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:
I can’t see that one analogy is any different than the other. Only the volumes are different; 1 tsp vs 0.5 litre. Also, the sawtooth chart of MLO CO2 looks pretty ‘discrete’ to me, so your analogy is no different than Bart’s.
April 4, 2012 at 1:44 pm
Bart, you are much better in the theory than I have ever been, most is too long ago and I haven’t practiced it for over 45 years, because of a quite different carrier. So I am a bit slow and need to think twice to ten times about what is said.
But I am a practical boy. Any increase in CO2 mass in the atmosphere over time is the integral of human additions + the integral of natural additions – the integral of natural sequestering of all known years in the past 50+ years. That may sound as a horror to you, who are thinking in linear equations, but as good as the old slide rule gives an approximation that 2 x 2 = 4 and a calculator gives a more exact result, your linear approach gives an approximation, while my much simpler approach gives the same result.
In the above you may combine the last two terms as the integral of (natural additions – natural sequestering) as that is what is known for each year in the past 50 years. And I made an error in the calculated k I sent, as that is the e-fold time, while the factor k is the reciprocal of that, thus the current k = 4 / 210 = 0.019. The smaller that k is, the more CO2 remains in the atmosphere.
But let us focus on
dM/dt := c*(N+A) – k*M
which can’t be solved, as both c and N are undefined, except if N ~ 0.
We have some historical integrations of N over time spans of 8-600 years in ice cores. These all show N ~ 0, except if the temperature changes. Then N integrates to new values in ratio with the temperature change.
For changes of about 10°C, there is a change of 80 ppmv (~170 GtC) over a period of 5,000 years, or average 0.034 GtC/year. Not really spectacular, compared to the 8 GtC/yr humans release nowadays. The MWP-LIA temperature change shows a change of ~6 ppmv (or ~13 GtC) over 50 years or de decrease of 0.26 GtC/year. Of course, the smoothing of the ice cores prevent the view on changes with higher frequenties.
We have some modern measurements too: mainly temperature driven year by year variations of +/- 2 GtC around the trend. Integrated over 2-3 years that gives near zero deviation from the trend.
While that isn’t a solid proof that N ~ 0, it looks quite like that over small to very long integrated periods.
smokey – in barts analogy the average volume in the bucket is half a litre, in mine it is half a teaspoon full, i you used 1ml pipette it would be half a millilitre, but the exchange is a litre in each case. Consider what happens when the exchange is performed one molecule at a time. The fact that the two almost identical analogies produce different results illustrates the flaw in the analogy.
The point is that the increase or decrease in the contents of the bucket depends on the difference between total flow into the bucket minus total flow out of the bucket. If you make the flow in the same as the flow out, you can have an exchange as large as you like, but it doesn’t change the level in the bucket.
smoky, also the saw tooth behaviour in the Mauna Loa series is due to annual growth/dieback in the region. However if you look at measurements from othe stations (e.g. in Antarctica there is no saw tooth pattern, just a steady rise with a small ripple in it).
The mass balance argument is usually described in terms of annual fluxes and changes, so that the irrelevant seasonal fluxes cancel out over the course of the year. The annual growth/dieback pretty much balances eachother out, if there is any imbalance it is reflected in the annual measurements.
gavincawley,,
Analogies are meant to simplify. Both analogies look to me to be the same. Maybe try a different one.
FerdiEgb says:
April 4, 2012 at 3:32 pm
“…which can’t be solved, as both c and N are undefined…”
But, solutions can be determined in the limit as k either goes to zero or becomes large. Those solutions are
k small: M approaches c*integral(N + A)
“c” is assumed to be constant here.
k large: M approaches (c/k)*(N + A)
“We have some historical integrations of N over time spans of 8-600 years in ice cores.”
As you say, the smoothing of the ice cores prevent the view on changes with higher frequenties. For modern measurements, I see no reason the trend cannot itself be due to N.
gavincawley says:
April 4, 2012 at 3:40 pm
“… but the exchange is a litre in each case.”
