Guest Post by David Middleton
Fingerprints are admissible evidence in criminal trials because of their uniqueness. The probability of two human beings having identical fingerprints is very low.
Measurements of δ13C depletion have often been cited as anthropogenic “fingerprints,” proving human culpability for the rise in atmospheric CO2 over the last 200 years or so…
While δ13C depletion certainly could be evidence of the Suess Effect, it is not a unique solution; therefore, not a “fingerprint.”
Examples of geologically recent δ13C depletion not of anthropogenic origin…
δ13C depletions were associated with warming events ~5,000 years ago in India, ~9,100 years ago in Poland and ~150,000 years ago in the Indian Ocean. It appears to me that δ13C depletion has been a fairly common occurrence during periods of “global warming.” It also appears that δ13C increases have occurred during periods of global cooling…
The red curve in Figure 5 is the Flinders Reef δ13C that was cited as “Human Fingerprint #1” in Skeptical Science’s The Scientific Guide to Global Warming Skepticism. The rate of δ13C depletion is quite similar to that of the lacustrine deposit on the Yucatan. The Flinders Reef data do not extend back before the Little Ice Age; so there is no way to tell if the modern depletion is an anomaly, if the δ13C was anomalously elevated during the 18th and 19th centuries and the depletion is simply a return to the norm or if δ13C is cyclical.
Is it possible that Skeptical Science’s “Human Fingerprint #1” is not due to the Suess Effect? Could it be related to the warm-up from the Little Ice Age?
References
Cook, J. et al., 2010. The Scientific Guide to Global Warming Skepticism. Skeptical Science.
Banakar V., 2005. δ13C Depleted Oceans Before the Termination 2: More Nutrient-Rich Deep-Water Formation or Light-Carbon Transfer? Indian Journal of Marine Sciences. Vol. 34(3). September 2005. pp. 249-258.
Enzel, Y. et al. High-Resolution Holocene Environmental Changes in the Thar Desert, Northwestern India. Science 284, 125 (1999); DOI: 10.1126/science.284.5411.125.
Apolinarska, K. δ18O and δ13C Isotope Investigation of the Late Glacial and Early Holocene Biogenic Carbonates from the Lake Lednica Sediments, Western Poland. Acta Geologica Polonica, Vol. 59 (2009), No. 1, pp. 111–121.
Hodell, D.A., et al., 2005. Climate change on the Yucatan Peninsula during the Little Ice Age. Quaternary Research, Vol. 63, pp. 109-121. doi:10.1016/j.yqres.2004.11.004
Pelejero, C., et al. 2005. Flinders Reef Coral Boron Isotope Data and pH Reconstruction. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2005-069. NOAA/NCDC Paleoclimatology Program, Boulder CO, USA.
Bart, I agree that the carbon cycle is a dynamical system, as I said in my paper I use a one-box model of the carbon cycle (essentially the same as Prof. Essenhigh’s) to capture the first order dynamics of the system, defined by a differential equation, which provides a crude model of the expansion of the sinks. It gives the same story as the mass balance argument.
I’m glad we agree that the environment is a net carbon sink. You have yet to explain how the natural environment can be causing atmospheric CO2 to rise whilst being a net sink. It is a bit like saying I can cause my bank balance to increase by withdrawing more money than I deposit (see the last part of my post for a more detailed explanation).
It is important to note that the mass balance analysis is not a model of the carbon cycle, and it applies equally well whether the carbon cycle is static or dynamic. It doesn’t predict anything, it just uses a principle of physics (conservation of mass) that allows you to infer the difference between natural uptake and natural emissions. This is true whether natural emissions are constant or whether they are variable.
As for the carbon cycle being dynamic, rather than M in your equation, it should be dM as it is the change in the mass of the atmospheric reservoir, rather than the mass itself. The equation is then more properly represented as
dM = A + N – U
This is a difference equation, and hence does define a simple dynamical system if you want to view it that way. If A, N and U were constant, then dM would also be constant, but of course nobody is claiming that any of these quantities are constant. N-U changes from year to year, as clearly demonstrated by the figures you were invited to investigate in my previous post.
