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.
Oh, this is great information. Thank you David. It is one of the key points that is always brought up when CO2 is discussed.
So it is elevated in association with the Little Ice Age……. and it is still elevated compared to 0 – 1400 AD. Note the many precipitous drops far greater that what is seen in the 20th century. There is obviously another mechanism controlling c13/C12 ratio.
Hold it now … I just realized that the scales are different.Flinders reef was 0 around 1700 and is now <-1 in 2000. Yucatan makes an arch between -2.5 and -4.5 with extreme variability between 1500 and 2000. The Flanders Reef series isn't long enough to say anything meaningful when it is compared to the Yucatan record. Variability of 2 full units in the ratio is very common. If the ratio goes negative due to fossil fuel input then why has the Flinders reef dropped from 0 to -1 while in the Yucatan it was in the -5 range for 1400 years ……. must have been a lot of Aztecks (sp?) burning a lot of coal. Mind you the Yucatan area is full of gypsum …wonder what the C ratio is in gypsum, ie does C12 – C13 speciate when gypsum crystallizes in the evaporite forming process or alternatively what was the C13 – C12 ratio when the gypsum formed in ocean water?
Is the ratio a regional thing versus a global proxy?
Hold it again. The Flinders Reef (Great Barrier Reef) in the SKS post has the ratio from -1.2 to -3.6. That doesn’t agree with the right hand scale where the curve is placed in Figure 5?
Ditto the thanks David…… I had no idea there were so many examples of the ratio change…. minus human influence. More stuff well within natural variability. I’ve always argued that the isotope doesn’t matter. I think we assume we know more than what we really know.
The Yucatan graph is a bit off if anyone is trying to argue the isotope ratio, at least for that place, is indicative of warming or cooling. And, it is problematic. Not only is the vertical divergence off, so is the frequency.
Just from experience, looking at the graph, I’d say a methodology of some sort, or sampling size changed for gathering information prior to about 1200-1400 as opposed to after. It doesn’t invalidate much of anything…. other than going back beyond 1200.
For those that can’t see, what I’m on about, the intersession between the RWP and MWP is missing, but if you look, @ur momisugly about 1200-1400….. the graph changes its characteristics.
I hate graphs that look like that…..
To worry about the origin of CO2 is to imply that present (or forecast) concentrations are a cause for concern. Elevated CO2 is an issue only for those who insist on misinterpreting temperature-CO2 cause-and-effect, and those who hate food.
This is something I’ve been considering spending more time on. But if I start, I may never finish. ‘Cold’ isotope-labels are frequently used as probes and internal standards in Chemistry, but the number of processes that can cause isotope fractionation is more than you can shake a stick at.
Deuterated hydrocarbons can be separated by liquid chromatography. For many enzymes/biological-catalysts I would expect fluctuating isotope effects to be the norm, not the exception. It’s a minefield.
It’s pretty annoying there is no actual calendar year 0; we jump to 1 BC, skipping 0.
Get out of the weeds. What is the point of criticizing the Yucatan v Flinders chart? It’s not published peer reviewed work. It’s an interesting comparison just to get people thinking. Isn’t it interesting the curves can be placed on top of each other relatively easily? What the overlay really means, if anything, hasn’t been determined. It serves to help people view the red curve in a larger context. The overlay makes the point the red curve doesn’t necessarily indicate the δ13C decline is due to human influence. Isn’t that the point of the story?
I think the isotope ratio is interesting and worth thinking about. It does possibly reflect human origin, and should be taken seriously as an argument. However . . .
We do not know enough about total CO2 sources and sinks to determine whether the increase in overall CO2 *would not have happened* but for human fossil fuel use. Further we do know that CO2 has risen at a remarkably steady pace in recent decades, despite ups and downs in fossil fuel use. Both of these facts should give us pause.
Finally, many argue that the amount of human emissions is greater than the total increase and, therefore, humans are responsible for the increase (meaning, the biosphere is able to handle part of the human emissions, but not all). However, even if the isotope ratio changes (more CO2-12), consider this analogy:
I run a small business on a cash basis. At the beginning of the year I have $1000, 3 of which are marked with a red dot. Throughout the course of the year I exchange thousands of dollars with many vendors and customers, including occasional transactions with one tiny customer who marks red dots on all his bills. At the end of the year, after thousands of transactions of cash flowing in and out, I count my cash, and it turns out I have $1001, 4 of which are marked with a red dot. According to AGW advocates, the tiny customer who pays only with bills marked with a red dot (i) *must* be the sole source of my $1 profit, and (ii) but for that tiny customer, I would not have made my $1 in profit. It should be easy to see that this is not a valid conclusion. The conclusion is even more shaky if David Middleton’s post is correct, because then we would have to say that there might even be another customer (we’re not quite sure) who sometimes also pays with bills marked with a red dot.
