# The Bern Model Puzzle

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.

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There’s a massive CO2 sink that resides over Siberia during winter, it is rapidly ‘taken up’ by foliage during Spring and Summer.

R. Shearer

We affect the partition in many different ways, on what we plant and harvest and what we do with the harvest. Numerous other biological systems do as well and none are fully understood.

Latitude

excellent thought post Willis……..
I still can’t figure out how CO2 levels rose to the thousands ppm….
….and crashed to limiting levels
Without man’s help……….

David McKeever

The categories are fixed so that you can see net effects.

Henry Clark

Their graph is made in a manner which would make readers not realize how much biomass growth occurs from human CO2 emissions.
Human emissions averaged around 27 billion tons a year of CO2 during the decade of 1999-2009 (on average 7 billion tons annually of carbon), which amounted to about 270 billion tons of CO2 added to the atmosphere. Meanwhile there was a measured increase in atmospheric CO2 levels of 19.4 ppm by volume, 155 billion tons by mass, an amount about 57% of the preceding but only 57% of it.
If one looks at where the other 115 billion tons went, it was a mix of uptake by the oceans and it going into increased growth of biomass (carbon fertilization from higher CO2 levels) / soil.
Approximately 18% (49 billion tons CO2, 13 billion tons carbon) went into accelerated growth of biomass / soil, and about 25% went into the oceans.
To quote TsuBiMo: a biosphere model of the CO2-fertilization effect:
The observed increase in the CO2 concentration in the atmosphere is lower than the difference between CO2 emission and CO2 dissolution in the ocean. This imbalance, earlier named the ‘missing sink’, comprises up to 1.1 Pg C yr–1, after taking land-use changes into account.” “The simplest explanation for the ‘missing sink’ is CO2 fertilization.
http://www.int-res.com/articles/cr2002/19/c019p265.pdf
In fact, global net primary productivity as measured by satellites increased by 5% over the past three decades. And, for example, estimated carbon in global vegetation increased from approximately 740 billion tons in 1910 to 780 billion tons in 1990:
http://cdiac.esd.ornl.gov/pns/doers/doer34/doer34.htm
Other observations include those discussed at http://www.co2science.org/subject/f/summaries/forests.php

Earle Williams

The categories are fixed so that one can import a sense of order and predictability to a collection of processes that lack both. I can just as easily categorize the residence time of foodstuffs in my refrigerator as beverage, pre-packaged, and leftovers. That doesn’t mean I can predict whether the salsa will become empty within three months or stick around to generate new life forms. It presumes a level of understanding of the “carbon budget” that doesn’t exist. But with such a model I can calculate how much milk will be in my fridge in 2050. Regardless of that result, the dried clump of strawberry jam on the third shelf won’t be inconsistent with my projection.
Turtles, indeed.

DirkH

Ah! A warmist recently told me that the residence time of CO2 is 2 to 500 years. I replied that that is quite the error bar. He probably had looked up that Bern model and got his information from there. But it really doesn’t make any sense and I would file it under make-work schemes or epicycles. A product of the Warmist Works Progress Administration.

“what is the physical mechanism that is partitioning the CO2 so that some of it is sequestered quickly, and some is sequestered slowly?”
“PV=nRT” basically dashes such a fantastic model on the rocks. A classic example of the modeller’s propensity to assume something corny in order to make the model do their bidding. One school assumes “well mixed” while its class clown decides to countermand the principles behind partial pressures. Hocus-pocus, tiddly-okus, next it’ll be a plague of locusts.

“Calculating” to 4.16 or 1.33 years indicates a remarkable of “accuracy” 3.65 days residence time for “some” CO2. The oceans do NOT absorb CO2 from the atmosphere. The oceans have “vast pools of liquid CO2 on the ocean floors” which keep constant supply of dissolved CO2 and other elemental gases in the water column ready to disperse. See Timothy Casey’s excellent “Volcanic CO2” posted at http://geologist-1011.net While there visit the “Tyndall 1861” actual experiment with Casey’s endnotes and the original translation of Fourier on greenhouse effect. Reality is different than the forced orthodoxy.

