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CO2: "WHY ME?"


by Jeffrey A. Glassman, PhD

Revised 3/14/10.


Myles Goodman at Drexel posted the following question as a comment to the Acquittal of Carbon Dioxide:


The Acquittal shows that carbon dioxide did not accumulate in the atmosphere during the paleo era of the Vostok ice cores. If it had, the fit of the complement of the solubility curve might have been improved by the addition of a constant. It was not. And because the CO2 presumably still follows the complement of the solubility curve, it should be increasing during the modern era of global warming in recovery from Earth's various ice epochs. These conclusions find support in a number of points in the IPCC reports.

So the answer to the post begins with supporting background on why CO2 is known not to accumulate in the atmosphere, and then goes on to other aspects of the model that global warming causes increases in CO2, which accounts for the last 100 years or so.

Rocket Scientist’s Journal


1. Estimates vary, but climatologists in the Consensus say that the atmosphere contains 730 Gtons (PgC) of carbon and the uptake to the oceans alone is at least 90 Gtons/year. It's a ninth grade algebra problem to calculate how long it takes to empty a bucket with 730 units at the rate of 90 units per year. If you throw in uptake by photosynthesis at 120 Gtons/year and perhaps leaf water at the IPCC figure of 270 Gtons/year, thus including everything in the IPCC's Third Assessment Report, 480 Gtons a year is pouring out of the bucket.

{Rev. 6/5/09a}

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.{end Rev. 6/5/09a}

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. {Rev. 6/5/09b} This is a different question from residence time, elevated to a mass balance problem. {end Rev. 6/5/09b}

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

2. In 1985, Keeling provided two estimates of the residence time (the reciprocal of his global air-sea transfer coefficient) and uptake of CO2 in the entire oceans, based on different methods from different locale. They were 7.9 years for 2 Gtons/year and 5.2 years for 4.35 Gtons/year. Keeling, C.D. and R. Revelle, Effects of El Nino/Southern Oscillation on the Atmospheric Content of Carbon Dioxide, Meteoritics, Vol. 20, No.2, Part 2, June 30, 1985. No one today uses such small numbers for the uptake, so the residence time must be much less than Keeling suspected.

3. There are no separate, physical paths to pipe natural CO2 and anthropogenic CO2 in the atmosphere or to segregate them in other reservoirs. There is a theory of plant isotopic preference, and a hypothesis of isotopic bias in the dissolution of natural and manmade CO2, but the Consensus has not posited such an effect in the carbon cycle exchange between the atmosphere and the reservoirs. In fact, the Consensus accounts for the difference in the concentrations in carbon isotopes in the atmosphere and the ocean not by selective solubility but by selective photosynthesis in the ocean. Climate Change 2001, Box 3.6, p. 207. Natural and anthropogenic are indiscriminately mixed in the atmosphere, and undergo similar if not identical residence times.

4. Sidebar: By losing its long residence time assumption, the Consensus finds its well-mixed conjecture invalidated. The admission in the TAR of CO2 gradients over the globe also contradicts its well-mixed claims. Independently, gradients must exist because of the highly concentrated outgassing of CO2 from equatorial waters, and the balancing concentrated polar uptakes. Consequently, the concentration of CO2 depends on where it is measured. Keeling himself warned not to mix CO2 measurements without regard to sinks and sources. He used calibration techniques to mix records. {Begin rev. 3/14/10} Recent results at 8 km from the AIRS (Atmospheric Infrared Sounder) satellite show dense clouds of CO2 emerging from below. This should be just one more nail in the coffin for the well-mixed/long-lived assumption. See RSJ response to James Daniel, 6/17/09, IPCC's Fatal Errors ; RSJ response to David, 8/24/08, The Acquittal of Carbon Dioxide . {End rev. 3/14/10}.

5. The TAR says,

CO2 naturally cycles rapidly among the atmosphere, oceans and land. However, the removal of the CO2 perturbation added by human activities from the atmosphere takes far longer. This is because of processes that limit the rate at which ocean and terrestrial carbon stocks can increase. Anthropogenic CO2 is taken up by the ocean because of its high solubility (caused by the nature of carbonate chemistry), but the rate of uptake is limited by the finite speed of vertical mixing. Climate Change 2001, Technical Summary of the Working Group I Report, p. 51.

The first sentence is semantic gamesmanship to imply that CO2 cycles rapidly only if the CO2 is natural. That conjecture is made specific in the next sentence. The rest is fraught with error.

The well-established physics of gas solubility in water should not be changed to suit the AGW conjecture. {Begin rev. 6/5/09c} Henry's Law states that at equilibrium the solubility of a gas, here CO2, in a solvent, here sea water, is proportional to the partial pressure of the gas adjacent to the solvent. The constant of proportionality is an empirical number, maximum at zero ºC or less, strongly and exponentially dependent on temperature and, for sea water, weakly dependent on salinity. Salinity reduces solubility about 10% at the cold end (3.41 to 3.28 g/kg at 0ºC), and about 1% (1.20 to 1.17 at 28ºC) at the hot end. DoE, Handbook of Methods for the Analysis of the Various Parameters of the Carbon Dioxide System in Sea Water, v. 2.11, 9/29/97; Lefevre, N., Functions to calculate equilibrium constants and solubility of carbon dioxide in sea water, 4/5/95, http://www.ipsl.jussieu.fr/OCMIP/phase1/distrib/funcchem.f. {End rev. 6/5/09c} The partial pressure of CO2 in sea water is a variable taken to mean, and computed from, the partial pressure of CO2 in an atmosphere in equilibrium with the sea water. See for example, Takahashi, T., et al., Method of underway pCO2 Measurements in Surface waters and the atmosphere during the AESOPS expeditions, 1996-1998 in the Pacific sector of the Southern Ocean and the Ross Sea, 4/25/00. http://usjgofs.whoi.edu/PI-NOTES/southern/Takahashi-pco2.html. The concept of the partial pressure of CO2 in sea water is a consequence of Henry's Law.