Finger prints may be on the gun, but the alleged murder victim is happily moving about as if nothing has happened.
It seems obvious that the Seuss effect is not just an anthropogenic fingerprint; instead it is the fingerprint of Life. Most plants and virtually all animals consist almost entirely of C12 and are depleted of C13 and C14. Hence when the global biomass increases, the proportion of total atmospheric carbon that is C12 increases, and the proportion that is C14 declines accordingly. The Seuss effect provides conclusive proof that a warm Earth enables life to thrive.
I get so worn out reading BS from the Gaia worshippers and rent seekers on the subject of CAGW. This article is just one more reason to be skeptical of the ‘man made’ part. I know we do have some effects such as Urban Heat Island Effect (UHIE) and I am sure our contribution to the Satanic Gases must have some effect, but I am skeptical that it rises above signal to noise ratio of the data itself.
Since Coal is from dead plants so that is not the origin, I was wonder where the C-13 actually came from and ran into this little gem…
That mess brings to mind this article:
No wonder CAGW has spread so easily.
Gail combs quotes that bit about “every C-14 atom losing an electron” and seems to suggest it’s not correct. She’s right that it makes the naive reader think the atom is losing a shell electron, but of course what is actually going on is nuclear decay, as a neutron becomes a proton by beta decay, emitting an electron and an electron anti-neutrino. Textbooks have a lot of sins for which they should answer, such as watering down the facts to make them” easier.”
I am gravely concerned that the concentration of CO2 is below 500ppm. To me, this means we are in a highly vulnerable state. This concentration (or lack of) has been fine during this fairly benign period of Geological History we’ve been in now since the commencement of the Quaternary. We have not had any really major disturbances other than the general dominance of high latitude Continental Glaciation for much of the Q. But no really big extraterrestrial strikes, no widespread volcanic catastrophes, etc. Not if but when the next one of these happens, if we are still below 500ppm I worry that photosynthesis will behave as if the level were far lower (e.g. due to the impacts of the disturbance). From there, a mass die off of photosynthesis based life could occur.
I personally believe that the isotopic signature in the current atmosphere is probobably anthropogenic. But you have hit on one of the most important mysteries in earth science: the PETM isotopic “excursion”. It has been asserted that the PETM was caused by fossil fuel burning as rifting in the north Atlantic separated Greenlandfrom Europe, but the timing really doesn’t work and current rifting through Africa and the Red Sea does not seem to be producing clouds of smoke from the ample petroleum in the region.
I once suggested tounge-in- cheek on Sks that a burst of cosmic rays converted nitrogen to C14, but this would not explain the C13, would it?
The increase in light isotope C must be caused by fossil fuel burning because we can’t think of any other reason.
Except that warming seas become more stratified and starve the calcareous phytoplankton which usually preferentially fix light C and export it to the deep ocean. So, fewer phytos, less light C pull down, more 12C in the atmosphere.
Oh, yes, we’ve disrupted vegetation cover causing a lot of dust. Dissolved silica runs into the oceans where it feeds diatoms which are the little beasties that get first helpings of nutrients until the silica runs out. Diatoms are not as discriminatory against 13C as the calcareous phytos, so they export proportionately less 12C, signal in atmosphere goes up.
Oh, and of course there’s the fact that oil and surfactant polluted seas warm faster, stratify more, starving the phytos. And waves break less, less CO2 is driven into the ocean which means that phytos are CO2 starved. Some change their metabolism to C4 ( a better way of fixing carbon in times of C famine), C4 phytos outcompete C3 types and, as any fule know, C4 metabolism is less discriminatory against 13C which means proportionately more heavy C is exported to the deep ocean.
And oil polluted seas engage less with the wind,: this reduces currents, pulling up less nutrient-rich water from below. So this starves the phytos which export less light C.
But it must be us burning fossil fuel, because we can’t think of anything else it can be.
Unless the introduction of European earth worms has altered the silica run-off from those areas where they have been introduced to improve agriculture.
Or something else is happening we haven’t noticed yet.
But it must be us.
The graph used on Sceptical Science should be compared with others: far be it from me to suggest that Mr Cook would use sharp practice in his articles, but other depictions show that the ‘anthropogenic’ 12C signal begins in about 1700AD. Which is odd as even the intelligent men in Ironbridge hadn’t yet started destroying Gaia at that date. But it must be us. We can’t think of anything else. [puts fngers in ears] I’m not listening.