You have explained this very poorly. I think you are saying that you first put in 1 liter + 1 teaspoon, then empty it, so that cycle averages to 1/2 of 1 liter plus one teaspoon. Then, the next cycle, you put in 1 liter minus 1 teaspoon, so the average is 1/2 of 1 liter minus 1 teaspoon, so the average over two cycles is still 1 liter.
If that is the case, it is trivially true, but has no bearing on the problem at hand, where there is continuous upward plant growth due to continuous increase in CO2.
“The annual growth/dieback pretty much balances eachother out, if there is any imbalance it is reflected in the annual measurements.”
Not if there is a sustained increase in growth. Again, go for the reductio: Are you telling me there would be no difference in CO2 concentration if the Earth were a dead planet, with no vegetation at all, compared to what it is now?
“Are you telling me there would be no difference in CO2 concentration if the Earth were a dead planet, with no vegetation at all, compared to what it is now?”
Understand – there is copious carbon tied up in all the living creatures on Earth. If you get more and bigger plants and animals, that is more carbon tied up in them. It does not matter if they live and die. If the population is stable, the carbon is continuously deposited there.
And, that doesn’t even get into the fact that much of that carbon does not return to be recycled through the system. E.g., the creation of fossil fuels, which is one of many permanent or semi-permanent carbon sinks which exist both in the oceans and on land. New sinks are being discovered all the time. Here is one which particularly piqued my interest. I have read recently that rock weathering sinks far more carbon than scientists previously thought.
We just do not know everything about the Earth and all the very complex processes happening on it.
smokey, the standard analogy is that of having a basin with a hot tap (representing anthropogenic emissions) a cold tap (representing natural emissions) and a drain (representing natural uptake). Start with the hot tap being shut, then if the water flowing in through the cold tap balances the flow of water through the drain, then the level of water in the basin will remain constant. This is true regardless of the magnitude of the flows, it is true for 1 litre per hour, or 10 or 1000 etc. In order for the level of water to change there needs to be a difference between the flow into the basin and the flow out of the basin, if total inflow exceeds total outflow then the level will rise, if total outlow exceeds total inflow, then the amount will fall.
So consider the case where we have a flow-meter that tells us how much water is flowing through the hot tap, and a depth guage which allows us to work out the volume of water in the basin. We don’t know how much water is flowing into the basin through the hot tap nor how much is flowing out through the drain, but we know that if the rate at which the volume of water in the basin is rising at a rate less than is flowing through the hot tap, then we know that there must be more water flowing out through the drain is greater than the amount flowing in through the cold tap. This is simple artihmetic.
Note that as I have said multiple times before, we can know that natural uptake, U, is greater than natural emissions, N, without knowing the values of either U or N, provided we assume conservation of mass.
This is also true whether the rate at which water is flowing through the drain and cold tap is constant or varies in some way. That is because conservation of mass holds regardless of the flow rates.
gavincawley says:
April 5, 2012 at 2:43 am
“This is simple artihmetic.”
Very simple. Way, way too simple.
Water flows out of the bottom in proportion to the pressure at the outlet. And, pressure is proportional to the height of the water column above the hole.
If you have 100 parts cold water flowing in and have stabilized at the appropriate level, and you add an additional 1 part hot water, then the water level will rise at most 1 part in 100 or 1%.
If the water level rises 2%, then you know someone has turned up the cold water, because the hot water cannot raise it more than 1%.
This is your flaw. This is your mistake. You have assumed that any rise must be attributable to the hot water, because the cold water incoming rate is constant. But, you do not know that rate, and have no means of determining whether it is constant or not. And, you do not know take account of the fact that the outflow rate increases with the added pressure.
This is a dynamic system. It does not respond based on simple accounting principles.
It helps to use the language of mathematics, so let’s parse this:
“We don’t know how much water is flowing into the basin through the hot tap (we do, let’s call it H) nor how much is flowing out through the drain(call it D) , but we know that (1) if the rate at which the volume of water in the basin is rising (call it Vdot) at a rate less than is flowing through the hot tap (H, again), then (2) we know that there must be more water flowing out through the drain is greater than the amount flowing in through the cold tap (call it C).”
Since I cannot use less than – greater than signs with html, I will use .lt. and .gt. instead.
