Guest Post by Willis Eschenbach
There’s a new open access paper in Nature Magazine, entitled “A tighter constraint on Earth-system sensitivity from long-term temperature and carbon-cycle observations“, by Wong et al., hereinafter Wong2021. Gavin Schmidt, GISS programmer to the stars, lauds it on Twitter. The Abstract says:
The long-term temperature response to a given change in CO2 forcing, or Earth-system sensitivity (ESS), is a key parameter quantifying our understanding about the relationship between changes in Earth’s radiative forcing and the resulting long-term Earth-system response. Current ESS estimates are subject to sizable uncertainties. Long-term carbon cycle models can provide a useful avenue to constrain ESS, but previous efforts either use rather informal statistical approaches or focus on discrete paleoevents. Here, we improve on previous ESS estimates by using a Bayesian approach to fuse deep-time CO2 and temperature data over the last 420 Myrs with a long-term carbon cycle model. Our median ESS estimate of 3.4 °C (2.6-4.7 °C; 5-95% range) shows a narrower range than previous assessments. We show that weaker chemical weathering relative to the a priori model configuration via reduced weatherable land area yields better agreement with temperature records during the Cretaceous. Research into improving the understanding about these weathering mechanisms hence provides potentially powerful avenues to further constrain this fundamental Earth-system property.
So I got to thinking about their paper. The first thing that made my urban legend detector start ringing was a statement in the Abstract above that you might have gone right past, viz:
We show that weaker chemical weathering relative to the a priori model configuration via reduced weatherable land area yields better agreement with temperature records during the Cretaceous.
Translated from Scientese into English, one possible meaning of this is:
We adjusted the climate model’s tunable parameters so the output agrees better with our theory that CO2 controls the climate.
Not an auspicious start …
All of this is based around a computer model called GEOCARBSULF, which is a long-term (millions of years) carbon and sulfur cycle model used to estimate past CO2 levels. So I got to wondering … just how many tunable parameters are there in the GEOCARBSULF model?
But before I discuss the number of GEOCARBSULF tunable parameters, why is the number of tunable parameters important? There’s a famous story about Freeman Dyson and Enrico Fermi that explains this issue well. Here it is in Dyson’s own words:
We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.
When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our newborn baby son, now fifty years old.
Then he delivered his verdict in a quiet, even voice. “There are two ways of doing calculations in theoretical physics”, he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.”
I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a self-consistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.”
In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students.
So … how many tunable parameters does the GEOCARBSULF model have? From the Wong2021 paper …
There are 68 GEOCARB model parameters, of which 56 are constants and 12 are time series parameters. The constant parameters have well-defined prior distributions from previous work, and the time series parameters have central estimates and independent uncertainties defined for each time point15.
Hmmm, sez I … 68 parameters … not a good sign.
So to see if “the constant parameters have well-defined prior distributions from previous work” as claimed above, I went to look at reference 15 listed in the above quote. It’s called “ERROR ANALYSIS OF CO2 AND O2 ESTIMATES FROM THE LONG-TERM GEOCHEMICAL MODEL GEOCARBSULF“. There, the Abstract concludes by saying:
The model-proxy mismatch for the late Mesozoic can be eliminated with a change in GYM within its plausible range, but no change within plausible ranges can resolve the early Cenozoic mismatch. Either the true value for one or more input parameters during this interval is outside our sampled range, or the model is missing one or more key processes.
Hmmm, sez I … doesn’t sound like that backs up the Wong2021 claim that “the constant parameters have well-defined prior distributions from previous work, and the time series parameters have central estimates and independent uncertainties defined for each time point15.”
So, setting aside the fact that the model has enough tunable parameters to make an elephant put on a tutu and do the Swan Lake ballet, I looked at their results. First, here is their graph of their results.

Figure 1. This is Figure 4 in Wong2021. ORIGINAL CAPTION: “Model hindcast, using both CO2 and temperature data, for precalibration and a %outbound threshold of 30% (shaded regions). The gray-shaded regions show the data compilations for CO2 (ref. 26) and temperature12. The lightest colored shaded regions denote the 95% probability range from the precalibrated ensemble, the medium shading denotes the 90% probability range, the darkest shading denotes the 50% probability range, and the solid-colored lines show the ensemble medians. To depict the marginal value of each data set, the dashed lines depict the 95% probability range from the precalibrated ensemble, when only temperature data is used (a) and when only CO2 data is used (b).”
