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Adjustment time greater than residence time?

In the debate about the human contribution to the CO₂ increase, many discussions concern the adjustment time or recovery time of the atmosphere, i.e. the time it takes to restore the balance after a perturbation. In a particular case: how long does it take before the CO₂ added by humans is reabsorbed by nature. Here we will show that this adjustment time can never be longer than the normal residence time of around 4 years.

The adjustment time is sometimes defined as the time that nature needs to absorb the surplus of CO₂ above pre-industrial levels (270 ~ 280 ppm), e.g. Cawley, G.C. (2011). The current level of 425 ppm therefore represents a surplus of approximately 150 ppm, or 320 PgC. To determine the speed at which this happens, the net absorption by nature (net sink) is then taken into account, which is assumed to be currently 6 PgC/year. At that speed and without new CO₂ it will take 320/6 = 53 years, but if that speed decreases and/or we continue to emit CO₂, the recovery time will be much longer.

In all cases, the adjustment time is much greater than the residence time. But that is not consistent with a very simple numerical simulation, as described below. It turns out that the adjustment time is shorter than the residence time. It is also not consistent with the evidence given by Stallinga that the adjustment time is always shorter than the residence time.

The confusion about the long adjustment time is the result of the sloppy and incorrect definition of the term as it is used here. Normally the adjustment time is defined as the time it takes to restore the balance after a perturbation. The self-invented definition by Cawley c.s. leads to all sorts of flaws. It starts with talking about the excess of CO₂ above pre-industrial levels. As indicated in the piece No accumulation of human CO₂ in nature, the increase is not at all the result of human emissions. CO₂ does not accumulate in the atmosphere. Moreover, there is no one specific natural balance. In the Impact of greening we showed that this balance depends on the amount of vegetation. Due to greening, the natural balance is now much higher than 200 years ago.

But if we were to calculate with a disruption of 320 PgC compared to an equilibrium level of 580 PgC (275 ppm), then the downflow as a result of that disruption is much greater than the 6 PgC per year that is being calculated. The disturbance increases the amount of CO₂ in the atmosphere by 55% (320/580), so if the residence time remains the same, the downflow will also increase proportionately.

The problem is that the calculation is based on the formula:

Equation

Normally the time constant is equal to the size of the reservoir divided by the entire flow, while here it is divided by the net flow, i.e. the difference of two flows. If those flows are in equilibrium, the recovery time in this equation is even infinitely long.

There is no physical justification for an adjustment time as defined here, and it is not consistent with the concepts in the IPCC reports, or with any other comparable system in nature. There is also no other gas in the atmosphere for which the adjustment time is calculated in this way.

What happens in the event of a disruption?

Stallinga provides evidence that the adjustment time is always shorter than the shortest residence time of the two reservoirs (atmosphere and sink). He shows that for the adjustment time τadj it holds that 1/τadj = 1/τa + 1/τs . Here τa and τs are the residence times of the atmosphere and the sink. Because the residence time of the sink is many times greater than that of the atmosphere, the adjustment time is virtually equal to the residence time of the atmosphere (Stallinga, P. (2023)).

To better understand the impact of human emissions, we consider a situation in which the natural flows are exactly in balance, and where this balance is disturbed by a single large (human) emission of, in this case, 100 PgC of CO₂. The other data are from the 2023 Global Carbon Project, but the exact values ​​are not very decisive for the simulation.

According to these data, the average time that a CO₂ molecule remains in the atmosphere is 4.1 years. This corresponds to a downward flow of 216 PgC per year (216 = 885 / 4.1). The residence time in the land/ocean reservoir (Sink) is 190 years (216 = 41,000 / 190).

What happens in the event of a disruption due to a large one-off emission
Figure 2: What happens in the event of a disruption due to a large one-off emission

  • Imagine that the up and down currents are in balance.
  • At some point 100 PgC is added to the atmosphere.
  • The mass in the atmosphere increases from 885 to 985 PgC.
  • The downward current is proportional to the mass and will therefore increase to 240 PgC/y (=985/4.1).
  • This reduces the mass in the atmosphere and increases the mass in the land ocean reservoir.
  • A (simple) simulation from year to year is given in the Excel table.
  • The mass in the atmosphere decreases to almost the old level (after 10 years 2% remains), blue bars in the graph.
  • Most of the added CO₂ (98%) ends up in land/ocean, green line.
  • The adjustment time (= time to re-equilibrate) is 4.0 years, slightly shorter than the residence time.

Simulation of a one-time disturbance in Excel
Figure 3: Simulation of a one-time disturbance in Excel
Simulation of a one-time disturbance in Excel
Figure 4: The result of the simulation of a one-time disturbance. The blue bars indicate the mass in the atmosphere. Most of the added CO₂ (98%) ends up in land/ocean, green line.

The recovery time to regain equilibrium after a disturbance (adjustment time) is shorter than the residence time. Stallinga (2023) shows that the adjustment time is always shorter than the residence times. The additional CO₂ is distributed between the atmosphere and the land/ocean reservoir in proportion to the size of the reservoirs. In this case, land/ocean absorbs about 50 times more than the atmosphere.

This means that human CO₂ does not accumulate in the atmosphere. Only a small percentage of human CO₂ remains in the atmosphere.

  • Since 1750, humans have emitted approximately 700 PgC of CO₂ (including land use changes). Of the emissions up to 10 years ago, only 2% is still in the atmosphere. Over the last 10 years, a larger portion has been in the atmosphere.
  • If we stabilize human emissions at current levels, about 7% of the CO₂ in the atmosphere is human-made. If we were to stop emitting today (net zero), the human contribution would quickly drop to less than 2%. Source: Stallinga, P. (2023).



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