I’ve been getting a lot of requests to cover this story, probably 20 or so now with wonderings about “why haven’t you covered this yet?”
How quickly you all forget. WUWT was the very first to cover this story back on November 10th, 2009.
Everybody else in the media today is playing catch-up. So if you’d like to read the original press release and participate in the already ripe comments left then, see this WUWT story:
Joel Shore (15:28:23)
“At the very least, you should read and understand the scientific literature on the carbon cycle so that you can explain where the accepted science is supposedly wrong.”
And, you should delve into the math.
But, I do not need to know the proposed theory for a perpetual motion machine to tell you it is not going to work. That is what we are talking about here: fundamental limitations of reality.
Ferdinand, thanks for your patient explanations. Regarding the C13/C12 ratio and deep ocean exchange, it is a nice analysis and chart, but the 40Gt calculated exchange with the deep ocean needs to be validated independently in order to validate your assumptions that went into the analysis (the primary one being that 100% of the CO2 increase is manmade and the corollary that the natural cycle is balanced).
The “+ 5 ppmv CO2 and + 1 C” numbers are indeed real,. The 5 presumably includes biosphere and ocean warming and both have the possibility of asymmetry each year which I will demonstrate below. Although your model assumes symmetry and no natural long term rise, that assumption needs to be validated by matching the results (e.g. the 40Gt above) with some other physical process analysis, the same way that manmade fluxes are independently validated.
Now for the mass balance equation: Cincrease = Cemiss + Cin – Cout
I defined two seasonal states above to make my analysis easier. In the warm season the mass balance is
15 = 8 + 10 – 3
where 15 is the measured atmospheric increase, 8 is manmade emissions, 10 is natural emissions and 3 is natural absorption of manmade emissions.
In the cool season I have
-11 = 8 – 14 – 5
where -11 is the measured decrease, 8 is the manmade emissions, -14 is the natural absorption and -5 is natural absorption of manmade emissions. The peak to trough is -11 or roughly the height of the natural sinusoid. The natural absorption of the manmade CO2 is independent of the natural CO2 flux (i.e. if the manmade CO2 were not produced, nature would still absorb -14.
Both equations are balanced. Manmade emissions are constant at 8. In my simple model, manmade emissions are absorbed seasonally, less (-3) when nature is outputting more CO2 and more (-5) when nature is outputting less CO2. Nature itself releases +10 in the warm season and absorbs (-14) in the cool season (unbalanced, contrary to your assumption). Finally man outputs an unvarying 8, and the long term rise is 4 corresponding with independent calculations and measurements.
Joel says “At the very least, you should read and understand the scientific literature on the carbon cycle so that you can explain where the accepted science is supposedly wrong.” I have read the scientific literature on the carbon cycle and it isn’t wrong. This picture is a little old http://cdiac.esd.ornl.gov/pns/graphics/c_cycle.htm but there is nothing wrong with it except the numbers are a bit out of date.
My paraphrase of your understanding of the picture linked above is “since the manmade emissions are greater than the observed atmospheric rise, 100% of the rise must be manmade”. But the seasonal rise and fall which is the same order of magnitude as the manmade emissions. That fact alone should make you question your assumption (or perhaps that is a conclusion). If you have any quantitative argument or take issue with any of my assumptions or conclusions above, please write it up.
Eric (skeptic) (20:08:24) :
As you suggest, spreadsheet analysis simply does not work for dynamic systems. This is not an exercise in accounting. It is not algebra, it is calculus.
Bart (16:57:00) :
Ferdinand Engelbeen (14:00:29) :
There are no problems with my formula. It’s pure math. It’s as certain as 2 + 2 = 4. The only option you have is alternative interpretations, but realistic scenarios are constrained by the formula
Well I agree: it is pure math. As good as a mass balance is pure math:
C = Co + Cem + Cin – Cout
Where
804 = 800 + 8 + x – y GtC
Thus x – y = – 4 GtC and there is zero addition from nature and the full increase is due to human emissions.
