For a another view on the CO2 issue, please see also the guest post by Tom Vonk: CO2 heats the atmosphere…a counter view -Anthony
Guest Post by Ferdinand Engelbeen
There have been hundreds of reactions to the previous post by Willis Eschenbach as he is convinced that humans are the cause of the past 150 years increase of CO2 in the atmosphere. For the (C)AGW theory, that is one of the cornerstones. If that fails, the whole theory fails.
This may be the main reason that many skeptics don’t like the idea that humans are the cause of the increase and try to demolish the connection between human emissions and the measured increase in the atmosphere with all means, some more scientific than others.
After several years of discussion on different discussion lists, skeptic and warmist alike, I have made a comprehensive web page where all arguments are put together: indeed near the full increase of CO2 in the atmosphere is caused by the human emissions. Only a small part might have been added by the (ocean) warming since the LIA. That doesn’t mean that the increase has a tremendous effect on the warming of the earth’s surface, as that is a completely different discussion. But of course, if the CO2 increase was mainly/completely natural, the discussion of the “A” in AGW wouldn’t be necessary. But it isn’t natural, as the mass balance proves beyond doubt and all other observations agree with. And all alternative explanations fail one or more observations. In the next parts I will touch other items like the process characteristics, the 13C and 14C/12C ratio, etc. Finally, I will touch some misconceptions about decay time of extra CO2, ice cores, historical CO2 measurements and stomata data.
The mass balance:
As the laws of conservation of mass rules: no carbon can be destroyed or generated. As there are no processes in the atmosphere which convert CO2 to something else, the law also holds for CO2, as long as it stays in the atmosphere. This means that the mass balance should be obeyed for all situations. In this case, the increase/decrease of the CO2 level in the atmosphere after a year (which only shows the end result of all exchanges, including the seasonal exchanges) must be:
dCO2(atm) = CO2(in1 + in2 + in3 +…) + CO2(em) – CO2(out1 + out2 + out3 +…)
The difference in the atmosphere after a year is the sum of all inflows, no matter how large they are, or how they changed over the years, plus the human emissions, minus the sum of all outflows, no matter how large they are, wherever they take place. Some rough indication of the flows involved is here in Figure 1 from NASA:
From all those flows very few are known to any accuracy. What is known with reasonable accuracy are the emissions, which are based on inventories of fossil fuel use by the finance departments (taxes!) of different countries and the very accurate measurements of the increase of CO2 in the atmosphere on a lot of places on earth, including Mauna Loa.
Thus in the above CO2 mass balance, we can replace some of the items with the real amounts (CO2 amounts expressed in gigaton carbon):
4 GtC = CO2(in1 + in2 + in3 +…) + 8 GtC – CO2(out1 + out2 + out3 +…)
Or rearranged:
CO2(in1 + in2 + in3 +…) – CO2(out1 + out2 + out3 +…) = – 4 GtC
Without any knowledge of any natural flow in or out of the atmosphere or changes in such flows, we know that the sum of all natural outflows is 4 GtC larger than the sum of all natural inflows. In other words, the net increase of the atmospheric CO2 content caused by all natural CO2 ins and outs together is negative. There is no net natural contribution to the observed increase, nature as a whole acts as a sink for CO2. Of course, a lot of CO2 is exchanged over the seasons, but at the end of the year, that doesn’t add anything to the total CO2 mass in the atmosphere. That only adds to the exchange rate of individual molecules: some 20% per year of all CO2 in the atmosphere is refreshed by the seasonal exchanges between atmosphere and oceans/vegetation. That can be seen in the above scheme: about 210 GtC CO2 is exchanged, but not all of that reaches the bulk of the atmosphere. Best guess (based on 13C/12C and oxygen exchanges) is that some 60 GtC is exchanged back and forth over the seasons between the atmosphere and vegetation and some 90 GtC is exchanged between the atmosphere and the oceans. These flows are countercurrent: warmer oceans release more CO2 in summer, while vegetation has its largest uptake in summer. In the NH, vegetation wins (more land), in the SH there is hardly any seasonal influence (more ocean). There is more influence near ground than at altitude and there is a NH-SH lag (which points to a NH source). See figure 2:
The net result of all these exchanges is some 4 GtC sink rate of the natural flows, which is variable: the variability of the natural sink capacity is mostly related to (ocean) temperature changes, but that has little influence on the trend itself, as most of the variability averages out over the years. Only a more permanent temperature increase/decrease should show a more permanent change in CO2 level. The Vostok ice core record shows that a temperature change of about 1°C gives a change in CO2 level of about 8 ppmv over very long term. That indicates an about 8 ppmv increase for the warming since the LIA, less than 10% of the observed increase.
As one can see in Fig. 3 below, there is a variability of +/- 1 ppmv (2 GtC) around the trend over the past 50 years, while the trend itself is about 55% of the emissions, currently around 2 ppmv (4 GtC) per year (land use changes not included, as these are far more uncertain, in that case the trend is about 45% of the emissions + land use changes).
We could end the whole discussion here, as humans have added about twice the amount of CO2 to the atmosphere as the observed increase over the past 150 years, the difference is absorbed by the oceans and/or vegetation. That is sufficient proof for the human origin of the increase, but there is more that points to the human cause… as will be shown in the following parts.
Please note that the RULES FOR THE DISCUSSION OF ATTRIBUTION OF THE CO2 RISE still apply!
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Dikran/Ferdinand
Well, I’ve explained it as carefully as I can, and at great length. The following is my last word.
Dikran and Narkid produced mathematically equivalent (similar to their names) equations, both of which were true. It was the conclusions they made based upon those equations, namely that the equations provided “sufficient proof for the human/volcano origin of the increase”, not the equations themselves, that were in error.
I think the root of your error is in the special status you afford to human actions.
Both humans and the volcano take fossil carbon (ie carbon that has not been part of the short-term carbon cycle for a very long time) and add it to that short-term cycle. It is not correct to assign a particular status to one source of fossil carbon (human) whilst lumping the other (volcano) in with the rest of the environment. That asymmetry in your analysis is wrong.
You analyse the situation (8GtsC/year human emissions, 4GtsC/year atmospheric gain) and say “4/8ths ie 50% of the additional C remains in the atmosphere”. The equivalent analysis with the volcano (80GtsC/year volcano, 8GtsC/year human emissions, 4GtsC/year atmospheric gain) should declare “4/88ths ie 4.55% of the additional C remains in the atmosphere”. If that were done, then it would be clearer that, in this hypothetical example, the fractional human contribution to the 4Gt rise was 8/88 (ie one eleventh) and the volcano contribution was 80/88 (ie ten elevenths).
The mass balance equation does not allow you to escape the messiness of the real environment: in order to show that the recent rise in atmospheric carbon has been (overwhelmingly) caused by human actions (which, of course, is the case) you need to quantify and give due status to all other possible sources of the increase. Simply asserting that the non-human environment as a whole has been a net sink for carbon, whilst true, brushes those assessment problems under the carpet. That is not correct.
Slioch wrote:
“I think the root of your error is in the special status you afford to human actions.”
There is a special status afforded to human actions. Government action on climate change will involve only human actions rather than asking the natural environment to solve the problem for us (assuming there is a problem) as the natural environment won’t be listening and will do its own thing regardless of our wishes. If we are not the cause of the rise, then why will cutting emissions help?
It is a shame you are bowing out, as I still haven’t quite worked out exactly where our views diverge. If you could explain in what sense the natural environment is a cause of the observed increase in atmospheric CO2, whilst also being a net sink (IIRC we agree that it is a net sink), that would help me to better understand your position (and hence better explain mine).
But if you are bowing out, it was a pleasure discussing it with you.
1. Ferdinand Engelbeen says:
August 11, 2010 at 11:57 am
Arthur Rörsch says:
August 11, 2010 at 4:49 am
But the fact remains that a tiny fraction of extra inflow (8/150) seems to disturb the system in such a way, that (also) non anthropogenic CO2 is accumulating strongly. That makes many people think by intuition that the extra inflow can not be the only cause of accumulation and do search for other causes of the unbalance, with many different in and outflows in the system and reservoirs that store the CO2 above the deep sea.
Arthur, what you are mixing up is the origin of the molecules with the origin of the increase in mass. Many before you have been confused by this, including Paul Birch as it seems now.
No Ferdinand I am not mixing up the origin of the molecules with the origin of the increase in mass. I hope to explain the difference of opinion mentioned above in due course with the further consideration of your presentation of the global mass balance.
2 Ferdinand Engelbeen says:
August 11, 2010 at 4:03 pm
Smokey,
Thanks, I agree that it is time to end this discussion. It differs the attention from the real question. But as I have said several times to Arthur Rörsch: the insistence on a possible non-human origin of the increase of CO2 in the atmosphere, where the evidence is overwhelming, makes that the credibility of all skeptics is undermined, not only of those who still believe that alternative explanations exist. Therefore this discussion is necessary, to weed out misconceptions in the skeptics world
No Ferdinand, I do not insist that the human emission is not contributing to the accumulation. What you name ‘overwelming’ evidence is in my opinion restricted to the coincidence between accumulation and the rise of human emission over half a century, and that the human emission has left a foot print (13C/12C) in the atmosphere.
About the credibility, I think that damage is done to the credibility of science as a whole if one abstains from the ‘Socratic doubt’ that things may be different than they may look at first sight, by oversimplifying a complex system. That is a misconception I want to weed out in general. Please give me a few more days to produce a post on these matters. I have to focus my attention today on a review of a manuscript for a lecture, on the request of the lecturer, on what you name the ‘real question’ (on which we agree). What is the role of CO2 in establishing a change in the greenhouse effect?
Arthur Rörsch writes:
“About the credibility, I think that damage is done to the credibility of science as a whole if one abstains from the ‘Socratic doubt’ that things may be different than they may look at first sight, by oversimplifying a complex system.”
Any orator is free in a rhetorical debate is thus free to arbitrarily ignore ANY simplified representation of a complex system on the grounds that it left “socratic doubt” through oversimplification. However, one would hope this is not a rhetorical discussion, where victory depends on oratory, but a scientific discussion aimed at discovering truth. As such, one cannot disregard an example that demonstrates a fundamental flaw in our position without first engaging in a proper discussion. One is duty bound to engage in constructive discussion and understand your opponents position, and if at the end of the discussion you can’t refute the argument, then you should concede that you can’t.
If you don’t currently have the time to discuss the matter, that is fine, however dismissing a counter example without properly engaging with it is not science, it is rhetoric.
Note my last response to slioch – I am still trying to find out the exact point of divergence so I can identify why we don’t agree, I haven’t ruled out the posibility he is right, its just that neither of us is yet convinced by each others arguments – so I acknowledge it is in the balance. Neither of us ought to be free of absolutely doubt regarding our position and I don’t think either of us are (for a start if we were, would we be trying so hard to understand where the divergence arises?).
I do have doubts about whether I am right, the greatest is that the data are wrong (I’m pretty certain about conservation of mass). It could be that our estimates of emissions are an over-estimate bu 100% (which is what would currently be needed for the conclusions of the mass balance argument to change), but there has been little argument provided to suggest that is likely to be the case. I am also a Bayesian, which means I am never certain about anything unless it is a logically necessity.
Where is your doubt regarding your own position?
Arthur Rörsch: “No Ferdinand, I do not insist that the human emission is not contributing to the accumulation. What you name ‘overwelming’ evidence is in my opinion restricted to the coincidence between accumulation and the rise of human emission over half a century, and that the human emission has left a foot print (13C/12C) in the atmosphere.”
Your opinion of Ferdinand’s evidence is a misrepresentation of the evidence he has presented. The mass balance argument demonstrates that the natural environment is a net sink, taking in more CO2 than it emits, and so it is not merely a coincidence between the accumulation and the rise of human emissions, we know* that the natural environment has been activaly opposing the rise (as one would expect from a system in approximate equilibrium that is peturbed – in this case by anthropogenic emissions).
* This knowledge is conditioned on the assumptions of conservation of mass and that the emissions data and atmospheric CO2 data is sufficiently accurate to be confident that human emissions exceed the annual growth. There is always “socratic doubt”, but that doesn’t mean it isn’t negligible. In this footnote I have identified the weakpoint in the argument to help you to attack it.
Dear Slioch,
Dikran and Narkid produced mathematically equivalent (similar to their names) equations, both of which were true.
Agreed. But the problem is that Narkid didn’t know of the human emissions and lumped all together as natural. If he had known of the human emissions, his equation would have reflected that and substracting the human emissions as not natural, would have shown more sink than source for all natural fluxes, including the 80 GtC volcano one-way emission.
The root of the difference in opinion indeed is that you don’t separate the human input from the natural inputs and we do, while others like Paul and Arthur even see all input fluxes as adding to the increase, but forget that many of the largest output fluxes are to the same reservoirs which act as sources ánd sinks: oceans and vegetation. Without human emissions, no increase, all the rest remaining equal (we know that wouldn’t be forever, but the evidence is clear that we are now operating above equilibrium). Without the 80 GtC volcano, a big drop in CO2 levels, all the rest remaining equal. But as long as the increase is above zero and less than the emissions, the increase is entirely from the emissions, all the rest remaining equal.
If that were done, then it would be clearer that, in this hypothetical example, the fractional human contribution to the 4Gt rise was 8/88 (ie one eleventh) and the volcano contribution was 80/88 (ie ten elevenths).
Be careful not to fall in the same trap as many before you: Both the human emissions and the volcano add to the input fluxes and the fraction human in these input-only flows indeed is 8/88. The fraction is what the origin of the molecules indicates. If we forget that the throughput fluxes also have a (near equal) output besides the inputs, it is even 8/238 (8 human, 80 volcano, 90 oceans, 60 vegetation). That doesn’t tell us anything about the cause of the increase, as the inputs are balanced with the outputs:
238 – (92 oceans + 62 vegetation + x unknown sink)= 4 GtC. Thus x in this case is 80 GtC of unknown sink capacity and the volcanic inputs are fully compensated with some unknown sink with equal capacity. It even doesn’t matter if vegetation was a net source and the oceans a larger sink, the mass balance tells us that the extra volcanic CO2 is absorbed somewhere else in nature (where absorbed means as mass, not as “volcanic type” molecules). That only holds as long as one separates the human emissions from the total of natural sources/sinks.
If the volcano and the human emissions had the same “fingerprint” it would be impossible to separate the origin of the CO2 molecules of these two sources in the atmosphere. But they don’t: volcanic CO2 in general is not 13C depleted (it comes often from chalk deposits), fossil fuel is. The separation of human emissions and vegetation is impossible on the basis of 13C/12C ratio’s (both are firmly depleted) but it is possible on the basis of 14C/12C ratio’s and oxygen use. But that will be for one of the next parts, if we ever can end this one…
BTW, there is a maxim in science known as Occam’s razor, which implies that if two explanations both fit the data equally well, then we should prefer the more simple.
Firstly, there is the injunction that both theories should fit the data equally well. Any theory that suggests the natural environment is a net source of CO2 into the atmosphere is not consistent with the data. So if your theory suggests that the netural envrionment is a net source, then it fails at the first hurdle, as Ferdinand has already pointed out.
The second part arises because ANY set of observations can be explained by an arbitrarily complicated explanation, regardless of whether the explanation is actually correct or not. In statistics this is called “over-fitting”. Thus, pointing out that there may be aliens from the planet Zog, or robbers who might ruin bank-balance related analogies is in direct contravention of a very well known principle of science. Now if you can argue that there is good reason to believe the aliens from Zog have a genuine parallel in the real world system being modelled, that is one thing, but just rejecting the model is “too simple” is unscientific.
GEP Box said “all models are wrong, but some are useful”. Here he is acknowledging that all models are wrong because they simplified versions of reality. So if it is valid that models leave “socratic doubt” and thus can be ignoring; then the same argument can be used to ignore any scientific finding you like outside the world of pure maths.
But as long as the increase is above zero and less than the emissions, the increase is entirely from the emissions, all the rest remaining equal.
All the rest of the natural emissions and sinks don’t even need to remain equal, they may vary widely, as long as the sum of all in/out fluxes remains equal to the difference between the increase in the atmosphere and the emissions, obeying the mass balance, i.e. negative over the past 50 years…
Arthur Rörsch says:
August 12, 2010 at 3:45 am
1. But the fact remains that a tiny fraction of extra inflow (8/150) seems to disturb the system in such a way, that (also) non anthropogenic CO2 is accumulating strongly.
You still confuse matters: the addition of (increasing) human emissions adds to the total inflow ánd to the increase in the atmosphere, as there is no similar human sink to compensate for the human emissions. The addition of natural releases (increasing or not), adds to the total inflow, but not to the increase, as the natural sinks more than compensate for the releases, because larger than the releases. Thus there is no accumulation of non-anthro CO2 as mass in the atmosphere, but there may be a huge increase in non-anthro molecules, as about 20% of the whole atmosphere is replaced per year. That replaces 20% of the anthro CO2 with non-anthro CO2 per year, without increasing the total mass of CO2 (to the contrary, it takes some 4 GtC CO2 away). Thus the increase in CO2 mass in the atmosphere is entirely caused by the anthro releases, but the bulk of the increase still is largely by non-anthro CO2 molecules. The example of Dikran, August 10, 2010 at 7:34 am describes exactly the mechanism behind it.
2. No Ferdinand, I do not insist that the human emission is not contributing to the accumulation. What you name ‘overwelming’ evidence is in my opinion restricted to the coincidence between accumulation and the rise of human emission over half a century, and that the human emission has left a foot print (13C/12C) in the atmosphere.
Indeed you don’t say that human emissions are not contributing, but you insist that there “may” be other (known or unknown) sources of the increase. Which is impossible, as that would be a violation of the mass balance.
The human emissions fit all known observations: the mass balance, the 13C/12C ratio (atmosphere and upper oceans), the pre-1945 14C/12C ratio (atm), the pH decreases and DIC increases (upper oceans) and the process characteristics of the carbon cycle.
Any alternative theory needs to fit all the above observations. If there is one contradiction, then the theory fails. Until one has a solid alternative that fits all observations, it is very unwise to come out with some vague ‘Socratic doubt’ that there ‘may’ be alternatives, when the ‘consensus’ on this point is very solid. That is what I fear.
Paul Birch writes
Oh, OK, if we are admitting what I call “invisible fairies” hypotheses (in the sense of, “We don’t know that objects fall due to gravity, because nobody has proved that it isn’t due to invisible fairies”), then I suppose that there are other hypotheses. But you agree that if we limit ourselves to realistic possibilities, then for CO2 to increase by a similar amount in the absence of a human contribution, then the absence of that human contribution would somehow have to trigger either an increase in inflows, a decrease in outflows, or some combination of the two.
OK, I understand that you are not using “equilibrium” according to its formal meaning, but in a colloquial sense that corresponds to what would be considered to be a steady state in the thermodynamic sense. I’ll continue to call it a steady state, with the understanding that we are talking about essentially the same thing.
So I think we are back to the problem that troubled me before with your hypothesis, which as I understand it is that, absent anthropogenic CO2 emissions, some natural process would increase natural CO2 inputs and/or decrease outputs so that the environment would become a net source of CO2, resulting in something approaching to the current +4GtC mass balance. You are making the argument that if the increase would have happened anyway, then the human influence cannot be considered causal. (I’m not entirely sure about the latter part, by the way. I’m pretty sure that if you shot somebody and he died, your lawyer would have little success defending you on the grounds that there was another guy behind you who would surely have killed the guy if you had missed. But let’s accept it for the sake of argument.)
We know from the mass balance that the environment is acting as a net CO2 sink, which tells us the atmospheric CO2 level already exceeds the current steady state value. Under your hypothesis, if human emissions were to drop out, the steady state atmospheric CO2 value would have to shift to above its current level in order for the environment to become a net source of CO2. This seems very strange. Normally, when an input is eliminated, the steady state point is reduced, but you would have it moving in the opposite direction to overshoot the current atmospheric CO2. I can’t imagine any way something like this could happen, without invoking “invisible fairies.”
Slioch says:
“You analyse the situation (8GtsC/year human emissions, 4GtsC/year atmospheric gain) and say “4/8ths ie 50% of the additional C remains in the atmosphere”. The equivalent analysis with the volcano (80GtsC/year volcano, 8GtsC/year human emissions, 4GtsC/year atmospheric gain) should declare “4/88ths ie 4.55% of the additional C remains in the atmosphere”. If that were done, then it would be clearer that, in this hypothetical example, the fractional human contribution to the 4Gt rise was 8/88 (ie one eleventh) and the volcano contribution was 80/88 (ie ten elevenths).”
You appear to be using an “attribution” formula very similar to that of Arthur Rorche, which I demonstrated to be misleading (at best) here: here
This concerns my rereading of the mass balance arguments. I begin to understand the reasoning why in the flow system through the atmosphere a contribution of an increased natural flow is supposed to be excluded by the argument that the natural system is a net sink. But let’s consider two cases.
Case 1
Let’s start from a balanced situation. The accumulation in the atmosphere Fa=0 because a large (standard) inflow FSin equals an outflow FSout. (order of magnitude 100-150 GtC/y)
[1] Fa=0 = FSin – FSout
Then we add to the inflow a value dFin (a natural inflow that disturbs the equilibrium state Fa=0) .
[2] Fa = (FSin + dFin) – FSout
If FSin and FSout do not change
[3] Fa = dFin All extra inflow is accumulating. The CO2 in the atmosphere increases.
We can expect however, that this causes a increase in FSout, named dFout .
If there is no constraint on the out flow we may still consider a situation that dFout equals dFin
[4] Fa = (FSin + dFin) –(FSout+dFout) and the Fa returns to 0
If there is a constraint , dFout will not rise to dFin, but still we may expect some rise, having the CO2 increase in the atmosphere as a driving force.
Now Fa gets a value
[5] Fa= (FSin – FSout) + (dFin-dFout) = 0 +dFin – dFout
With the consequence
[6] dFout < dFin Thus dFout – dFin 0
Conclusion [A] Thus the extra flow FemIN is expected to change the sign of (dFout-dFin), by the rise of dFout, but still below the value (FemIN+dFin) and that is considered to be the signal that the FemIN is the (single) cause of the accumulation Fa.
Case 2
We start again from the balanced situation but replace in [2] dFin by FemIN
[9] Fa = FemIN +FSin – FSout
As yet there is not an ‘natural’ additional flow considered.
If FSout does not change [3] becomes
[10] Fa = FemIN (All FemIN is accumulating.)
Again we assume that the rise of CO2 in the atmosphere produces a increased FSout again named dFout . Then [5] becomes
[11] Fa= FemIN – dFout
Fa can only get a value below FemIN if
[12] dFout <FemIN ( compare [6])
Next we assume an extra natural flow in, dFin and we come to the same equations as [7]
[13] Fa= (FemIN +dFin) – dFout
In which dFout further increases under the force of added dFin and may be above dFin. But still dFout dFin. (see [13]
The question is how much each FemIN and dFin are contributing to the value for dFout.
An exercise. (with the assumption that the dFin plays a role to obtain a value for Fa).
We split the dFout in two parts, dFoutA caused by the FemIN and dFoutN, caused by the dFin. Then [13] reads:
[14] Fa= FemIN-dFoutA + dFin-dFoutN
We assume that dFoutA is a fraction x of FemIN and dFoutN is also a fraction x of dFin
[15] Fa= FemIN(1-x) + dFin(1-x)
Then we can calculate how much dFin is required to bring Fa to a value of Fa=3.5 with an FemIN =7 (The situation in the year 2000, with 370 ppmv in the atmosphere.)
[16] dFin = {(Fa-FemIN(1-x)}/(1-x)
Next we assume that half of the FemIN is taken out x=0.5 but also it may have a higher value 0.5<x0.7
My view.
The argument that the net result for outflow and inflow is positive is not proof that a current imbalance in the natural cycle (which persists for some time) is not playing a role in the amount of accumulation in the atmosphere. The ‘proof’ is based on the assumption there is no natural imbalance and that half of an extra emission (FemIN) above the balanced state (FSin=FSout) is sequestered only for 50%.
If the response of the natural system is so, that it can sequester more than 50% of an extra emission , than we can explain the level of Fa (accumulation in the atmosphere) only by a contribution of the unbalance in the natural cycle.
The question was raised previously, why consider a more complicated case than based on the assumption that only FemIN is producing a value for Fa? (Why not apply Ockham razor? ).
The ‘razor’ rule states that in reasoning no arguments should be used which are not based on logic deduction or observation. (The rule is NOT that the most simple explanation should be preferred.)
The observations show that the CO2 cycles are complex and may be influences by many different forces, which deserve further investigation. There is little doubt that over half a century both FemIN and Fa have increased. (from 1960-2000 FemIN from 3 to 7 GtC/y. Fa (as an average) from 2 to 3.5 GtC/y. ). The FemIN increase is steady (R^2 = 0.95), but the Fa is not (R^2 = 0.27). It shows from year to year large fluctuations which are of the order of magnitude of the Fa itself. (The largest: 1998 Fa= 5.8 GtC/y 2000: 2.5 GtC/y) . It leads to the conclusion that also the introduced ratio x may be subject to strong variation. But not necessarily so exclusively. It has been pointed out previously that in the global mass balance equation
[7] Fa = (FemIN +dFin) – dFout
we are dealing with one equation with two unknowns, dFin and dFout.
We do not know whether (dFout-dFin) is, to what extend, or was during certain periods, positive or negative
The accumulation of CO2 in the atmosphere can be due in principle not only to increased up welling (dFin) from, but also by decreased down welling (dFout) to the deep sea, processes which are not controlled only by definition by the concentration of the CO2 in the atmosphere but also by the of incidence of weather events and ocean currents which ‘carry’ the gas.
In the overall global CO2 circulation, up welling from the deep sea near the equator, down welling to the deep sea, do participate many compartments which are involved in the exchange op CO2. Equation [7] is a very strong simplification of an interaction among the compartments, e.g., the air, the biosphere, the soils and the boundary (mixing) layer of the oceans, all behaving differently from 90 degree South to 90 degree North.
An interesting question is how much of total human emission in the atmosphere after being produces by burning of fossil fuels, reaches the sink in the major global cycle. It has been suggested that the FemIN, with its low 13C/12C has a preference to be taken up by the vegetation in the neighbourhood of its sources. And that the FemIN has increased the vegetation + soil reservoir. It means that the amount of FemIN that reaches the global (ocean) cycle is less than 7 GtC/y. This is one of the arguments why the FemIN may not upset the global cycle as expected at first sight, because of its preferential absorption in the biosphere.
Lastly, to summarize, in our current dispute on this blog, the most essential theoretical element is the ratio (x): to what extend an increased flow into the atmosphere, will itself contribute to an forced outflow. (This point is not dealt with in metaphors about contributions to, and withdrawals from a bank account).
I think it is premature to deduce from current (global) observations a value for x. Too easily creeps in the preposition that the human emission is the sole cause of rise of CO2 in the atmosphere, which then is considered a circular argument to prove that preposition. The ratio x may be much larger than the value 0.5. That will lead to the conclusion that the CO2 balance is pretty robust to meet changes of extra inflow. On the other hand, in theory we could also face the situation that x<0.5. There may be, at current levels of CO2, a very strong constraint to absorb from the atmosphere, because, according to the law of diminishing profit, there is a maximum value for this absorption. (Explained in our E&E paper 16(2) 2005)
My feeling is that belief in this constraint is in fact the intuitive base for the preposition of the major influence of the human emission on the accumulation. They who oppose this, belief in a more robust reaction of the system on minor disturbances.
Arthur Rörsch says:
August 15, 2010 at 4:31 am
Dear Arthur,
The problem starts at equation [13]:
[13] Fa= (FemIN +dFin) – dFout
In which dFout further increases under the force of added dFin and may be above dFin. But still dFout dFin. (see [13]
The question is how much each FemIN and dFin are contributing to the value for dFout.
The last question is easily answered, as we know Fa and FemIN for each year in the past 50 years. For the year 2000 that makes:
3.5 = (7 + dFin) – dFout
or dFin = dFout -3.5 GtC
Thus whatever the changes in dFin, dFout must follow the mass balance and for any amount of Fin, or any change in Fin, the result for the year 2000 is 4.5 GtC more outflow than inflow, thus we have an equation with one unknown, as one of the unknowns directly depends of the other. The contribution of dFin to dFout may be huge, but the contribution of dFin to Fa still is zero, as dFin is less than dFout in all cases over the past 50 years.
Thus dFin plays no role in Fa at all…
In the following equations [14]-[16] you confuse between the origin of the CO2 molecules which contribute to Fa (which for Fem indeed is about 7/150) and the contribution to the total mass increase of Fa (which is for Fem 7/3.5)…
Dear Ferdinand
[13] Fa= (FemIN +dFin) – dFout
AR: “The question is how much each FemIN and dFin are contributing to the value for dFout.”
FE: “The last question is easily answered, as we know Fa and FemIN for each year in the past 50 years. For the year 2000 that makes”:
[13a] 3.5 = (7 + dFin) – dFout
or dFin = dFout -3.5 GtC
Thus whatever the changes in dFin, dFout must follow the mass balance and for any amount of Fin, or any change in Fin, the result for the year 2000 is 3. 5 GtC more outflow than inflow, thus we have an equation with one unknown, as one of the unknowns directly depends of the other. The contribution of dFin to dFout may be huge, but the contribution of dFin to Fa still is zero, as dFin is less than dFout in all cases over the past 50 years.
Thus dFin plays no role in Fa at all “
AR: I think this is the base of the circular argument.
Consider again my reasoning, that IF dFin plays a role and dFout is partly due to FemIN and partly to dFin to the same proportion factor x of of FemIN and dFin
dFout = x*FemIN + x*dFin
then [13] reads:
Fa= (FemIN+dFin) – (x*FemIN+x*dFin)
Fa = (FemIN + dFin) * (1-x)
Filling in [13a]
3.5 = (7+dFin) * (1-x)
If x= 0.5 then dFin = 0.
That is your statement: x = 0.5 and therefore dFin=0
But if x>0.5 than you need a contribution of dFin to reach the level of Fa=3.5. And there is no reason to assume beforehand that any extra inflow would not be sequestered above the ratio x=0.5. With higher values of x, the mass balance is still satisfied.
Again, the ratio x=0.5 arises from the assumption that the FemIN is the only cause for the value of Fa.
PS
I see to my surprise that part of my former post, has been deleted. May be that has confused you.
It reads after equation [16] in the exercise:
An exercise. (with the assumption that the dFin plays a role to obtain a value for Fa).
We split the dFout in two parts, dFoutA caused by the FemIN and dFoutN, caused by the dFin. Then [13] reads:
[14] Fa= FemIN-dFoutA + dFin-dFoutN
We assume that dFoutA is a fraction x of FemIN and dFoutN is also a fraction x of dFin
[15] Fa= FemIN(1-x) + dFin(1-x)
Then we can calculate how much dFin is required to bring Fa to a value of Fa=3.5 with an FemIN =7 (The situation in the year 2000, with 370 ppmv in the atmosphere.)
[16] dFin = {(Fa-FemIN(1-x)}/(1-x)
Next we assume that half of the FemIN is taken out x=0.5 but also it may have a higher value 0.5<x0.7
I see to my surprise that again the post refuses to produce the reasoning after equation [16]. Why?
I shall have another try.
Dear Ferdinand
I have another try to bring a deleted part of my former post to your attention . An for the sake of clarity I also repeat my previous counter argument.
[13] Fa= (FemIN +dFin) – dFout
AR: “The question is how much each FemIN and dFin are contributing to the value for dFout.”
FE: “The last question is easily answered, as we know Fa and FemIN for each year in the past 50 years. For the year 2000 that makes”:
[13a] 3.5 = (7 + dFin) – dFout
or dFin = dFout -3.5 GtC
Thus whatever the changes in dFin, dFout must follow the mass balance and for any amount of Fin, or any change in Fin, the result for the year 2000 is 3. 5 GtC more outflow than inflow, thus we have an equation with one unknown, as one of the unknowns directly depends of the other. The contribution of dFin to dFout may be huge, but the contribution of dFin to Fa still is zero, as dFin is less than dFout in all cases over the past 50 years.
Thus dFin plays no role in Fa at all “
AR: I think this is the base of the circular argument.
Consider again my reasoning, that IF dFin plays a role and dFout is partly due to FemIN and partly to dFin to the same proportion factor x of of FemIN and dFin
dFout = x*FemIN + x*dFin
then [13] reads:
Fa= (FemIN+dFin) – (x*FemIN+x*dFin)
Fa = (FemIN + dFin) * (1-x)
Filling in [13a]
3.5 = (7+dFin) * (1-x)
If x= 0.5 then dFin = 0.
That is your statement: x = 0.5 and therefore dFin=0
But if x>0.5 than you need a contribution of dFin to reach the level of Fa=3.5. And there is no reason to assume beforehand that any extra inflow would not be sequestered above the ratio x=0.5. With higher values of x, the mass balance is still satisfied.
Again, the ratio x=0.5 arises from the assumption that the FemIN is the only cause for the value of Fa.
PS
I see to my surprise that part of my former post, has been deleted. May be that has confused you.
It reads after equation [16] in the exercise:
An exercise. (with the assumption that the dFin plays a role to obtain a value for Fa).
We split the dFout in two parts, dFoutA caused by the FemIN and dFoutN, caused by the dFin. Then [13] reads:
[14] Fa= FemIN-dFoutA + dFin-dFoutN
We assume that dFoutA is a fraction x of FemIN and dFoutN is also a fraction x of dFin
[15] Fa= FemIN(1-x) + dFin(1-x)
Then we can calculate how much dFin is required to bring Fa to a value of Fa=3.5 with an FemIN =7 (The situation in the year 2000, with 370 ppmv in the atmosphere.)
[16] dFin = {(Fa-FemIN(1-x)}/(1-x)
Next we assume that half of the FemIN is taken out x=0.5 but also it may have a higher value 0.5<x0.7
Dear Ferdinand,
Again, the post deleted part of my text. What the hell is happening? Question to the moderator.
I shall send you now my previous post directly to your own e-mail adress.
Dear Arthur,
There may be a problem with the “less than” and “greater than” signs, which the HTML language sees as command tags. Especially after the “less than” sign, this may delete all following text…
Have a look where it happens and replace the “less than” sign with plain text…
Dear Arthur,
Here follows the missing part in your comment of August 15, 2010 at 4:31 am, indeed it was caused by the second less than sign :
Next we assume that half of the FemIN is taken out x=0.5 but also it may have a higher value 0.5 less than x less than 1
And that the same ratio has to be applied to dFin
The result for several values of x in [16] is presented here
Fem=7 . .Fa=3.5
x . .dFin ,
0.5 0
0.6 1.75
0.7 4.666667
0.8 10.5
0.9 28
If x = 0.5 than dFin = 0. As expected, if half of the amount of the FemIN is sequestered and there is no natural dFin.
With increasing ratio x of sequestration of FemIN, a dFin has to contribute to reach the value Fa=3.5 (see [15])
See for example that with x= 0.7, (70 % of the 7 GtC/y FemIN is absorbed) than 4.7 GtC/y extra ‘natural’ inflow is required to reach the accumulation value Fa=3.5 GtC/y.
In principle there is no reason to assume a priori that the absorption ratio is not larger than half of the amounts of the inflows, or even >0.7
Dear Arthur,
There is an essential problem in equation [13a]:
dFout is not proportional to FemIN, neither to dFin, but to the difference in total CO2 mass (pCO2) over the “equilibrium” CO2 level, whatever that might be (but probably around 300 ppmv). Thus we need to look at the total balance:
Fa = Fin + FemIN – Fout were the difference between Fin and Fout is proportional to the difference between the current amount in the atmosphere and the equilibrium level, or about 3.5/(800-580) = 3.5/220
(I know that it is more difficult than that, but for the atmosphere-deep oceans this is about right). But the real equilibrium level doesn’t matter much for the current balance, only matters for the evolution of Fin-Fout.
The 3.5 GtC unbalance thus is not directly dependent of Fin/FemIN/dFin, but is taken from the bulk of CO2 in the atmosphere, currently 800 GtC, thus only 3.5/800 or 0.4% of total CO2. That is also 0.4% of an eventually increase caused by (Fin + FemIN + dFin – Fout).
This all makes that dFin doesn’t play much role in establishing dFout and equation [15] can be solved, because x is quite low (0.4%):
[15] Fa= FemIN(1-x) + dFin(1-x)
or
[15] Fa ~= FemIN + dFin
Because FemIn is larger than Fa and Fa is larger than zero in the past 50 years, dFin must be negative and between zero and FemIN in absolute value.
We have looked now at dFin only, implying that dFout is more or less fixed, but the same reasoning applies to any natural variability in sink rate dFout. But in reality it applies to the combination of dFin and dFout: the net result of both together must be +/- around the trend of Fa. If positive, then less than the emissions minus Fa, if negative then less than Fa. That is what we see as natural variability around the trend in the past 50 years…
In all cases, there is no contribution of dFin or dFout or the net effect of both to the increase in the atmosphere, as long as the increase in the atmosphere is less than the human emissions.
That the sequestering is quite constant at about 55% of the emissions is not coincidence: the emissions are increasing slightly exponential (even if temporarely reduced by an economical crisis), which results in this case in a slighlty exponential increase in the atmosphere. That indicates that the whole natural carbon cycle reacts as a simple linear process, disturbed (a little) by temperature and (largely) by the emissions.
Figure 1 which you have attributed to NASA I believe needs some attention. Lumping fossil fuels and cement together does not aid understanding. From my research total world recoverable reserves of fossil fuels are about 1000GtC and calcite deposits are about 6,000,000 GtC. This compares with 40,000 GtC in the oceans and 750 GtC in the air.
It occurs to me that if all the recoverable world resource of fossil fuel were dumped into the biosphere the impact would be negligible once equilibrium was re-established.
Jim McK says:
August 15, 2010 at 9:16 pm
It occurs to me that if all the recoverable world resource of fossil fuel were dumped into the biosphere the impact would be negligible once equilibrium was re-established.
This is one of the controversies with the Bern model: the Bern model includes very fast equilibrium with the upper part of the oceans (the “mixed layer”), but its capacity is only 10% of the increase of CO2 in the atmosphere. A larger part is going into the deep oceans (about 30%) which needs much longer time frames, and the rest is going into deposits or are absorbed via rock weathering. And some part even will stay forever in the atmosphere. That is the Bern model, which is used by the IPCC.
But the Bern model is based on 3000 to 5000 GtC, that is burning all available oil and most of the available coal. In reality, until now, the total accumulated burning of all fossil fuels added a part to the atmosphere and half of it is already absorbed by the deep oceans and vegetation. If we stop the emissions today, the level in the atmosphere would probably go down to the temperature controlled equilibrium with a rate of about 40 years half life time (mostly in the deep oceans), but that will increase the deep ocean CO2 level with about 1%. That comes back some time (~1000 years) later in upwelling zones and the new equilibrium then might be some 1% higher than the pre-industrial level of 300 ppmv. Hardly a problem.
See the discussion of Peter Dietze at the late John Daly’s website:
http://www.john-daly.com/carbon.htm
Thus how much remains in the atmosphere after the equilibrium is re-established is mainly a matter of total emitted quantity, as the deep oceans are the main buffer for the atmospheric levels, the other reactions (except more permanent sequestering by plant carbon) are much slower.
Dear Ferdinand,
You still state “In all cases, there is no contribution of dFin or dFout or the net effect of both to the increase in the atmosphere, as long as the increase in the atmosphere is less than the human emissions”
And your argument is: “There is an essential problem in equation [15]:
dFout is not proportional to FemIN, neither to dFin, but to the difference in total CO2 mass (pCO2) over the “equilibrium” CO2 level, whatever that might be (but probably around 300 ppmv). Thus we need to look at the total balance:
[15] Fa= FemIN(1-x) + dFin(1-x)
I do not think there is a problem in the equation.
For sure, the fraction of FemIN going out (x*FenIN) is not directly correlated to FemIN, neither the fraction of dFin is, to what is going out x*dFin, by a cause-effect equation. The CO2 concentration in the atmosphere will be in such an equation.
But nevertheless we can define a ratio what of each is going out and in, at a particular moment. (Or as an average over 50 years). And I think that we must assume that the ratio FemA/FemIN will have the same value x as dFinN/dFin, because the sinks will not discriminate between the CO2’s from different origins. (The biosphere might, but I think that this is a minor component) .
(FemA is the amount anthropogenic CO2 going out, dFinN the amount of ‘natural’CO2 going out.)
I really think I have now identified the background of the circular argument.
It is that you take it for granted that half of the amount of the FemIN is accumulation as Fa. Thus x-0.5
In [15] the equation reads:
[15a] 3.5 = 7*(1-0.5) + dFin*(1-0.5) with the result that dFin =0
If the system is less sensitive to changes in inflow , say x=0.75
[15b] 3.5 = 7*0.25 + dFin*0.25 than dFin has a value
7+dFin = 3.5/0.25 . dFin=14-7= 7
Note that also [15b] fulfils the requirement that Fa<FemIN.
I am not saying that [15b] is proof that there is a contribution from a natural source. (x is greater than 0.5 is an arbitrary choice. But so is x=0.5). I am saying that the equation [15a] is based on a circular argument.
I think it is important to reckon with a possible natural unbalance contributing to the accumulation. The human emission provides for a valuable tracer to investigate all flows in the system and one may come to wrong conclusions if one adheres to x=0.5 only.
Note, I speak of a natural unbalance, not necessary of an increased natural flow. Indeed, x may be smaller than 0.5 . x is smaller when there is over some time a strong constrained on the sinks.
I have explained in my original post on the subject what may be the cause of an x below or above the value 0.5. In the first case the system is operating near a saturation point (for the sinks) In the second case at a considerable distance from saturation.
Since the Fa shows an annual fluctuation of the same order of magnitude as the average (increasing) Fa I favour for the time being the second case.
Arthur Rörsch says:
August 16, 2010 at 2:38 am
I really think I have now identified the background of the circular argument.
It is that you take it for granted that half of the amount of the FemIN is accumulation as Fa. Thus x-0.5
Not at all: what is accumulating is the emissions FemIN + any extra natural inflow dFin – dFout
where dFout is 0.4% of the total amount of CO2 in the atmosphere. That is hardly influenced by any moderate increase in FemIN and/or change in dFin and may be smaller or larger or much larger than FemIN or dFin or the sum of both.
In all cases, dFout thus is only 0.4% of 800 GtC + 0.4% of FemIN + 0.4% of dFin
Thus in [15] the equation reads:
[15a] 3.5 = 7*(1-0.004) + dFin*(1-0.004) with as result that dFin is much less than 0
In other words: you can’t make dFin positive as long as the emissions are higher than the increase in the atmosphere.
Of course, dFin can be positive in some circumstances, but then the result would be larger than the emissions alone.
Dikran/Ferdinand
Well, I said my post of August 12, 2010 at 12:00 am would be my last word, since I didn’t seem to be getting through, and I had other things to do, but I will spend a few minutes on a slightly different track. Previously I used the reductio ad absurdum on your mass balance equation. The problem with that tack is that, of course, it produces scenarios which are absurd and which may therefore be as unrealistic without the realisation that they expose a logical error.
So, I will now abandon reductio ad absurdum and propose a far more feasible scenario, but before I do so, let me remind you where I’m coming from. I have been attempting, on forums such as this, to persuade people of the overwhelmingly human responsibility for recent increases in atmospheric CO2 for some years. See, for example, my first post ( Slioch says: August 5, 2010 at 10:30 am ) in this thread, which a copied an example of the reasoning I have employed to that end previously. So, my concern about your use of the mass balance equation is that it does not BY ITSELF adequately address that issue.
So, here is another scenario, unlikely, though not altogether impossible, to illustrate why the mass balance equation by itself is insufficient and why, therefore, SOLE reliance on it to try to persuade people of human responsibility for the increase in atmospheric CO2 is likely to be counter-productive.
You use the following data (which I will accept for the sake of argument):
annual human emissions of fossil C to atmosphere = 8Gtons
annual increase in C in atmosphere = 4Gtons
and you therefore correctly state that the non-human environment is a net sink of CO2.
Where we differ is your insistence that THIS proves that the increase in atmospheric CO2 is entirely caused by human actions.
So, consider this scenario: a supervolcano (eg Yellowstone) or somewhere in the Pacific suddenly starts to erupt and adds 1Gton of CO2 to the atmosphere annually (the figure is not important as long as it is large enough that you would recognise its contribution as significant). How would the atmosphere/environment react to such a new source of CO2?
Human emissions (we assume) would continue at 8Gtons/pa, but now they are joined by an extra 1 Gton/pa of fossil C from our new volcano, making 9Gtons in total. There is no reason to suppose that the environment would act in any different way to this new source of fossil CO2 than it does to the new source of fossil CO2 produced by humans – ie it would absorb about half of it per annum.
So, the new figures would be:
Annual emission of fossil C to atmosphere = 9Gtons (8Gtons human and 1Gton new volcano)
Annual increase in atmospheric carbon = 4.5Gtons
and we therefore correctly state that the non-human environment is a net sink of CO2.
And you would STILL claim that THIS proves that the increase in atmospheric CO2 is entirely caused by human actions. And it that you would be wrong: in this case one ninth of the increase will have been caused by this new supervolcano. The mass balance equation alone cannot by itself lead to the conclusion you claim for it. Only when supplemented by knowledge of the wider environment, in particular a) the past history of atmospheric CO2 levels as well as b) sources of fossil carbon or carbon that has not been involved in the short-term C-cycle for a long time, or even c) extra-terrestrial C (eg from carbonaceous chondrites – it doesn’t have to be aliens from the planet Zog), – only when knowledge of these is included can we with confidence claim that the increase in atmospheric CO2 is overwhelmingly anthropogenic.
The mass balance equation alone cannot lead to that conclusion, and your insistence that it can is, in my view, a block to progress in showing people that human emissions are responsible for the recent rise in atmospheric CO2.