What this says is
Vdot .lt. H
We can say
Vdot = H + C – D
(1) says
Vdot .lt. H
Does this imply, as the final statement (2) says, that
D .gt. C
?
Yes. It says
H + C – D .lt. H
or
C .lt. D
Does this tell us that the observed rise is attributable to H? No. Because D is variable. It has a part which has responded to C, and a part which has responded to H. Call them DH and DC. We have
C .lt. DC + DH
If we send H to zero, will Vdot go negative?
Initially, yes. But, when H goes to zero, DH also goes to zero, with a characteristic time dependent on the feedback (sink) strength, and we are left with
Vdot = C – DC
Now, can we say
C .lt. DC
?
No, we cannot. We only know that
C .lt. DC + DH0
where DH0 is DH evaluated at the time H was being input.
Bart wrote “C .lt. D Does this tell us that the observed rise is attributable to H? ”
Yes (as you agree) more is flowing out through the drain than is coming in through the cold tap. Thus if it were not for the water coming in through the hot tap H, the level in the basin would be falling instead of rising. For most people who have ever run a bath, this would be entirely obvious.
If I half fill my bath, pull out the plug and then adjust the cold tap so that the level in the bath is falling at 1cm per minute Your argument appears to be that if I then put the hot tap on full that the resulting rise in the level of water in the bath cannot be attributed to the hot tap being on. That conclusion would be to say the very least “counterintuitive” to most people!
Note in this case the amount of water flowing out through the drain would have increase slightly as the level of water in the bath rose. It is still the water from the hot tap that is responsible for the rise.
gavincawley says:
April 5, 2012 at 10:57 am
“Yes (as you agree) more is flowing out through the drain than is coming in through the cold tap. Thus if it were not for the water coming in through the hot tap H, the level in the basin would be falling instead of rising.”
I showed that was not the case. Read.
Of course, H is responsible for some rise.
The point is, its responsibility can be infinitesimal.
It all depends on the rate of sequestration, which is what I have been telling you.
Bart, you last post does not address my analogy at all, it is just bluster to hide the fact that your position has been demonstrated to be absurd. H is responsible for ALL of the rise, because if not for the water coming from the hot tap, the level in the bath would be FALLING instead of rising.
Maybe some sims will help. Here is a notional CO2 model. I could play with the parameters all day and produce different results, but this will do to demonstrate the concepts.
The model is in Simulink, an industry standard dynamical systems modeling software package to solve differential equations.
At the left, I first generate a natural input and an anthropogenic input. At top, I feed the natural input alone into the model
Mdot = (1/2)*(N + A) – k*M
I chose k = 0.1 to be a fairly strong sink feedback.
In the middle, I add in the anthropogenic input.
At bottom, I feed in 1/2 the accumulation of the anthropogenic input.
As may be seen in the output plot here, the effect of the natural input and the integral of 1/2 the anthropogenic input is roughly comparable (yellow and cyan lines). The output of the model with both anthropogenic and natural effect is just a little greater than with the natural input alone.
I could play around the with parameters and make the gap infinitesimal. But, hopefully, this will illustrate my point. With an arbitrary natural input, and rapid feedback in the system, I can make the output dance to whatever tune I choose.
Does the anthropogenic input increase the output? Yes. But not necessarily significantly. Everything which is true about the Earth’s CO2 system is true about this one.
Bart, ignoring the issue won’t make it go away. We know the water coming in through the hot tap is responsible for 100% of the rise becase the amount of water coming out of the cold tap is less than the amount flowing out through the drain. Thus if not for the water from the hot tap, the level of water in the bath would be falling, not rising.
The same is true of the carbon cycle. Natural emissions are less than natural uptake, so if it wasn’t for anthropogenic emissions, CO2 levels would be falling rather than rising. It isn’t hard to see why this should be the case, the uptake of CO2 by the oceanic sink depends on the difference in partial pressure between the atmosphere and the surface waters. If we stopped all anthropogenic emissions today, this difference in partial pressures would still exist, so natural emissions would still be less than natural uptake and CO2 levels would be falling. So there again we know that anthropogenic emissions are solely responsible for the observed rise, at least over the last 50 years.