The average time molecules remain in the atmophere as a gas is probably a matter of hours. Think how fast a power plant plume vanishes to a global background level. Think about how clouds absorb and transport CO2. It is the different lengths of reservoir changing cycles that is changing the amount of gaseous CO2 we measure in the atmosphere. I have evidence that most of anthropogenic emissions cycle through the environment in about ten years and, at present, contribute less than 10% to atmospheric levels. Click on my name for details.

mfo

I’m way out of my depth here, but The Hockey Schtick wrote about The Bern Model with advice from “Dr Tom V. Segalstad, PhD, Associate Professor of Resource and Environmental Geology, The University of Oslo, Norway, who is a world expert on this matter.”

Nullius in Verba

Imagine you have three tanks full of water: A, B, and C. A and B are connected with a large pipe. A and C are connected with a narrow pipe. The water levels start off equal.
We dump a load of water into tank A. Quite quickly, the levels in tanks A and B equalise, A falling and B rising. But the level in tank C rises only very slowly. Tank A drops quickly to match B, but then continues to drop far more slowly until it matches C.
Dumping an extra load in A while this is going on would again lead to another fast drop while it matched B again. It ‘knows’ which is which because of the amount in tank B.
I gather the BERN model is more complicated, and the parameters listed are an ansatz obtained by curve-fitting a sum of exponentials to the results of simulation. But I think the choice of a sum of exponentials to represent it is based on the intuition of multiple buffers, like the tanks.
John Daly wrote some stuff about this – I haven’t worked my way through it, so I can’t comment on validity, but I thought you might be interested.
http://www.john-daly.com/dietze/cmodcalc.htm

alex

“Partitioning” is trivial
The simple case of a single exponent corresponds to a first-order linear equiation, but this does not describe the complex nature.
CO2 evolves according to a higher-order linear equation (or a system of first-order linear equations that is the same). Very reasonable. That is where the “partitioning” comes,
You write down these quations and look for eigenmodes. These are the exponents. IPCC effectively claims, there are 6 first order equations or a single 6th order linear equation. OK, no objection, although there can be even more eigenmodes, but let us assume these are the major 6.
Now, the general solution is a sum of these exponents with ARBITRARY pre-factors at each exponent. How to define these pre-factors?
The pre-factors are defined by the initial conditions: the particular CO2-level and 5 (6-1) derivatives (!). IPCC claims, these are 14%, 13%, 19%, 25%, 21%, and 8%. What does it mean?
Effectively IPCC claims to know the 5th derivative of CO2 population down to 1% accuracy level!!!
Sorry, as a physicist I cannot buy such accuracy in derivatives of an experimental value.

LetsGoViking

Two words… Occam’s Razor

Edim

CO2 is determined by climatic factors. Temperature-independent CO2 fluxes into/out of the atmosphere (especially minor ones like the human input) are compensated by the system (oceans).
If we could magically remove 100 ppm of the CO2 from the atmosphere in one day, what would be the transient system response (after 10 days, 1 month, a year…)?

alex

IPCC claims to Bern model to find out these “prefactors” in simulations with a “CO2-impulse”.
The point is, the linear exponential solutions are valid only in the vicinity of an equilibrium. This means, IPCC must use an infinitesimal CO2-impulse to define the system response.
They assume the “CO2-impulse” being an instantaneous combustion of ALL POSSIBLE FOSSILE FUELS.
The response is in no way linear then and the results are just crap.
They even introduce some model for “temperature increase” due to higher CO2. The higher temperature means there is less absorption of CO2 by oceans etc…
This is not a science, but a clear misuse of it.

