphere. Let me start by recapping the main point, which is the theory of why increasing CO2 must perforce lead to surface warming.

• The amount of atmospheric CO2 and other greenhouse gases (methane, CFCs, etc.) is increasing.

• This absorbs more upwelling longwave radiation, which leads to unbalanced radiation at the top of the atmosphere (TOA). This is the TOA balance between incoming sunlight (after some of the sunlight is reflected back to space) and outgoing longwave radiation (OLR) from the surface and the atmosphere.

• In order to restore the balance so that incoming solar radiation equals outgoing longwave radiation (OLR), the surface perforce must, has to, is required to warm up until there’s enough additional upwelling longwave to restore the balance.

In my last post, I showed what I believed was the relationship between the CERES surface temperature and the OLR. Here’s that graphic:

Figure 1. Scatterplot, monthly top-of-atmosphere outgoing longwave radiation (TOA LW) versus surface temperature. Seasonal variations have been removed from both datasets

Now, I mentioned above that I wanted to correct an error and a claim in my previous post. The claim was that although the change in OLR at the troposphere from a doubling of CO2 was shown by MODTRAN to be about 3.7 W/m2, the change at the top of the atmosphere (TOA) was much smaller.

However, since then I’ve found a paper entitled “Radiative Forcing of Quadrupling CO2” that says:

Note that the forcing and adjustment in this paper are analyzed using the radiation fluxes at the TOA instead of the tropopause. However, it can be shown that after the stratosphere equilibrates, the stratosphere-adjusted forcing is identical at the two levels.

Unfortunately, they neglect to reference just how or where “it can be shown”. And I see no reason to assume that it is true—why should the upwelling longwave radiation be the same, both somewhere in the upper middle of the atmosphere and also at the top of the atmosphere? That would assume that the stratosphere makes no contribution either way to the OLR … ?? Seems doubtful.

But to take a very conservative position, by which I mean one that increases calculated climate sensitivity, I’ll assume for the sake of this discussion that they are correct and that the top of atmosphere (TOA) OLR is reduced by 3.7 W/m2 from a doubling of CO2, the same as at the tropopause.

So that was the claim … what about the error?

Well, my error was that I used the actual TOA OLR figures to calculate the relationship between surface temperature and OLR. But assuming that the prevailing theory is correct, those OLR values have already been reduced by the effect of the greenhouse gases. So to get the true relationship between temperature and OLR, we need to add back in the amount of the reduction in OLR due to the greenhouse gases.

In order to get a more accurate answer from a longer period of record, this time I’ve used the Berkeley Earth surface temperature data and the NOAA OLR data. This gives us about twice as much data as we have from the CERES satellite observations. Figure 2 shows that result.

Figure 2. Scatterplot, NOAA OLR adjusted for well-mixed greenhouse gases (WMGHG) versus Berkeley Earth Surface temperature. Seasonal variations have been removed from both datasets

As expected, adjusting the OLR data to include the effect of the WMGHGs has increased the trend of OLR vs surface temperature.

As a check on the Berkeley/NOAA data, I took just the part of that data that overlaps the CERES data and I plotted up both of them. As you can see, the agreement between the two is better than what is generally found between different climate datasets.

Figure 3. Comparison of Berkeley/NOAA values and CERES values. Seasonal variations have been removed from both datasets

So … according to Figure 2, in order to offset a doubling of CO2, which presumably decreases the TOA OLR by 3.7 W/m2, the temperature has to rise by 3.7 W/m2 divided by 4.2 W/m2 per °C, which is 0.9 °C per doubling of CO2.

Is this the long-term “equilibrium climate sensitivity” and not the short-term “transient climate response”? I say yes because it is independent of how long it takes for the temperature to rise. Whether the temperature goes up by 0.9°C in a month, a year, or a decade, the data above shows that it will increase the OLR by 3.7 W/m2.

And that’s all the news I have for you today.

My best regards to everyone,

AS ALWAYS: I can defend and explain my words and I am happy to do so. I cannot defend or explain your interpretation of my words. So when you comment, please QUOTE THE EXACT WORDS that you are discussing. This avoids endless misunderstandings.

MATH: As discussed in my previous post, Where Is The Top Of The Atmosphere, I’ve used Deming regression instead of Ordinary Least Squares regression because of the presence of significant uncertainty in the x-axis of the graphs.

DATA:

via Watts Up With That?

February 12, 2022