With some more (nightly) thinking, I suppose that I now know where your error is:
In the case of the bathtube example, the system is in equilibrium when output flows are equal to input flows at a certain height of water in the bathtube. That is the basic system.
Now we add a small extra stream to the bathtube. That doesn’t induce an extra outflow in itself (as your formula suggests), but in first instance it increases the height of the water in the bathtube. That increases the pressure at the drain and that increases the flow.
Something similar for CO2 in the atmosphere: if you add a small quantity of CO2 to a system in equilibrium, the CO2 level must go up first, or there is no reason why the CO2 “drains” would remove more CO2 from the atmosphere.
That is what is lacking in your formula (and what is present in mine).
Further, the equilibrium flows as seen in seasonal changes, deduced from O2 and d13C changes are temperature dependent, not pressure dependent. Temperature changes the equilibrium Co with 4-8 ppmv/K, but that doesn’t say anything about what an extra C does. It is like increasing the temperature of the bathtube: the height will increase, due to lower density of the water, but that doesn’t tell you what the height in the bathtube will do if you add an additional flow.
And that is -again- the difference between temperature induced exchange rates (of about 150 GtC/season) and pressure induced removal rates (of about 4 GtC/yr)…
Eric (skeptic) (19:51:42) :
Both equations are balanced. Manmade emissions are constant at 8. In my simple model, manmade emissions are absorbed seasonally, less (-3) when nature is outputting more CO2 and more (-5) when nature is outputting less CO2. Nature itself releases +10 in the warm season and absorbs (-14) in the cool season (unbalanced, contrary to your assumption). Finally man outputs an unvarying 8, and the long term rise is 4 corresponding with independent calculations and measurements.
Eric, I have not the slightest problem with your calculations. Indeed, globally more CO2 is absorbed in one season that in another. I didn’t make any seasonal assumptions, as these have no influence on the year-by-year balance. Only the year-by-year temperature changes have an influence: in warm (1998 El Niño) years, less CO2 is absorbed and in cold (1992 Pinatubo eruption) years more is absorbed. That doesn’t change the fact that even if in some months more may be released by nature than absorbed, the overall balance over 50+ years is that nature was a strong absorber of about 50% of the extra CO2 induced by humans.
Eric (skeptic) (19:51:42) :
Ferdinand, thanks for your patient explanations. Regarding the C13/C12 ratio and deep ocean exchange, it is a nice analysis and chart, but the 40Gt calculated exchange with the deep ocean needs to be validated independently in order to validate your assumptions that went into the analysis (the primary one being that 100% of the CO2 increase is manmade and the corollary that the natural cycle is balanced).
You’re welcome… Indeed the d13C graphs are based on the assumptions that there is a balance (more natural sinks than sources) and the increase is man-made. But it shows that it is quite easy to determine how much deep ocean flow is needed to dilute the atmospheric 13C/12C rate to what is measured. It will be quite difficult to prove that, as that involves measurements of CO2 releases/uptake at the air/ocean surface, which are more dependent of surface water mixing due to wind speed than for the pCO2 differences.
Some more on that can be read from Feely at:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
Anyway, there are some useful estimates, based on tracers like CFK’s which track (and thus follow ocean flows) can be followed from the polar surface to the deep oceans, but it remains largely guessing.