Now if you wanted to make even the simplest model of the carbon cycle, it would have to include the expansion of the sinks (as you point out) due to the rise in atmospheric CO2, so lets do that. Essenhigh forms his one-box model by making U proportional to M (if you look at the data this clearly isn’t a reasonable assumption, which is why I use a linear relationship with an intercept). We then have
dM = A + N – kM
where k is a constant. Now if you want a continuous time model, you can use a differenttal equation instead, which gives you (c.f. equation 4 in my paper).
dM/dt = A + N – kM
If you solve the equation you will still find that if the rate of growth of atmospheric CO2 is less than the rate of anthropogenic emissions then the rate of natural emissions must be less than the rate of natural uptake. That is because conservation of mass applies to both static and dynamical systems, and the mass balance argument is merely an application of conservation of mass, nothing more.
Now if you want to separate natural uptake into uptake of “anthropogenic” CO2 and “natural” CO2, then that is fine. Indeed that is exactly what I do in my paper (c.f. equations7 and 8). If you do that, you still end up with a situation where if the rate at which CO2 is increasing in the atmosphere is less than the rate of anthropogenic emissions then the rate of natural uptake must be greater than the rate of natural emissions.
you write “So, we only know N-UA-UN. Suppose UA = A. Then M = N – UN, N is greater than UN, and the rise is entirely natural.” This is an absurd argument, which we can see if we recast it in a more familiar setting (as indeed I did in my paper in an analogy adapted from one of Ferdinands):
Consider a husband and wife that share a jar in which they keep their savings. He deposits 8 euro per month, all in Belgian minted coins, and never makes any withdrawals. She on the other hand deposits 1000 euro a month, all in French minted coins (so we can tell the difference) but withdraws 1004 euros a month from the jar. Clearly the total amount in the jar will rise by 4 euro a week, and most people would agree that the rise in their savings is purely due to the husband (as his deposits exceeded his withdrawals) and not his wife (as her withdrawals exceed her deposits).
Your argument is akin to saying that if the wifes withdrawals contained 8 Belgian coins then that particular month the increase in their savings was purely due to her having taken four more coins out of the jar than she had put in, which is clearly absurd.
Bart says:
April 2, 2012 at 10:03 am
UA = natural uptake of anthropogenic emissions
UN = natural uptake of natural emissions
So, we only know N-UA-UN. Suppose UA = A. Then M = N – UN, N is greater than UN, and the rise is entirely natural.
Let us use your own example of the bucket. Some huge, clear, waterflow is added at the top of a bucket and flows away via a hole in the bottom. At steady state, the height of the water in the bucket is constant and delivers the right pressure to make that the outflow exactly matches the inflow.
Now we add a smaller blue colored waterflow at the top of the bucket. That mixes readily with the inflow of clear water, giving a fainted blue color, its intensity depending of the ratio between the inflows. The extra inflow also causes an increase of the water height in the bucket, INdependent of the height of main inflow or the height already in the bucket, which only accomodates the extra inflow, until a new steady state is reached where the extra outflow = extra inflow.
Alternatively, we add the extra blue waterflow at the bottom of the bucket, near the output hole. The blue water is immediately gone into the drain, but despite that, we see exactly the same rise in height of total water in the bucket, still near only composed of clear water. Thus according to your reasoning, the rise is only due to clear water. According to our reasoning, the rise still is the result of the addition of blue water, no matter how fast it is replaced by clear water.
To this example one can add the variability of the clear water inflow and the slightly exponentially increasing blue water inflow over time, to make it more realistic, but the basic point remains the same…
Phil. says:
April 2, 2012 at 10:52 am
gavincawley says:
April 2, 2012 at 11:05 am
FerdiEgb says:
April 2, 2012 at 11:36 am
I honestly can’t see how to answer you fellows without becoming churlish and abusive, so I will be brief: This is pitiful stuff.
Go back and read what I wrote at 10:03 am, this time for comprehension. Because, you guys are embarrassing yourselves.
