Ole Humlum on CO2 Lagging Temperature

Ole Humlum published a paper about 10 years ago attempting to show that CO2 always lags temperature and therefore the increase in CO2 substantially comes from an increase in temperature, not the other way around. In the words of Humlum's paper,

As cause always must precede effect, this observation demonstrates that modern changes in temperatures are generally not induced by changes in atmospheric CO2. Indeed, the sequence of events is seen to be the opposite: temperature changes are taking place before the corresponding CO2 changes occur.

Papers like this almost always have multiple flaws. First, they ignore the empirical data we have for our own carbon emissions, and second, they compare monthly and/or annual changes in CO2 and temperature, rather than the overall increases in CO2 and temperature. By looking at monthly changes in CO2 and temperature, they essentially detrend the data, removing the increases in CO2 and temperature, which is precisely the data you need to look at. Instead these papers consider seasonal and annual variability in CO2 and temperature. Given that CO2 is less soluble in warmer temperatures, we'd expect to see more CO2 degas from the oceans when they are warmer, and since global temperatures are warmer in NH summers than in NH winters, we'd expect to see seasonal increases CO2 lagging NH summers. And since El Nino years are warmer than La Nina years, we'd expect to see increases in CO2 lagging the warm months of El Nino years. Ole Humlum's graph showing a seasonal lag of CO2 behind temperatures may well be valid, but it's also completely unsurprising and not an argument that the overall increase in CO2 is from an increase in temperature. Below I did my own version of Humlum's graph. I took data from the Keeling Curve and calculated running annual slopes for the graph and then added 12-month smoothing. Then I took HadCRUT5 and HadSST4 and did the same thing to these. Here's the graph from 1960 to 2023; here you can see that the CO2 portion of the graph not fully detrended but temperature is.

An evaluation of Humlum's graph (or mine above) essentially refutes the paper. Let's do some back of the envelope calculations from what Humlum's graph shows. The scale on the left shows a change in temperature (ΔT) range of 1.4°C/year. The scale on the right shows a corresponding ΔCO2 of 4.5 ppm/year. If we assume that these scales are properly chosen, then we can say that the ΔCO2 and ΔT relationship is in the neighborhood of 4.5/1.4 or ~3.2 ppm/°C. This would mean seasonal variability in temperature corresponds to seasonal variability in CO2 at a rate of about 3.2 ppm for every 1°C change in GMST. If we assume that this means that the 140 ppm increase in CO2 above preindustrial levels (~280 ppm) is due to changes in temperature, then things get absurd pretty quickly. For ΔCO2 to be caused entirely by ΔT, then we'd have to have a 140/3.2 or 44°C increase in GMST to produce a 140 ppm increase in GMST at the rate implied by Humlum's chart. But the planet has only warmed by about 1.2°C. In other words, using Humlum's graph to argue that the overall increase in CO2 is substantially caused by increases in temperature is objectively ridiculous. Humlum is confusing causes of seasonal variability in CO2 with the cause of the overall increase in CO2 concentrations. In the graph below I show data from the 2023 Carbon Budget[2] with human emissions on the positive side of vertical scale and with sinks and atmospheric growth on the negative. You can see there's a significant amount of annual variability in the sinks and atmospheric growth compared to the emissions sources, but overall, total anthropogenic emission sources from fossil fuels and industry (FFI) and land use change (LUC) are about the same magnitude as the land/ocean sinks with atmospheric growth. The budget balances if human activity is responsible for virtually all the increase in CO2.

It turns out that the relationship between how the solubility of CO2 in seawater is affected by temperature is pretty well understood. As the oceans warm, the ocean to atmosphere flux (Foa) increases linearly with temperature. This is governed by the following equation (per Millero and Roy):

Foa = 0.3*ΔSST gCO2/m^3

So if SSTs have increased by 1°C, then Foa has contributed 0.3 gCO2/m^3 to the atmosphere, which amounts to 0.3*600*360/1000 = 64.8 GtCO2 (17.7 GtC). However, Henry's Law states that at equilibrium the amount of CO2 dissolved in sea water will increase proportionately with the partial pressure of CO2, and the amount of CO2 in the oceans is strongly affected by the behavior of the HCO3-/CO3-- buffering system. Increasing atmospheric CO2 also causes an atmosphere to ocean CO2 flux (Fao) which is governed by the following equation:

Fao = 8.66*ln (C/280) gCO2/m^3

At 420 ppm, therefore, the ocean sink will take up 3.51 gCO2/m^3 or 758 GtCO2 (207 GtC). Overall the oceans are a carbon sink taking up about 693 GtCO2 (189 GtC). In other words, the flux of CO2 from the atmosphere to the oceans caused by the increase in atmospheric CO2 is about 10x greater than the flux of CO2 from the oceans to the atmosphere due to increasing temperature.

The 2023 Carbon Budget has updated cumulative information for 1750-2022. According to this, humans have emitted a total of 703 GtC from both fossil fuel/industry (FFI) emissions and land use change (LUC). The total land sink is 247 GtC and the total ocean sink is 189 GtC, with a budget imbalance of about 16 GtC. Using round numbers total human emissions has added 700 GtC to the climate system, of which about 57% goes to the land and ocean sinks, leaving 302 GtC in the atmosphere from human emissions. We can convert this to ppm if we multiply by 3.67 GtCO2/GtC and then divide by 7.81 GtCO2/ppm to get 142 ppm CO2 above preindustrial levels. Since CO2 was about 278 ppm in 1750, the 2023 carbon budget clearly shows that virtually all the increase in CO2 above preindustrial levels is caused by human emissions. It is preposterous to suggest that the increase in CO2 is caused by an increase in temperature.

There are numerous other problems with this paper that are described in two comments[3][4]. However, while the paper is flawed on so many levels, it is interesting to me that the graph does illustrate something meaningful. Rates of CO2 variability do appear to lag temperature variability by a few months. Equally interesting is that a paper got published that attempts to show that the long-term increase in CO2 is caused by increases in temperature using a methodology that removed the long-term trends in CO2 and temperature. In the words of Richardson's comment, "Humlum et al., 2013 identify natural controls on short term variation in atmospheric CO2 using a differential method that removes long term trends and emphasises short term changes. They proceed to make conclusions about the long term change in atmospheric CO2 since January 1980, despite having removed most of the long term contribution through differentiation."[3] That sums it up quite nicely.

 

References:

[1] Ole Humlum, Kjell Stordahl, Jan-Erik Solheim, The phase relation between atmospheric carbon dioxide and global temperature, Global and Planetary Change, Volume 100, 2013, Pages 51-69, ISSN 0921-8181. https://doi.org/10.1016/j.gloplacha.2012.08.008.

[2] 2023 Carbon Budget. https://essd.copernicus.org/articles/15/5301/2023/

[3] Richardson, M. (2013). Comment on “The phase relation between atmospheric carbon dioxide and global temperature” by Humlum, Stordahl and Solheim. Global and Planetary Change, 107, 226–228. doi:10.1016/j.gloplacha.2013.03.0

[4] Masters, T., & Benestad, R. (2013). Comment on “The phase relation between atmospheric carbon dioxide and global temperature.” Global and Planetary Change, 106, 141–142. doi:10.1016/j.gloplacha.2013.03.010