(A short digression. Looking at Figure 1, I considered the fact that dinosaurs lived on the planet from about 245 million years ago to 66 million years ago. Mammals first appeared 178 million years ago. During that time, according to Figure 1, temperatures were between 6°C and 12°C warmer than at present. And folks hyperventilate about a further half of a degree °C warming being an “emergency” that will ruin our lives and drive extinctions through the roof? … but I digress.)
Now, their claim is that their results gave tighter constraints on the sensitivity of the planetary temperature (lower panel) to atmospheric CO2 levels (upper panel). Squinting at that graphic, I said “Hmmm …”. Didn’t look too likely.
So I did what I usually do when the authors are not conscientious enough to archive their results. I digitized the Wong 2021 temperature and CO2 data, and I graphed it up. Figure 2 shows that result.

Figure 2. Scatterplot, paleo temperatures versus the log (base 2) of paleo CO2 levels from Wong2021
Now, if CO2 levels actually were the control knob regulating the global temperature, we’d see all of the points falling on a nice straight line … but we don’t, far from it. There’s no statistically significant relationship between the temperature and the CO2 levels reported by Wong et al.
So I gotta say, the data reported in the Wong2021 paper is a long, long way from establishing the claims made in their Abstract. In fact, even after they’ve carefully adjusted the tunable parameters of the GEOCARBSULF model in their favor, their results support the null hypothesis, which is that CO2 is not the global temperature control knob.

My best to everyone, dinosaurs and mammals alike,
w.
PLEASE: When you comment, quote the exact words you are discussing. I can and am happy to defend what I wrote. But I can’t defend your interpretation of what I wrote.
Nice report, not too hard for Sunday morning.
Does anybody know how the Nature Magazine decides what papers will be “open access”?
Wong 2021–what science looks like when it is published in The Onion.
Just plain Wong ?
😉
Not even Wong
So is Wong white or wong ?
I’m confused by Confucius.
He must’ve been on the wong side of the woad.
Reminds me of what I just read in “Simplified Climate Modelling – Part 1.”
Same here — prb’ly recent orders from the marxist science-bosses to now try the “carbon-cycle observations” angle.
One more addition is needed for the Onion:
The CO2 control knob only goes to “10”… as we have all learned from Spinal Tap, the maximum should be “11”.
+1 for the Spinal Tap reference
Looks like Willis carefully adapted the Men vs. Women control panels without accreditation. Good job, Willis, you avoided going to woke jail!
I thank you for your informed, ongoing efforts in these matters, Mr. Eschenbach.
Seconded.
Loved the Fermi story. Showing what REAL science … EXPERIENCED science looks and sounds like.
Me, too. I have such great respect for Freeman Dyson, and it’s striking learning about how such a brilliant man was dressed down at one time by an even more brilliant man. Or maybe not more brilliant, but more experienced, is the way it should be put.
Yes, love the story.
Two Giants of Science.
Ditto
Great job, WE! One additional observation about dinosaurs and mammals, drawn from your figure 1(a) gray ‘Foster data’. It is shown experimentally that plant photosynthesis starts to fail at 150ppm, and fails utterly below 100ppm. IF Foster’s data are to be believed, than all life on earth failed from starvation (plants eating CO2 and animals eating plants) before there ever were dinosaurs and mammals. Oopsy.
Figure 2 is fairly conclusive. A very weak correlation between CO2 and temperature, even after stroking.
Not with CO2 on a log scale and T on a linear one. In fact it’s a negative correlation
Hahaha ha … you said “stroking”. I suspect a LOT of stoking goes on with these climate scientists
You said: “There’s no statistically significant relationship between the temperature and the CO2 levels reported by Wong et al.”
It looks to me that there is a good relationship [straight line] up to log CO2 = 10, and no correlation thereafter. So, at that point something must be regulating temperature apart from CO2. Perhaps tropical thunderstorms…
Possible … or more possibly, it’s just a chance correlation …
w.