Others use N – P – DIC cycles/reactions to estimate what happens where, but that is even more difficult. See Gruber e.a (10 MB file, not easy stuff):
http://www.atmos.ucla.edu/~gruber/publication/pdf_files/gruber_thesea_02.pdf
Ferdinand Engelbeen (01:29:40) :
C = Co + Cem + Cin – Cout
Of course, the Co in this case is not the equilibrium Co, but the concentration of carbon (as CO2) in the previous year…
Bart says:
I have looked at the math, as described in L.D. Danny Harvey’s book. I haven’t bothered with your math because I already know that the basic problem is that you are missing a very important part of the whole picture, which is that the large natural flows that you are fascinated by are just exchanges between the different subsystems of the biosphere, (near-surface) soils, and the ocean mixed layer, whereas the carbon released through our burning of fossil fuels is a new source being added to this entire combined system (biosphere + soils + ocean mixed layer). This new source of carbon is quite rapidly transported and equilibrated within this combined system but the rate-limiting step is then the transfer of the carbon from this combined system to the deep ocean.
No…We are talking about fundamental limitations in your ability to understand reality. In fact, we are talking about fundamental limitations in your ability to even try to understand reality. You would rather believe in your own convenient fiction.
Just out of curiosity, do you think that there is some grand conspiracy among scientists on this issue? Or, do you believe you are the only one who has such mathematical insight that all these other scientists are missing?
Ferdinand, thanks for checking the equations which were
warm: 15 = 8 + 10 – 3
cool: -11 = 8 – 14 – 5
But I made an unintentional mistake. Only half of the manmade CO2 is released in each season. The equations could be something like:
warm: 15 = 4 + 12 – 1
cool: -11 = 4 – 12 – 3
Or if the natural sinks exceed the natural sources by a little, and nature only absorbs 3/8 of the manmade, we get:
warm: 15 = 4 + 12 – 1
cool: -11 = 4 – 13 – 2
There is no way with these equations for the observed rise to be due, in any part, to the natural sources as long as there is manmade CO2 being absorbed in some manner by nature, e.g. strictly seasonal:
warm: 15 = 4 + 11 – 0
cool: -11 = 4 – 11 – 4
or e.g. not seasonal at all:
warm: 15 = 4 + 13 – 2
cool: -11 = 4 – 13 – 2
So Joel’s simple notion is correct, at least as far as these simple equations go. And here I thought he was oversimplifying because he’s a physicist!
Ferdinand Engelbeen (01:29:40) :
… but in first instance it increases the height of the water in the bathtube. That increases the pressure at the drain and that increases the flow.”
Of course it does. Remember, I am not saying anthropogenic emissions do not add to the overall level. I am saying they cannot account for the full 30% rise we have seen. The question is, how much do they increase the level? The answer is, they are constrained, in the linear no-stimulated-emissions case, to increase it no more than 3%.
“That is what is lacking in your formula (and what is present in mine).”
As I just explained, that is not lacking in mine.
“Further, the equilibrium flows as seen in seasonal changes, deduced from O2 and d13C changes are temperature dependent, not pressure dependent.”
That is the temperature dependent forcing, which I removed from my model because it does not affect the sensitivity to “adot”, the anthropogenic rate of CO2 input to the system.
Joel Shore (07:32:06) :
” I haven’t bothered with your math…”
It isn’t “my math”. It is math.
“…the large natural flows that you are fascinated by are just exchanges between the different subsystems of the biosphere…”
Groan… that is an incorrect picture. Those exchanges evolved as part of the overall feedback system. They reached their present levels because they fought against each other until an equilibrium was established. They did not just “happen”. There is no immaculate conception.
“Just out of curiosity, do you think that there is some grand conspiracy among scientists on this issue? Or, do you believe you are the only one who has such mathematical insight that all these other scientists are missing?”
I never attribute conspiracy to that which can be explained by incompetence. No, I do not believe I am the only one with the mathematical capability to see this. But I believe the loudest voices, which are dominating the debate, are not as mathematically adept as they are adept in their role as gatekeepers for the orthodoxy.
Tell me why you find this so fantastic a possibility? Here are two examples: plate tectonics and the implication of h. pylori in the formation of ulcers. How long did it take these now well established theories to gain acceptance? And, why, when they are now so intuitively obvious?
