How Natural Carbon Sinks Respond to Carbon Emissions

In a previous post, I evaluated a recently published MDPI paper claiming that we could with minimal effort limit CO2 concentrations to 475 ppm and warming to 1.5 C above preindustrial levels. The paper was horribly flawed, but it was based on the assumption that natural sinks will increase more rapidly than our continued emissions. I thought it would be an interesting exercise how scientists expect natural sinks to respond as CO2 concentrations (and global temperatures) increase.

I want to show expected changes in sinks as CO2 concentrations rise. As noted in that previous post, the 2021 carbon budget values are estimated per year, and converting these values so that they reflect the size of sinks in terms of atmospheric CO2 concentrations potentially introduces biases into the data. I do not want to go into a lot of detail. Instead I want to cover the land and ocean sink in general terms. I'm also only considering the impact of CO2 without evaluating the effect of increases in other GHGs or changes in other relevant forcings.

Cumulative Land Sink

The land sink (Sl) refers to processes on land that take up CO2 from the atmosphere (aCO2). Annual data in the 2021 carbon budget contains much more variability than the ocean sink data. In recent years, the land sink has been increasing linearly with CO2, at about 4 GtCO2/ppm:

Sl = 4*ΔaCO2 GtCO2

Since the size of Sl fluctuates significantly every year, it's significantly affected by environmental factors, especially land use change and precipitation. Deforestation decreases plant biomass, whether by decomposition or burning, so deforestation increases aCO2 concentrations. Likewise, reforestation increases plant biomass, and therefore reduces aCO2 concentrations. Plants both photosynthesize and respire, and photosynthesis depends on aCO2 and aH2O:

6CO2+6H2O→C6H12O6+6O2.

The difference between photosynthesis and respiration is generally the biomass of the plant. Droughts limit photosynthesis and increase risk of fires. Increasing humidity and rainfall can potentially improve photosynthesis rates, though associated flooding can be harmful to plant life. Multiple studies show significant "greening" in the 20th century due to many factors, including elevated CO2. However, some studies[1] are showing that greening is slowing down globally in the 21st century, so we cannot assume that the trend of 4 GtCO2/ppm will continue indefinitely into the future. There's some good evidence that it may decrease.

In the 2021 carbon budget, I binned the values for the land sink in 10 ppm increments and totaled the estimated sink for each bin. I did this to minimize bias from converting annual values to concentration values. On the basis of this, I set the land sink to 7.75 GtCO2/ppm for 280-316 ppm and to 5 GtCO2/ppm for 317-400 ppm. I set it to a constant 4 GtCO2/ppm for 410-500 ppm. Since land sink has had a decreasing trend, I set it to 3.8 GtCO2/ppm for 500-560 ppm. This should overestimate the size of the sink and thus underestimate the airborne fraction. The following table contains the values for the cumulative land sink on the basis of these assumptions at four aCO2 concentrations.

So much of these values depend on our land use policies that I think these should be treated as very approximate, but they are consistent with observations that the land sink is becoming less efficient at absorbing our carbon emissions as CO2 concentrations increase.

Cumulative Ocean Sink

The ocean CO2 sink is dominated by two factors: 1. the behavior of the HCO3-/CO3-- buffering system, which is pretty well understood, and 2. the ocean current systems which transport CO2 (and AGW heat) vertically. As CO2 levels increase, two things happen related to Henry's Law and the solubility of CO2. First, since CO2 concentrations in the ocean are proportional to the partial pressure of aCO2 above the ocean surface, as aCO2 increases, the atmosphere to ocean CO2 flux (Fao) increases. The relationship is logarithmic. Doubling CO2 causes a 6 gCO2/m^3 increase in the mass of CO2 in the oceans. In other words the increase in mass of CO2aq (Fao) above the levels found at 280 ppm aCO2 is governed by the following equation:

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

Second, as SSTs warm CO2 becomes less soluble in ocean water, so as the oceans warm, the ocean to atmosphere flux (Foa) increases linearly with temperature. This is governed by the following equation:

Foa =  -0.3*ΔSST gCO2/m^3

The net flux is simply the sum of Fao and Foa. And positive Fnet shows the net flux is a carbon sink; a negative value shows the oceans to be a carbon source:

Fnet = Fao + Foa 

The value of the carbon sink down to 600m then can be calculated as 

So = Fnet *600*360/1000 GtCO2

With these equations, we can estimate the change in the ocean sink (So) above 280 ppm. The following table assumes SSTs increase by 1.6 C for a doubling of CO2:

Notice that as aCO2 increases by 140 ppm above preindustrial levels, So increases by ~700 Gt, but a 280 ppm increase does not double the size of So. It increases by only 69%, so the ocean sink becomes progressively less efficient at removing aCO2. 

Since these values are calculated, I thought it would be good to compare these values to those that in the 2021 carbon budget. I used the same binning procedure I described above to collect the empirical ocean sink data and then plotted both together. As you can see the model calculations above slightly over estimate the size of the cumulative ocean sink. This should mean that by using the land sink and ocean sink values I'm being a bit conservative. That is, I'm overestimating the size of the sink and thus underestimating how much the airborne fraction will increase as CO2 concentrations increase.

Cumulative Airborne Fraction

From these values we can calculate how the airborne fraction changes with increasing CO2. To do this we need to convert aCO2 to GtCO2, which can be easily done by noting that 1 ppm = 7.81 GtCO2 - that is the mass of CO2 increases at a rate of 7.81 GtCO2/ppm. Some fraction of our carbon emissions from fossil fuels, industry and land use change remains in the atmosphere; the rest is taken up by the land and ocean sinks (a small amount is taken up by concrete carbonization, but that is a small amount).  The airborne fraction can be can be calculated as

AF = aCO2/(aCO2 + Sl + So)

Based on the above calculation, we can see how the airborne fraction increases as aCO2 concentrations increase:

The above table calculates the cumulative fraction of our emissions above 280 ppm that remains in the atmosphere when reaching that concentration of aCO2. Using these simple values, we can observe that for every 50% increase in CO2 concentration, AF increases by 2-4%. 

I constructed a toy model in a spreadsheet to show how the expected atmospheric growth and size of the land and ocean sinks at increasing CO2 concentrations through 560 ppm CO2. 

Conclusion

I don't want to make too much of this. This is a simple model I made in a spreadsheet, and it doesn't account for other forcings besides CO2 or many of the biological processes that can affect the size of the ocean and land sinks. I think there is good reason think that my simple analysis underestimates the rate at which the cumulative airborne fraction will increase as GHG concentrations rise. As an example, here is how the IPCC expects the airborne fraction to increase at higher cumulative CO2 emissions. They expect the airborne fraction to reach 56% under SSP3-7.0 and to 62% under SSP5-8.5.

Of course, these projections are based on scenarios that account for more than just changes in CO2 concentrations, so this is somewhat of an apples to oranges comparison. My main goal here is show some of the reasons why climate scientists expect the airborne fraction to increase as CO2 levels increase. We cannot count on the oceans to fix the mess we're causing, and we cannot expect global "greening" to fix the problem either.

References:

[1] Winkler, A. J., Myneni, R. B., Hannart, A., Sitch, S., Haverd, V., Lombardozzi, D., Arora, V. K., Pongratz, J., Nabel, J. E. M. S., Goll, D. S., Kato, E., Tian, H., Arneth, A., Friedlingstein, P., Jain, A. K., Zaehle, S., and Brovkin, V.: Slowdown of the greening trend in natural vegetation with further rise in atmospheric CO2, Biogeosciences, 18, 4985–5010, https://doi.org/10.5194/bg-18-4985-2021, 2021.o 0%.

[2] Global Carbon Budget 2021. https://essd.copernicus.org/articles/14/1917/2022/essd-14-1917-2022-metrics.html