dmmcmah

The idea CO2 is partitioned in any way sounds like complete bull to me – CO2 is quickly well mixed in the atmosphere. But its possible some CO2 sinks could be diminishing, that might help explain some of the increase in atmospheric concentration (plus as others have pointed out higher temperatures mean less absorption by the oceans).
I don’t think any discussion of the carbon cycle should be without mention of Salby’s work, if you haven’t seen it:
http://youtu.be/YrI03ts–9I
[REPLY: It was discussed here on April 19. -REP]

Legatus

The basic assumption of this model seems to be that there is some “perfect” amount of CO2 that the earth tries to return to. Otherwise, if adding CO2 causes it to slowly go away, we should have no CO2 now, right? Thus, they must believe that it does down to this “perfect” amount and just stays there. Why does it stop diminishing? What mechanism could cause it to do so? For that matter, what mechanism would cause it to try and return to some “perfect” amount?
If CO2 goes down to this “perfect” amount and just stays there, CO2 over time should mostly be at that level all throughout history, is it? In fact, it goes up and down all the time, why is that? In fact, even in recent history it has gone up and down, that being the case, how can we even vaguely estimate how fast it will do so, much to the accuracy they claim here. In fact, since we know that CO2 goes up and down, if it does go down over time, we should be able to tell over a long enough time period how fast it goes down on average.Since we do have records of CO2 in the past, we should be able to compare this idea to the real world, and if what they are saying is true, that it goes down steadily over time (despite the actual records that say it does not), should we not be able to check this real world record against this model? Has it been checked? If it has not been checked, is this science? If it has not been checked, this model is fiction.
Also, their idea is that if CO2 increases, it then decreases, well, where does it go? The only place it can go is into the ground as oil, coal, natural gas, etc. This if we burn these, we are merely returning to the atmosphere what came from the atmosphere. This should return to the atmosphere what they claim here is being steadily removed. We need to keep doing this, otherwise we will run completely out of CO2, right? If this is not true, they need to demonstrate that CO2 will go down to this mythical “perfect” amount and just stays there.
Also, if CO2 is decreasing all the time, as they claim, yet it goes up and down over time (and note that the world does not end when it does), then something must be adding it, what, and is it enough to keep us from running out completely? Since we know that in the distant past there was far more CO2 (yet life flourished, go figure), yet now it is near to the level where all life on earth will die, we cannot rely on whatever natural processes add CO2 to bring it back up, since it obviously is not working, CO2 is dangerously low. We need to invent a way to return the CO2 back to the atmosphere. Occording to the IPCC, we have, now they are trying to stop us from doing what this model claims we must do to survive.
Once you understand the logical underlying assumption of this, that there must be a “perfect” level of CO2 that the earth tries to return to, the actual logic is:
The history of the earth shows that there is no perfect amount of CO2 that the earth tries to return to.
We the IPCC however, say that there is.
We say that because we wish it to be so.
We wish it to be so because if it is true, we can tax you and regulate you if it is not perfect.
We are the only authority on when it is perfect.
Ignore that real world behind the curtain!

Canman

Peter Huber used to make the controversial claim that North America is a carbon sink, based on a 1998 article in Science. This was based on prevailing winds blowing from West to East, with higher concentrtions of CO2 found on the West coast than the East. Later papers doing carbon inventories have disputed this. Huber responded that there was plenty of ways to miss inventory. Whoever is right, Huber makes a good case that the US does a better job than the rest of the world of replacing farmland with trees.

JimTech

Isn’t just like a bunch of resistors in parallel? 1/R =1/r1+1/r2+1/r3…..