JF
PETM: sea erosion breaches a major oil reservoir. Kriegesmarine Effect happens. Big temperature rise. Would such a small event have such a large effect? Well, we are dumping enough light oil down our rivers every fortnight to cover the entire ocean surface and that’s giving us about .2 deg C/decade. During WWII the spilled oil was enough to drive the temperature up by .3 deg C in a few months. I think. All wwe need to do is clean up our act and watch what happens. I bet on cooling.
There is also the question of diffusion, i.e., how long it takes for the C12 rich gas input to disperse throughout the system. This topic was discussed on a recent thread.
An analogy is as follows. Suppose you have a bucket of water with an incoming flow at the top, and an equal outgoing flow from a hole at the bottom. To the incoming flow, you add about 3% more of blue dyed water. A new equilibrium will be established when the height of the water in the bucket increases 3%. But, before the dye has thoroughly diffused, the water will be bluer at the top than it is at the bottom.
Now, pump in an additional clear water flow near the bottom from an unknown source at a rate which continually increases the level in the bucket over the observation time interval. Where does the blue water now aggregate?
Can anyone please explain to me why the measured increase in atmospheric CO2 is almost linear; yet the worlds population increase & usage of CO2 generating fuels would more likely be exponential during the 20th C?
Something is not right!
The SUESS effect was first noticed to correct carbon dating before the 1950s when bomb testing first started. C14 is naturally produced by cosmic rays in the upper atmosphere and about 10kg are produced each year this way. After the industrial revolution the concentration of C14 began to get diluted slightly as fossil fuels were burned. This is because fossil fuels essentially contain no C14. The effect was first noticed by Suess who introduced a correction for carbon dating. A recent study from 2002[6] has measured that the effect up until 1950 was to decrease C14 concentrations by 2.4+- 0.35%. By 1950 CO2 levels had risen above pre-industrial values by about 12%. This also provides evidence that just 20% of the increase in CO2 levels by 1950 was due to fossil fuels.
Both these results imply that a maximum of just one quarter of the increase in CO2 concentrations since 1750 are of fossil fuel origin. This means that at least 75% of the observed increase in CO2 is of natural origin. Perhaps a further 15% of this could also be due to human causes – land change, deforestation but it is hard to avoid the conclusion that the majority of it is natural. How can this be ? Have we disrupted the overall carbon cycle such that each year there is a surplus in the recycling of natural CO2 ? Or is this 60% effect due to natural warming which would have occurred anyway ? It seems to me that there could be an error in the estimates that the IPCC use for the lifetime(s) of CO2 in the atmosphere?
The lifetime of a given sample of CO2 molecules is the time needed for 1/e of the CO2 molecules to leave the atmosphere. An unintended experiment was carried out in the 1960s due to nuclear testing which released large amounts of radioactive C14 into the atmosphere. C14 measurements show how this pulse of CO2 decayed with time and derive a lifetime value. The evidence from the delta C13 measurements, and the Seuss effect would support a lifetime of about 7 years. The direct C14 measurements give a value around 10 -14 years. In both cases the fraction of CO2 molecules in the atmosphere for current emission levels reaches a limit of < 10% of today’s atmosphere. It is only by assuming much higher lifetimes of over 100 years that the IPCC predictions are possible.
So the whole AGW model depends on a long lifetime for CO2. The IPCC carbon model (WG1) is described on page 213 of WG1 states :
a0 + sum(i=1,3)(ai.exp(-t/Taui)) , Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, Tau1 = 172.9 years, Tau2 = 18.51 years, and Tau3 = 1.186 years.
If you look carefully at this formula you will see that it is made up of 3 independent CO2 lifetimes each with different amplitudes, plus a constant term implying that 22% of anthroprogenic CO2 will remain in the atmosphere for ever!
One objection I have to the form of this model is the concept of using 3 different lifetimes purely from a logical viewpoint, as it kind of assumes that there are 3 different types of CO2 molecule in different queues waiting to leave the atmosphere. I suspect that the model in this form also violates the second law of thermodynamics, since whether there are 3 holes in a bucket of water or just 1 large hole is irrelevant to the rate at which the water leaks out of the bucket !
