
From Watts Up With That?
Guest Post by Willis Eschenbach
Well, every time I go to look at the climate models, I come away more confused. And today is no exception. I decided to take a look at the relationship between the change in forcing (downwelling radiation) and the change in temperature.
Forcing datasets are somewhat hard to come by, but the Computer Model Intercomparison Project 5 (CMIP5) forcings for the GISS-E2 model areย here. The sum of all the forcings is shown in Figure 1, along with the CEEMD smooth of the data.

The big dips in the forcings are the theoretical changes in forcing due to volcanic eruptions.
Next, here is the average surface temperature output of six runs of the GISS E2 model using those forcings, available from the marvelous KNMI websiteย here.

Already, although the model does a decent job hindcasting the past global surface temperature, we have problems. The difficulty is, back here in the real world, the volcanoes have not had that large an effect on the surface temperature.

Why the exaggeration of the volcano effects? Me, I say it is because as the eruptions cool the surface, the climate responds by the daily tropical cumulus field forming later in the day, and the tropical thunderstorms also forming later or not at all. This warms the surface, counteracting the effects of the eruptions. However, YMMV โฆ
But none of that is what I started out to look at. I wanted to see if the CMIP5 modeled temperatures slavishly follow the forcings. Thirteen years ago, I showed that the temperature output of the CCSM3 climate model could be very closely emulated by a simple one-line formula, viz:
T(n+1) = T(n) + ฮป โF(n+1) * (1- exp( -1 / ฯ )) + ฮT(n) * exp( -1 / ฯ )
See the linked post for the description of what the formula means.
So I used that formula, to see how well I could emulate the temperature output using nothing but the forcing applied to the model. Hereโs the result:

So the situation is unchanged. An R^2 of 0.97 says the emulation is doing a most excellent job. In passing, itโs interesting that the volcanic action in the model averages is a bit larger than in the calculations from the forcing, just as happened with the model average compared to the real world.
In any case, to recap the bidding: The GISS-E2 climate model has 440,000+ lines of code. It has over two million gridcells representing the world, and it takes a whole day to do just one model run on a parallel-processing computer with 88 processors.
And after all that, it merely spits out a lagged and resized version of the input forcing.
Hmmm โฆ
Now, in the formula used to emulate the model output, the variable โlambdaโ (ฮป) is the change in temperature resulting (in modelworld) from a 1 watt per square meter (W/m2) increase in forcing. This is a measure of the โtransient climate responseโ (TCR), how the temperature responds in the short term to a change in forcing. Itโs usually expressed as the amount of change from a doubling of CO2 (2xCO2).
And the doubling of CO2 is said by the IPCC to increase forcing by 3.7 W/m2. This would make the TCR have a value of 0.41 ยฐC/Wm2 * 3.7 W/m2 per 2xCO2 = 1.5ยฐC / 2xCO2.
Now, I wanted to calculate the equilibrium climate sensitivity (ECS) from that TCR value. However, when I went to research that โฆ let me say I was shocked. Thereโs a good discussion of the issues in an article with the long title โEmergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 modelsโ.
What was shocking? Well, several things. First, according to the article, every different model uses a different value for the increase in forcing from a doubling of CO2. Remember above where I noted that the IPCC says forcing increases by 3.7 W/m2 from a doubling of CO2 (2xCO2)? Hereโs what the models say:

Zowie! The models are all over the place, with values for 2xCO2 forcing ranging from 2.6 to almost 4 W/m2. And the range of the uncertainty on the median value (width of the notch in the sides of the box) doesnโt even include the canonical IPCC value of 3.7 W/m2 โฆ how these jokers have the nerve to call climate science โsettledโ is a mystery. Not only do we not have agreement on the values of the ECS and the TCR, but we donโt even agree on how much the forcing changes when CO2 doubles! Who knew? I remember Steve McIntyre asking for an engineering-level derivation of the 3.7 W/m2 figure for 2xCO2, but I had no idea that the models disagreed so much on this central figure.
Then there was another surprise. It turns out that the ECS is not some fixed multiple of the TCR. Instead, the ECS of small values of TCR is a smaller multiple of the TCR than for large values of the TCR. Figure 5 shows that relationship.

This relationship would mean that the GISS E2 model would have an ECS on the order of 2ยฐC / 2xCO2 โฆ but of course, thatโs only if the 2xCO2 forcing is 3.7 W/m2, when in fact we have values from 2.6 to almost 4 W/m2.
To compound the problem, as you can see, the different models give widely different values for equilibrium climate sensitivity (ECS). They range from 1.8ยฐC to 5.7ยฐC for a doubling of CO2, more than a three-to-one variation.
Hereโs the final impossibility. Despite the different models having wildly different equilibrium climate sensitivities and different transient climate responses and different forcing changes from doubling CO2 โฆ somehow they all do a pretty good job of hindcasting the actual temperature record.
And if the models were actually โphysics-basedโ as every modeler claims, this would not be possible. I call this โDr. Kiehlโs Paradoxโ, since he noted it first, and I discuss this impossible result here.
Gotta love that settled science โฆ
Look, the ECS is a central, vitally important number in mainstream climate science. The forcing change from doubling CO2 is another central, vitally important number in mainstream climate science. Theyโve been studying the subject for a half-century, and both numbers still have an enormous uncertainty range.
And worse than that, the uncertainty of the ECS has gotten wider with more study, not narrower โฆ

In any other science, a half-century spent studying such a central number would result in reduced uncertainty โฆ but in climate science, itโs going the other way.
To me, this is evidence that the basic paradigm of climate science is wrong. This basic paradigm is the claim that the temperature change is a linear function of the forcing change. I donโt think thatโs true. I think thatโs simplistic nonsense. I think that the climate actively responds to changing conditions and that there are a host of emergent climate phenomena that oppose any warming from any source, including changes in forcing.
Anyhow, thatโs the story of my latest wandering through the models โฆ I ended up knowing less than when I started.
Here in the US, itโs Motherโs Day, so my gorgeous ex-fiancee and I are going for a bike ride and then out for dinner โฆ whatโs not to like?
Best to all, and remember, when you comment please quote the exact words youโre discussing. It makes everything much clearer.
w.

































You must be logged in to post a comment.