Guest Post by Willis Eschenbach
There seem to be a host of people out there who want to discuss whether humanoids are responsible for the post ~1850 rise in the amount of CO2. People seem madly passionate about this question. So I figure I’ll deal with it by employing the method I used in the 1960s to fire off dynamite shots when I was in the road-building game … light the fuse, and run like hell …
First, the data, as far as it is known. What we have to play with are several lines of evidence, some of which are solid, and some not so solid. These break into three groups: data about the atmospheric levels, data about the emissions, and data about the isotopes.
The most solid of the atmospheric data, as we have been discussing, is the Mauna Loa CO2 data. This in turn is well supported by the ice core data. Here’s what they look like for the last thousand years:
Figure 1. Mauna Loa CO2 data (orange circles), and CO2 data from 8 separate ice cores. Fuji ice core data is analyzed by two methods (wet and dry). Siple ice core data is analyzed by two different groups (Friedli et al., and Neftel et al.). You can see why Michael Mann is madly desirous of establishing the temperature hockeystick … otherwise, he has to explain the Medieval Warm Period without recourse to CO2. Photo shows the outside of the WAIS ice core drilling shed.
So here’s the battle plan:
I’m going to lay out and discuss the data and the major issues as I understand them, and tell you what I think. Then y’all can pick it all apart. Let me preface this by saying that I do think that the recent increase in CO2 levels is due to human activities.
Issue 1. The shape of the historical record.
I will start with Figure 1. As you can see, there is excellent agreement between the eight different ice cores, including the different methods and different analysts for two of the cores. There is also excellent agreement between the ice cores and the Mauna Loa data. Perhaps the agreement is coincidence. Perhaps it is conspiracy. Perhaps it is simple error. Me, I think it represents a good estimate of the historical background CO2 record.
So if you are going to believe that this is not a result of human activities, it would help to answer the question of what else might have that effect. It is not necessary to provide an alternative hypothesis if you disbelieve that humans are the cause … but it would help your case. Me, I can’t think of any obvious other explanation for that precipitous recent rise.
Issue 2. Emissions versus Atmospheric Levels and Sequestration
There are a couple of datasets that give us amounts of CO2 emissions from human activities. The first is the CDIAC emissions dataset. This gives the annual emissions (as tonnes of carbon, not CO2) separately for fossil fuel gas, liquids, and solids. It also gives the amounts for cement production and gas flaring.
The second dataset is much less accurate. It is an estimate of the emissions from changes in land use and land cover, or “LU/LC” as it is known … what is a science if it doesn’t have acronyms? The most comprehensive dataset I’ve found for this is the Houghton dataset. Here are the emissions as shown by those two datasets:
Figure 2. Anthropogenic (human-caused) emissions from fossil fuel burning and cement manufacture (blue line), land use/land cover (LU/LC) changes (white line), and the total of the two (red line).
While this is informative, and looks somewhat like the change in atmospheric CO2, we need something to compare the two directly. The magic number to do this is the number of gigatonnes (billions of tonnes, 1 * 10^9) of carbon that it takes to change the atmospheric CO2 concentration by 1 ppmv. This turns out to be 2.13 gigatonnes of carbon (C) per 1 ppmv.
Using that relationship, we can compare emissions and atmospheric CO2 directly. Figure 3 looks at the cumulative emissions since 1850, along with the atmospheric changes (converted from ppmv to gigatonnes C). When we do so, we see an interesting relationship. Not all of the emitted CO2 ends up in the atmosphere. Some is sequestered (absorbed) by the natural systems of the earth.
Figure 3. Total emissions (fossil, cement, & LU/LC), amount remaining in the atmosphere, and amount sequestered.
Here we see that not all of the carbon that is emitted (in the form of CO2) remains in the atmosphere. Some is absorbed by some combination of the ocean, the biosphere, and the land. How are we to understand this?
To do so, we need to consider a couple of often conflated measurements. One is the residence time of CO2. This is the amount of time that the average CO2 molecule stays in the atmosphere. It can be calculated in a couple of ways, and is likely about 6–8 years.
The other measure, often confused with the first, is the half-life, or alternately the e-folding time of CO2. Suppose we put a pulse of CO2 into an atmospheric system which is at some kind of equilibrium. The pulse will slowly decay, and after a certain time, the system will return to equilibrium. This is called “exponential decay”, since a certain percentage of the excess is removed each year. The strength of the exponential decay is usually measured as the amount of time it takes for the pulse to decay to half its original value (half-life) or to 1/e (0.37) of its original value (e-folding time). The length of this decay (half-life or e-folding time) is much more difficult to calculate than the residence time. The IPCC says it is somewhere between 90 and 200 years. I say it is much less, as does Jacobson.
Now, how can we determine if it is actually the case that we are looking at exponential decay of the added CO2? One way is to compare it to what a calculated exponential decay would look like. Here’s the result, using an e-folding time of 31 years:
Figure 4. Total cumulative emissions (fossil, cement, & LU/LC), cumulative amount remaining in the atmosphere, and cumulative amount sequestered. Calculated sequestered amount (yellow line) and calculated airborne amount (black) are shown as well.
As you can see, the assumption of exponential decay fits the observed data quite well, supporting the idea that the excess atmospheric carbon is indeed from human activities.
Issue 3. 12C and 13C carbon isotopes
Carbon has a couple of natural isotopes, 12C and 13C. 12C is lighter than 13C. Plants preferentially use the lighter isotope (12C). As a result, plant derived materials (including fossil fuels) have a lower amount of 13C with respect to 12C (a lower 13C/12C ratio).
