In modelling the growth of CO2 in the atmosphere from emissions data it is standard practice to model what remains in the atmosphere since after all it is the residual CO2 that is of concern in climate studies. In this post I turn that approach on its head and look at what is sequestered. This gives a very different picture showing that the Bern T1.2 and T18.5 time constants account for virtually all of the sequestration of CO2 from the atmosphere on human timescales (see chart below). The much longer T173 and T∞ processes are doing virtually nothing. Their principle action is to remove CO2 from the fast sinks, not from the atmosphere, in a two stage process that should not be modelled as a single stage. Given time, the slow sinks will eventually sequester 100% of human emissions and not 48% as the Bern model implies.
If emissions were switched off today the fast sinks would continue to pump down CO2 quickly, assuming they are not saturated, until a new equilibrium between the fast sinks is reached where the eventual CO2 concentration of the atmosphere may still contain 19% of total emissions over and above the pre-industrial baseline, that is until the slow sinks have time to pump that residual CO2 away.
The chart shows the amount of annual emissions removed by the various components of the Bern model. Unsurprisingly the T∞ component with a decline rate of 0% removes zero emissions and the T173 slow sink is not much better. Arguably, these components should not be in the model at all. The fast T1.2 and T18.5 sinks are doing all the work. The model does not handle the pre-1965 emissions decline perfectly, shown as underlying, but these too will be removed by the fast sinks and should also be coloured yellow and blue. Note that year on year the amount of CO2 removed has risen as partial P of CO2 has gone up. The gap between the coloured slices and the black line is that portion of emissions that remained in the atmosphere.
This is Part 2 of the mini series on CO2 in the atmosphere. What’s up with the Bomb Model coming next.
The Bern Model
The Bern Model for sequestration of CO2 from Earth’s atmosphere imagines the participation of a multitude of processes that are summarised into four time constants of 1.2, 18.5 and 173 years and one constant with infinity (Figure 1). I described it at length in this earlier post The Half Life of CO2 in Earth’s Atmosphere. T173 and T∞ constants are supposed to account for 48% of the CO2 that is sequestered. In fact, on the human time scale these slow processes sequester virtually zero manmade emissions. It is traditional when modelling the atmosphere to model what is left and not what has been sequestered. Doing this gives the perception that the T173 and T∞ time slices dominate the non-sequestered CO2 and give the impression that these components may linger in the atmosphere for a very long time (Figure 1). This is a false impression.
Figure 1 The Bern model has 4 components representing sequestration at different rates by different geological and biological processes. The wedge labelled “underlying” represents the pre 1965 emissions that in the model go back to 1910 and these are simply declined at 3% per annum which is an imperfect approximation. The line labelled atmosphere is the actual atmosphere trend based upon Mauna Loa CO2 and IPCC Grid Arendal carbon cycle. The model does not easily convey the fact that the T1.2 process is actually one of the most important for sequestering CO2 (see Figure 2). Nor does it convey the fact that the T173 and T∞ slices remove virtually zero CO2 on this time scale.
Modelling what is actually sequestered gives a totally different and truer picture (Figure 2). The vast bulk of CO2 is sequestered by the fast T1.2 and T18.5 sinks. The T173 and T∞ sinks do nothing on this human time scale and should not be in the model at all. The gap between the sequestered CO2 and the emissions in Figure 1 represents those emissions that the fast sinks have not yet had time to sequester. If CO2 emissions are turned off, the fast sinks will continue to operate, for so long as they are not saturated, and CO2 in the atmosphere will drop like a stone, but not to pre-industrial levels (see below).
Figure 2 Plotting the annual emissions that are sequestered shows which processes are doing all the work. See caption for the figure up top for further clarification. This chart opens the possibility of examining the % of emissions sequestered each year (Figure 3).
We can now look at the percentage of annual emissions removed each year (Figure 3) that have fallen from 70% in 1966 to 40% today according to the Bern model. This looks alarming, but it is just a model and not reality.
Figure 3 A derivative of Figure 2 showing the percentage annual amount of emissions sequestered by the Bern model. The gradient in the data may look worrying but is an artefact of the model that does not necessarily represent reality.
From an earlier post:
In 1965 the mass of CO2 in the atmosphere was roughly 2400 Gt (billion tonnes) and today (2010) it is roughly 2924 Gt. That is an increase of 524 Gt. And we also know that we have added roughly 1126 Gt of CO2 to the atmosphere through burning FF and deforestation (emissions model from Roger Andrews). And so while Man’s activities may have led to a rise in CO2 the rise is only 46% of that expected from our emissions. Earth systems have already removed at least 54%.
In the period 1966 to 2010 the Bern model on average removed 51% of emissions which is not a good match to observations.
The fast sink equilibrium theory
In a comment to an earlier post retired NASA astronaut Phil Chapman proposed that there should be an equilibrium distribution of CO2 between the fast sinks. If that equilibrium is disturbed by the addition of CO2 to the atmosphere (emissions) the system adjusts until the CO2 is redistributed between the reservoirs and a new equilibrium is reached. We see this as sequestration of CO2 from atmosphere into the fast sinks (bio mass and ocean water). Since there is a net addition of CO2, at equilibrium each sink, including the atmosphere will contain more CO2 than at the outset.