Bart, to help me understand where we disagree, please can you give a direct answer to this question:
Consider a husband and wife that share a jar in which they keep their savings. He deposits 8 euro per month, all in Belgian minted coins, and never makes any withdrawals. She on the other hand deposits 1000 euro a month, all in French minted coins (so we can tell the difference) but withdraws 1004 euros a month from the jar. Clearly the total amount in the jar will rise by 4 euro a month, and most people would agree that the rise in their savings is purely due to the husband (as his deposits exceeded his withdrawals) and not his wife who was actively opposing the rise (as her withdrawals exceed her deposits).
In this particular analogy (forgetting for the moment whether it is appropriate to a discussion of the carbon cycle) would you agree that it would be absurd to claim that the wife was responsible for the rise in the couples savings, even if she deliberately took out the 8 Belgian coins that had been deposited each month by her husband, despite the fact that she withdrew four more Euro coins than she deposited each month?
A “yes” or “no” answer would be best, if “no”, explaining why.
gavincawley says:
April 2, 2012 at 2:33 pm
Gavin – why don’t you try reading and understanding what I wrote at 10:03 am? You’re just digging your hole deeper.
Your analogy fails because you have artificially contrived a situation in which all of the inputs and outputs are known. It is equivalent, in my example, to saying you know both N and U individually. You DO NOT.
There are children pilfering coins from the jar. The taxman steals in occasionally to grab his share. And, a rich uncle occasionally makes a contribution. You have no idea how much each of these is contributing or taking away, so you have excluded them from your calculation. And, your result is useless for drawing up a budget, or determining which coins came from where or from whom.
Furthermore, this a DYNAMIC SYSTEM we are talking about. in effect, the jar shrinks and expands based on inputs and outputs, automatically drawing more coins in and expelling them in response to the inputs.
Before we go further down the road of trying to make your jar analogy apply better to the actual system, read my post at 10:03 am until you understand it!!!
Bart says:
April 2, 2012 at 1:49 pm
Bart, I have reread that comment:
UA = natural uptake of anthropogenic emissions
UN = natural uptake of natural emissions
So, we only know N-UA-UN. Suppose UA = A. Then M = N – UN, N is greater than UN, and the rise is entirely natural. Equality would never be precisely the case, but it depends on the sequestration time.
What you suppose there is that the anthro CO2 is sequestered near instantly, while the natural CO2 largely remains in the atmosphere. That is impossible. Both anthro and natural CO2 are 99% 12CO2. Natural sinks don’t make any differentiation between anthro or natural 12CO2. And the differences in the 13CO2 are too small to make a substantial difference in mass transfer. Thus there is no practical difference in sequestration time between anthro and natural CO2.
The current amount sequestered by oceans and biosphere together is about 4 GtC/year. With a current CO2 level about 210 GtC above steady state (for the current temperature), that gives an e-fold time of about 52.5 years, far from instantly. No matter the origin of the CO2 molecules flying around in the atmosphere.
Thus we have a yearly, growing, addition of 8 GtC of human CO2 and a natural sink capacity of only 4 GtC/year (growing in near constant ratio with the emissions) at the current extra CO2 pressure in the atmosphere. There is no way that you can explain that any natural source is responsible for the increase in the atmosphere, while the human emissions are not…
Bart, I wrote in my post “forgetting for the moment whether it is appropriate to a discussion of the carbon cycle”, I even put it on bold to make sure you didn’t miss it. Thus complaining that “Your analogy fails because you have artificially contrived a situation… “ is merely evasion.
A minimal answer to the question would have required only two or three characters, depending on your view, so the effort of typing a response could not be the issue as your actual response was much longer than that, without actually introducing any more information to the discussion.
The reason I asked the question was to see whether the concept of being “the cause of the increase” meant something different to you than it does to me. So any direct answer you could have given would have been helpful in understanding your point of view.
So please, give a direct answer to the question as posed. A “yes” or “no” answer would be preferred, if “no” an explanation would be appreciated.
To reinforce Ferdinand’s comment above, I also agree that the uptake doesn’t significantly differentiate between anthropogenic CO2 and natural CO2 (indeed it can’t 12C is 12C is 12C, it isn’t labelled by source). So the one box dynamical model of the cabon cycle used in my paper divides the uptake according to the mixing ratio.