It is claimed (I have not looked very deeply into this) that since about 1850 the amount of 12C in the atmosphere has been increasing. There are several lines of evidence for this: 13C/12C ratios in tree rings, 13C/12C ratios in the ocean, and 13C/12C ratios in sponges. Together, they suggest that the cause of the post 1850 CO2 rise is fossil fuel burning.
However, there are problems with this. For example, here is a Nature article called “Problems in interpreting tree-ring δ 13C records”. The abstract says (emphasis mine):
THE stable carbon isotopic (13C/12C) record of twentieth-century tree rings has been examined1-3 for evidence of the effects of the input of isotopically lighter fossil fuel CO2 (δ 13C~-25‰ relative to the primary PDB standard4), since the onset of major fossil fuel combustion during the mid-nineteenth century, on the 13C/12C ratio of atmospheric CO2(δ 13C~-7‰), which is assimilated by trees by photosynthesis. The decline in δ13C up to 1930 observed in several series of tree-ring measurements has exceeded that anticipated from the input of fossil fuel CO2 to the atmosphere, leading to suggestions of an additional input ‰) during the late nineteenth/early twentieth century. Stuiver has suggested that a lowering of atmospheric δ 13C of 0.7‰, from 1860 to 1930 over and above that due to fossil fuel CO2 can be attributed to a net biospheric CO2 (δ 13C~-25‰) release comparable, in fact, to the total fossil fuel CO2 flux from 1850 to 1970. If information about the role of the biosphere as a source of or a sink for CO2 in the recent past can be derived from tree-ring 13C/12C data it could prove useful in evaluating the response of the whole dynamic carbon cycle to increasing input of fossil fuel CO2 and thus in predicting potential climatic change through the greenhouse effect of resultant atmospheric CO2 concentrations. I report here the trend (Fig. 1a) in whole wood δ 13C from 1883 to 1968 for tree rings of an American elm, grown in a non-forest environment at sea level in Falmouth, Cape Cod, Massachusetts (41°34’N, 70°38’W) on the northeastern coast of the US. Examination of the δ 13C trends in the light of various potential influences demonstrates the difficulty of attributing fluctuations in 13C/12C ratios to a unique cause and suggests that comparison of pre-1850 ratios with temperature records could aid resolution of perturbatory parameters in the twentieth century.
This isotopic line of argument seems like the weakest one to me. The total flux of carbon through the atmosphere is about 211 gigtonnes plus the human contribution. This means that the human contribution to the atmospheric flux ranged from ~2.7% in 1978 to 4% in 2008. During that time, the average of the 11 NOAA measuring stations value for the 13C/12C ratio decreased by -0.7 per mil.
Now, the atmosphere has ~ -7 per mil 13C/12C. Given that, for the amount of CO2 added to the atmosphere to cause a 0.7 mil drop, the added CO2 would need to have had a 13C/12C of around -60 per mil.
But fossil fuels in the current mix have a 13C/12C ration of ~ -28 per mil, only about half of that requried to make such a change. So it is clear that the fossil fuel burning is not the sole cause of the change in the atmospheric 13C/12C ratio. Note that this is the same finding as in the Nature article.
In addition, from an examination of the year-by-year changes it is obvious that there are other large scale effects on the global 13C/12C ratio. From 1984 to 1986, it increased by 0.03 per mil. From ’86 to ’89, it decreased by -0.2. And from ’89 to ’92, it didn’t change at all. Why?
However, at least the sign of the change in atmospheric 13C/12C ratio (decreasing) is in agreement with with theory that at least part of it is from anthropogenic CO2 production from fossil fuel burning.
CONCLUSION
As I said, I think that the preponderance of evidence shows that humans are the main cause of the increase in atmospheric CO2. It is unlikely that the change in CO2 is from the overall temperature increase. During the ice age to interglacial transitions, on average a change of 7°C led to a doubling of CO2. We have seen about a tenth of that change (0.7°C) since 1850, so we’d expect a CO2 change from temperature alone of only about 20 ppmv.
Given all of the issues discussed above, I say humans are responsible for the change in atmospheric CO2 … but obviously, for lots of people, YMMV. Also, please be aware that I don’t think that the change in CO2 will make any meaningful difference to the temperature, for reasons that I explain here.
So having taken a look at the data, we have finally arrived at …
RULES FOR THE DISCUSSION OF ATTRIBUTION OF THE CO2 RISE
1. Numbers trump assertions. If you don’t provide numbers, you won’t get much traction.
2. Ad hominems are meaningless. Saying that some scientist is funded by big oil, or is a member of Greenpeace, or is a geologist rather than an atmospheric physicist, is meaningless. What is important is whether what they say is true or not. Focus on the claims and their veracity, not on the sources of the claims. Sources mean nothing.
3. Appeals to authority are equally meaningless. Who cares what the 12-member Board of the National Academy of Sciences says? Science isn’t run by a vote … thank goodness.
4. Make your cites specific. “The IPCC says …” is useless. “Chapter 7 of the IPCC AR4 says …” is useless. Cite us chapter and verse, specify page and paragraph. I don’t want to have to dig through an entire paper or an IPCC chapter to guess at which one line you are talking about.
5. QUOTE WHAT YOU DISAGREE WITH!!! I can’t stress this enough. Far too often, people attack something that another person hasn’t said. Quote their words, the exact words you think are mistaken, so we can all see if you have understood what they are saying.
6. NO PERSONAL ATTACKS!!! Repeat after me. No personal attacks. No “only a fool would believe …”. No “Are you crazy?”. No speculation about a person’s motives. No “deniers”, no “warmists”, no “econazis”, none of the above. Play nice.