Because solubility theory by definition applies at equilibrium, it is a steady state model, and hence static. While IPCC assumes the surface layer is equilibrium, it nevertheless recognizes the importance of kinetics in dissolution, a subject of extensive research over the years. IPCC says with regard to both the kinetic and static processes,


IPCC shows the result of the determining CO2 flux using the Wanninkhof gas exchange rate model in the beautiful Takahashi diagram. AR4, Figure 7.8, p. 523.

[IPCC] Figure 7.8. Estimates (4° X 5°) of sea-to-air flux of CO2, computed using 940,000 measurements of surface water pCO2 collected since 1956 and averaged monthly, together with NCEP/NCAR 41-year mean monthly wind speeds and a (10-m wind speed)2 dependence on the gas transfer rate (Wanninkhof, 1992). The fluxes were normalised to the year 1995 using techniques described in Takahashi et al. (2002), who used wind speeds taken at the 0.995 standard deviation level (about 40 m above the sea surface). The annual flux of CO2 for 1995 with 10-m winds is –1.6 GtC yr-1, with an approximate uncertainty (see Footnote 1) of ±1 GtC yr-1, mainly due to uncertainty in the gas exchange velocity and limited data coverage. This estimated global flux consists of an uptake of anthropogenic CO2 of –2.2 GtC yr-1 (see text) plus an outgassing of 0.6 GtC yr-1, corresponding primarily to oxidation of organic carbon borne by rivers (Figure 7.3). The monthly flux values with 10-m winds used here are available from T. Takahashi at http:// www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/pages/air_sea_flux_rev1.html. Notes: Scale revised to make height proportional to width of range and to show number of cells by range and in total. Click on figures to enlarge.

Figure 1

At this point, IPCC conspicuously ignores its data that the ocean outgasses 90.6 GtC yr-1 and absorbs 92.2 GtC yr-1. AR4, Figure 7.3, p. 515. That's a flux difference of exactly 90 GtC yr-1 in each direction, apparently IPCC's additive, balanced, background of natural CO2 flux. IPCC asserts that Takahashi's uptake is of anthropogenic CO2, and by computing the difference with the outgassing, implying that Takahashi measured and computed anthropogenic CO2. None of Takahashi's measurements nor computational parameters discriminate between CO2 and ACO2, and none can. IPCC offers no explanation for how the 90 GtC yr-1 might be distributed around the globe, how 90 GtC annually moves into and out of the atmosphere without its theoretically associated pCO2 disequilibrium, nor how Takahashi's measurements failed to detect that flux or huge pressure difference.

IPCC does not provide the area of the individual Takahashi cells. However, a similar chart with supporting data files is available on-line from the Carbon Dioxide Research Group, Lamont-Doherty Earth Observatory of Columbia University. http://www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/air_sea_flux/sumflux_2006.txt. This chart provides each cell area as well as the total flux per cell (called the Box flux). The total uptake is -2.42 GtC yr-1 and the total outgas is 1.01 GtC yr-1, which is within a few percent of IPCC's claim for its Takahashi chart. Consequently, the only application IPCC makes of the kinetic theory of solubility, the Takahashi chart, fails to support its total flux estimates by a wide margin.

{Begin rev. 11/12/09} Takahashi's results confirm the model of the role of the Thermohaline Circulation in the global distribution of CO2. See RSJ, The Acquittal of Carbon Dioxide , Figure 23. The density of Takahashi cells by type in Figure 1 show a gradual increase corresponding to a gradual uptake of CO2 across the surface of the ocean in the cooling, poleward circulations, and a precipitous drop corresponding to the bursts of CO2 outgassed dominantly (about 80%) in the Eastern Equatorial Pacific (EEP). As shown in the legend to Figure 1, Takahashi's cells have a width of 0.5 mol m-2yr-1, except his maximum uptake cell is eight times as wide (4 mol m-2yr-1), dominantly placed in the polar regions, and his maximum outgassing cell is seven times as wide (3.5 mol m-2yr-1), and are dominantly clustered in the EEP.

However, the Takahashi cells need to be recalibrated to account for the full volume of outgassing (90.6 GTC/yr) and uptake (92.2 GTC/yr) as reported by IPCC. AR4, Figure 7.3, p. 515. For the minimum values of each Takahashi cell, the total outgassing, uptake, and net would be (-4.11, 6.64, -3.44) GgmC/yr, at average they are (-3.32, 1.20, -2.12) GgmC/yr, and at maximum, (-2.54, 1.73, -8.05) GgmC/yr. {Begin rev. 12/30/09}The values should be on the order of 90 PetagmC/yr, an unresolved discrepancy of 10^7. A possible recalibration of the Takahashi diagram that agees with IPCC data is shown in Figure 1A:

An example of the Takahashi chart with the scale recalibrated to preserve the general shape of cell values, but with the total outgassing set to 90.6 GtC/yr and the total uptake set to 92.2 GtC per IPCC AR4 Figure 7.3, p. 515.

