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.
gavincawley says:
April 5, 2012 at 2:27 pm
Good. Bye. Gavin.
Actually Bart, it points out that your model is useless (any model that can explain absolutely anything is of no value for the same reason that astrology is meaningless even though it can explain anything). The mass balance argument however cannot explain everything. It can only explain what is consistent with conservation of mass and the observations of anthropogenic emissions and the observed rise in atmospheric CO2.
gavincawley says:
April 5, 2012 at 2:43 pm
Nope.
Bart says:
April 5, 2012 at 2:11 pm
Sorry Bart, but I disagree: there are indeed constraints in the output to the ocean surface (which is saturated with a factor 0.1 against the atmospheric increase), but not in the input to the atmosphere. And not in the deep oceans (at least not on short term) or vegetation.
The saturation of the ocean surface is very fast, in the order of 1.5 years half life time and as the ocean surface contains ~1000 GtC, its concentration increased with ~3% (30 GtC) where the atmosphere increased with 30% (210 GtC) in the same period.
That part of the oceans thus is only of minor interest, the bulk of the current sinks is in the deep oceans (via the THC in the NE Atlantic), and in vegetation. These have, at least for now, no constraints in mass accumulation. The deep oceans take at least 800 years to return any change in CO2 mass increase back to the surface and vegetation can store any amount of carbon indefinitely.
The only constraints are the speed of transfer to the deep oceans and of CO2 (semi) permanent sequestering by photosynthesis (regardless that a large part returns in another season). Both seems directly in ratio with the distance between current M and Mo (whatever that may be). Thus -kM is the only term of interest for the uptake flow.
I didn’t realize that in the mat, but your scheme makes it pretty clear: if the human emissions are halved at the input, where then goes the other halve? Theoretically your scheme might be right for the ocean surface layer with restricted uptake, but practically it is impossible…
FerdiEgb says:
April 5, 2012 at 2:56 pm
“I didn’t realize that in the mat, but your scheme makes it pretty clear: if the human emissions are halved at the input, where then goes the other halve?”
Into the oceans..
Anyway, it’s a moot question (see post @ur momisugly April 5, 2012 at 2:33 pm). The mass balance argument still does not eliminate the possibility that the rise is natural.
Bart says:
April 5, 2012 at 4:35 pm
Into the oceans…
Sorry, but that is not what your scheme says. What you have done is that you transferred a part of the observed change in increase of M from the output to the inputs. That may be mathematically sound and even the overall mass balance may not be violated (for halve the inputs), but it violates the mass balance of the total inputs. Whatever happens with the inputs, even if any human (or natural) input was catched by oceans or vegetation within a second, it must be added to the total mass of M before it can be removed.
Your scheme only shows halve the real inputs to the atmosphere, where the increase in mass partly is removed into the oceans, while the other halve isn’t shown and bypasses the whole process to disappear spontaneously into the same oceans. That can’t be true. Your scheme doesn’t reflect reality.
About the possibility that the rise is natural: that can be right momentarily, when the C input rises, but it can’t be right integrated over the longer term, as long as the increase in M is less than expected from H alone. Thus the C input may give a short rise during the positive flank of the variability (the AC component), but doesn’t give a rise due to the natural throughput (the DC component).
Bart wrote “Anyway, it’s a moot question (see post @ur momisugly April 5, 2012 at 2:33 pm). The mass balance argument still does not eliminate the possibility that the rise is natural.”
So even though we know that natural uptake exceeds natural emissions (via the mass balance argument) and that atmospheric CO2 would be falling if not for anthropogenic emissions (because the partial pressures of CO2 in the oceans and atmosphere are not in equilibrium), that doesn’t rule out the possibility that the rise is natural?