Bart

FTA: “Anyhow, that’s my problem with the Bern model—I can’t figure out how it is supposed to work physically.”
It is because the process of CO2 sequestration is not solved by an ordinary differential equation in time, but by a partial derivative diffusion equation. It has to do with the frequency of CO2 molecules coming into contact with absorbing reservoirs (a.k.a. sinks). If the atmospheric concentration is large, then molecules are snatched from the air frequently. If it is smaller, then it is more likely for an individual molecule to just bob and weave around in the atmosphere for a long time without coming into contact with the surface.
This gives rise to a so-called “fat-tail” response. Such a fat-tail response can be approximated as a sum of exponential responses with discrete time constants.
I am not, of course, advocating the Bern model parameters. The modeling process is reasonable and justifiable, but the parameterization is basically pulled out of a hat.
What we actually see in the data is that CO2 rate of change is effectively modulated by the difference in global temperatures relative to a particular baseline. What is more likely? That CO2 rate of accumulation responds to temperatures, or that temperatures respond to the rate of change of CO2? The latter would require that temperatures be independent of the actual level of CO2, which is clearly not correct. Hence, we must conclude that CO2 is responding to temperature, and not the other way around.
In case anyone misses the point, let me spell the implications out clearly: fat tail or no, the response time for sequestering the majority of anthropogenic CO2 emissions is relatively short, and the system is having no trouble handling it. CO2 levels are being dictated by temperatures, by nature, not by humans.

Richdo

Interesting Willis. The problem reminds me of pharmacokinetics where the fate of drugs/toxins in the body are studied; wish I knew enough about pk to be more specific unfortunately it was only ancillary to my field of study. Any toxicologists around?

NetDr

Thanks. I thought I was the only one that didn’t believe this fallacy.
The fast processes will finish with it’s CO2 then go after the next batch !
The alarmists just want an excuse to say CO2 remains in the atmosphere for 100 years which is can’t possibly do.

Kelvin Vaughan

The different timings are only relevent for the first 376.1 years of the model after that they are totally irrelevant as all sinks will be working. In fact in the real world they will be totally irelevant as all the sinks will be working all of the time. It just padding for the report to make it look more technical.

NetDr

CO2 works like resistors in parallel.
1/RT=1/R1 + 1/R2+1/R3
So the total resistance can’t be more than the smallest resistor.
for CO2 the 1/2 life of the total can’t be greater than the 1/2 life which is shortest.

The Bern Model needs to introduced to the Law of Entropy (diffusion of any element or compound within a gas or liquid to equal distribution densities). And it should also be introduced to osmosis and other biological mechanisms for absorbing elements and compounds across membranes.
In fact, it seems to need a serious dose of reality

Bart

Bart says:
May 6, 2012 at 11:51 am
I want to repeat this part of my post, because people may miss it in with the other stuff, and I think it is important.
What we actually see in the data is that CO2 rate of change is effectively modulated by the difference in global temperatures relative to a particular baseline.
What is more likely? That CO2 rate of accumulation responds to temperatures, or that temperatures respond to the rate of change of CO2? The latter would require that temperatures be independent of the actual level of CO2, which is clearly not correct. Hence, we must conclude that CO2 is responding to temperature, and not the other way around.
In case anyone misses the point, let me spell the implications out clearly: fat tail or no, the response time for sequestering the majority of anthropogenic CO2 emissions is relatively short, and the system is having no trouble handling it. CO2 levels are being dictated by temperatures, by nature, not by humans.

Willis Eschenbach

Bart says:
May 6, 2012 at 11:51 am

FTA:

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

It is because the process of CO2 sequestration is not solved by an ordinary differential equation in time, but by a partial derivative diffusion equation. It has to do with the frequency of CO2 molecules coming into contact with absorbing reservoirs (a.k.a. sinks). If the atmospheric concentration is large, then molecules are snatched from the air frequently. If it is smaller, then it is more likely for an individual molecule to just bob and weave around in the atmosphere for a long time without coming into contact with the surface.

Thanks, Bart. That all sounds reasonable, but I still don’t understand the physics of it. What you have described is the normal process of exponential decay, where the amount of the decay is proportional to the amount of the imbalance.
What I don’t get is what causes the fast sequestration processes to stop sequestering, and to not sequester anything for the majority of the 371.6 years … and your explanation doesn’t explain that.
w.

rgbatduke

Surely they don’t serious use the sum of five or six exponentials, Willis. Nobody could be that dumb. The correct ordinary differential equation for CO_2 concentration $C$, one that assumes no sources and that the sinks are simple linear sinks that will continue to scavenge CO_2 until it is all gone (so that the “equilibrium concentration” in the absence of sources is zero (neither is true, but it is pretty easy to write a better ODE) is:
$\frac{dC}{dt} = - (R_1 + R_2 + ...) C$
Interpretation: Since CO_2 doesn’t come with a label, EACH process of removal is independent and stochastic and depends only on the net atmospheric CO_2 concentration. Suppose $R_1$ is the rate at which the ocean takes up CO_2. Left to its own devices and with only an oceanic sink, we would have:
$\frac{dC}{dt} = - R_1 C$
$\frac{dC}{C} = - R_1 dt$
$\int \frac{dC}{C} = - \int R_1 dt$
$ln(C) = - R_1 t + A$
$C(t) = e^{-R_1 t + A}$
$C(t) = C_0 e^{-R_1 t}$
where $A$ is the constant of integration. I mean, this is first year calculus. I do this in my sleep. The inverse of $R_1$ is the exponential decay constant, the time required for the original CO_2 level to decay to $1/e$ of its original value (for any original value $C_0$). If there are two processes running in parallel, the rate for each is independent — if (say) trees remove CO_2 at rate $R_2$, that process doesn’t know anything about the existence of oceans and vice versa, and both remove CO_2 at a rate proportional to the concentration in the actual atmosphere that runs over the sea surface or leaf surface respectively. The same diffusion that causes CO_2 to have the same concentration from the top of the atmosphere to the bottom causes it to have the same concentration over the oceans or over the forests, certainly to within a hair. So both running together result in:
$C(t) = C_0 e^{-(R_1 + R_2) t}$
If (say) trees and the ocean both remove CO_2 at the same independent rate, the two together remove it at twice the rate of either alone, so that the exponential time constant is 1/2 what it would have been for either alone. If there are five such independent sinks (where by independent I mean independent chemical processes), all with equal rate constants $R$, the exponential time constant is 1/5 of what it would be for one of them alone. This is not rocket science.
This is completely, horribly different from what you describe above. To put it bluntly:
$C(t) = C_0 e^{-(R_1 + R_2)t} \ne C_1 e^{-R_1t} + C_2 e^{-R_2t}$
Compare this when $R_1 = R_2 = R$, $C_1 = C_2 = \frac{C_0}{2}$:
$C(t) = C_0 e^{-2 R t}$
(correct) versus
$C(t) = C_0 e^{-R t}$
(incorrect). The latter has exactly twice the correct decay time, and makes no physical sense whatsoever given a global pool of CO_2 without a label. The person that put together such a model for CO_2 — if your description is correct — is a complete and total idiot.
Note that this would not be the case if one were looking at two different processes that operated on two different molecular species. If one had one process that removed CO_2 and one that removed O_3, then the rate at which one lowered the “total concentration of CO_2 + O_3” would be a sum of independent exponentials, because each would act only on the partial pressure/concentration of the one species. However, using a sum of exponentials for independent chemical pathways depleting a shared common resource is simply wrong. Wrong in a way that makes me very seriously doubt the mathematical competence of whoever wrote it. Really, really wrong. Failing introductory calculus wrong. Wrong, wrong, wrong.
(Dear Anthony or moderator — I PRAY that I got all of the latex above right, but it is impossible to change if I didn’t. Please try to fix it for me if it looks bizarre.)
rgb

Willis Eschenbach

Nullius in Verba says:
May 6, 2012 at 11:19 am (Edit)

Imagine you have three tanks full of water: A, B, and C. A and B are connected with a large pipe. A and C are connected with a narrow pipe. The water levels start off equal.
We dump a load of water into tank A. Quite quickly, the levels in tanks A and B equalise, A falling and B rising. But the level in tank C rises only very slowly. Tank A drops quickly to match B, but then continues to drop far more slowly until it matches C. ….