The SUESS effect was first noticed to correct carbon dating before the 1950s when bomb testing first started. C14 is naturally produced by cosmic rays in the upper atmosphere and about 10kg are produced each year this way. After the industrial revolution the concentration of C14 began to get diluted slightly as fossil fuels were burned. This is because fossil fuels essentially contain no C14. The effect was first noticed by Suess who introduced a correction for carbon dating. A recent study from 2002 has measured that the effect up until 1950 was to decrease C14 concentrations by 2.4+- 0.35%. By 1950 CO2 levels had risen above pre-industrial values by about 12%. This also provides evidence that just 20% of the increase in CO2 levels by 1950 was due to fossil fuels.
Both these results imply that a maximum of just one quarter of the increase in CO2 concentrations since 1750 are of fossil fuel origin. This means that at least 75% of the observed increase in CO2 is of natural origin. Perhaps a further 15% of this could also be due to human causes – land change, deforestation but it is hard to avoid the conclusion that the majority of it is natural. How can this be ? Have we disrupted the overall carbon cycle such that each year there is a surplus in the recycling of natural CO2 ? Or is this 60% effect due to natural warming which would have occurred anyway ? It seems to me that there could be an error in the estimates that the IPCC use for the lifetime(s) of CO2 in the atmosphere?
The lifetime of a given sample of CO2 molecules is the time needed for 1/e of the CO2 molecules to leave the atmosphere. An unintended experiment was carried out in the 1960s due to nuclear testing which released large amounts of radioactive C14 into the atmosphere. C14 measurements show how this pulse of CO2 decayed with time and derive a lifetime value. The evidence from the delta C13 measurements, and the Seuss effect would support a lifetime of about 7 years. The direct C14 measurements give a value around 10 -14 years. In both cases the fraction of CO2 molecules in the atmosphere for current emission levels reaches a limit of < 10% of today’s atmosphere. It is only by assuming much higher lifetimes of over 100 years that the IPCC predictions are possible.
So the whole AGW model depends on a long lifetime for CO2. The IPCC carbon model (WG1) is described on page 213 of WG1 and states :
a0 + sum(i=1,3)(ai.exp(-t/Taui)) , Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, Tau1 = 172.9 years, Tau2 = 18.51 years, and Tau3 = 1.186 years.
If you look carefully at this formula you will see that it is made up of 3 independent CO2 lifetimes each with different amplitudes, plus a constant term implying that 22% of anthropogenic CO2 will remain in the atmosphere for ever!
One objection I have to the form of this model is the concept of using 3 different lifetimes purely from a logical viewpoint, as it kind of assumes that there are 3 different types of CO2 molecule in different queues waiting to leave the atmosphere. I suspect that the model in this form also violates the second law of thermodynamics, since whether there are 3 holes in a bucket of water or just 1 large hole is irrelevant to the rate at which the water leaks out of the bucket !
I heard about ‘fingerprinting’ CO2 emissions from burning coal based on carbon isotope ratios, down to particular production regions about 10 years ago, but it didn’t strike me as being convincing (I probably didn’t understand the science!). But as I recall anything to do with carbon isotopes always needs a fair pinch of salt, it’s one of those ‘great in theory, but damn hard in practice’ things. Can one of the regular commentators provide an overview primer of carbon isotopes as a post? As a commentator on this thread has already pointed out, living organisms are good at altering isotope ratios. As another pointed out, anthropogenic sources for CO2 might be plausible, but have the other mechanisms been ruled out, or is this just another Climate Science mantra reinforced by repetition rather than hard science?
Has anyone sampled the isotope ratio in carbon being emitted from black smokers?
Interesting comment about spilled oil, I need to think that through…
Dixon wrote
‘spilled oil. I need to think that through.’
Search for the Ceres picture of the world, zoom in on the Mississippi overflow into the Gulf.
Find the earlier pictures of the Gulf oil spill and see the way the air above the slick is eating stratocumulus clouds at the edges.
Thinking is good! Wigley should have done it, then he would not have needed to ask ‘why the blip’.
JF
[You seem to be quick to think that your contributions are not being dealt with quickly enough . . they fall into the spam bin along with hundreds of other spam postings and it takes time to sift through the pile to release valid responses. . . reposting is pointless as are attempts to spur moderators to attend to your concerns . . everything is dealt with seriatim, you will be heard . . kbmod]
Well, it seems that this is one of the discussions which will return to WUWT every (few) month(s)…
One need to make a differentiation between direct measurements of the C13/C12 ratio and different proxies which have some relation with that ratio, but where confounding factors may be at work. That is especially the case for organic materials, influenced by a host of factors, like available light, nutritients even the CO2 concentration itself and also for inorganics made by organisms in shallow waters where pH, local concentration and depletion may play a role in de d13C ratio.
Ice cores give direct measurements of the C13/C12 ratio of CO2 in trapped air. These were measured by cold crushing the ice, cryogenic freezing, distillation of CO2 and measuring with a mass spectrometer.