Figure 1A

This recalibration extends the central uniform width of cells through the polar regions, no good reason being known for accelerated CO2 solubility there. Takahashi's polarity of the flux is maintained in each cell, so that the zero point is unchanged. The uniform height of 13.2 mol m-2yr-1 sets the total uptake to IPCC's estimate of -92.2 GtC/yr. The maximum outgassing of 944.6 mol m-2yr-1 causes the total outgassing to equal IPCC's 90.6. {End rev. 12/30/09.}

In March, 2007, Martin Durkin, a documentarian, produced a most controversial film titled The Great Global Warming Swindle in which he claims everything that the public has been told about CO2 causing global warming is a lie, leaving the Sun as the only climate driver. His film drew from about 34 individuals, mostly scientists, about 20 of whom appeared on camera. Included on camera was Professor Carl Wunsch, who, on the heels of the film's release, sided with IPCC and other believers in AGW to file a complaint with UK's Office for Communications (Ofcom) for breaches of the Ofcom Broadcasting Code and the British Communications Act. They claimed that they did not have adequate notice of the nature of the production, and that it mislead the public by presenting misinformation. Ofcom found merit to some of the complaints, parts dealing with inadequate notice. In its decision, Ofcom noted that complainants referred to its opposition as "global warming deniers", an appropriate contrast with believers in matters of faith but not science, and that Professor Wunsch did

describe the 'conveyor' as "a kind of fairy-tale for grownups".

Ofcom Broadcast Bulletin, Issue 114, 21 July 2008, p. 75 of 86. Professor Wunsch was not a contributor to IPCC's Third or Fourth Assessment Reports, although IPCC did cite several articles he authored or co-authored. Wunsch is a professor of oceanography at MIT, a visiting professor in oceanography at Harvard and University College London, a senior visiting fellow in mathematics and physics at Cambridge, and author of four text books on oceanography. His placing the word conveyor in quotation marks suggests a misnomer, but the word is used often in the TAR and AR4, with and without quotes, usually as conveyor belt. More than a few of IPCC's references include the word conveyor in the title, of course without the qualification of quotation marks.

Professor Wunsch's fairy-tale remarks are ambiguous, but in context appear to be a reference to the Gulf Stream, and not specifically the conveyor belt associated with the THC. However, the Gulf Stream is the North Western Atlantic warm circulation that serves as a collector for CO2, eventually to feed the northern headwaters of the THC. Wunsch in the documentary and his writings refers to climate memory in the ocean, stating that for some phenomena it can be as large as 10,000 years. Nowhere does he recognize the THC or conveyor belt role in the uptake and outgassing of CO2, nor the associated well-known transport delay of about 1,000 years. As well as these things are known today, the one millennium transport delay is the dominant signal in ocean memory.

Nothing Wunsch has said in the documentary is ambiguous nor appears context sensitive, yet his remarks are supportive of the theme of the documentary. He seems to have suffered thespian's remorse for his participation in an inconvenient exposè of a family dogma. As an oceanographer, his observations are surprising. The existence of the THC is firmly established, IPCC even publishing a graph of the volume of sea water that it carries according to nine different authorities. TAR, Figure 9.21, p. 563. The role of the THC in atmospheric CO2 presented in The Acquittal of CO2, and as partially validated by the Takahashi diagram have yet to be challenged.

In other articles on the Journal , IPCC has been faulted for its specific assumption that the surface layer of the ocean is in equilibrium. This assumption has many unfortunate consequences. IPCC uses it to cause Anthropogenic CO2 to accumulate in the atmosphere, but not natural CO2! This gives nCO2 and ACO2 measurably different solubility coefficients, a previously unknown property. Since the only difference known between the two species of the gas is their isotopic mix, IPCC gives sea water the previously unknown ability to fractionate. Another result from this assumption is that IPCC can invoke inappropriate chemical equilibrium equations to give the sequestering of sea water multiple simultaneous time constants, ranging from centuries to thousands in the IPCC reports, and up to 35,000 years in the papers of its key author, oceanographer David Archer, University of Chicago. The assumption is foolishness as shown by its consequences, but it tends to confirm oceanographer Wunsch's 10,000 year memory claim. The science should have influenced Wunsch to distance himself from IPCC, neither joining with it in the lawsuit, nor identifying himself as a supporter of its conclusion, the existence of AGW. {End Rev. 11/12/09}

It is the kinetic theory that has failed. As shown by the Lamont-Doherty data, Takahashi has used the following equation for CO2 flux as proposed by Wanninkhof in 1999:



The parameter k is the gas exchange coefficient, and s is solubility. Other forms of this equation are found in the literature, and Wanninkhof compares several forms for k, normalized to a Schmidt number of 660, in the Figure 2 next.

[Wanninkhof] Figure 1. Gas exchange relationships for steady winds reported in the literature. They include the general relationships of Smethie et al. [1985], Liss and Merlivat [1986], Wanninkhof [1992], and the relationships including specific parameterization of bubble mediated processes of Asher and Wanninkhof [1998], Monahan and Spillane [1984], and Woolf [1997]. The thick solid line (k = 0.0283 u10 3) is the deconvolved cubic relationship using the global mean gas transfer rate determined from 14C. Where applicable, a drag coefficient of 1.1 x 103 was used and all data were normalized to Sc = 660.

