by Pat Frank

Multiply not the entities — William of Ockham. paraphrased

This essay starts with a thank-you. Willis Eschenbach has very often been a source of insight or inspiration here at WUWT. Back on 23 February 2024, Willis posted “A Curious Paleo Puzzle,” in which he drew attention to the work of James Rae, et al., (2021) Atmospheric CO₂ over the Past 66 Million Years from Marine Archives.” Rae, et al., had compiled benthic d¹¹B and alkenone proxies to produce 66-million-year proxy record of Paleocene to Holocene atmospheric CO₂ (ppm). Willis’ introduction set the present study in motion. So — thank-you, Willis.

Rae, et al., (2021) also included a 66-million-year record of d¹⁸O proxy global average sea surface temperature (SST), which Jim Hansen and colleagues had published in 2013. The usual CO₂ –> T interpretation was advanced in both papers.

The solubility of CO₂ is temperature-dependent. The existence of both a paleo-SST record and a paleo-CO₂ record brought to mind the possibly that the rise and fall of SST was natural variation and atmospheric CO₂ just followed — the Null Hypothesis.

The Null Hypothesis

The idea is that some independent natural process drove SST. The partial pressure of atmospheric CO₂, P(CO₂), followed SST-driven solubility. The Null Hypothesis proposes a minimalist explanation for Cenozoic SST and P(CO₂). It requires no additional entity; namely the radiative forcing of CO₂. A preliminary analysis looked favorable.

The idea is worked out in Cenozoic Carbon Dioxide: the 66 Ma Solution, just published and open access in MDPI Geosciences. The state of the field requires attention to the basics of the typical criticism. Two anonymous reviewers asked for extensive revisions and clarifications. The highly qualified academic editors evaluated the revised manuscript. Submission-to-acceptance took just over a month. The whole process was completely professional. MDPI Geosciences was the second submission journal. The first submission journal held the manuscript for 3.5 months, but could not find a manuscript editor. So, that submission was stillborn.

This post sketches the results; details in the paper.

SST, CO₂, and Henry’s Law

Flood Basalt Volcanism: The first step was to find whether the oceans can warm without recourse to CO₂ forcing. Meet the North Atlantic Igneous Province (NAIP). The NAIP, Figure 1, contains the crustal remains of the flood basalts that erupted 56 to 52 million years before the present (MYr BP), when Greenland split off from the Eurasian land mass.

The eruptions of the NAIP produced about 6.6 million km³ of basaltic magma over a period of 3-4 million years. Typically, the main phase of flood basaltic eruptions occurred over about half the time of the full duration.

Liquid basaltic magma emerges at about 1620 K and crystallizes at 1470 K. Taking into account the heat capacity and the heat of fusion of basalt, each 1 million km³ of magma releases enough heat to warm the entire 1.338 billion km³ of the global ocean by about 0.97 C. If the thermal plume rises to occupy just the top 1 km of the world ocean, the temperature change is about 3.6 C. These numbers assume the ocean captures all the released heat, which may not be the case.

Nevertheless, the thermal impact of the 6.6 million km³ of NAIP basaltic magma alone can account for the entire increase in SST entering the post-Cretaceous Paleocene-Eocene Thermal Maximum (PETM) (discussed below).  Although the NAIP eruption was accompanied by large emissions of CO₂ and other gases, there is no need to invoke CO₂ forcing to account for the increased SST of the PETM.

Figure 1: Map of the North Atlantic Igneous Province (from Horni, et al., (2017))

The Miocene Climate Optimum is associated with the Columbia River flood volcanism. Evidence of flood basalt volcanism occurs throughout the Phanerozoic. Correlation of climate and submarine flood basalt magmatism across deep time is outside the scope of the paper, but would seem to be a fruitful area of research.

Henry’s Law: The next order of business was to derive the relation between SST and the atmospheric partial pressure of CO₂, P(CO₂), across the 66 million years of the Cenozoic. Figure 2 illustrates Henry’s Law, which describes the partition of CO₂, as a soluble gas, between the gas phase and the solution phase.

Typically, most dissolved CO₂ is the neutral molecule. However, a small fraction of the dissolved CO₂ reacts with water to produce carbonic acid (H₂CO₃). At the alkaline pH of the upper ocean, H₂CO₃ is converted into bicarbonate (HCO₃⁻) and carbonate (CO₃²⁻). Removal of H₂CO₃ into carbonate means additional CO₂ converts into carbonic acid (Le Chatelier).