OK, countdown to mayhem in 3, 2, 1 … I’m outta here.
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Hot of the press and just released ASAP today in Analytical Chemistry:
http://pubs.acs.org/doi/abs/10.1021/ac1001492
I think you need a subscription to read the whole thing, but it obviously pertains to this posting and should make for an interesting read.
-Scott
Obviously, I meant hot
ofoff the press!Willis Eschenbach says:
June 11, 2010 at 3:02 pm
and Joel,
thank you for the globalview-co2 link. I probably missed it before, though I always check if my nickname is quoted. I will check again later to see what other links have been provided that I missed.
http://www.esrl.noaa.gov/gmd/ccgg/globalview/co2/co2_intro.html
from their introduction:
To facilitate use with carbon cycle modeling studies, the measurements have been processed (smoothed, interpolated, and extrapolated) resulting in extended records that are evenly incremented in time. Be aware that information contained in the actual data may be lost in this process. Users are encouraged to review the actual data in the literature, in data archives (CDIAC, WDCGG), or by contacting the participating laboratories.
OK, and particularly after climate gate, I am allowed my doubts on the ability of climate scientists to be objective with the data, no?
I suppose I could find links for the publications entering in the squiggly lines to extract height of measurement and method of calibration and whether the Keeling values are somewhere implicitly assumed. I will hit pay walls and am too old to start spending days in libraries. 75% from 5 to 14 kilometers, if “well mixed” is nonsense, cannot be a show case for global trends.
1. The stomatal data agree very well with the Mauna Loa data that you say you don’t believe. You can’t have it both ways.
It is not a matter of belief. It is a matter of questioning the statistical methodology at Mauna Loa as they set it forth, and a question on the validity of theconcept of “well mixed” that is necessary for the splicing of two independent measurement methods to create “unprecedented”.
It is also a questioning on whether the whole field of CO2 measurements has been following the “throw away data that does not fit” methodology to agree with the guru’ directions. What has happened with temperatures.
2. The recent rise is unprecedented, whether you believe the stomatal data, the ice core data, or both.
The rise is not great, either in the stomatal records or in the ice records. It is the splicing that does the trick.
And not to forget Beck’s compilations.
At the moment “CO2 is well mixed” seems to be a belief not supported by three dimensional data. . The very concept of going where the air is “pure” and throwing away 2sigma outliers is scientifically invalid and suspect that it is not reflective of a real measurement on a real world. Satellite measurements should very soon clear the three dimensional picture.
I have had these discussing with other people before, so lets leave it at that. You will not convince me unless there is a 3d representation that shows unprecedented CO2 to the extent Maona Loa does, and I will not convince you. Everybody can do their own thinking and delving into data, to the extent that they can.
continued:
Have to take back about the stomata record because that one publication, W. Finsinger et al , and Wagner et al no1,2 in the figure, take off precipitously. I now have to decide how much time I want to spend chasing stomata publications to see if the methodology is Keeling biased, in throw away data and include data manner.
Anyway, my ending, that I am waiting for more and better 3 dimensional satellite data stands.
re anna v: June 11, 2010 at 10:04 pm
She makes good points, Willis. Two sigmas and the false positive issue with things that occur infrequently or in small quantities is a recipe for self-deception (to say nothing of the potential for purposeful deception). It needs more digging.
/dr.bill
Willis Eschenbach, on 6/7/10 at 1:25 pm, responding to a request by Steve Hempell to comment on “On Why CO2 is Known Not To Have Accumulated in the Atmosphere, etc.”, said,
>>Yes. Like many others, he is conflating e-folding time and residence time.
My paper dealt with IPCC’s crucial and often repeated claim that CO2 was a Long-Lived Greenhouse Gas. Neither IPCC’s reports nor my paper used the term or concept of e-folding time to have conflated it with anything.
Specifically I quoted from the following by IPCC:
>>[Aerosols] have a much shorter lifetime (days to weeks) than most greenhouse gases (decades to centuries) … . TAR, pp. 24-25.
And from the following,
>>Turnover time (T) (also called global atmospheric lifetime) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M / S. For each removal process, separate turnover times can be defined. In soil carbon biology, this is referred to as Mean Residence Time. AR4, Glossary, p. 948.
IPCC explicitly refers to the lifetime of CO2 in the atmosphere, not its e-folding time, and makes Lifetime equivalent to Turnover time and to Mean Residence Time, which IPCC explicitly defines.
I reported the following in my paper:
>>Regardless of which way one poses the problem, the existing CO2 in the atmosphere has a mean residence time of 1.5 years using IPCC data, 3.2 years using University of Colorado data, or 4.9 years using Texas A&M data. The half lives are 0.65 years, 1.83 years, and 3.0 years, respectively.
I used the identical term used and defined by IPCC, amplified by the half life figures, to show that IPCC was wrong and inconsistent about the Lifetime/Turnover Time/MRT of CO2 in the atmosphere. Furthermore, even had I converted to e-folding times, it would have effected no more than a scaling by 0.69, immaterial to whether CO2 persists a few years or “decades to centuries”, or why natural CO2 and anthropogenic CO2 might have, as IPCC implies, different lifetimes.
I conflated nothing, and Mr. Eschenbach’s dismissive criticism, resting on that single allegation, was disingenuous and unresponsive.