Ferdinand Engelbeen (01:29:40) :
Re: “That is the temperature dependent forcing, which I removed from my model because it does not affect the sensitivity to “adot”, the anthropogenic rate of CO2 input to the system.”
I explained this at Bart (11:47:35).
Ferdinand Engelbeen (01:29:40) :
Re: “The answer is, they are constrained, in the linear no-stimulated-emissions case, to increase it no more than 3%.”
I use 3% because that is my assumed ratio of anthropogenic emissions to natural emissions.
Bart (11:54:23) :
Ferdinand Engelbeen (01:29:40) :
Re: “The answer is, they are constrained, in the linear no-stimulated-emissions case, to increase it no more than 3%.”
I use 3% because that is my assumed ratio of anthropogenic emissions to natural emissions.
Except that the 97% natural aren’t emissions, but part of a temperature induced cycle. And the anthro 3% is the only part of the equation that really increases the pressure in the atmosphere…
Ferdinand Engelbeen (01:29:40) :
“C = Co + Cem + Cin – Cout
Where
804 = 800 + 8 + x – y GtC
Thus x – y = – 4 GtC and there is zero addition from nature and the full increase is due to human emissions.”
Never bring algebra to a calculus fight. This is just awful logic, Ferdinand.
In actual fact, Cin – Cout is a convolution integral of the impulse response of the system minus one times the rate of anthropogenic production. If you differentiate it, whatever its form may be, then at least locally (in a mathematical sense), you will get
Cdot = (Co-C)/tau + (adot + K[adot])
where K[ ] is a linear operator for which I substituted the dc (zero frequency) gain Ko in my equation.
You are trying to analyze a dynamic system using static and uncertain sums. It just does not work.
Ferdinand Engelbeen (12:05:38) :
“Except that the 97% natural aren’t emissions, but part of a temperature induced cycle. And the anthro 3% is the only part of the equation that really increases the pressure in the atmosphere…”
Yes, they are. See my comment on “immaculate conception” to Joel above.
They go into the air, just like anthropogenic emissions, do they not? They are emissions. And, they and the anthropogenic emissions must be treated the same way by the sinks.
The “cycle” comes about because the sinks act as regulating feedback. If there were no sink feedback, they would just accumulate, in the same way you think the anthropogenic emissions accumulate.
This division into “cyclic” natural and “secular” anthropogenic components is arbitrary and unphysical.
The feedback comes about because the sinks will expand in response to an increase, and contract in response to a decrease. They have to. That is what established an equilibrium in the first place.
“The feedback comes about because the sinks will expand in response to an increase, and contract in response to a decrease. They have to. That is what established an equilibrium in the first place.”
Moreover, if they did not, we would not be discussing the Knorr paper which is ostensibly the subject of this entire thread. The Knorr paper shows definitively that the sinks expand in response to increased forcing.
Bart:
Fine. They evolved. That’s irrelevant. What is relevant is the fact that these exchanges are exchanges within a relatively small subsystem (roughly 3000 Gt carbon, of which the atmospheric portion is about 20%) that exchanges carbon only very slowly with other larger reservoirs (the deep ocean and, if you want to take the geological view, the carbon locked up in rocks, in fossil fuels, etc). So, when you add a new slug of carbon to this subsystem, it will rapidly partition itself between the different components of the subsystem and then we will be back in equilibrium again. (Since we are adding carbon constantly, it is actually kind of being sustained slightly out of equilibrium.)
What you are missing with your 3% nonsense is that you are looking at things that are irrelevant. I thought of even a better analogy than the fountain one today while cross-country skiing. (Yea!!! We finally have enough snow here in Rochester.) Simply imagine a room divided into two sides A (“atmosphere”) and B (“ocean mixed layer + biosphere + soils) by a metal screen that allows air to pass through (like a screen) door. And, imagine this room is sealed so no air can get in or out of the room, except for a pump that can pump more air into the A side. Now, there are large exchanges of air back and forth between A and B. (To make them macroscopic, one could set up currents by running a fine blowing from A to B on one side and blowing from B to A on the other.)