Current oceanic ratios are: CO₂, 0.5%; HCO₃⁻,  87.4%, and; CO₃²⁻, 12.1%. In Figure 2, right, the thin aqua vertical bar shows the anticipated impact of so-called “ocean acidification” from doubled CO₂: slightly less carbonate, slightly more bicarbonate, and a hair more neutral CO₂. The change is pH 8.1 to pH 7.9. The surface waters remain alkaline. They will not have been acidificationized.

Figure 2: Left, Henry’s Law governs the equilibration of CO₂ between gas and solution phases (paired vertical blue arrows across the aqua-white interface). Right, the distribution of CO₂ and carbonate with pH in sea-water-like salt solution.

Henry’s Law is deceptively simple. In words:

Gas-phase Partial Pressure = solution-phase concentration x the Henry’s Law Constant.                     1

Henry’s Law constants vary with the molecule, with temperature, with the solvent, and with the presence of other solutes. Knowledge of any two Henry’s Law factors allows calculation of the third. Figure 3 shows the correspondence of the temperature-dependent Henry’s Law constants for CO₂ in sea water (H_S) with the trend of d¹⁸O proxy Cenozoic SSTs.

The temperature-dependent Henry’s Law constants for CO₂ plus sea water closely track the d¹⁸O proxy Cenozoic SST.

Cenozoic CO₂: The paper shows that Cenozoic P(CO₂) can be reconstructed as:

P(CO₂) = (fractional change in H_S) x (total change in P(CO₂)) + baseline offset                       2

at each point across the Cenozoic.

The Rae, et al., (2021) proxy construct gave a mean P(CO₂) ~1093 ppm at 66 MYr BP. At the end of the Cenozoic, the mean P(CO₂) was 231 ppm during the Quaternary glacial/interglacial cycles. The Cenozoic P(CO₂) = 1093 – 231 = 862 ppm.

The trend in Cenozoic P(CO₂) can then be calculated using the value-added equation 2. Specifically:

P(CO₂)_i = [(dH_0,i/dH_0,t)x 862 ppm] +231 ppm,                                                               3

where (dH_0,i/dH_0,t) is just the fractional change in the temperature-dependent Henry’s Law constant.

Figure 3: Blue line, d¹⁸O proxy estimate of Cenozoic SSTs (Hansen et al., (2013)). Red line, trend in Henry’s Law constant for equilibration of CO₂ across the atmosphere/sea surface interface during the Cenozoic. The right ordinate is descending upwards.

The proxy reconstruction of Cenozoic P(CO₂) proxy points of (Rae, et al., (2021)) provided a baseline reference series for the P(CO₂) trends calculated from Henry’s Law. Figure 4 shows the comparison.

Figure 4: (yellow points), proxy P(CO₂) over the Cenozoic from (Rae, et al., 2021)); (purple line), 15% weighted Lowess smooth. (blue line), Cenozoic P(CO₂) calculated using equation 3; red line, weighted Lowess smooth. Inset: expansion of the most recent 7.5 Ma.

Two proxy SSTs for the PETM are available. The PETM maximum SST reported by Bijl, et al. (2009) is 35 C, while the Hansen, et al., 2013 reported a PETM maximum of 28 C.

The Bijl SSTs (blue line) gave a much better match to the P(CO₂) proxy points. The PETM SSTs of Hansen, et al., (Figure 3), yielded PETM P(CO₂) levels generally too low.

The calculated P(CO₂) trend goes through the proxy CO₂ points across the first 36 MYr BP of the Cenozoic. After that, P(CO₂) declined all across the Cenozoic. At 30 MYr BP, the proxy suddenly dips about 300 ppm below the Henry’s Law line. However, after 22 MYr BP, the calculated and proxy slopes are nearly parallel.

At about 3 MYr BP, (inset), the proxy points and the Henry’s Law trend merge once again while P(CO₂) dereases precipitously through the Pleistocene.

[CO₂]_ocean of the Paleocene

Of further interest, at the beginning of the Cenozoic the mean proxy estimates of SST, 297 K, and of P(CO₂), 1093 ppm, allow a Henry’s Law estimate of the equilibrium concentration of CO₂ in the ocean 66 million years ago. This estimate is [CO₂]_ocean = 3.41×10^-5 Molar (M).

If the [CO₂]_ocean had remained constant at 3.41×10^-5 M up through the present, then Henry’s Law equation 4 can reveal how atmospheric P(CO₂) would have evolved through the Cenozoic given the variation in SST and under the condition of constant marine CO₂.