Jeff: Willis’s criticism is exactly right and what you are saying is confused and incorrect. The mean lifetime of a CO2 molecule in the atmosphere is short because of the large exchanges that occur between the atmosphere, the biosphere + soils, and the mixed layer of the ocean. However, the decay time for a pulse of CO2 such as produced by the burning of fossil fuels is governed by the much slower rate at which CO2 can be removed from these reservoirs into the deep ocean.
So, what happens when you add in some new CO2 from burning of fossil fuels is that it rapidly partitions itself between the atmosphere, biosphere + soils, and the mixed layer…and now all three of these reservoirs have an elevated level of CO2. And, the decay of this elevated level is very slow.
Jeff Glassman says:
June 12, 2010 at 2:30 pm
Contrary to your claim, the IPCC makes a clear differentiation between residence time on the one hand, and half-life or e-folding time on the other hand, although they give them slightly different names (“turnover time” and “adjustment (or response) time” respectively). The following is from the Glossary for the IPCC TAR. The same definition is given in the IPCC FAR Glossary. I’ve emphasised the relevant parts:
Note that they say “half-life or decay constant”. “Decay constant” refers to using something other than 0.5 (half, for half-life) as the constant for measuring the decay. The number “e” (2.71828) is the other commonly used decay constant in the form of 1/e, or ~ 0.37, hence “e-folding time”.
So as I said, you have conflated the two.
RE: Willis Eschenbach: (June 11, 2010 at 3:02 pm) Stomatal Data
The primary inference I draw from the included stomatal data plot is that this seems to confirm that CO2 levels in the past were probably much more variable than that indicated by ice-core data. It seems reasonable to suppose that ice-core data may have been subject to gradual in situ diffusion or annealing processes that would progressively degrade the temporal resolution of this data over long periods of time.
I do think that modern CO2 levels may well be unprecedented as maintained in this article, but perhaps a more balanced approach might be to say there also could be significant physiogenic (natural) as well as anthropogenic effects contributing to this change.
I know that it is possible to ‘force-fit’ a filtered SST data curve to account for most the recent CO2 variation, but it appears there is no readily-available historical data from BT drops over the years to show just how much past and recent thermal forcing has actually penetrated into the depths of the ocean. Without this data, I do not think we can make an intelligent estimate of the amount of CO2 that could have been forced out of the sea as a result of the recent warming.
Spector says:
June 13, 2010 at 8:41 pm
I do think that modern CO2 levels may well be unprecedented as maintained in this article, but perhaps a more balanced approach might be to say there also could be significant physiogenic (natural) as well as anthropogenic effects contributing to this change.
I will add to your comments volcanic activity as an unknown possible source of sudden increase. There is no reason to assume that the volcanoes , of which an estimate of over 200.000 vents in the ocean floors have been estimated, are in a steady state as far as CO2 exhausts go. That they are not in a steady state is evident by the occasional explosions. Maybe, if the Maona Loa etc data are not doctored out of reality, we are measuring an upswing in the chaotic mechanisms of magma circulation and venting.
Willis Eschenbach says:
June 7, 2010 at 12:59 pm
My language was extreme because, as a result of Dr. Ravetz’s inanities, I have suffered innumerable personal attacks because I don’t buy into his nonsense. In addition, his “post-normal science” theory is responsible in part for the destruction of good scientific practice we see in too much of climate science.
Just a quick comment; I hope that it’s not too far down the tail to be read.
First, greetings to my old sparring partner Willis. I’m glad that you didn’t consider your remarks to be ad hominem.
Then, I do regret that you were exposed to innumerable personal attacks, all because of me. As to my ‘inanities’ and ‘nonsense’, I suggest that you consult ‘Uncertainty and Quality in Science for Policy’ (co-authored with Silvio Funtowicz), and also the many publications of Jeroen van der Sluijs, including the ‘Guidance’ for uncertainty management adopted by the Dutch environmental agency. You will find there that I do not airily substitute a politically-correct ‘quality’ for Truth; but with others I try to develop standards and methods whereby quality can be assessed and ensured in those sciences where simple Truth is not so easily obtained. If you still believe that Truth is just a simple matter of applying Scientific Method in such areas as the evaluation of the CO2 record, then we still have some fundamental disagreements. If that be corruption, so be it.
I am now in dialogue, in terms of mutual respect, with some other severe critics. It’s a pity that you still consider me to be some mixture of villain and idiot.
All best wishes – Jerry Ravetz
Jerome Ravetz says:
June 14, 2010 at 7:34 am
Jerry, thank you for your note. I don’t consider you either a villain or an idiot. I consider your ideas very dangerous. They are much more dangerous because you are neither villainous nor idiotic. You are both smart and well intentioned, making you a perfect man for your present position, the man in charge of the paving job to the place of eternal perdition …
However, your “drive-by” style of posting sucks. You post your pearls of wisdom, and then tell us you can’t stay, you are running off to some secret location to impress some unknown folks who are willing to osculate your fundament in some mystical manner that I obviously don’t understand.
When you get up the nerve up to post something and then actually stick around to discuss it, please let me know, as you will be very welcome, and we will have what is called a “dialogue”. So far, all you have provided here are monologues. Monologues reveal that you don’t want to defend or discuss your ideas, just espouse them. I find it less than coincidental that this reluctance to answer questions and objections is rampant in climate science these days … the reason that you didn’t find a dialog here is that you posted, and then NEVER REPLIED to our questions and objections. You’d make a great mainstream climate scientist with that attitude. If you want a dialogue, you have to participate.
Which is why your style of posting sucks.