My thanks for your explanation. That was my first thought too, Nullius. But for it to work that way, we have to assume that the sinks become “full”, just like your tank “B” gets full, and thus everything must go to tank “C”.
However, since the various CO2 sinks have continued to operate year after year, and they show no sign of becoming saturated, that’s clearly not the case.
So what we have is more like a tank “A” full of water. It has two pipes coming out the bottom, a large pipe and a narrow pipe.
Now, the flow out of the pipe is a function of the depth of water in the tank, so we get exponential decay, just as with CO2.
But what they are claiming is that not all of the water runs out of the big pipe, only a certain percentage. And after that percentage has run out, the remaining percentage only drains out of the small pipe, over a very long time … and that is the part that seems physically impossible to me.
I’ve searched high and low for the answer to this question, and have found nothing.
w.

Faux Science Slayer says:
May 6, 2012 at 11:14 am
“Calculating” to 4.16 or 1.33 years indicates a remarkable of “accuracy” 3.65 days residence time for “some” CO2. The oceans do NOT absorb CO2 from the atmosphere. …

What about rain water, which, in its passage through the air dissolves many of the soluble gases e.g. CO2 present in the atmosphere, and which as part of ‘river waters’ eventually makes its way into the oceans?
River and Rain Chemistry
Book: “Biogeochemistry of Inland Waters” – Dissolved Gases
.

Richard G

“The IPCC, using the Bern Model, says that the e-folding time ranges from 50 to 200 years.”
**********************
Strikes me as a pretty wide ranging estimate. More like a ‘WAG’.
I file this Bern Model under “more BAF (Bovine Academic Flatulence)”.

Robert of Ottawa

The physiology of scuba diving divides body tissues into different categories, with different “half-lives”, or nitrogen abosrption rates. Some tissues absorb, and release Nitrogen rapidly, others more slowly; they are given different diffusion coefficients.
Nitrogen absorbed in your tissues in diving is the cause of the bends.
Maybe the Bern Conspiracy is thinking that some absorption mechanisms operate at different rates others. How fast do forests absorb CO2 compared to oceans? etc. Perhaps that is what they are thinking.

Willis Eschenbach

mfo says:
May 6, 2012 at 11:19 am

I’m way out of my depth here, but The Hockey Schtick wrote about The Bern Model with advice from “Dr Tom V. Segalstad, PhD, Associate Professor of Resource and Environmental Geology, The University of Oslo, Norway, who is a world expert on this matter.”

mfo, take a re-read of my appendix above. The author of the hockeyschtick article is conflating the residence time and the e-folding time. As a result, he sees one person saying four years or so for residence time, and another person saying 50 to 200 years for e-folding time, and thinks that there is a contradiction. In fact, they are talking about two totally separate and distinct measurements, residence time and e-folding time.
w.

Bart

Willis Eschenbach says:
May 6, 2012 at 12:07 pm
“What I don’t get is what causes the fast sequestration processes to stop sequestering, and to not sequester anything for the majority of the 371.6 years … and your explanation doesn’t explain that.”
The best I can tell you is what I stated:”It has to do with the frequency of CO2 molecules coming into contact with absorbing reservoirs (a.k.a. sinks). If the atmospheric concentration is large, then molecules are snatched from the air frequently. If it is smaller, then it is more likely for an individual molecule to just bob and weave around in the atmosphere for a long time without coming into contact with the surface.” The link I gave explains it from a mathematical viewpoint.

Bart

rgbatduke says:
May 6, 2012 at 12:12 pm
“The correct ordinary differential equation…”
It’s a PDE, not an ODE. See comment at May 6, 2012 at 11:51 am.

ferdberple

About 1/2 of the annual human emission are absorbed each year. If they weren’t the growth in CO2 as a % of total would be growing, which it isn’t.
Assuming an exponential rate of uptake, we have a series something like this:
1/2 = 1/4 + 1/8 + /16 + 1/32 ….
With each year absorbing 1/2 of the residual of the previous, to match the rate of the total.
ie: R = R^2 + R^3 + R^4 … R^n , where 0 < R infinity.
What this means is that tau is 2 years. 1/4 + 1/8 = 0.25 + 0.125.= 0.375 = approx 1/e