The d13C level in the atmosphere over the Holocene can be followed in the Taylor Dome ice core:
http://medias.obs-mip.fr/paleo/taylor/indermuehle99nat.pdf
The average variability is +/- 0.15 per mil over the Holocene, up to 1,000 years ago.
The next ice cores one can use are the Law Dome ice cores. The combination of ice cores, firn and direct measurements allows us to reconstruct the full Holocene d13C changes up to today with increasing better resolution:
http://www.mendeley.com/research/stable-isotope-constraints-on-holocene-carbon-cycle-changes-from-an-antarctic-ice-core-1/
This can be compared to a proxy that is living in shallow and deeper waters (down to 200 m) where coastal influences are minimal: coralline sponges. The calcite deposit is isotopic identical to the surrounding seawater, which in the Carribean is rather fast refreshed and largely similar over the whole North Atlantic Gyre. The resolution of the calcite d13C ratio is 2-4 years over the past 600 years:
http://www.agu.org/pubs/crossref/2002/2001GC000264.shtml the full article is pay walled, but the most important graph, combining ice cores, firn and air d13C measurements with ocean surface measurements is here:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/sponges.gif
This shows some small pre-industrial variability of +/- 0.15 per mil d13C. Since about 1850, there is a faster and faster continuous drop of d13C of nowadays already -1.6 per mil d13C. There is no knowledge of non-human reasons like burning down about 1/3rd of all land vegetation or a similar natural disaster involving gas, oil or coal burning, And human releases fit the equation more than necessary to explain the downward trend…
Thus all together, the ice cores show conclusively the influence of human activities on the d13C ratio of the atmosphere. Proxies in the oceans need to be used with caution, as the influence of temperature on the d13C ratio must be separated from the influence of the addition of fossil fuel burning. As the first influence on coralline sponges is rather limited (+/- 0.15 per mil d13C over 350 years) and there is a direct correlation (with lag) between the measured d13C change in the atmosphere and in the sponges for recent years, the sponges show that humans are responsible for the d13C changes in the ocean’s surface layer.
clivebest says:
March 29, 2012 at 2:00 am
A recent study from 2002 has measured that the effect up until 1950 was to decrease C14 concentrations by 2.4+- 0.35%. By 1950 CO2 levels had risen above pre-industrial values by about 12%. This also provides evidence that just 20% of the increase in CO2 levels by 1950 was due to fossil fuels.
The common problem with this is that one need to make a distinction between the origin of the CO2 molecules which are in the atmosphere and the origin of the increase in total amount of CO2 in the atmosphere. Look at the example that Bart showed: we add a some blue colored water to a bucket where clear water is added to the top and leakes away at the bottom and is recirculated via a huge tank with near unlimited capacity. The water in the bucket wil be colored somewhat by the blue addition (which shows the origin), how much, that entirely depends of the ratio between colored and clear water addition. But the addition of blue water also increases the height of the waterlevel in the bucket. That is INdependent of the original flow in- and out. The original height of course depends of the initial flow, but the increase in height only depends of the additional flow.
So what is important in this case? What rests in the atmosphere of original human emissions (the blue coloured ones…) is not important at all, only the total increase (the increase in height) is important. The bomb 14C decline ratio only shows how fast the atmosphere is exchanging CO2 with other reservoirs (about 20% per year or a residence time of ~5 years), but that doesn’t say anything about how fast an excess amount of CO2 in total is removed (that is 4 GtC/year of the total 800 GtC in the atmosphere, or a 1/e decay time of ~55 years). Two completely different time constants without any relationship. Here a graph which shows (based on realistic figures) the difference between what happens with the total amount of CO2 in the atmosphere if humans should add 200 GtC from fossil fuel at once to the pre-industrial atmosphere and what happens to the human “fingerprint”:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/fract_level_pulse.jpg where FA is the fraction of “human” CO2 in air, FL the fraction in the ocean surface (not important here), tCA total carbon in air and nCA natural carbon in air.
The human fingerprint is gone after some 50 years, but the effect of the one-time addition on the total amount still is measurable after 160 years…
While I don’t agree with the Bern model, what they do is comparing the decay time between the atmosphere and different compartiments: the fastest is for the ocean’s surface, but that has a limited capacity (~10% of the increase), the medium term for the deep oceans and vegetation and the lowest for long-term processes like rock weathering, carbonate sedimentation,… My objection is that there is currently no limit in sight for the deep ocean and vegetation uptake, thus the slowest and residual terms are highly questionable.