P(CO₂) = H_ix 3.41x10^-5 M                                                                                                         4

where H_i is the temperature dependent Henry’s Law constant. Figure 5 shows the result.

Figure 5: (points), proxy estimate of Cenozoic P(CO₂) from Rae, et al., (2021); (purple line), Lowess smooth; (blue line), evolution of Cenozoic P(CO₂) driven only by SST at constant [CO₂]_ocean = 3.41×10^-5 M; (red line), Lowess smooth. Inset: the most recent 7.5 Ma.

At the PETM maximum (52 MYr BP), the calculated line is close to the proxy smooth, but passes through the lower region of the proxy CO₂ points. This means SST alone seems unable to account for the full PETM increase in P(CO₂).  The volcanic activity of the NAIP probably released considerable CO₂.

Heading into the Eocene and Oligocene (50-35 MYr BP), the constant [CO₂]_ocean trend is close to the proxy points. But after 30 MYr BP, the constant CO₂ line is much higher than the proxy P(CO₂) smooth. This result shows that [CO₂]_ocean was not constant across the Cenozoic.

An interesting revelation is that if [CO₂]_ocean had remained constant at 3.41×10^-5 M, the post-glacial Holocene atmospheric CO₂ would have been about 775 ppm. This assumes the same decreasing trend in SST to its modern value. In the Null Hypothesis, cooling would have occurred because tectonic magmatism was generally low, apart from episodic excursions such as during the MCO.

Under this scenario, industrial emissions would have increased atmospheric CO₂ to about 900 ppm. There would have been no conceivable rationale at all for climate alarm, or for a war against fossil fuels. The world would also have been much greener, and the more prolific agriculture would have required conversion of far less arable wildland.

In any case, the decreasing SST alone clearly cannot account for the decline in P(CO₂) after 35 MYr BP.

The modern [CO₂]_ocean: Henry’ Law applied to the observed post-glacial mean Holocene SST (292 K) and P(CO₂) (295 ppm), yields the modern [CO₂]_ocean = 0.998×10^-5 M.

That is, the Cenozoic has seen a loss of [(3.41 – 0.998)/3.41]x100 = 71% of the equilibrating CO₂ that was present in the ocean of the Paleocene.

At constant pH, Le Chatelier says the concentration of oceanic CO₂ cannot decline without a loss of bicarbonate and carbonate (Figure 2).

Therefore, the 775 – 295 = 480 ppm difference, between the a modern P(CO₂) at constant [CO₂]_ocean, and the observed P(CO₂) of the pre-industrial Holocene, quantifies the known massive Cenozoic draw-down of carbonate, which is discussed in Bestland, 2020, Dutkiewicz, et al, 2018, von Strandmann, et al., 2021, and Rae, et al., 2021.

This process began around 30 MYr BP and continued right through the Pleistocene (Figure 5).

It is unlikely that the pH of the ocean has changed much. But the modern buffer capacity is greatly diminished relative to the deep past.

Quaternary Glaciation and CO₂

The falls and rises of P(CO₂) across the Quaternary glacial/interglacial cycles were driven by changes in SST alone, because they occurred without any significant change in [CO₂]_ocean.

The 420 kYr VOSTOK ice core records the ~100 ppm range of the global average P(CO₂) cycle during the last four glacial/inter-glacial periods.

Knowing the present [CO₂]_ocean (0.998×10^–5 M), and the d¹⁸O proxy SST over the 420 kYr period (Hansen, et al., (2013)), permits a direct calculation of the glacial/interglacial P(CO₂) cycle of the Quaternary.

If the proxy SSTs are correct, the Henry’s Law P(CO₂) should reproduce the VOSTOK record. The direct Henry’s Law calculation is:

P(CO₂) = H_ix 0.998x10^-5 M,                                                                                                      5

where H_i is the temperature-dependent Henry’s Law constant.

Figure 6a shows that the d¹⁸O proxy SSTs yielded P(CO₂) cycles that are compressed relative to the point-range of the VOSTOK record (Figure 6a, red line).

This means the temperature-dependent Henry’s Law constants were not correct. Therefore, the d¹⁸O proxy SSTs are not correct.

Figure 6: a. (points), 420 kYr of P(CO₂) from the VOSTOK ice core (Petit, et al., (1999); VOSTOK data). (red line), Henry’s Law P(CO₂) calculated using the d¹⁸O proxy SSTs of Hansen, et al, 2013, and the mean Quaternary [CO₂]_ocean = 0.998×10^-5 M. b. (points), VOSTOK ice core CO₂; (blue line), P(CO₂) calculated using equation 2; (green line), P(CO₂) directly calculated using [CO₂]_ocean = 0.998×10^-5 M, and Henry’s Law reflecting the SST adjusted to have an 11 C glacial/interglacial range.

