"A decade ago I wrote a post entitled “The Bern Model Puzzle”. It related to the following question.
Suppose we have a relatively steady-state condition, where the CO2 level in the atmosphere is neither rising or falling.
Now, suppose during that time, a volcano blows its top and dumps (lots) of CO2 into the atmosphere.
Over time, that pulse of CO2 will be absorbed by a variety of land and ocean sinks, and the status quo of atmospheric CO2 will be restored to the level it was before the eruption.
The “Bern Model” is a model used by the IPCC and various climate models. It purports to calculate how long it takes that pulse of CO2 to be reabsorbed by the natural sinks.
And that’s where things get curious.
First off, the Bern Model says that 15.2% of that pulse of CO2 will stay airborne forever.
If this were true, it seems to me that every volcanic eruption would lead to a new and higher permanent level of airborne CO2 … but that simply hasn’t happened.
For further evidence that the first claim of the Bern model is wrong, consider the annual swing of CO2 levels.
From a low point around October to a high point around May of each year, there is a short sharp natural pulse of CO2 that leads to an increase in CO2 levels of about 6 parts per million by volume (ppmv).
And this is matched by an equal sequestration of CO2 in natural sinks such that by the following October the previous CO2 level is restored.
If that were not the case, CO2 levels would have been increasing every year since forever.
And during that same seven month period, at present we emit a pulse containing enough CO2 to result in an increase in CO2 levels of about 1.3 ppmv.
The Bern Model says that 15.2% of the 1.3 ppmv anthropogenic CO2 pulse will stay in the air forever … but the ~ 6 ppmv pulse is gone very quickly.
So how does nature know the difference?
... It gets more curious. The Bern Model says that :
25.3% of the CO2 pulse decays back to the previous steady-state condition at a rate of 0.58% per year
another 27.9% of the pulse decays at 5.4% per year, and
a final 31.6% of the pulse decays back to the steady-state condition at 32.2% per year
... How does nature know the difference?
How is the CO2 partitioned in nature?
What prevents the CO2 that’s still airborne from being sequestered by the fast-acting CO2 sinks?
... the Bern Model simply doesn’t do a good job at representing reality.
... So I thought I’d take a look at the Bern Model, to see how well it could predict the airborne CO2 since 1850 from the emissions since 1850.
... Actual atmospheric CO2 values, and values according to the Bern Model
No bueno … the fact that the Bern Model results are so much smaller indicates that it is incorrectly pushing much of the effect far out into the future.
So, is there a better way?
...The better way is to use the standard lagging formula:
Using this formula, I find the time constant tau to be ~49 years.
Here’s the result of that calculation.
Actual atmospheric CO2 values, and values according to a standard lagging model
This puts the half life of a pulse of CO2 into the atmosphere at about 34 years …
Those are my questions and observations about the Bern Model."