Mydogsgotnonose

The mathematical and physical ability of climate scientists appears to be very poor.
The worst case is the assumption by Houghton in 1986 that a gas in Local Thermodynamic Equilibrium is a black body. This in turn implies that the Earth’s surface, in radiative equilibrium, is also a black body, hence the 2009 Trenberth et. al. energy budget claiming 396 W/m^2 IR radiation from the earth when the reality is presumably 63 of which 23 is absorbed by the atmosphere.
The source of this humongous mistake is here: http://books.google.co.uk/books?id=K9wGHim2DXwC&pg=PA11&lpg=PA11&dq=houghton+schwarzschild&source=bl&ots=uf0NxopE_H&sig=8vlpyQINiMyH-IpQrWJF1w21LQU&hl=en&sa=X&ei=6Z2mT7XyO-Od0AWX3LGTBA&ved=0CGMQ6AEwBA#v=onepage&q&f=false
Here is the [good] Wiki write-up: http://en.wikipedia.org/wiki/Thermodynamic_equilibrium
‘In a radiating gas, the photons being emitted and absorbed by the gas need not be in thermodynamic equilibrium with each other or with the massive particles of the gas in order for LTE to exist….. If energies of the molecules located near a given point are observed, they will be distributed according to the Maxwell-Boltzmann distribution for a certain temperature.’
So, the IR absorption in the atmosphere has been exaggerated by 15.5 times. The carbon sequestration part is no surprise; these people are totally out of their depth so haven’t fixed the 4 major scientific errors in the models.
And then they argue that because they measure ‘back radiation’ by pyrgeometers, it’s real They have even cocked this up: a radiometer has a shield behind the detector to stop radiation from the other direction hitting the sensor assembly. So, assuming zero temperature gradient, the signal they measure is an artefact of the instrument because in real life it’s zero. What is measures is temperature convolved with emissivity, and so long as the radiometer points down the temperature gradient, that imaginary radiation cannot do thermodynamic work!
This subject is really the limit of cooperative failure to do science properly. Even the Nobel prize winner has made a Big Mistake!

I’m not sure of the significance of the e-folding time. I presume it must be related to the rate at which a particular sink absorbs CO2, in which case why not use the absorption time? As for the partitions, I just don’t get it. Surely there must be a logical explanation in the text for the various percentages listed.

Bart

ferd berple says:
May 6, 2012 at 12:25 pm
“About 1/2 of the annual human emission are absorbed each year.”
In the IPCC framework, that 1/2 dissolves rapidly into the oceans. So, if you include both the oceans and the atmosphere in your modeling, there is no rapid net sequestration.
I agree with the IPCC on the former. But, I do not agree with them that the collective oceans and atmosphere take a long time to send the CO2 to at least semi-permanent sinks.

Willis Eschenbach

Bart says:
May 6, 2012 at 12:21 pm

Willis Eschenbach says:
May 6, 2012 at 12:07 pm

“What I don’t get is what causes the fast sequestration processes to stop sequestering, and to not sequester anything for the majority of the 371.6 years … and your explanation doesn’t explain that.”

The best I can tell you is what I stated:”It has to do with the frequency of CO2 molecules coming into contact with absorbing reservoirs (a.k.a. sinks). If the atmospheric concentration is large, then molecules are snatched from the air frequently. If it is smaller, then it is more likely for an individual molecule to just bob and weave around in the atmosphere for a long time without coming into contact with the surface.” The link I gave explains it from a mathematical viewpoint.

No, the link you gave explains simple exponential decay from a mathematical viewpoint, which tells us nothing about the Bern model.
w.

