Bern Model Puzzle

Once again we see different numbers but a general view that is added to the pile we have already.  The comment at the bottom sums it up a bit crudely:

The Bern Model Puzzle

Willis Eschenbach / May 6, 2012

Guest Post by Willis Eschenbach

Although it sounds like the title of an adventure movie like the “Bourne Identity”, the Bern Model is actually a model of the sequestration (removal from the atmosphere) of carbon by natural processes. It allegedly measures how fast CO2 is removed from the atmosphere.  The Bern Model is used by the IPCC in their “scenarios” of future CO2 levels. I got to thinking about the Bern Model again after the recent publication of a paper called “Carbon sequestration in wetland dominated coastal systems — a global sink of rapidly diminishing magnitude” (paywalled here ).

Figure 1. Tidal wetlands. Image Source

In the paper they claim that a) wetlands are a large and significant sink for carbon, and b) they are “rapidly diminishing”.

So what does the Bern model say about that?

Y’know, it’s hard to figure out what the Bern model says about anything. This is because, as far as I can see, the Bern model proposes an impossibility. It says that the CO2 in the air is somehow partitioned, and that the different partitions are sequestered at different rates. The details of the model are given here.

For example, in the IPCC Second Assessment Report (SAR), the atmospheric CO2 was divided into six partitions, containing respectively 14%, 13%, 19%, 25%, 21%, and 8% of the atmospheric CO2.

Each of these partitions is said to decay at different rates given by a characteristic time constant “tau” in years. (See Appendix for definitions). The first partition is said to be sequestered immediately.  For the SAR, the “tau” time constant values for the five other partitions were taken to be 371.6 years, 55.7 years, 17.01 years, 4.16 years, and 1.33 years respectively.

Now let me stop here to discuss, not the numbers, but the underlying concept. The part of the Bern model that I’ve never understood is, what is the physical mechanism that is partitioning the CO2 so that some of it is sequestered quickly, and some is sequestered slowly?

I don’t get how that is supposed to work. The reference given above says:

CO2 concentration approximation

The CO2 concentration is approximated by a sum of exponentially decaying functions, one for each fraction of the additional concentrations, which should reflect the time scales of different sinks.

So theoretically, the different time constants (ranging from 371.6 years down to 1.33 years) are supposed to represent the different sinks. Here’s a graphic showing those sinks, along with approximations of the storage in each of the sinks as well as the fluxes in and out of the sinks:

Figure 2. Carbon cycle.

Now, I understand that some of those sinks will operate quite quickly, and some will operate much more slowly.

But the Bern model reminds me of the old joke about the thermos bottle (Dewar flask), that poses this question:

The thermos bottle keeps cold things cold, and hot things hot … but how does it know the difference?

So my question is, how do the sinks know the difference?

Why don’t the fast-acting sinks just soak up the excess CO2, leaving nothing for the long-term, slow-acting sinks? I mean, if some 13% of the CO2 excess is supposed to hang around in the atmosphere for 371.3 years … how do the fast-acting sinks know to not just absorb it before the slow sinks get to it?

Anyhow, that’s my problem with the Bern model—I can’t figure out how it is supposed to work physically.

Finally, note that there is no experimental evidence that will allow us to distinguish between plain old exponential decay (which is what I would expect) and the complexities of the Bern model. We simply don’t have enough years of accurate data to distinguish between the two.

Nor do we have any kind of evidence to distinguish between the various sets of parameters used in the Bern Model. As I mentioned above, in the IPCC SAR they used five time constants ranging from 1.33 years to 371.6 years (gotta love the accuracy, to six-tenths of a year).

But in the IPCC Third Assessment Report (TAR), they used only three constants, and those ranged from 2.57 years to 171 years.

However, there is nothing that I know of that allows us to establish any of those numbers. Once again, it seems to me that the authors are just picking parameters.

So … does anyone understand how 13% of the atmospheric CO2 is supposed to hang around for 371.6 years without being sequestered by the faster sinks?

All ideas welcome, I have no answers at all for this one. I’ll return to the observational evidence regarding the question of whether the global CO2 sinks are “rapidly diminishing”, and how I calculate the e-folding time of CO2 in a future post.

Best to all,

w.

APPENDIX: Many people confuse two ideas, the residence time of CO2, and the “e-folding time” of a pulse of CO2 emitted to the atmosphere.

The residence time is how long a typical CO2 molecule stays in the atmosphere. We can get an approximate answer from Figure 2. If the atmosphere contains 750 gigatonnes of carbon (GtC), and about 220 GtC are added each year (and removed each year), then the average residence time of a molecule of carbon is something on the order of four years. Of course those numbers are only approximations, but that’s the order of magnitude.

The “e-folding time” of a pulse, on the other hand, which they call “tau” or the time constant, is how long it would take for the atmospheric CO2 levels to drop to 1/e (37%) of the atmospheric CO2 level after the addition of a pulse of CO2.  It’s like the “half-life”, the time it takes for something radioactive to decay to half its original value. The e-folding time is what the Bern Model is supposed to calculate. The IPCC, using the Bern Model, says that the e-folding time ranges from 50 to 200 years.

On the other hand, assuming normal exponential decay, I calculate the e-folding time to be about 35 years or so based on the evolution of the atmospheric concentration given the known rates of emission of CO2.  Again, this is perforce an approximation because few of the numbers involved in the calculation are known to high accuracy.  However, my calculations are generally confirmed by those of Mark Jacobson as published here in the Journal of Geophysical Research.

Section for a video or follow-on comment

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