Hi Willis, a friend has written a significant piece on the issue of the greenhouse effect energy balance and sent me a copy for comments before he submits.
But reading through it i feel that the subject matter here is really what you have been writing here on wuwt.
Would you be willing to review the paper? It’s long.
If so may I have an email address where I can send it? My email is chaamjamal@yahoo.com
You two share a very similar research interest.
Cheers.
Done.
w.
Apply the confidence intervals from Figure 1 to both variables in Figure 2, and things get a bit hazy. Some sort of relationship might be salvaged over the fact that confidence intervals are smaller at lower temperature, but the lower temperatures are all recent observations, so adding the rest of Earth’s history didn’t accomplish anything.
The uncertainty monster is right there in their Supp Figure 3.
Cherry-picking I see
Or perhaps below about 900 ppmv the CO2 level in the atmosphere is driven by the temperature of the oceans.
It may be another chicken vs. egg
Does Co2 cause temperature changes or does temperature changes cause Co2 production?
On Gavin’s linked Twitter thread the takeaway seems to be that the CO2 levels are dropping over these timescales.
Not exactly the intended message, methinks.
The Quaternary’s Ice Age would seem like a big warning flag. CO2 is not the problem, but it may be the answer.
Some years ago I sat in a geology department seminar given by a fellow whose research was trying to close the Earth surface volatiles budgets. All sorts of volatiles, CO2, Sulfur, Chlorine, etc. His take was that the subduction zones take a great deal of volatiles back into the mantle, and that the big return mechanisms, like volcanoes, are not sufficient to keep a steady surface inventory — unless, as he speculated, there are many distributed return flows that we simple don’t know about.
Suppose for a minute that the volatiles budget for CO2 is not in balance and we are continually burying CO2 in the mantle. It would explain some of the paleo CO2 concentration and temperature trends. Scary thought, long term. Longer term than I have anyway.
Good work, Willis, and I especially appreciate your digress to talk about dinosaurs, etc. As a geologist who has walked many miles through the preserved strata of the Cretaceous, and marveled at the abundance and scale of the life preserved as fossilized bones and tree trunks, I am always on the verge of a hissy fit when someone messes with the Cretaceous. Remember the Lone Ranger? “Return with me now to those thrilling days of yesteryear…”.
It is clear that all the carbon in coal came from CO2 in the atmosphere. Did the carbon in limestone and dolomite also come from CO2 in the atmosphere or did it come directly from carbonaceous ions in the ocean?
I don’t know the exact numbers … but large amounts of CO2 is carried down the rivers to the oceans via organic matter (leaves etc.). Calcium weathering out of the rocks combined with CO2 creates CaCO3 i.e. Calcium Carbonate i.e. Limestone.
keywords ‘limestone rock fossils’ revealed this “Limestone is a sedimentary rock made almost entirely of fossils”
So this model only has 68 parameters. That’s nothing. My model has 3793 parameters and the latest model run has the oceans boiling by next Thursday. We’re all doomed, I tell you.
And Bill have you named your model “The Lemon”?
(If you haven’t yet registered this name, I suggest you get an application in quickly, because as Wills demonstrates here, there are many, many other candidates for this name)
My model is called the Climate Reproducing Autonomous Program.
You mean CRAP?!!👍
There appear to be quite a few climate scientists spending lots of *ahem* Autonomous time … with themselves. Is that redundant?
Already superseded by my Biggest Underlying Latitudinal Longitudinal Climate Reproducing Program which really puts the squeeze on them all. Particularly the grants program.
Ha ha, good take down Willis, this is why I stopped reading 100% modeling based papers long ago, they hurt my brain with their tuned baloney,
I hope are you are feeling well despite reading it.
Speaking of models, the ‘usual suspects’ at LLNL have just published a paper
[ https://scitechdaily.com/satellites-may-have-underestimated-global-warming-in-the-lower-atmosphere-over-the-last-40-years/ ] where they are basically claiming that they can judge the quality of data sets by how well a data set agrees with their models. On that basis, they further claim that the temperature of the lower troposphere has been underestimated for the last 40 years because the warmer data set agrees better with the model.