The bath analogy I gave earlier demonstrated that this argument is absurd, which is why Bart is unwilling to address it. It isn’t difficult to come up with another one:
Consider I share a savings jar with my wife (with video surveilance and a team of loyal ninja to make sure that nobody else interfers with it*). If I put in £8 a week and notice that the balance is only rising at £4 as week, then that DOES rule out the possibility that that the rise in our savings is in any way due to my wife. Whatever the amount of money she has put into the jar, conservation of money means that she must have taken more out of the jar than she put in, and hence she is OPPOSING the rise in our savings, not causing it. If you disagree, I a have a business proposal for you ;o)
* yes I included that bit to prevent the inevitable over-extension of the analogy by those who want to avoid the key issue, for instance by saying that thieves may be taking money out of the jar without my knowledge. However if you relate that back to the carbon cycle it would be like saying that in addition to anthropogenic and natural sources and sinks there are other sources/sinks. However, if these sources and sinks aren’t anthropogenic and they are not natural, that only leaves exraterrestrial or supernatural inluences, so it is like saying space-pixies are stealing CO2 from the atmosphere. I’d say that wasn’t exactly the strongest argument ever made in the climate debate! ;o)
FerdiEgb says:
April 6, 2012 at 12:03 am
“Sorry, but that is not what your scheme says.”
Yes, it is exactly what it says. By assuming “a” is much greater than “k”, I am assuming the dynamics for movement of the mass into the oceans is “fast”. The system described by the first order differential equation
Mdot = c*(N + A) – k*M
is merely an approximation to the output “M” from the set of equations
Mdot = N + A + a*(O – 0.5*M/c)
Odot = a*(0.5*M/c – O) – 2*k*O
when the exchange into the ocean is “rapid”. Mass is conserved because
Mdot + Odot = N + A – 2*k*O
which is the natural and anthropogenic inputs minus the amount which gets permanently sequestered in the oceans.
gavincawley says:
April 6, 2012 at 2:40 am
Nope.
Ferdinand, what I have told you above is not controversial. These are standard equations. If you do not understand what I am doing, you should not be opining so strenuously on the topic.
Without at least a familiarity with the math involved, you are a blind man trying to describe a rainbow. Gavin is blind, and deaf as well. I urge you not to stop up your ears as he has.
Sorry Bart, your behaviour is *exactly* the kind of thing that Singer says gives the skeptics a bad name, and on that point he is right (although as I said I wouldn’t use his terminology).
It is you that is ignoring the arguments posed against you. “nope” and rhetorical posturing is no substitute for a substantive response. The reason you won’t reply to either of the two analogies I have posted is simply becuase your position is absurd and your evasion is tacit admission that you know it.
Bart, in your equation
Mdot = c*(N + A) – k*M
the first term assumes there is some mechanism that somehow knows was anthropogenic and natural emissions actually are and automatically takes up half of it. This is clearly nonsense as the mechanisms that govern the sinks respond to the concentration of carbon dioxide in the atmosphere, and have no way of telling what either N nor A are at any particular time, only M. Therefore your model bears no relation to reality to the physical world.
Yes, I know that the airborne fraction is about a half, but my model reproduces that as a concequence of the emissions, and doesn’t need a bodge to hardcode it into the model.
I am going to make an amendment to the equations here. I originally started with
Mdot = N + A + a*(O – M)
Odot = a*(M – O) – 2*k*O
This is the standard form which usually appears in the literature, and assigns 1/2 of the input to the atmosphere and 1/2 to the oceans, in superficial agreement with observations.The output “M” of this model can be reliably approximated by the first order differential equation
Mdot = (1/2)*(N + A) – k*M
whe a is much greater than k.
I then worked out on my own equations
Mdot = N + A + a*(O – 0.5*M/c)
Odot = a*(0.5*M/c – O) – 2*k*O
and said the output “M” here could be approximated by the rist order differential equation
Mdot = c*(N + A) – k*M
when a and a/c are much greater than k. I made an ERROR here. The second order set of equations should have been
Mdot = N + A + (a/c)*(c*O – (1-c)*M)
Odot = (a/c)*((1-c)*M – c*O) – (k/(1-c))*O
The output “M” for this set of equations can be approximated by
Mdot := c*(N + A) – k*M
when a is much greater than k*c/(1-c). It may be seen that, when c = 1/2, these equations become the first ones on this page.