Therefore, if we stopped emissions today, fast sink sequestration will continue until equilibrium is reached and CO2 will decline, quite rapidly, in the atmosphere but not to pre-industrial levels since the overall amount of CO2 in the fast sinks has increased. Phil suggested that since the atmosphere currently has 19% of the CO2 in the fast sinks that at the new equilibrium point it may still contain 19% of the total additions with the caveat that this will only occur if the redistribution processes between the sinks are linear. Furthermore, the slow sinks are continually removing CO2 from the fast sinks although on human time scales these slow processes are trivial to the outcome (Figure 2). The distribution of CO2 between the fast sinks is shown below. Note that Phil originally used a NASA carbon cycle model while I am using data from the IPCC Grid Arendal model that are slightly different.
Atmosphere Land biomass Biodetritus Shallow ocean
GtCO2 750 550 1580 1020
% 19.2 14.1 40.51 26.15
I have taken Phil’s idea and built a simple two Tau model where 19% of emissions remain in the atmosphere (T∞) and the model is balanced by varying the exponential decline rate of T2. It was found that applying a decline rate of 4% to 81% of emissions balanced the model and it was surprisingly easy to achieve this balance (Figure 4). One weakness with this model is that it assumes equilibrium is continually reached but I still think it is conceptually useful. It might also appear that I am following the same procedure adopted by Bern by mixing fast and slow sinks in a single model. I do not believe that I am doing this since my “T∞” is not modelling a slow sequestration process but residual CO2 in the atmosphere left behind by the fast process and so it should accumulate at the same rate as removal.
Figure 4 This two component model has 1 time constant set to ∞ for 19% of emissions and the other set to 17 years which would represent an average figure for the fast sinks applied to 81% of annual emissions. In 2010 the model removed 40% of emissions added which is close to observations.
With this model we can do fun things like switch off emissions to see what would happen (Figure 5).
Figure 5 In this example, emissions are switched off in 1990 and it can be seen that atmospheric CO2 drops like a stone (top of red band). The black line shows how the atmosphere actually was with emissions on.
The fast sinks continue to pump seeking that new equilibrium between the fast sinks. Projecting this into the future it can be seen that according to the equilibrium distribution theory, 19% of CO2 emissions will remain (red band) and the atmosphere will not return to pre-industrial levels until the slow processes have time to achieve that. Emissions from 1965 to 2010 are 1126 Gt. 19% of that = 214Gt equivalent to about 29 ppm CO2 in the atmosphere for this time span.
Note that in this model 19% of emissions linger because the overall amount of CO2 in the system has increased and a new equilibrium is reached. That equilibrium can then only be moved by the slow sinks pumping down the fast sinks.
To complete the story Figure 6 shows the sequestered emissions for the 2Tau model and derived from that the % of emissions sequestered each year are shown in Figure 7. In the 2Tau model virtually all of the emissions that are sequestered are sequestered by fast sinks with a mean Thalf of 17 years. The underlying (pre-1965) emissions will be sequestered by these same processes. The T∞ portion with 0% decline sequesters nothing in this time frame. Interestingly the sequestered profile is similar to Bern but they are not the same even although both models match the actual atmosphere.
Figure 6 The sequestered emissions for the 2Tau model. All the work is done by the T17 fast sinks. The T∞ sink does no work at all.
Subtracting the sequestered from the emissions provides a picture of the annual removal with time. Interestingly, the 2Tau model is flat (Figure 7) and does not have the gradient evident in Bern and the mean sequestration rate is 54.9% per annum that matches observations almost exactly.
Figure 7 Derivative of Figure 6 showing the percentage of emissions sequestered each year.
- Modelling the CO2 evolution of the atmosphere by looking at what is sequestered provides insight to what is actually going on. Models that rely on unsequestered residuals left behind in the atmosphere are unlikely to have any skill at describing the processes that left these residuals behind.
- Examining CO2 sequestration in the Bern model shows clearly that virtually all the work is done by the fast sinks (T1.2 and T18.5). The slow T173 sink does hardly anything on human time scales and the T∞ process removes no CO2 at all (decline = 0%).
- CO2 is removed from the atmosphere by fast sinks and slow sinks remove CO2 from fast sinks over longer time scales. The slow sinks in fact remove virtually no CO2 from the atmosphere. This two stage process should not be modelled as a single stage in the way that the Bern model functions. Given sufficient time, slow sinks will remove 100% of human emissions and not the 48% implicit in Bern.
- A fast sink equilibrium model is presented that assumes the total amount of CO2 in the fast sinks rises with increasing emissions but the distribution of CO2 between the four fast sinks will be the same at T2 compared with T1 when equilibrium is restored. This leads to the conclusion that if emissions were halted today that fast sinks would continue to sequester CO2 that would fall to a baseline above pre-industrial levels represented by 19% of total emissions.
- A two component model is developed where 81% of emissions are removed by a fast T17 sink (17 year half life, 4% per annum decline). This may be the average of a number of sinks of various speeds. The T17 sink reduces CO2 to a baseline at T2 that is 19% higher than T1.
- The fit of model to observations is excellent. And the model removes 54.9% of annual emissions that is also a close match to observations.
- Just because a model seems to give the correct result does not mean it is valid.