A couple of observations: They are claiming that models are more trustworthy than actual observations, and they may have provided a clue as to why models have a history of running warm.
Took a look. For sure, the usual suspects. TY.
One thing this new paper did NOT mention, but UAH actually did in developing their lower troposphere estimates, was compare their satellite estimates to many actual radiosonde temperatures at various altitudes up continental North America from Southern Mexico all the way to Alaska. The large ‘latitudinal swath’ fit is excellent when the radiosondes are averaged to reproduce the satellite lower troposphere. The Christy and Spencer paper can be found in some footnote to the penultimate climate chapter of The Arts of Truth. As far as I can tell, Mears and RAH did no such validation, and a couple of years back adjusted their results upward based on a spurius orbital drift argument that Spencer corrected in about UAH v3. Now Mears says maybe not enough?!?
I believe Mears and Co. did do a comparison with radiosonde data about a decade ago and found they were running just a little hot. They then ignored this finding when they adjusted their results to be even hotter.
That is along the same crap modeling science claims of Micky Mann that if a Climate model doesn’t reproduce some internal variability, like the AMO, then it doesn’t exist.
Willis and/or WUWT editor,
My kudos to you on the most-excellent choice of photo that appears at the end of the above article. That single photo is worth a
thousandmillion words about all “scientific” attempts to model climate toward the purpose of claiming that CO2 is the dominant driver of climate change. Of course, it isn’t, as objective scientific data clearly shows.Of course, Willis presents a good-read, science-based, great article per his established reputation for laser focused, cut-to-the-case, often-witty criticisms of “junk science” publications. So thanks for that too.
Great photo, but I am worried about the on/off switch !
THAT switch is only for God’s use.
Thanks, Willis!
Just the thing for a Sunday morning after some huevos rancheros! Walt Disney is smiling in his grave at the reference to elephants in tutus dancing to Swan Lake!
It is kind of you to complete the work that Wong et al. failed to complete in their study! Proposing an hypothesis is all good and well, but a REAL scientist would have tested it by trying to disprove it! Instead these jamokes did everything in their power to prove their thesis and avoided any attempts at the null hypothesis! That makes them true climastrologists, not scientists!
They’re just trying to produce evidence that past temps and CO2 levels were more in line modern ones. That’s not gonna happen with the wizards of WUWT blocking their path forward!
“Instead these jamokes did everything in their power to prove their thesis and avoided any attempts at the null hypothesis! That makes them true climastrologists, not scientists!”
Our guy (Willis) looks at it and immediately sees the flaws in the claims, but Nature Magazine apparently can’t do the same.
Who is running these “science” organizations? It’s got to be politicians masquerading as scientists. They know the ways of politics, not the ways of science.
Happily for us, Willis *does* know the ways of science.
Thanks, Willis.
Regards,
Bob
“tuneable parameters”
Not only are tuneable parameters problematic, they become downright scary when you use a tuning feedback method like gradient descent optimization looking to reduce a global error.
Gradient descent optimization across a large number of parameters is essentially how AI works and allows a very large complex network to exhibit extraordinary ability to match or near match very different input series.
I’d be curious to know what process they use to tune these parameters and if its based on any kind of feedback changes using error derivatives and multiple small step change runs I’d suggest they are doing a form AI back propagation.
Note their graph is about right over the last 200 Myr. 3000 ppm CO2 reduction results in 3 degrees cooling. Quite a long ways from their current prediction for increasing CO2.
Shhhh. They think the credulous only notice increases.
Thanks for your work Willis, again. Crowd review beats peer review once more.
Willis, if you don’t stop revealing the man behind the curtain after every act, the climate calamity vaudeville audiences will soon go elsewhere for their fright night thrills.
Have some consideration for the ongoing financial wellbeing of the climate showbiz personalities, please.
The “god knob” presumes an invariant nature outside of a limited frame of reference, thus statistics, thus inference, thus plausible, thus modern science, infilled with brown matter to smooth the missing links.
Lead Author: Ben Santer, a known fraud. The study just goes downhill from there. “Who you gonna believe, my model or your lie’n eyes.” [Clyde’s referenced study.]