The accepted global average glacial/interglacial d¹⁸O proxy SST range is 4-5 C. But this range is clearly too small to reproduce the VOSTOK P(CO₂) record.

Testing alternatives, only an SST with an 11 C glacial/interglacial range did a good job of reproducing the VOSTOK record (Figure 6b).

Also, only 11 C cycles yielded the correct 280 ppm P(CO₂) of the pre-industrial Holocene at 0 kYr BP.

In support of this result, Cuffey et al. 2015 reported an 11.3 ±1.8 C glacial/interglacial range for West Antarctica, which they described as, “two to three times the global average.“

However, it was the Cuffey West Antarctica 11 C range that reproduced the VOSTOK global P(CO₂) series (Figure 6b). This implies that 11 C is a global average range of glacial/interglacial SST, rather than confined to Antarctica.

Figure 6b shows two calculated lines. The blue line was calculated under the Null Hypothesis, equation 6

P(CO₂)_i = [(dH_0,i/dH_0,t)x 116.5 ppm] +182 ppm                                                                          6

where 116.5 ppm is the VOSTOK P(CO₂) range and 182.5 ppm is the VOSTOK offset minimum.

The green line used equation 7 — the direct Henry’s Law calculation, with the modern value of [CO₂]_ocean = 0.998×10^-5 M and Henry’s Law constants reflecting SSTs with a global average 11 C glacial/interglacial range:

P(CO₂)_i = H_ix 0.998x10^-5 M,                                                                                                     7

where H_i is the temperature-dependent Henry’s Law constant.

The lines of the alternative calculations almost superimpose.

An aside

The Quaternary ice ages began only after about 45 million years of ocean cooling. Equivalently large Milankovitch orbital forcing must have been present in the Cretaceous and throughout the Cenozoic, but did not produce glaciations.

Possibly, glaciations appeared because the cooling ocean eventually entered a potential energy surface that includes a bifurcation of climate states. In this view, Milankovitch orbital forcing with a lower energy flux produces a glacial icehouse climate. When orbital forcing moves to a higher energy flux, an interglacial cool-house climate is produced. The energy transition causing the climate state shift can be 100 Wm^–2 at northern latitudes, and the sensitivity to the flux change appears to have been brought into being by the low SST of the Quaternary. Extended ocean cooling due to long-term quiescence of submarine flood basalt magmatism may also explain snowball Earth events.

Conclusion

The behavior of P(CO₂) across the 66 million years of the Cenozoic is consistent with the Null Hypothesis.

High SSTs are produced by large scale submarine flood basalt magmatic events capable of warming the entire global ocean — about 1 C for each million km³ of eruptive basaltic magma. When an extreme magmatic event warmed the global ocean, marine CO₂ outgassed into the atmosphere. When flood basaltic magmatism was quiescent, the global ocean cooled and atmospheric CO₂ was absorbed.

The rises and falls of P(CO₂) can be understood as physical re-equilibrations across the ocean surface in response to variations in SST, and changes in the concentrations of oxides of carbon caused by volcanism or carbonate drawdown.

Although extreme volcanic events released copious CO₂, radiative forcing by CO₂ is not needed to explain the high SSTs of the PETM, or of the Oligocene warm period, or of the Miocene Climate Optimum.

During the Quaternary, the cycling of P(CO₂) is entirely consistent with Henry’s Law re-equilibration, as SST varied over an 11 C glacial/interglacial range.

For the past 66 million years, atmospheric CO₂ can be understood as a neutral spectator molecule, right up through the present.

A short commentary

What current research reveals about consensus climatology:

1. Climate models cannot predict air temperature: here, here, here, here, here, here, and here.

2. Absent climate models, there is no evidence whatever that CO₂ emissions have done, are doing, will do, or can do, anything to global air temperature.

3. The surface air temperature record is climatologically useless: here, and here, and the published field calibration experiments referenced in those papers.

4. Absent a reliable historical air temperature record, the rate or magnitude of modern climate warming are unknowable. Only the poleward migration of the northern tree line and a lengthened growing season indicate a recently warmed climate.

5. The record of the past 66 million years shows that atmospheric CO₂ is driven, not a driver. This work.

As a general and unavoidable conclusion: the dogma that the radiative forcing of CO₂ controls global mean surface air temperature should be set aside.

The party’s over.