The equation for “O” becomes approximately
Odot := (1-c)*(N + A) – k*O
Approximately a fraction of “c” goes into the atmosphere, and (1-c) goes into the oceans. Mdot + Odot in this approximate model is equal to N+A – k*(M+O), the natural plus anthropogenic inputs minus the part which is sequestered, so mass balance holds here, too.
gavincawley says:
April 6, 2012 at 10:08 am
Gavin – you are flailing. When you find yourself in a hole, stop digging. It is painful to watch.
Bart, all you have done is show you have no answer to that criticism either.
BTW, your new model still has the airborne fraction hard-coded into the model. What you don’t seem to realise is that the constant airborne fraction is not a law of physics, it is a consequence of exponentially rising emissions. The model I use in my paper produces a constant airborne fraction as a consequence of the observed emissions (or at least an exponential approximation to those observations, which is a pretty good approximation). So why do you need to hard-code it into your model?
Hint: If you drive a first order linear system with an exponential signal, you get out an exponential signal with the same time constant, but different amplitude. Divide one exponential by another exponential with the same timeconstant and the result is a constant value – the airborne fraction.
This is before we get to the issue that the oceans can only see M, so they can’t obey a law that says its uptake is determined by A and N.
Of course, the model I have presented only takes into account atmosphere and ocean. Including land will alter the allocations and time constants. If broad decoupling assumptions hold, I would expect something like
Mdot := c1*(N + A) – (k1+k2)*M
Odot := c2*(N + A) – k1*O
Ldot := (1-c1-c2)*(N + A) – k2*L
In addition, I expect that the decay is not really simple exponential, and k1 and k2 might need to be expressed as differential equation operators rather than simple gains to give a “long tail” response. The terms c1 and c2 might be similarly more complicated than simple gains.
But, the basic conclusion still holds: If ocean and land permanent and semi-permanent sinks are sufficiently active, then there is no reason that the rise we have observed should necessarily be due to anthropogenic forcing.
gavincawley says:
April 6, 2012 at 11:00 am
Gavin, you have completely lost touch with reality.
I’ve done all I can for your two. I have given you a lot of my time (which generally costs dearly, I can assure you). I have shown you using rigorous mathematics why your assumptions have been overly simplified. I have led you to the water, but it is up to you to drink. There is nothing more I can do.
So, until we meet again, I am signing off and deleting this link from my queue.
Bart says:
April 6, 2012 at 11:20 am
Gavin, you have completely lost touch with reality.
Bart, as said by Gavin, there is no physical way that the oceans or vegetation know what the input flows are. Thus your constants c, c1, c2,… on the input flows are physically impossible, however nice the math sounds. The only way to have a sink in any of the (semi) permanent storages is by a pressure difference between the atmosphere and the oceans and/or water in the plant alveoles. That is the term -kM, whatever k may be.
BTW, k is observed to be ~4/210 or ~0.02 if we may assume that the current levels are 100 ppmv above steady state.
All,
There will be a post up on my site tomorrow which should add something more to this debate. Feel free to stop by and contribute.
Cheers
Rog Tallbloke
All:
I’m putting up a new post tomorrow which will hopefully add to this debate. Feel free to drop by and comment.
Cheers
TB
fraction that belongs to humans?
gavincawley says:
April 3, 2012 at 2:21 pm
tallbloke, read a bit further, where I wrote “Another one of the arguments that Prof. Singer says should be dropped is the argument that the rise in CO2 is natural, perhaps you should ask him to expand on this in a blog post here?.”
I mentioned the second law thing as it is the first “denier argument” that Prof. Singer mentions. The argument that the rise in CO2 is natural is if anything worse than the second law canard; anyone capable of balancing a bank account ought to understand how we know the rise in CO2 is anthropogenic.
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How can you know?