Figure 2

All of the representations of the gas exchange coefficient except the Monahan curve, which Takahashi did not use, are asymptotic to zero as the wind speed goes to zero. For these, as shown by Equation (1), the CO2 flux is zero for no wind, and the no wind flux is not included as a background for the wind enhanced flux. The dependence of gas exchange on IPCC's "other factors" (in bold at p. 528, above) is not represented in Equation (1) with any of the coefficients, except perhaps Monahan's, and it is not represented in the Takahashi diagram. Under the same proviso, the flux of Equation (1) and in Tagahashi's analysis relied on by IPCC is an additive flux enhancement due to the wind, and not the total flux. {End rev. 6/5/09c}

{Rev. 6/10/09} Man's CO2 emissions of about 6 GtC/yr might be lost just in IPCC's errors in estimating the massive natural emissions: 90 GtC/yr from the ocean, 120 GtC/yr from the land, not including 270 GtC/yr from leaf water. To show a danger from ACO2, IPCC adopted the Revelle conjecture about a bottleneck in the atmosphere-ocean CO2 exchange. It suppressed established solubility physics and resuscitated the Revelle buffer factor, the troubled anthropogenic conjecture in, and the essence of, Revelle and Suess's 1957 pitch for an International Geophysical Year grant. Revelle, R., H. E. Suess, Carbon Dioxide Exchange between Atmosphere and Ocean and the Question of an Increase of Atmospheric CO2 during the Past Decades, Tellus, 9, 1957, pp. 18-27. Regardless, IPCC embraces the "Revelle factor (or buffer factor)" as if it had been validated. AR4, ¶ Carbon Cycle Feedbacks to Changes in Atmospheric Carbon Dioxide, p. 531. IPCC illustrates its conclusion with this duplex figure:

[IPCC] Figure 7.11. (a) The Revelle factor (or buffer factor) as a function of CO2 partial pressure (for temperature 25°C, salinity 35 psu, and total alkalinity 2,300 µmol kg–1) (Zeebe and Wolf-Gladrow, 2001, page 73; reprinted with permission, copyright 2001 Elsevier). (b) The geographical distribution of the buffer factor in ocean surface waters in 1994 (Sabine et al., 2004a; reprinted with permission, copyright 2004 American Association for the Advancement of Science). High values indicate a low buffer capacity of the surface waters.

Figure 3

IPCC defines the Revelle factor by its Equation 7.3,



"relating the fractional change in seawater pCO2 to the fractional change in total DIC after re-equilibration (Revelle and Suess, 1957; Zeebe and Wolf-Gladrow, 2001)". The rectangular brackets, [], designate "concentration of", and DIC stands for Dissolved Inorganic Carbon, which is equal to [CO2]+[HCO3 ]+[CO3 --]. IPCC does not provide symbols to distinguish gaseous from aqueous CO2, such as CO2(g) and CO2(aq). Wolf-Gladrow uses CO2(aq) and "CO2 in air". In this section of Chapter 7, IPCC mixes the parameters, at one point referring to a hybrid "gaseous seawater CO2 concentration".

Revelle & Suess introduce their buffer factor by saying,

Because of the peculiar buffer mechanism of sea water, however, the increase in the partial CO2 pressure is about 10 times higher than the increase in the total CO2 concentration of sea water when CO2 is added and the alkalinity remains constant, so that under equilibrium conditions at a given alkalinity



γ being a numerical factor of the order of 10 for r and s small compared to A0 and S0 respectively. Bold added, R&S, id., pp. 24-25.




The authors define their variables as follows:

S0:         Total carbon of the marine carbon reservoir at equilibrium condition, at time zero.
A0:         Atmospheric CO2 carbon at time zero.
i:         Annual amount of industrial CO2 added to the atmosphere.
t:         Time in years.
s=St–S0:         Amount of CO2 derived from industrial fuel combustion in the sea at time t.
r=it-s:         Amount of CO2 derived from industrial fuel combustion in the atmosphere at time t.

R&S discovered and reported that they could not set the parameters for the peculiar exchange they sought without causing a "too fast exchange rate" or "unexpectedly short mixing times for the ocean". R&S's problem was pure speculation at the outset, having never observed an ocean in equilibrium. The Revelle factor was a phantom.

IPCC's version of the Revelle buffer factor is functionally different than the original. At equilibrium pCO2(g) equals pCO2(aq) by definition, and the ratio of pCO2(g) to [CO2(g)] approximates the ideal gas relationship, being nearly equal to the product of the gas constant and the absolute temperature, RT. But no such simple relationship exists between [CO2(g)] and [CO2(aq)]. Furthermore, the model for the CO2 flux arises out of the disequilibrium all across the ocean, where pCO2(g) ≠ pCO2(aq). Wanninkhof, 1999.

In its Second–Order Draft, the illustration comprised three graphs:

[IPCC] Figure 7.3.10. The Revelle factor (or buffer factor) as a function of seawater temperature (S=35, pCO2=230 μatm, TAlk=2300 μmol kg–1) (a), as a function of pCO2 (TC = 25º, S = 35, TAlk = 2300 μmol kg–1) (b), and with its geographical distribution for year 1994 (c). With increasing partial pressure of CO2 and decreasing temperature, the Revelle factor increases and thus the buffering capacity of the seawater decreases. Source: (a) and (b) from Zeebe and Wolf-Gladrow (2001), (c) from Sabine et al. (2004a).