Latitude

Willis said: What I don’t get is what causes the fast sequestration processes to stop sequestering, and to not sequester anything for the majority of the 371.6 years … and your explanation doesn’t explain that.
================================
Either there are five different types of CO2…..or CO2 is not well mixed at all……or each “tau” has a low threshold cut off point
The only things that can have a low threshold cutoff point are biology

stumpy

Cos the other sinks are fully saturated, or already absorbing all they can, so they leave the rest behind for the other longer sinks – then they can claim the natural sinks are saturated and we are evil despite it making no sense. Its all based on the assumption that before 1850 co2 levels were constant and everything lived in a perfect state of equilibirum just on the very the systems absorbtion capacity. Ahhh the world of climate science!

Bart

I must step away, so apologies if anyone has a question or challenge to anything I have written. Will check the thread later.

Mydogsgotnonose says May 6, 2012 at 12:26 pm:

The worst case is the assumption by Houghton in 1986 that a gas in Local Thermodynamic Equilibrium is a black body. … And then they argue that because they measure ‘back radiation’ by …

All I’ve got time for today is: Here we go again …
Welcome to the ‘troop’ which denies the measurable EM-nature of bipolar gaseous molecules, e.g. is studied in the field of IR Spectroscopy.
.

ferdberple

The rate of each individual sink is meaningless. What is important is that the total increase each year remains approximately 1/2 of annual emissions. Everything else is simply the good looking girls the magician uses to distract the audience from the sleight of hand.
As Willis points out, the thermos cannot know if the contents are hot or cold. Similarly, the sinks cannot know how long the CO2 has been in the atmosphere, so you cannot have differential rates depending on the age of the CO2 in the atmosphere.
1/2 the increased CO2 is absorbed each year. therefore 1/2 the residue must also be absorbed year to year. The sinks cannot tell if it is new CO2 or old CO2.

son of mulder

What are the mechanisms for removing CO2 from the atmosphere?
1. Asorbsion at the surface of seas and lakes
2, Absorbsion by plants through their leaves
3, Washed out by rain.
Any others?
What is the split in magnitude between these methods because I’d expect some sort of equilibrium for each of 1 & 2 whereas 3 seems to be one way.

Every year this lady named Mother Nature adds a whole lot of CO2 to the atmosphere, and every year she takes out a whole lot. The amount she adds in a given year is only loosely correlated with the amount she takes out, if at all. Year after year we add a little more CO2 to the atmosphere, still only around 4% of the average amount MN does. There is no basis for contending that the amount we add is responsible for what may or may not be an increased concentration with respect to recent history. All we know is that CO2 frozen in ice averages around 280 ppm, but this is definitely an average value as the ice can take hundreds of years to seal off. The only numbers in this entire discussion that have a basis in fact are 220 gT in and out, and an average four year residence time. All else is speculation/conjecture/WAG.
Occam’s Razor rules as always.

ferdberple

Bart says:
May 6, 2012 at 12:32 pm
In the IPCC framework, that 1/2 dissolves rapidly into the oceans.
Nonsense. The oceans cannot tell if that 1/2 comes from this year or last year. If the oceans rapidly absorb 1/2 of the CO2 produced this year, then they must also rapidly absorb 1/2 the remaining CO2 from last year in this year. And so on and so on, for each of the past years.
The ocean cannot tell when the CO2 was produced, so it cannot have a different rate for this years CO2 as compared to CO2 remaining from any other year.

Willis Eschenbach

rgbatduke says:
May 6, 2012 at 12:12 pm

Surely they don’t seriously use the sum of five or six exponentials, Willis. Nobody could be that dumb.

Thanks, Robert, your contributions are always welcome. Unfortunately, that is exactly what they do, with the additional (and to my mind completely non-physical) restriction that each of the exponential decays only applies to a certain percentage of the atmospheric CO2. Take a look at the link I gave above, it lays out the math.
Your derivation above is the same one that I use for the normal addition of exponential decays. I collapse them all into the equivalent single decay with the appropriate time constant tau.
But they say that’s not happening. They say each decay operates only and solely on a given percentage of the CO2 … that’s the part that I can’t understand, the part that seems physically impossible.
w.