When we turn on the pump, the air pressure in the rooms will start to increase. A portion of what we pump into A will of course end up in side B, so the pressures in both sides will increase. Even if the pump is injecting air into the room at a rate of only 3% relative to the amount that the fan is transferring from B to A, the reason for the entire pressure increase in A will be the pump…And, in fact, the only reason that the pressure in A doesn’t increase more than it does is that there will be a net flow now from A to B, i.e., side B now acts as a “sink” for part of what we pump into A.
Of course, in the real system, there is also a small hole that allows air to escape out of side B (representing transfer of carbon to the deep ocean). And, when the pressure builds up in the room, it will start to increase the amount of air escaping out of the hole…But, if the hole is small, the pressure of the room would have to rise quite a bit before a new equilibrium were established.
Neither of those cases involved as simple mathematical arguments as you claim apply here. Furthermore, the real story in the Wegener case (and probably the ulcer case too) are more complex than you make them. I read something written by a physicist that noted both that Wegener’s ideas did find acceptance in parts of the scientific community fairly quickly although other parts were more resistant. The second point, even more important, is that Wegener’s picture was quite incomplete. There were lots of gaps in the logic and it was probably realistic for scientists to be skeptical until the understanding evolved to fill in those gaps.
In that sense, plate techtonics and AGW actually have a lot in common. After all, it was way back around 1900 that Arrhenius proposed the notion of the burning of fossil fuels increase CO2 in the atmosphere and enhancing the greenhouse effect. However, it did not gain immediate acceptance because there were legitimate gaps in the theory. For example, nobody had good experimental evidence that CO2 was building up and the ocean chemistry and dynamics were not understood sufficiently well to counter the notion that all the CO2 that we were emitting could be absorbed by the oceans. It took the development of good measurement techniques for CO2 levels and a better understanding of ocean chemistry to recognize that such a buildup was, and indeed was expected to be, occurring.
Eric (skeptic) says:
We physicists (usually) know when we can “cheat” and get away with it. 😉
Bart says:
Ah, Bart…Are you aware of the fact that the Knorr paper is based on the standard scientific notion that we are responsible for the increase in CO2 in the atmosphere? The only point that they are addressing is whether the fraction of our emissions that remains in the atmosphere has been changing over time or whether it has been remaining constant…and their conclusion is that, within errorbars, it has been remaining constant.
I have no clue how someone who thinks that we could only be responsible for at most 3% of the rise in atmospheric CO2 levels could find any comfort whatsoever in the Knorr paper. I am quite positive that every author on that paper would tell you that you are utterly and completely wrong.
Joel Shore says:
Or, better yet, one could forget the “fine” and go with a “fan” instead. (Why don’t my fingers type what I tell them to?)
Bart (11:34:18) :
That is the temperature dependent forcing, which I removed from my model because it does not affect the sensitivity to “adot”, the anthropogenic rate of CO2 input to the system
You didn’t remove it from your model, as you assume that still 97% is natural non-temperature dependent “emissions”, while these amounts are largely temperature dependent and counter-current, which makes that the momentary natural “emissions” are of the same order as the human ones… If there were no temperature induced seasons, how large would the natural emissions and sinks be? I don’t know and you don’t know…
As the Knorr paper says, over the past 160 years, about halve the anthro emissions (as mass, not as individual molecules…) were absorbed, halve remained in the atmosphere. That is the result of the total carbon cycle, whatever the underlying equilibria and natural in/out flows were or are. That simply means that in the past 160 years, and as long as the anthro emissions increase as they did in the past, that all measured increase is due to human emissions.
Again, my formula with all known changes in temperature and emissions fits the observed increase and d13C changes in the atmosphere and upper oceans (and vegetation), and the d14C changes (until 1950) in the atmosphere. I am eager to see the results of your calculations where everything fits reality…
Joel Shore (13:28:45) :
Joel, I cannot help you. Your mind is closed.