Figure 4

Dieter Wolf-Gladrow reproduced this omitted inset in a presentation available online. D. Wolf-Gladrow, CO2 in Seawater: Equilibrium, Kinetics, Isotopes, 6/24/06, Chart 58, T dependence of Revelle factor. It is identical to Figure 7.3.10(a) except that he added the symbol RF0 to the ordinate, "Revelle or buffer factor". He also provided inset (b) (Wolf-Gladrow, id., Chart 59), and both are attributed to Zeebe and Wolf-Gladrow, 2001. Earlier in the presentation, Wolf-Gladrow provides this next illustration on the subject of solubility:

Figure 5

Wolf-Gladrow, D., id., Chart 11, faithfully reproduced. The curves are identical, with the Revelle factor being a simple linear transformation of Henry's coefficient, K0: RF0 = 3.86 + 183.9*K0. Climatologists set about to measure the Revelle factor, but what they measured was solubility.

In response to a reviewer's criticism of the draft Fourth Assessment Report, IPCC provides the explanation for removing the solubility-like curve.

Comment: "buffer factor decreases with rising seawater temperature…" This is a common misconception. The buffer factor itself has almost no temperature sensitivity (in an isochemical situation). In contrast, the buffer factor strongly depends on the DIC to Alk ratio. The reason why there is an apparent temperature sensitivity is because of the temperature dependent solubility of total DIC (note that (a) is not isochemical, it is done with a constant pCO2, i.e. DIC will decrease with increasing temperature). In the ocean, surface ocean DIC and Alk are controlled by a myriad of processes, including temperature, so it is wrong to suggest that the spatial distribution of the buffer factor shown in Figure 7.3.10c is driven by temperature . [Nicolas Gruber (Reviewer's comment ID #: 307-70)]

[Editor's] Notes: Taken into account. The buffer factor has a considerable T dependency (see Zeebe and Wolf-Gladrow, 2001). However, it is right that in the real ocean, this T dependency is overridden often by other processes such as pCO2 changes, TAlk changes and others. The diagram showing the T dependency of the buffer factor was omitted now in order not to confuse the reader. The text was changed.

Bold added, AR4, Expert and Government Review Comments on the Second-Order Draft, Chapter 7, 6/15/06, #7-1027, p. 70 of 132. Isochemical means the chemical products are not varying, which would be one of the prerequisites for equilibrium.

So the editor contradicts a criticism of one of IPCC's senior, contributing author's to this chapter, and leaves the matter unsettled. The final resolution is to delete old figure (a) "in order not to confuse the reader."

IPCC leaves the reader with empirical evidence, directly and through references, that the Revelle buffer is a linear transformation of solubility, and conceals part of that evidence. No evidence exists that the Revelle buffer factor is anything but solubility and Henry's law, nor that it should be peculiar to ACO2 instead of all CO2. IPCC relies on a conjecture inherited from the original authors that the Revelle factor buffers against anthropogenic CO2(g), but not natural CO2(g), and IPCC's Third and Fourth Assessment Reports ignore Henry's law, which denies IPCC a method to discriminate between the two species of CO2.

Moreover, Henry's law, coupled with fundamentals of system science, dictate that ACO2 and natural CO2 may not be modeled as additive and be faithful to physics. CO2 emissions, presumably lighter weight, add to the local, existing CO2 in the atmosphere to create a new isotopic mixture. Thereafter the two gases share a combined partial pressure, pCO2(g), to effect absorption proportional to pCO2(g) and outgassing inversely proportional to pCO2(g), a nonlinear phenomenon dictated by Henry's law. A linear fit to the nonlinear phenomenon might suit some special application, but any such parametrization needs to be justified against the full model. In general, being nonlinear, a natural carbon cycle may not be reliably added to an anthropogenic carbon cycle as IPCC has done and as its radiative forcing paradigm necessitates. ACO2 is absorbed into the water with, and outgassed against, the partial pressure equivalent of about 380 ppmv.{End rev. 6/10/09}

{Rev. 6/11/09} So who won the argument, Gruber or the editor? It's a draw. Whether IPCC's formulation (Eq. 2) or Revelle's (Eq. 3), the Revelle factor is a relationship between measurable or estimable parameters. It has an existence as an empirical formula, but not one derivable as a consequence of an à priori model. But to call it a buffer is to add another ambiguity. Buffer can be used in the sense of storage or an accumulator, referring here to the accumulation of either CO2(g) or CO2(aq). IPCC said as the Revelle factor increases "the buffering factor of the seawater decreases." Caption, Figure 7.3.10; Figure 4, above. IPCC puts it this way: "The lower the Revelle factor, the larger the buffer capacity of seawater." AR4, ¶, Carbon Cycle Feedbacks to Changes in Atmospheric Carbon Dioxide, p. 531.

The Revelle factor increases as the water temperature decreases or as pCO2 increases, just as solubility does, and as it increases, the concentration of CO2 in seawater increases. Consequently buffer in the context of the Revelle buffer factor means to buffer against the storage of CO2, to act as a barrier to the uptake of CO2, and hence to cause CO2, specifically ACO2, to accumulate in the atmosphere. The phrase "buffer capacity" seems self-contradictory.

Revelle & Suess's "peculiar mechanism of sea water" had no basis in physics, and didn't work out numerically. IPCC has found a physical basis for the Revelle buffer factor: marine carbon chemistry. It says,

The ocean will become less alkaline (seawater pH will decrease) due to CO2 uptake from the atmosphere (see Box 7.3). The ocean's capacity to buffer increasing atmospheric CO2 will decline in the future as ocean surface pCO2 increases (Figure 7.11a). This anticipated change is certain, with potentially severe consequences. Bold added, AR4, ¶ Carbon Cycle Feedbacks to Changes in Atmospheric Carbon Dioxide, p. 531.

IPCC's Box 7.3 contains equations (IPCC #7.1 and #7.2) for the marine carbon chemistry and discusses how the acidity level and buffering capacity change due to added CO2. AR4, p. 529. Wolf-Gladrow provides a more complete set of equations, including the important stoichiometric equilbrium constants for each reaction. Wolf-Gladrow, id., Chart 3. These equations are readily solved, and the solution diagrammed in the Bjerrum plot. Wolf-Gladrow provides several examples in his presentation, including the following:

Wolf-Gladrow Bjerrum plot, Chart 7, showing DIC by carbonate fraction, temperature, and salinity.

Figure 8

Wolf-Gladrow Bjerrum plot, Chart 21, comparing fresh water and seawater, proton levels, and pH. Notes: zlp refers to the "zero level of protons" at the top of the chart; the pKi are the base 10 logarithms of the two equilibrium constants in the reactions producing the two carbonate ions.

Figure 9

IPCC doesn't use the Bjerrum plot in either its Third or Fourth Assessment Report, however the plot serves well to illuminate IPCC's discussion of the marine carbon chemistry. AR4, ¶7.3.4 Ocean Carbon Cycle Processes and Feedbacks to Climate, pp. 527-532. The plot provides the carbonate fraction determined by the independent variable, pH. If the CO2 fraction rises, it must be accompanied by a decrease in pH at equilibrium. IPCC's conclusions (1) that the ocean buffers against ACO2 absorption because the absorption causes the ocean to become less alkaline, (2) that the buffering is measured by the Revelle factor, and (3) that the addition of ACO2 causes potentially harmful acidification (AR4, Box 7.3, p. 529) all rest on assumed equilibrium chemistry in the surface layer, also known as the mixed layer.

IPCC models climate from equilibrium point to equilibrium point, but computes CO2 flux according to a disequilibrium between pCO2(g) and pCO2(aq). IPCC assumes that the mixed layer is in equilibrium at some fractional distribution according to a Bjerrum plot, when that can never be the case. The Bjerrum model only applies to a dead, stagnant, and isolated body of water. The mixed layer exchanges heat with its environment through short wave radiation from the Sun and long wave radiation to space. Every point on the surface is fed by horizontal and vertical currents. Wind, wave action, and entrained air, along with living flora and fauna, add to the dynamics. No model exists for marine chemistry of a real surface layer, and no reason exists to accept equilibrium chemistry as even approximating the real ocean.

Equilibrium is not a continuous measure like pressure, temperature, and concentration. It is a state of a system, as is linear in models. Expressions like "highly nonlinear" or concepts of near equilibrium have no objective meaning. In equilibrium, no work, no heat exchange is being done with the environment. A system is either in equilibrium, or it is not. It is an idealization.

Science dictates that IPCC should abandon its model of additive natural CO2 and anthropogenic CO2 cycles, and abandon its reliance on equilibrium. It needs to abandon its model that the mixed layer must have any specific fraction of carbonate products, and allow the CO2 molecular concentration to vary freely and as necessary to satisfy the laws of solubility. It needs to scrap the Revelle factor and apply Henry's law. It needs to model the carbon cycle using mass balance calculations applied to the ever-changing mixture of natural and anthropogenic CO2, and according to Henry's law. IPCC's global circulation models, formerly known as global climate models, have the carbon cycle wrong. {End rev. 6/11/09}

{Begin rev. 11/12/09} Next in computing the greenhouse effect of CO2, IPCC needs to abandon its assumption that the radiative forcing effects are logarithmic with respect to the gas concentration. For example, a claim with respect to CO2 at AR4, ¶2.3.1 Atmospheric Carbon Dioxide, p. 140; an approximation with respect to water vapor at AR4, Box 8.1: Upper-Tropospheric Humidity and Water Vapour Feedback, p. 631, and at ¶ Water Vapour and Lapse Rate, p. 633; and previously a claim with respect ot water vapor at TAR, ¶ Representation of water vapour in models, p. 426. The physics of absorption are governed by the Beer-Lambert Law, nowhere used by IPCC. This law applied to the radiative forcing yields the following equation, including a decaying exponential: RF = RF0 + ΔRF*(1-e-kx), where x is the normalized concentration (or depth). In a small region, this equation can be approximated by a logarithmic function. But the logarithmic function goes on forever. As IPCC says,

It has been suggested that the absorption by CO2 is already saturated so that an increase would have no effect. This, however, is not the case. Carbon dioxide absorbs infrared radiation in the middle of its 15 mm band to the extent that radiation in the middle of this band cannot escape unimpeded: this absorption is saturated. This, however, is not the case for the band's wings. It is because of these effects of partial saturation that the radiative forcing is not proportional to the increase in the carbon dioxide concentration but shows a logarithmic dependence. Every further doubling adds an additional 4 Wm-2 to the radiative forcing.