Bart says:
April 5, 2012 at 12:12 pm
Maybe some sims will help. Here is a notional CO2 model. I could play with the parameters all day and produce different results, but this will do to demonstrate the concepts.
Bart I have looked at that conscept, but I don’t see how picture 1 can be true: the human input, directly injected into the atmosphere is twice what the endresult is. As said before, there is no reason why that should be halved. What happens is that the input of any source into the atmosphere as a whole gives more pressure to push more CO2 into the oceans and vegetation. That is the term -kM which is also implemented on the combined inputs. If you halve the inputs ánd implement -kM you are double accounting in the sinks.
gavincawley says:
April 5, 2012 at 1:13 pm
Gavin, I have explained to you in excruciating detail why you are wrong. If repetition ad nauseam is the best you can do, then there is no point in continuing.
Bart, your post is merely a tacit admission that you have no answer to the argument I made in my preceding point.
The natural sources are less than natural sinks, CO2 levels would be falling if it were not for anthropogenic emissions. Thus it is obvious that anthropogenic emissions are the cause of the rise.
The error in your model (double accounting of the uptake) was pointed out to you earlier in the thread. It is a pity that you are unable to accept criticism, being wrong and understanding your error is a very good way of learning.
FerdiEgb says:
April 5, 2012 at 1:45 pm
“As said before, there is no reason why that should be halved.”
Ferdinand – I explained the origin of the 1/2 factor in, again, excruciating detail at April 3, 2012 at 12:30 pm. I noted at April 3, 2012 at 1:35 pm that, in fact, the factor “c” could be anything, but that climate modelers prefer a value of 1/2 because of the superficial agreement with observations. Phil pointed out at April 3, 2012 at 2:23 pm that the number should, in fact, be much smaller to be in agreement with Henry’s law, and I agree that he is probably right.
The conceptual problem you are having is when you say “the term -kM which is also implemented on the combined inputs”. But, the dissolution into the ocean is not a function of the atmospheric concentration alone, but in the weighted difference of the ocean concentration and the atmospheric concentration. If that were not the case then, in the absence of inputs, the oceans would continue absorbing until all the CO2 was gone from the atmosphere. But, we know quite well the dissolution would only continue until an equilibrium has been established with some CO2 in the air, and some dissolved in the oceans.
If it helps you conceptualize it, use the equations I gave at April 3, 2012 at 1:35 pm
Mdot = N + A + a*(O – 0.5*M/c)
Odot = a*(0.5*M/c – O) – 2*k*O
If you simulate this, choosing the constant “a” to be much greater than “k”, you will find that the output M is very nearly approximated by
Mdot = c*(N + A) – k*M
gavincawley says:
April 5, 2012 at 2:05 pm
I have no more time for such foolishness. Good-bye, Gavin.
“If you simulate this, choosing the constant “a” to be much greater than “k”, you will find that the output M is very nearly approximated by
Mdot = c*(N + A) – k*M”
And, do please note, Ferdinand, that this is only a side issue. I insist on putting a factor “c” in there because it is the correct way to create the model. But, it is not necessary to prove the point. I have complete freedom to choose a time varying input “N” and a constant “k”. As I said, I can make the output dance to any tune I please with that.
Bart wrote: “If that were not the case then, in the absence of inputs, the oceans would continue absorbing until all the CO2 was gone from the atmosphere.”
Which is why in the model I used in my paper I made U a linear function of atmospheric concentration, rather than simply being proportional. However it is no excuse for you to put a fiddle factor into your model to double-count the uptake. I know you have explained your reasoning for putting c into the D.E. but that doesn’t mean that your reasoning right, and ignoring criticism of your model is deeply unconvincing.
Ferdinand – if it will make you happy, here is a bogus CO2 model with c = 1.
Here is the output. I also tuned the feedback to be stronger so I could show than I can make the gap arbitrarily close, and the anthropogenic input less and less important, that way. And, I adjusted the natural input to produce the agreement with all the outputs you see.
As you see, with feedback and a properly selected natural input, I can make the output do anything I please to within an arbitrary tolerance.
I can do this so easily. It is why I have been after you about this silly mass balance business all along. Now, maybe you can see.