Is that ad hominem? As I said before, I don’t think your ideas are dangerous because of who you are, that would be ad hominem and it is meaningless in any case. I think your ideas are dangerous because they mislead scientists into coming up with “scary scenarios” and not revealing their doubts, because they say that facts are meaningless and “quality” (as defined by you) is all-important …
Which is why I am surprised that your dialogues are monologues. I thought you espoused “quality”, but your postings reveal that you don’t care about quality in the slightest, you care about pushing and promoting your ideas at the expense of having a quality discussion about those ideas.
Jerry, the invitation for a dialogue is always open here. But please, spare us your monologues … they’re too low quality for me.
PS – Let me disabuse you of your convenient notion that I have not read your work with Funtowicz, or that of van der Sluijs. The reason that I dislike your ideas is not that I am not familiar with them. It is because I know them very well, and I find them both puerile and dangerous. We could have a discussion about why, but you don’t seem to want to discuss things, only pontificate about them.
Spector says:
June 13, 2010 at 8:41 pm (Edit)
Thanks, Spector. Anyone espousing your idea would have to explain why the historical stomata data vary so quickly and so far, while both the modern stomata and Mauna Loa data vary so little. What are your ideas on that question?
Jerome Ravetz says:
June 14, 2010 at 7:34 am:
If you still believe that Truth is just a simple matter of applying Scientific Method in such areas as the evaluation of the CO2 record, then we still have some fundamental disagreements.
Dr. Ravetz, if you think you can approach Truth in the case of CO2CAGW without applying the Scientific Method – a defect which characterizes ipcc Climate Science – then you are not even interested in the search for Truth to begin with, nor in the wellbeing of Humanity. It’s as simple as that.
Jerome Ravetz said;
“If you still believe that Truth is just a simple matter of applying Scientific Method in such areas as the evaluation of the CO2 record, then we still have some fundamental disagreements.”
I wonder if, when you were working towards your PHD, your lecturer had said that the scientific method could be set aside as irrelevant in some instances, would you have protested against this?
Would you have said that if a theory can not stand up to the scientific method it should be discarded and another one examined?
The notion that the scientific method is irrelevant in some cases is extraordinary to many of us. I wonder if Willis could do an article enumerating the other areas of science where this proven method has been set aside after vast resources have been thrown at it, in order to follow the much less time honoured system of post normality? A short article I think Willis.
What I find concerning is the obfuscation that surrounds climate science. In particular the rewriting of history to demonstrate that there was only the merest hiccup to represent the Little Ice age or the Medieval Warm period. No doubt the melting of the glaciers that allowed the Romans to march their armies across the High Alps was also an illusion, and the well trodden path I attempted to take to follow in their footsteps did not exist?
If the case for radiative physics is so strong why does it need to be shorn up with the nonsenses of temperature manipulation as our climate history is rewritten to suit the new post normal ‘facts’ Why has sea level history been allowed to be based on absurd reconstructions from three highly disjointed northern hemisphere tide gauges which are then taken to represent the whole globe? The pillars of present climate science are very shaky. Temperatures have been rising since the depths of the LIA around 1690. Whoever would have thought it?
Cast your mind back to your student days Mr Ravetz and and see for yourself how far the path you have now chosen to tread in pusuing post normal science lies from the methods you would have learnt at your University.
As Willis says it would be good if you stuck around for a normal dialogue as surely we all have much to learn from each other?
Tonyb
100612 ESCHENBACH WUWT 100616
Willis Eschenbach says on June 12, 2010 at 8:31 pm
>>>>Adjustment time or response time (Ta) is the time-scale characterising the decay of an instantaneous pulse input into the reservoir. The term adjustment time is also used to characterise the adjustment of the mass of a reservoir following a step change in the source strength. Half-life or decay constant is used to quantify a first-order exponential decay process. See: →Response time, for a different definition pertinent to climate variations. The term lifetime is sometimes used, for simplicity, as a surrogate for adjustment time. [Quoting from IPCC glossaries]
>>Note that they say “half-life or decay constant”. “Decay constant” refers to using something other than 0.5 (half, for half-life) as the constant for measuring the decay. The number “e” (2.71828) is the other commonly used decay constant in the form of 1/e, or ~ 0.37, hence “e-folding time”.
>> So as I said, you have conflated the two.
Mr. Eschenbach reaches into IPCC’s glossaries for a term IPCC explicitly excludes from use in climate. IPCC does not violate its edict. It never uses e-folding time with respect to CO2. As a result, and combined with the fact that I didn’t use the term e-folding time either, I could not have conflated e-folding time, or any synonym of it, with anything as Mr. Eschenbach imagines. Mr. Eschenbach reads “e-folding time” where it is not written to make a false accusation.
Next, Mr. Eschenbach conflates “e”, a number, with a “decay constant”, a parameter. Even Wikipedia manages to get this straight where it says “(lambda) is a positive number called the decay constant: … N(t) = N_0*e^(-lambda*t). Accord: HyperPhysics, Britannica Online, Weisstein’s World of Physics, etc., etc. The number e, appropriately dimensionless, and the decay constant, which has the dimension of time, are quite different, and should not have been conflated.
Mr. Eschenbach never responds to the fact that using half-life vs. e-folding time is a matter of a small scale factor (0.69 = ln(2)). Even if I had conflated the terms, as he wrongly alleges, it would have caused no substantive difference in my argument that CO2 lasts a few days, supported by IPCC’s formula, vs. “decades to centuries” as IPCC concludes. His accusation, in which he persists, that I conflated terms is not only false, but immaterial.
Correction: lambda has the units of reciprocal time.