TAR, ¶1.2.3 Extreme Events, p. 93. Thus IPCC attributes a logarithmic effect to the emergence of weaker absorption regions for CO2 in the longwave band. The argument is unnecessary and fallacious. The absorption grows in any subband according to the RF equation above. As formulated by IPCC, CO2 can absorb more LW radiation than exists in its band as if its effect spread outside its band, adding 4 Wm-2 for every doubling to infinity. The logarithmic function never saturates, and as a result IPCC doesn't have to determine an operating point for CO2 as a greenhouse gas. Instead the laws of physics provide for saturation, and an operating point is essential. The absorption of any GHG in a particular band can be no greater than the relative width of the band, and is further reduced by the relative blackbody radiation in that band. As the critics that IPCC acknowledged said, CO2 appears to be well into saturation. IPCC needs to compute the marginal effects of additional CO2 instead of adding 4 Wm-2 for every doubling. IPCC needs to respect the Beer-Lambert Law. {End rev. 11/12/09}

Nor does solubility favor natural CO2 over anthropogenic CO2 based on the rate of vertical mixing. It is the same for both. There is no centrifuge effect to segregate heavy CO2 from light CO2.

One would expect no chemical reaction between ions in the ocean and molecular CO2 in the atmosphere. Solubility should be a purely kinetic process bringing CO2 into solution where it can dissociate first and then participate in the chemical reactions.

6. The IPCC provides the following data in Climate Change 2001:

Parameter   Value    Page
Fossil fuel CO2 uptake to emissions ratio [u/e]      50%    187
Ocean CO2 uptake, PgC/yr      90    188
Land CO2 uptake, PgC/yr      120    188
Calculated total uptake, nominal      210          
Fossil fuel emissions, 1980-1989, PgC/yr      5.4    185
Fossil Fuel emissions, 1990-1999, PgC/yr      6.3    185
Calculated Fossil Fuel emissions, average      5.8        
Ratio CO2 total increase to Fossil Fuel emissions, 50%/yr      2.9    187
Total ACO2 = Fossil Fuel emissions/(3/4)      7.8    185
El Niño reduced emissions, min, PgC/yr      0.2    185
El Niño reduced emissions, max, PgC/yr      1    185
Estimated El Niño incidence      50%        
Calculated El Niño reduced emissions, weighted average, PgC/yr      .3          
Net gain in CO2, PgC/yr      3.3    185

Note: 1 Petagram (Pg) = 1 Gigaton (Gton)

So the natural

u/e = 210/207.8 = 101.06%,


a net uptake of CO2 from the atmosphere. Adding ACO2 emissions and crediting the El Niño reduction in natural emissions,

u/e = 211.9/215.2 = 98.41%,


is a net addition (denominator - numerator) of 3.3 PgC/yr.

Next IPCC segregates anthropogenic parts in both the numerator and denominator

u/e = (2.9 + 209.2)/(5.8 + 209.4)


but converts it into

2.9/5.8 + 209.2/209.4 =

50% explicit fossil fuel CO2 emission reduction +

99.80% implicit natural CO2 emission reduction.


Only in IPCC algebra does

(a+b)/(c+d) = a/c + b/d.


This is the result of assigning net transactions, whether fluxes or radiative forcings, to individual components in the transaction without physical justification. Consensus physics here is no better than its algebra. Because measured increases in CO2 concentration appear to be correlated with reasonable estimates for the growth of anthropogenic emissions, the Consensus assumes it has established a cause and effect relationship. Assuming correlation implies cause and effect is the same error the Consensus made in assuming that the increase in CO2 caused the increase in temperature in the Vostok ice core reductions.

Until the Consensus can show that the solubility of CO2 in water depends on the carbon isotope or some other as yet unknown property differing between natural and manmade CO2, the IPCC data support the conclusion that all CO2 is reduced by the same number, approaching 98.41% per year.

7. The Consensus says,


This argument, at the crux of the Anthropogenic Global Warming alarm, is contradicted by the Consensus' own data. Considering the uptake to the ocean alone, which is at least 90 Gtons/year, the Mean Residence Time of the 730 Gtons of atmospheric CO2 is 8.1 years, and the half life is 5.3 years. The CO2 concentration is down to one quarter in twice the half-life, or 10.6 years, more than an order of magnitude less than several centuries.

Thus the Consensus bases its key argument on its fallacious 50% calculation, which it then applies to its scenarios of accelerating anthropogenic CO2. That calculation nakedly assumes different residence times for anthropogenic and natural CO2. Instead of centuries, the Mean Residence Time of both kinds of CO2 is 8.1 years, based on elementary mathematics applied to the Consensus' own data on the oceanic uptake alone. Relative to the Consensus model, CO2 does not accumulate in atmosphere.

8. The Consensus says in the same section of the TAR,

Before the Industrial Era, circa 1750, atmospheric carbon dioxide (CO2) concentration was 280 ±10 ppm for several thousand years. It has risen continuously since then, reaching 367 ppm in 1999.

The present atmospheric CO2 concentration has not been exceeded during the past 420,000 years, and likely not during the past 20 million years. Climate Change 2001, p. 185.