If anybody ought to be sued over Climate Change Fraud, it should be Ben Santer. He is the one who lied and said there was evidence that humans are causing the Earth’s climate to change, and the Western World is currently planning on wasting Trillions of Dollars on the Climate Change Fraud based soley on Ben Santer’s say so.
The UN IPCC scientists come out with their report and the report says they cannot find a CO2 human signal in the Earth’s climate.
Then, Ben Santer, who is writing the summary of the IPCC report, which is what most people and politicians read, inserted a statement into the summary that said the human signal was in evidence, based on nothing.
Santer said the exact opposite of what the report said, and Santer’s version is the one the whole world is working on now.
Santer is responsible for this lie, and the waste it has caused, and will cause, and he should have to pay damages.
How do they know whether they’re measuring cause or effect?
Or other confounding factors not considered.
I love it!!! I have to make a stand-alone comment just to acknowledge that one!
It was kind of a take on my friend Matt Briggs, whose web site says he’s “Statistician to the Stars” … except in his case, he actually is.
w.
I note the likes of Griff et al are notably AWOL when Willis discusses real science.
Griff is only interested in arctic sea ice and windmills.
“yields better agreement with temperature records during the Cretaceous.”
Those Cretaceous weather observers, studiously making temperature records, must have been better than our grandparents making temperature records from the 1910-1940’s that have to be frequently re-adjusted.
If they are considering the entirety of time since the Cambrian, hasn’t there been a goodly amount of rearrangement of continents and oceans by way of Plate Tectonics?
Wouldn’t that have a big effect on weather trends and in turn climate?
This has come up in observations of change in the Moon’s orbit and the length of the day on Earth resulting from Earth-Moon tidal interaction. There is fossil evidence of a much shorter day and month (orbit of the Moon) based coral growth rings or some such evidence, but if you extrapolated the trend, you would get an age of the Earth-Moon system in the hundred of million years, not the 4+ billion years that radioactive isotopes indicate.
The explanation is that tidal drag depends on the arrangement of oceans, and for much of geologic history, the land is pile up into one big supercontinent before it splits off, rearranges and the reforms a supercontinent? And we are in one of the split-off and rearranging epochs?
Dunno about the Moon, but do know about plate tectonics. Wrote up Wegener’s continental drift theory as a major example in the Recognition chapter of The Arts of Truth. No less a prominent geologist than Princeton’s Dyeffies presented compelling arguments in his last book that the present ice ages started about 2mya with the closure of what is now the Panama Isthmus, drastically changing ocean circulation patterns. After the closure, Pacific and Atlantic could only ‘communicate’ via the very cold Arctic ocean or the very cold Drake Passage.
They use a time series parameter that estimates sea floor spreading rates (tectonics), as Supp Figure 1 k. And also subducting carbonate bearing plates into the mantle as CO2 volcanic outgassing rates, as Supp Fig 1 L. Apparently CO2 outgassing from carbonate bearing plates did NOT begin subducting/outgassing until just 150 Myr ago and has been a ramp function ever since. Who knew??
These are all part of the a priori tuning that was done. total junk.
The model accounts for land mass fractions as a time series parameter. You can see them in their Supplement. They also write about the problems in the Discussion,:
“However, several of the time series parameters’ distributions change substantially. Specifically, we find that changes were required in the time series for the land area relative to present (fA), global river runoff relative to present (fD), the response of temperature change on river runoff (RT), and the fraction of land area that undergoes chemical weathering relative to present (fAW/fA).”
Talking of temperature control knobs.
Check out the the band of thunderstorms within the ITCZ over the Atlantic.They appear to have become so powerful that their having a impact on the jet stream up at 250 pHa.This suggests to me they must be pumping one hell of alot of heat out of the ocean. As l have suggested before in a other comment it is looking like when the jet stream goes into LIA mode it makes the mid Atlantic ITCZ thunderstorms work harder. Which increases the amount of heat been taken out of the ocean.
What is pHa? Did you mean hPa (hectoPascals – the standard atmosphere (atm) is a unit of pressure defined as 101,325 Pa (1,013.25 hPa))? (250 hPa corresponds to an altitude a bit over 10 km.)