Jeff,
I doubt your sophistry in the above post will convince anyone (except perhaps yourself). Frankly, it’s embarrassing. You write a whole post about half life vs. e-folding time as if that is the primary subject of the argument. It is not. You are the king of trouncing strawmen.
The primary point is your inability to distinguish between the characteristic time (whatever you want to define it as, e-folding, half-life, or whatnot) that a CO2 molecule spends in the atmosphere vs. the characteristic time it takes for a pulse of CO2 to decay. The two are very different because there are fast processes of exchange between the atmosphere, the land sink (biosphere + soils), and the mixed layer of the oceans. So, when you add some additional CO2 to the atmosphere, it rapidly partitions between these three reservoirs. However, the slow rate-limiting process is the transfer from the ocean mixed layer to the deep oceans. So, what you get well after the CO2 has equilibrated within these three reservoirs is a rise in the “height” (i.e., CO2 level) in all three reservoirs and it is this that then takes a long time to decay.
It’s easy to make an analogy with reservoirs containing water: Take two reservoirs that each contain 10 gallons of water and two pumps, one that pumps from the reservoir A to reservoir B and one that pumps from reservoir B to reservoir A, each at 1 gallon / minute. Now, imagine adding 1 gallon of water to reservoir A. The half-life of an individual molecule in that added gallon will be on the order of 5 minutes or so. (Actually, I think the precise answer is ~6.93 minutes, assuming the reservoirs are perfectly well-mixed, but we won’t quibble on the details.) However, it is wrong to conclude that after, say, 1 hour (when nearly all…~99.75%…of the molecules from the added gallon would have gone through the pump from reservoir A to B) that the amount of water in reservoir A will be essentially 10 gallons. In fact, as the problem is strictly stated, Reservoir A would remain with 11 gallons in it forever. (A better analogy would have the pump from A to B pump at a higher rate than the pump from B to A when there is more water in reservoir A than B and vice versa. In that case, the long term limit would have 10.5 gallons in each reservoir. So, the additional gallon has been divided between the two reservoirs but then remains in them forever.)
In this simple analog, the half-life of a water molecule added to reservoir A is only about 7 minutes but a “pulse” of water persists in that reservoir forever (after, possibly, dividing itself equally between the two reservoirs); in the real system, the pulse of CO2 does not persist in the atmosphere forever (because there are processes that remove it from the reservoirs) but it does persist for a lot longer than the characteristic time for a molecule of CO2 to be in the atmosphere.
Jeff Glassman says:
June 16, 2010 at 2:25 pm
Jeff, thanks for your reply. I did not say you were conflating half-life and e-folding time. My exact statement was:
As you point out, half-life and e-folding times are just different ways of measuring exponential decay of a pulse of CO2 into the atmosphere. You are correct that the IPCC uses half-life rather than e-folding time, although other researchers in the field use the latter. My point was that you are conflating exponential decay (whether it is measured by half-life or e-folding) and residence (what the IPCC calls “turnover”) time.
For example, you say:
First, you gave no citations for those figures. The IPCC says (op. cit.):
More to the point, you are still conflating residence (turnover) time, and half-life. One is how long the average CO2 molecule remains in the air. The other is how long it takes a pulse of CO2 to decay back to equilibrium. They are very different things, as seen in the IPCC definitions. You go so far as to calculate (on some unexplained basis) what you refer to as the half-life of the residence time, a number which makes no sense …
For more on this subject, including the equations to calculate the half-life, see Jacobson.
RE: Willis Eschenbach: (June 15, 2010 at 8:23 pm) “Thanks, Spector. Anyone espousing your idea would have to explain why the historical stomata data vary so quickly and so far, while both the modern stomata and Mauna Loa data vary so little. What are your ideas on that question?”
I think the lack of variation in the two modern data sets is because that data was taken during a single monotonic CO2 increase interval and we probably have a better handle on the dates represented by the stomata. Perhaps we need a third proxy or a more robust collection of stomata data to get a better picture of what was going on in the past.
It might be interesting to take several CO2-free ice-cores and expose the open end-faces on one side to a pure CO2 atmosphere for several months, say at -5, -15, and -40 degrees C and see just how much and how far CO2 is absorbed into each core.
Spector,
I think your diffusion experiment could put some numbers to what some of us postulate to explain “trapped” gas bubble ages being always younger than the ice containing it and the age differences increaseing with age. Also, the observation of C14 in ice older than 5000 years old. The mechanism that has been postulated is that as pressure is released on the ice cores, the highly compressed gases expand creating microcracks in the ice into which modern air diffuses.
Re Willis Eschenbach on 6/16/10 at 7:53 pm and Joel Shore on 6/12/10 at 7:59 and 6/16/10 at 7:23 pm:
Mr. Eschenbach continues not to respond to Steve Hempell’s request for his comments on my paper, “On Why CO2 Is Known Not To Have Accumulated in the Atmosphere, etc.”. Clearly Mr. Eschenbach did not read it, yet was able to conclude that I had conflated two bits of physics. He quoted the following paragraph from my email,
>>>> Regardless of which way one poses the problem, the existing CO2 in the atmosphere has a mean residence time of 1.5 years using IPCC data, 3.2 years using University of Colorado data, or 4.9 years using Texas A&M data. The half lives are 0.65 years, 1.83 years, and 3.0 years, respectively.
omitting the following introductory part,
>>I reported the following in my paper.
Then he says,
>> First, you gave no citations for those figures.
He shows no evidence of reading emails either.
>>You go so far as to calculate (on some unexplained basis) what you refer to as the half-life of the residence time, a number which makes no sense …
My paper says,
>>>>Turnover time (T) (also called global atmospheric lifetime) is the ratio of the mass M of a reservoir (e.g., a gaseous compound in the atmosphere) and the total rate of removal S from the reservoir: T = M / S. For each removal process, separate turnover times can be defined. In soil carbon biology, this is referred to as Mean Residence Time. AR4, Glossary, p. 948.
>>Now throw in approximately 100% replenishment, and you have an eleventh grade physics or chemistry problem where the level in the bucket is only slowly changed but the solution is quickly diluted. This is a different question from residence time, elevated to a mass balance problem.
>> Regardless of which way one poses the problem, the existing CO2 in the atmosphere has a mean residence time of 1.5 years using IPCC data, 3.2 years using University of Colorado data, or 4.9 years using Texas A&M data. The half lives are 0.65 years, 1.83 years, and 3.0 years, respectively. This is not “decades to centuries” as proclaimed by the Consensus. Climate Change 2001, Technical Summary of the Working Group I Report, p. 25. See The Carbon Cycle: past and present, http://www.colorado.edu/GeolSci/courses/GEOL3520/Topic16/Topic16.html & Introduction to Biogeochemical Cycles Chapter 4, http://www.colorado.edu/GeolSci/courses/GEOL1070/chap04/chapter4.html, UColo Biogeochem cycles.pdf; The Carbon Cycle, the Ocean, and the Iron Hypothesis, http://oceanworld.tamu.edu/resources/oceanography-book/carboncycle.htm
The “unexplained basis” is IPCC’s formula, quoted and cited. The sources for all the data are cited specifically.
That the number makes no sense is Mr. Eschenbach’s personal limitation.
He quotes from IPCC, omitting the first sentence, included next:
>> In more complicated cases, where several reservoirs are involved or where the removal is not proportional to the total mass, the equality T = T_A no longer holds. Carbon dioxide (CO2) is an extreme example. Its turnover time is only about four years because of the rapid exchange between the atmosphere and the ocean and terrestrial biota.
This is a violation of Henry’s Law, the law of solubility, and a law which IPCC not only never uses but suppressed when it arose in an AR4 draft. The uptake of CO2 is proportional to its partial pressure in the atmosphere, and its partial pressure is the equivalent of its total mass. (See for example AR4, ¶7.3.4.3, p. 532, where IPCC gives a change in pCO2 in units of ppm.) Furthermore, IPCC makes leaf water the largest flux in that uptake at 270 Gtons/year (TAR, ¶3.2.2.1, p. 191), and then never uses leaf water in its carbon cycle (see for example TAR, Figure 3.1, p. 188; AR4, Figure 7.3, p. 515). By omitting that 270 Gtons/year, IPCC’s data yield a turnover time, which is the same thing (and according to IPCC specifically for “soil carbon biology” and SO2 aerosol), of 3.55 years (“about four”) instead of the 1.5 years IPCC data and formula yield.
Mr. Eschenbach says,
>>More to the point, you are still conflating residence (turnover) time, and half-life. One is how long the average CO2 molecule remains in the air. The other is how long it takes a pulse of CO2 to decay back to equilibrium. They are very different things, as seen in the IPCC definitions.
To the contrary, neither the glossary in the Third nor the Fourth Assessment Report refers to the lifetime of a CO2 molecule in any respect.
Similarly, Mr. Shore says,
>> The primary point is your inability to distinguish between the characteristic time (whatever you want to define it as, e-folding, half-life, or whatnot) that a CO2 molecule spends in the atmosphere vs. the characteristic time it takes for a pulse of CO2 to decay. The two are very different …
and
>>in the real system, the pulse of CO2 does not persist in the atmosphere forever (because there are processes that remove it from the reservoirs) but it does persist for a lot longer than the characteristic time for a molecule of CO2 to be in the atmosphere.
The model under discussion here is the exponential decay of a pulse, slug, or mass of CO2 in the atmosphere by its uptake into other reservoirs. The pulse, slug, or mass is given by the number of molecules. Computing the average lifetime of a molecule from the decay of the pulse is trivial. It is precisely the mean residence time, which is identically the half-life divided by ln(2), and the reciprocal of the decay constant, for the pulse. One wonders how Eschenbach and Shore might think the mean molecular lifetime of a molecule might be defined and calculated if not by observing a large mass of them being absorbed.
The notion that the characteristic time for a CO2 molecule is different than the characteristic time for a pulse, slug, or mass of them is foolishness. It is an invention, repeated here and there, and now by Eschenbach and Shore, to salvage IPCC’s justification for and reliance on anthropogenic CO2, but not natural CO2, accumulating in the atmosphere. It is related to IPCC claims that MLO data are global, that atmospheric CO2 is well-mixed, and that CO2 is a Long Lived GreenHouse Gas (LLGHG), and to IPCC’s implication that the ocean uptake of natural and manmade CO2 are significantly different. These are all false.
Jeff Glassman says:
June 18, 2010 at 11:12 am
My friend, if after all of this you continue to claim that the residence (or turnover) time is the same thing as the pulse decay time (half-life), I’m afraid that you need more help than either Joel or I can give you. I have given references to a variety of sources, along with a simple basin model. In both, there is a clear distinction between how long a molecule stays in a given reservoir (residence or turnover time), and how long it takes a pulse to decay back to equilibrium (half-life). For CO2, the residence time is on the order of six or eight years or so.
The half-life of a pulse of CO2, however, is variously estimated between 30 and over a hundred years. My figures put it in the 30’s.
Neither I nor Joel “invented” the difference between residence time and half-life. It is found in the textbooks, in the scientific papers, and in the popular press.
Finally, the IPCC does not say that only anthropogenic CO2 “accumulates” in the atmosphere. That’s a misunderstanding, fairly common to be sure, but wrong none the less.
Willis Eschenbach on 6/19/10 at 1:40 pm said,
>> My friend, if after all of this you continue to claim that the residence (or turnover) time is the same thing as the pulse decay time (half-life), I’m afraid that you need more help than either Joel or I can give you.
I never made the claim asserted, and consequently could not have continued to make it. To the contrary, I quoted from by paper specific pairs of values for residence time and half-life, and the numbers were not the same. To be helpful to anyone, a teacher must cite precisely and accurately.
Mr. Eschenbach says,
>> The half-life of a pulse of CO2, however, is variously estimated between 30 and over a hundred years. My figures put it in the 30′s.
Mr. E. has made no point, and the use of the passive voice here doesn’t help his argument. I had already cited in my posts here and on my blog, that IPCC puts the characteristic time of CO2 in the range of “decades to centuries” (citing TAR p. 25). This contradicts IPCC’s own formula. The fact that Mr. E. adopts IPCC’s figures is not to his credit.
Mr. Eschenbach says,
>> Neither I nor Joel “invented” the difference between residence time and half-life. It is found in the textbooks, in the scientific papers, and in the popular press.
I’m sure neither of them did. Half-life is mean residence time multiplied by ln(2), a fact about as old as Euler (1707-1783) and the Euler number, e. If Mr. E. is responding to my post, he misunderstands what I wrote. I actually said,
>> The notion that the characteristic time for a CO2 molecule is different than the characteristic time for a pulse, slug, or mass of them is foolishness. It is an invention, repeated here and there, and now by Eschenbach and Shore, to salvage IPCC’s justification for and reliance on anthropogenic CO2, but not natural CO2, accumulating in the atmosphere.
What I claimed was invented is the silly notion that the half-life of a molecule was different than the half-life of a pulse of CO2. And I did not claim that either Eschenbach or Shore invented it, only that they repeated it.
Mr. Eschenbach says,
>> Finally, the IPCC does not say that only anthropogenic CO2 “accumulates” in the atmosphere. That’s a misunderstanding, fairly common to be sure, but wrong none the less.
Quite to the contrary, IPCC refers to CO2 accumulation when it says,
>>Assuming that accumulation of CO2 in the ocean follows a curve similar to the (better known) accumulation in the atmosphere, the value for the ocean-atmosphere flux for 1980 to 1989 would be between −1.6 and −2.7 PgC/yr. TAR, ¶3.5.1 Atmospheric Measurements and Global CO2 Budgets, p. 207.
More specifically, IPCC makes the following analysis and attribution:
>>From 10 kyr before present up to the year 1750, CO2 abundances stayed within the range 280 ± 20 ppm. During the industrial era, CO2 abundance rose roughly exponentially to 367 ppm in 1999 and to 379 ppm in 2005. Citations deleted, AR4, ¶1.3.1 The Human Fingerprint on Greenhouse Gases, p. 100.
>>Cumulative carbon losses to the atmosphere due to land-use change during the past 1 to 2 centuries are estimated as 180 to 200 PgC and cumulative fossil fuel emissions to year 2000 as 280 PgC, giving cumulative anthropogenic emissions of 480 to 500 PgC. Atmospheric CO2 content has increased by 90 ppm (190 PgC). Approximately 40% of anthropogenic CO2 emissions has thus remained in the atmosphere; the rest has been taken up by the land and oceans in roughly equal proportions. Citations deleted, TAR, Box 3.2, p. 192.
So IPCC attributes all the observed rise in CO2 that has accumulated in the atmospheric during the industrial era to ACO2. The 119.6 PgC/yr from terrestrial sources, the 90.6 PgC/yr from the ocean do not accumulate. See AR4, Figure 7.3 p. 515. Nor does the 270 PgC/yr from leaf water. Op. cit. In summary, and contrary to Mr. Eschenbach’s guess, IPCC does indeed say that only ACO2 accumulates in the atmosphere.
A misunderstanding certainly exists. It lies in physics, and it belongs to IPCC and its disciples.
Jeff Glassman:
So IPCC attributes all the observed rise in CO2 that has accumulated in the atmospheric during the industrial era to ACO2.
Yes, the IPCC does attribute the total of the rise to aCO2. That is about the increase of the total amount. That doesn’t mean that all individual molecules of aCO2 emitted in the past 150 years or so, still are in the atmosphere. Most of them were exchanged by “natural” CO2 during the seasonal exchanges at a rate of near 20% per year or about 150 GtC/800 GtC in the atmosphere (or a half live slightly over 5 years). But seasonal exchanges don’t change the total amount of CO2 (whatever the source) in the atmosphere when in equilibrium.
But we know from the CO2 emissions inventory and the CO2 measurements (at a lot of places) that nature aborbs about halve the emissions (as mass!): nature as a whole is a net sink for CO2. Whatever the source of the extra CO2, the current sink capacity of nature is about 4 GtC/year of the 800 GtC already present. That is only about halve the human emissions and forms a long(er) decay time (near 40 years average half life) if we should stop all emissions today.
It is like the difference between the turnover and the gain/loss of a bank/factory or anything you want: the amount of turnover of natural CO2 is not important at all, only the difference between the natural contributions and natural sinks is important, which is negative: there is zero net contribution by nature to the total amount of CO2 in the atmosphere and humans are (near) totally responsible for the increase.