The crucial test of any scientific hypothesis is whether its predictions match real-world observations. If empirical evidence doesn’t confirm the predictions, the hypothesis is falsified. The scientific method then demands that the hypothesis be either tossed out, or modified to fit the evidence. This post illustrates just such an example of the scientific method at work.

The hypothesis in question is a model of the carbon cycle, which describes quantitatively the exchange of carbon between the earth’s land masses, atmosphere and oceans, proposed by physicist Ed Berry and described in a previous post. Berry argues that natural emissions of CO₂ since 1750 have increased as the world has warmed, contrary to the CO₂ global warming hypothesis, and that only 25% of the increase in atmospheric CO₂ after 1750 is due to humans.

One prediction of his model, not described in my earlier post, involves the atmospheric concentration of the radioactive carbon isotope ¹⁴C, produced by cosmic rays interacting with nitrogen in the upper atmosphere. It’s the isotope commonly used for radiocarbon dating. With a half-life of 5,730 years, ¹⁴C is absorbed by living but not dead biological matter, so the amount of ¹⁴C remaining in a dead animal or plant is a measure of the time elapsed since its death. Older fossils contain less ¹⁴C than more recent ones.

Berry’s prediction is of the recovery since 1970 of the ¹⁴C level in atmospheric CO₂, a level that became elevated by radioactive fallout from above-ground nuclear bomb testing in the 1950s and 1960s. The atmospheric concentration of ¹⁴C almost doubled following the tests and has since been slowly dropping – at the same time as concentrations of the stable carbon isotopes ¹²C and ¹³C, generated by fossil-fuel burning, have been steadily rising. Because the carbon in fossil fuels is millions of years old, all the ¹⁴C in fossil-fuel CO₂ has decayed away.

The recovery in ¹⁴C concentration predicted by Berry’s model is illustrated in the figure below, where the solid line purportedly shows the empirical data and the black dots indicate the model’s predicted values from 1970 onward. It appears that the model closely replicates the experimental observations which, if true, would verify the model.

However, as elucidated recently by physicist David Andrews, the prediction is flawed because the data depicted by the solid line in the figure are not the concentration of ¹⁴C, but rather its isotopic or abundance ratio relative to ¹²C. This ratio is most often expressed as the “delta value” Δ¹⁴C, calculated from the isotopic ratio R = ¹⁴C/¹²C as

Δ¹⁴C = 1000 x (R_sample/R_standard – 1), measured in parts per thousand.

The relationship between Δ¹⁴C and the ¹⁴C concentration is

¹⁴C conc = (total carbon conc) x R_standard x (Δ¹⁴C/1000 + 1).

Unfortunately, Berry has failed to distinguish between Δ¹⁴C and ¹⁴C concentration. As Andrews remarks, “as Δ¹⁴C [calculated from measured isotope ratios] approaches zero in 2020, this does not mean that ¹⁴C concentrations have nearly returned to 1955 values. It means that the isotope abundance ratio has nearly returned to its previous value. Therefore, since atmospheric ¹²CO₂ has increased by about 30% since 1955, the ¹⁴C concentration remains well above its pre-bomb test value.”

This can be seen clearly in the next figure, showing Andrews’ calculations of the atmospheric ¹⁴CO₂ concentration compared to the experimentally measured concentration of all CO₂ isotopes, in parts per million by volume (ppmv), over the last century. The behavior of the ¹⁴CO₂ concentration after 1970 is unquestionably different from that of Δ¹⁴C in the previous figure, the current concentration leveling off at close to 350 ppmv, about 40% higher than its 1955 pre-bomb spike value, rather than reverting to that value. In fact, the ¹⁴CO₂ concentration is currently increasing.

At first, it seems that the ¹⁴CO₂ concentration in the atmosphere should decrease with time as fossil-fuel CO₂ is added, since fossil fuels are devoid of ¹⁴C. The counterintuitive increase arises from the exchange of CO₂ between the atmosphere and oceans. Normally, there’s a balance between ¹⁴CO₂ absorbed from the atmosphere by cooler ocean water at the poles and ¹⁴CO₂ released into the atmosphere by warmer water at the equator. But the emission of ¹⁴C-deficient fossil-fuel CO₂ into the atmosphere perturbs this balance, with less ¹⁴CO₂ now being absorbed by the oceans than released. The net result is a buildup of ¹⁴CO₂ in the atmosphere.

As the figures above show, the actual ¹⁴C concentration data falsify Berry’s model, as well as other similar ones (see here and here). The models, therefore, must be modified in order to accurately describe the carbon cycle, if not discarded altogether.

The importance of hypothesis testing was aptly summed up by Nobel Prize winning physicist Richard Feynman (1918-88), who said in a lecture on the scientific method: