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,


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.

via Watts Up With That?

May 30, 2021