FerdiEgb says:
April 2, 2012 at 3:19 pm
“What you suppose there is that the anthro CO2 is sequestered near instantly, while the natural CO2 largely remains in the atmosphere.”
Size matters. A small input to a negative feedback system with adequate bandwidth to respond can be easily attenuated to negligibility, whereas a large input creates… a larger excursion. Since we do not have any direct measurement of everything that is coming in from nature (e.g., an extended expulsion from upwelling of deep ocean currents), we cannot rule out the possibility.
FerdiEgb says:
April 2, 2012 at 3:19 pm
“With a current CO2 level about 210 GtC above steady state (for the current temperature)…”
How do you calculate the steady state for the current temperature? If it is based on ice core data, I would consider such an estimate tentative and unproven, at the very least.
Before we get too far afield, let us pause to make the current point. You are now arguing, Ferdinand, that you have a problem with the sequestration rate being what you think is required. That’s fine, and a valid argument to have. But, in doing so, we must acknowledge that the mass balance argument is insufficient to convict anthropogenic emissions of the crime of increasing atmospheric concentrations, and you must rely upon other data to prosecute the case.
If I can only get that concession from you, I will be happy for now.
FerdiEgb says:
April 2, 2012 at 3:19 pm
One final point on your last post:
“The current amount sequestered by oceans and biosphere together is about 4 GtC/year.”
How do we know what the current amount is? Don’t list for me all the known sinks and their estimated capacities. Justify that the list is exhaustive (something more compelling than “we don’t know of any others”), and that the estimates are supremely accurate (remember, it takes less than 3% variation of what we currently “know” to completely swamp the anthropogenic input).
Bart wrote: “How do we know what the current amount is?” The figure of 4GtC per year is the difference between natural uptake and natural emissions. You have already conceded that the mass balance argument allows us to infer this from knowledge of anthropogenic emissions and the observed rate of increase, and that is indeed how the figure is estimated.
Bart says:
April 2, 2012 at 4:39 pm
FerdiEgb says:
April 2, 2012 at 3:19 pm
One final point on your last post:
“The current amount sequestered by oceans and biosphere together is about 4 GtC/year.”
How do we know what the current amount is? Don’t list for me all the known sinks and their estimated capacities. Justify that the list is exhaustive (something more compelling than “we don’t know of any others”), and that the estimates are supremely accurate (remember, it takes less than 3% variation of what we currently “know” to completely swamp the anthropogenic input).
We don’t need to know what it is, just that on an annual basis over the last 50yrs it has never exceeded the growth in anthropogenic input! That’s the point of the mass balance equation, you’re looking at the result. You don’t need to know a detailed breakdown of all the known non-anthropogenic sinks and sources because what the results of the mass balance tells you, with certainty, is that sinks exceed sources, whether they are all known or not.
gavincawley says:
April 2, 2012 at 4:46 pm
“The figure of 4GtC per year is the difference between natural uptake and natural emissions.”
This is circular logic.This is N – U, not U. You have built in the a priori assumption that N = 0.
Phil. says:
April 2, 2012 at 5:14 pm
“We don’t need to know what it is, just that on an annual basis over the last 50yrs it has never exceeded the growth in anthropogenic input!”
I do not doubt that is all you need to know. People who understand the issue need more.
gavincawley says:
April 2, 2012 at 4:10 pm
“So please, give a direct answer to the question as posed.”
No. It is a red herring. Read my post at 10:03 am. When you understand it… I was going to say, get back to me, but when you do, you will have no further questions.
gavincawley says:
April 2, 2012 at 11:05 am
Perhaps it will help you to grasp what I have been telling you by addressing the problem on your own ground.
“dM/dt = A + N – kM
If you solve the equation you will still find that if the rate of growth of atmospheric CO2 is less than the rate of anthropogenic emissions then the rate of natural emissions must be less than the rate of natural uptake.”
No. You won’t.
