Of Emissions and CO2

Guest Post by Willis Eschenbach (still banned from X aka Twitter, see here)

The most excellent reef and ocean scientist Jennifer Marohasy put up a Facebook post recently on the lack of much effect on the atmosphere CO₂ levels from the 2020 emissions drop due to COVID. She says this shows human CO₂ emissions have very little effect on atmospheric CO₂ levels. However, I fear her graph is greatly misleading.

The problem is that she is showing the full range of two related but very different variables. Let me see if I can clear up the confusion.

To begin with, we need to change the CO₂ emissions to parts per million by volume (ppmv) of CO₂. To do that, we need to divide the gigatonnage (billions of tonnes) of CO₂ by 7.81 gigatonnes of CO₂ emissions per each 1 ppmv increase.

Next, we need to account for the fact that the earth is constantly absorbing and sequestering CO₂. I find there’s an excellent fit to be had by using the following procedure. The underlying assumption is that every year, a certain small percentage of “excess” airborne CO₂ is being sequestered by natural processes, with the rest of prior emissions remaining in the air. What is “excess CO₂“? Well, it is the amount in excess of some undetermined baseline, which we expect to be on the order of the historical value of about 285 ppmv.

So I set up an Excel spreadsheet to use Solver to search for the value of the unknown percentage which remains after the ongoing sequestration, as well as the value of the unknown baseline, that give the best fit to the actual airborne CO₂. You can download my spreadsheet here, it’s only 23 kbytes. I get the following values:

Unknown baseline: best fit = 286.8 ppmv

Given that the fitting process could have come up with a very wide range of values, that is a very good indication that atmospheric CO₂ levels are indeed related to human emissions.

Unknown percentage remaining after each year’s sequestration: best fit = 98.1%

And here is what those values give as a result. Remember, I’m calculating the best fit of human emissions to the actual airborne CO₂ values using just two fitted variables—the amount remaining after annual sequestration, and the pre-industrial baseline.

Now, on my planet at least, that’s a very good fit. At all points, it’s within 1.5 ppmv of observations, and the R² of the estimate and the observations is 0.997

A couple of comments on that. First, for a two-parameter fit between emissions and CO₂ level, with one of the fitted parameters coming out very near the expected value, that seems clear evidence that the rise in CO₂ levels is MAINLY a result of human emissions.

I say “mainly” because as you note, the observed CO₂ level goes both above and below the estimate. I assume this is because of changes in both emissions and sequestration rates.

Now, as you can see, Jennifer is right that the estimate for the time of the dip due to COVID is slightly below the actual values. How much? The largest difference is the year after COVID, when observations are a whopping 0.7 ppmv above the value estimated from the emissions … be still my beating heart.

However, the same is true during a number of periods in the record.

Why doesn’t the COVID drop make much difference? Four reasons.

First, the e-folding time “tau” for the slow decay of a pulse of CO₂ is ~ 50 years, so any year is greatly affected by the previous years.

Second, the drop in the emissions was small, only about 5%. Such small changes occur throughout the emissions record, and are smoothed over by the natural process of sequestration.

Third, the emissions dip was short, only one year long, with the next year returning to normal amounts.

Fourth, there are other factors at play, changes in natural emissions and sequestrations.

In closing, folks may ask about “tau”, the time constant being only 50 years when the scientific solons say excess CO₂ remains in the air for hundreds and hundreds of years. So are they correct? Well … yes …and no. Excess CO₂ remains, just not very much. Given the annual decay rate calculated above, .981, here’s how that plays out for the excess carbon.

(Yes, I know that’s different from what the standard “Bern Model” of CO₂ sez … see my post on that model, including the previous post linked therein.)

My best wishes to Jennifer Marohasy despite her claims in this one case—she’s a most valuable and insightful scientist.

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Me, I’m not only in the very remote Solomon Islands near the Equator, north of Australia, where I worked for eight most wonderful years. I’m in the even more remote Western Province of the Solos, chewing betel nut with lime and leaf, and having a great time. I also, for the first time in three weeks, have reasonable Internet. Why?

My friend with whom I’m staying has Starlink. So for all you Elon haters out there, he’s done a huge service for mankind.

Best of the South Pacific to all, going scuba diving tomorrow, back to the US next week.

w.

AS IS MY CUSTOM, I ask that when you comment you quote the EXACT WORDS you are discussing. It avoids endless misunderstandings.