Ferdinand Engelbeen (14:22:04) :
Ferdinand, you do have a point. But, you are not taking into account that CO2 production has both a cyclical, temperature dependent quality, and a steady production, because the entire globe does not experience summer and winter at the same time.
Let me put the temperature dependent part back into my equation
Cdot = (Co-C)/tau + (1+Ko)*adot + S*dT
You will recall from earlier I left this out because, I said, this does not affect the sensitivity to adot. It does, however, affect the calculation of the magnitude of the time constant, because of the cyclical temperature dependence you have brought up.
Now, you are correct, to some extent, that I should be calculating adot as less than or equal to 3% of Co/tau plus the integral of the positive part of S*dT divided by 1 year. If we take S*dT = alpha*cos(omega*t), where omega = 2*pi rad/year and t is time in years, then the requirement becomes
adot (is less than or equal to) 3% of Co/tau + alpha/pi/P
where P = 1 year.
How much does this change things? It depends upon the value of alpha, and the value of tau.
If we take the Mauna Loa data as representative, the variation of C due to S*dT is less than 5 ppmv. Because S*dT is cyclical with a period of 1 year, sensitivity of C to S*dT is tau/sqrt(1+(2*pi*tau)^2), with tau in years. Thus, we have approximately
alpha (is proportional to) 5*sqrt(1+(2*pi*tau)^2)/tau
Let me also presume Co is proportional to 280 ppmv. I am told that the roughly 100 ppmv rise of the last 50 years is proportional to 45% of adot integrated over time, so I set adot proportional to (100/50/0.45) = 4.4 ppmv/year.
So, I have the inequality
4.4 (is less than or equal to) 0.03*(280/tau + 5*sqrt(1+(2*pi*tau)^2)/(pi*tau))
Moving everything to the right side, we can easily show graphically that this inequality requires tau less than or equal to about 2 years.
For the max value of tau, Co/tau is proportional to 140 ppmv/year. alpha/pi/P (is propotional to) 5*sqrt((2*pi)^2+(1/2)^2)/pi= 10 ppmv/year, which is 7% of the Co/tau value, so it is small.
The ratio adot/(Co/tau) is less than or equal to 3.1%. So, in the linear, no stimulated emissions case, I have to amend my projection of the effect of anthropogenic forcing from 3% to 3.1%.
Mea culpa. I am not infallible. But, you will pardon me if I still do not see a justification for the anthropogenic attribution hypothesis.
Now, how do you get a 100 ppmv rise? Well, in this model, you can put in a secular dT trend.Temperature records, such as this, indicate cyclical temperature rises and falls +/- about 0.1 degC each year. In actual fact, the yearly variation in C due to S*dT is more like +/- 3 ppmv – I gave you 5 ppmv in the calculations above to be conservative. This suggests the sensitivity parameter S is proportional to about 3 ppmv/0.1 degC times sqrt(1+(2*pi*tau)^2)/tau = 189 ppmv/deg_C.
The rise in global temperature since 1970 has been about 0.6 degC. This suggests, according to the equation above, that atmospheric CO2 concentration should have increased about 0.6*189 = 113 ppmv. Anthropogenic forcing should have contributed about 0.015*280 = 4.2 ppmv (I used 1.5% instead of 3% because anthropogenic production has actually been ramping up to 3%, and has not been 3% all the time). So, we have a total expected delta of about 117 ppmv from a base of 280 ppmv, or 397 ppmv.
Not too shabby, given all the approximations I have made. It follows that, if temperatures genuinely start to decline, after 2-6 years lag time (3 time constants is commonly referred to as “settling time” in systems theory), you should expect to see the CO2 levels decline as well.
If that doesn’t do it for you, I don’t know what will. In any case, I think we are done here.