Let us begin by stipulating that this model is way too simplified to capture the actual system. But, we will make do for now. At the very least, you have to modify it for ocean dynamics, making it
dM/dt = c*(A + N) – kM
where c is a factor of perhaps roughly 1/2, which models the relatively rapid dissolution of a portion of the atmospheric CO2 into the oceans. Now, you have stipulated that
dM/dt < A
What does this tell us? Not much.
In fact, dM/dt is observed to be approximately equal to c*A, but this is not actually known to be more than happenstance. If k is large (high bandwidth, rapid sequestration), then the solution will have M approximately equal to (c/k)*(A+N). The larger k is, the bigger N has to be in order that observations of M show it to be roughly equal to the integral of A times c. Furthermore, to maintain pace with the integral, N has to be increasing.
Perhaps you might think it is unlikely that N would be increasing similarly to a scaled and biased plot of the integral of A. But, it is not. When you are dealing with functions which behave like a low order polynomial expansion, the set of all possibilities which produce similar results relative to bias and scaling is large.
Now, if k is small, then, and only then, is M approximately the integral of c*(A+N), which would necessitate N being small.
It all depends on the rate of sequestration, which is what I have been telling you.
Bart wrote: “This is circular logic.This is N – U, not U. You have built in the a priori assumption that N = 0.
No Bart, the 4GtC/year is the amount sequestered by the natural environment, not the amount taken in, they are not the same thing. If you were familiar with carbon cycle you would know that the total uptake U is much larger than that, so it is obviously not an estimate of U itsel.
Consider the oceans, according to fig 7.3 in the IPCC AR4 WG1 report, the oceans emit about 90.6 GTC/year into the atmosphere, but also takes about 92.2 GTC/year out of the atmosphere. So most of the flux between the oceans and atmosphere is an exchange flux that exchanges molecules of CO2 from the atmosphere, however an exchange does not alter the mass of the atmopsheric reservoir. However ocanic uptake is 1.6GTC/year higher than oceanic emissions, so 1.6CTG/year of carbon goes into the ocean and doesn’t come back out again. So the amount sequestered is the difference between the amount taken in and the amount taken out.
Sequestration and uptake are not the same thing; sequestration is N-U, uptake is U. We don’t need to know the precise value of U to know the value of N-U, as you have already conceded the mass balance argument tells us that.
Bart wrote “No. It is a red herring”
Bart, I explicitly said in the question that an answer was wanted forgetting for the moment whether the analogy was appropriate or not. So yet again you have filed to give a direct answer to a direct question, and typed a much longer answer than would have been required to answer the question.
In a rhetorical debate, the object is simply to win, regardless of whether you are actually correct. In rhetorical arguments it is common to ask direct questions to paint your opponent into a corner, but it is very common for your opponent to give a direct answer to the question as (i) it gives a hostage to fortune in that you then have to remain consistent with that answer to avoid contradicting yourself and (ii) you will be painted into a corner. So in a rhetorical debate, it is common for your opponent to engage in evasion and avoid anserwing direct questions at all costs.
In a scientific discussion however, both parties are seeking the truth and trying to identify errors in both their opponents reasoning and their own. Thus is again common to ask direct questions to try and understand your opponents argument and to narrow down on the precise source of error in the argument. The difference between a rhetorical and scientific debate is that in a scientific debate, your opponent ought to be keen to give a direct answer to your question, as they are as interested in getting to the truth as you are.
In a scientific discussion it is also common to go through an argument, step by step, testing each link in the chain of reasonong one by one, as this is the easiest way to find a weakness in one of the links, but if you can’t to reach the conclusion that the chain of reasoning is sound.
So constantly avoiding answering questions, of avoiding point-by-point analysis of the argument is making it look as if you are engaging in a rhetorical debate and are only interested in winning the argument, rather than a scientiic debate where you are interested in determining the truth. Was this what you intended?
Bart wrote: ”
dM/dt = c*(A + N) – kM
where c is a factor of perhaps roughly 1/2, which models the relatively rapid dissolution of a portion of the atmospheric CO2 into the oceans.
No bart, i you did that your model would violate the principle of conservation of mass. The original equation
dM/dt = A + N – U
was a restatement of conservation of mass, so if you arbitrarily halve A and N then obviously that principle no longer holds.
Bart says:
April 2, 2012 at 6:11 pm
gavincawley says:
April 2, 2012 at 4:46 pm
“The figure of 4GtC per year is the difference between natural uptake and natural emissions.”
This is circular logic.This is N – U, not U. You have built in the a priori assumption that N = 0.
Your differentiation between N and U is artificial, it doesn’t make any difference for the sinks if an increase in the atmospheric mass above setpoint is from N or U. It only matters that there is an increase in mass. And in this case it is proven that N is smaller than 0, for every year in the past 50+ years. That is not an a priory assumption, that is measured.
The equation is:
dM/dt = A + N – kM
if we start at point zero without any A, the zero time equation is:
dM/dt = N – kM
where M is the increase in mass above the steady state, whatever that may be.
at the first step of injecting A we have:
dM/dt = A + N – kM
where dM/dt and A are known:
1/2 A = A + N – kM
or
N – kM = -1/2 A
thus the sink rate in natural sinks kM is larger than the extra supply N from natural sources. With a small ratio of A in the total mass Mt (thus not only with the mass M above steady state), most of the removed CO2 is from Mt + N, only a small fraction is from A:
kM = k((Mt + N + A) – Msts)
where Msts is the mass at steady state and Mt is the current mass, all natural, and N is all natural and A is only a small fraction of the total Mt. Thus more natural CO2 is removed from the atmosphere than the theoretical supply by N. Which is not a net supply, as the overall natural balance is negative.
You may repeat that for the 50+ measured steps, but that doesn’t change the negative balance, whatever N was, some sinks were growing more than N was increasing (if N increased at all) over the past 50+ years. Even if the fraction of A in the current atmosphere is growing, that hardly matters, until an equilibrium is reached between A and the removal of A via kM. That means that only at an 100% fraction of A in the atmosphere, there would be a reduction of 50% in A mass in the atmosphere. Excluding simple back and forth exchanges with other reservoirs.
Bart says:
April 2, 2012 at 4:21 pm
Size matters. A small input to a negative feedback system with adequate bandwidth to respond can be easily attenuated to negligibility, whereas a large input creates… a larger excursion. Since we do not have any direct measurement of everything that is coming in from nature (e.g., an extended expulsion from upwelling of deep ocean currents), we cannot rule out the possibility.
We don’t know the variability of most natural inflows and outflows with sufficient accuracy, but we do know the variability of the net natural balance. That is +/- 1.5% of the estimated total inflows and outflows. Or a variability of about halve the human emissions total inflow. Thus any response to a change in the natural balance must be equal to or faster than a response to the human emissions…
A response from the natural sinks to any increase in the atmosphere must be the same whatever caused the increase. The current response is about 4 GtC/year, while the emissions are at about 8 GtC/year…
Bart says:
April 2, 2012 at 4:24 pm
How do you calculate the steady state for the current temperature? If it is based on ice core data, I would consider such an estimate tentative and unproven, at the very least.
Ice cores have only one real problem: they are smoothing the results over 8-600 years, depending of the accumulation rate. That doesn’t change the average, only the resolution. Within all resolutions, we see about 290 ppmv for the current temperature. With backcalculation we can estimate 300 ppmv at zero human emissions…
Bart says:
April 2, 2012 at 4:31 pm
Before we get too far afield, let us pause to make the current point. You are now arguing, Ferdinand, that you have a problem with the sequestration rate being what you think is required. That’s fine, and a valid argument to have. But, in doing so, we must acknowledge that the mass balance argument is insufficient to convict anthropogenic emissions of the crime of increasing atmospheric concentrations, and you must rely upon other data to prosecute the case.
If I can only get that concession from you, I will be happy for now.
The mass balance itself is sufficient to prove that the human emissions are the sole cause of the increase in the atmosphere, as long as the increase is less than the emissions. It is as simple as that. If the increase in the atmosphere was more than the emissions, then we would have a part from the emissions and a part from nature adding to the increase. In both cases, the sequestering is less than the emissions or less than the sum of the emissions + extra natural supply. If there was no increase or even a decrease in the atmosphere, then the sequestration rate was larger than the emissions and any additional supply by nature.