The 420,000 year figure was the greatest age of the Vostok CO2 data, which achieved peaks of about 300 ppm. See IPCC Figure 3.2(d) on page 201. A rough straight line fit to the Mauna Loa data (Figure 3.2(a), page 201) shows the measurements have exceeded 300 ppm for roughly 50 years.

Check the Vostok data: ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/co2nat.txt

{Err. 12/8/09}.

The CO2 samples number 283, covering 414,085 years. The average spacing is 1463 years. The chances of sampling an epoch like the present 50 year record, if it existed, is about 50/1463 or 3.4%.

That translates into a 3.4% confidence level for the statement that the present CO2 trend was unprecedented in the last 420 Kyears. That confidence level does not begin to rise to an acceptable standard for a scientific conclusion.

This unprecedented claim is a mantra of the Consensus. It made a normal scatter plot of the Vostok data, but then seduced itself by connecting the dots!

9. The Vostok record (Figure 3.2(d)) shows five peaks in 420,000 years. What are the chance that the peaks shown are below the true maximum given that the average sample interval is a millennium and a half? Ans: The chances are about 96.6%. Thus the confidence is greater than 95% that any measured maximum is more than 50 years from the peak CO2.

10. So the question about the CO2 record for the last century asks for an explanation of an implicit exaggeration of an exaggeration. The measured record is actually only 50 years old, and it may show a high rate of CO2 growth. The elements of a model to fit the record should accommodate all the following.

11. The CO2 growth rate at Mauna Loa is unprecedented because no comparable measurements exist.

12. The CO2 level at Mauna Loa is substantially higher than the calculations from Vostok ice cores. Because Mauna Loa sits in the plume of the massive CO2 outgassing from the Eastern Equatorial Pacific, and because Vostok sits inside one of the great polar CO2 sinks, Mauna Loa should be higher than Vostok records for the same average, global CO2 concentration. How much higher is for further study by climatologists. The origin of the CO2 at Mauna Loa is dominated by Eastern Equatorial Pacific outgassing.

13. As shown in The Acquittal of Carbon Dioxide , the CO2 concentration lags global warming and is shaped like the complement of the solubility curve. The current epoch of global warming is just one more such epoch shown several times in the Vostok data, and the increase in CO2 concentration is similar to the paleo record, within the resolution of that record.

The Consensus had no explanation for the increase in CO2 it alleged caused the historical ice epoch recoveries. Once the Consensus accepts those new results from The Acquittal of Carbon Dioxide , it will have an explanation for the CO2 but no satisfactory explanation for the global warming at any time.

14. Also, small changes in ocean or atmospheric currents could have an additional profound effect on the CO2 measured at Mauna Loa. The center of the CO2 plume may now be moving toward Hawaii, causing an increase in CO2 concentration there. This could also account for the seasonal effects evident in the Keeling curve.

15. The CO2 rich atmosphere rises near the equator and splits into north and south plumes. As it rises in each hemisphere, it enters a Hadley Cell, carrying it first poleward, and then down into and to feed the westerly trade winds. The trade winds carry the CO2-rich atmosphere across Hawaii. However, the trade winds are also seasonal, varying cyclically in direction and magnitude. The seasonal fluctuations Keeling attributed to the biosphere growing seasons might be better correlated with the trade wind vector at Hawaii.

16. Anthropogenic CO2 may be an additional component of the 3.3 PgC/yr seen at Mauna Loa. It is at most 7.8 parts in 90, or less than 9%. The 3.3 PgC/yr is not unabsorbed ACO2.

17. To the extent that the record at Mauna Loa is influenced by the venting of CO2 from the Thermohaline Circulation, the changes in plume intensity may be due to events a millennium old.

18. The Consensus assumes anthropogenic changes act in a state of climate equilibrium. It assumes that both the CO2 and the global temperature are in equilibrium but for man. Instead, climate change forecasts must operate in the state of Earth's on-going, triple recovery from the last ice age, the last glacial epoch, and the Little Ice Age, whatever the causes might be. Any valid forecast must first account for that natural warming.

Kyoto-like arrangements can have no measurable effects on the rise in CO2. To stop the rise in CO2, man must stop global warming.

The Consensus weaves a tangled web.


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Comments (26)

yonason wrote wrote:


If CO2 caused global warming, why wouldn't the resting state of the earth be at max temp; only to fall during periods of increased vulcanism or such, but then to rise back when they subside?

The reason this seems reasonable to me is that 1. if CO2 caused temp elevations 2. which subsequently induced CO2 loss from oceans 3. which caused temps to rise 4. etc., until a steady state is achieved at MAX temp, then high temp should be the norm, not low.

And an earth at low temp and low CO2 would then be in a metastable state which, once the CO2 trigger was pulled, could NOT be reset short of some geologic (vulcanism) or cosmic process (meteor) or maybe out of control vegetation. I.e., if those who blame CO2 for the warming are correct, it should already be too late to do anything, even if we were to end all human contribution.

I've never heard anyone discuss this, but it seems like a reasonable thesis. Did I miss something?

Regards, and thanks in advance for your input.

[RSJ: 4/30/08. What you describe in layman's terms is a system with positive feedback. Feedback control systems are commonplace in nature, and widespread in technology. It occurs in the atmosphere with the secondary greenhouse gas, CO2, as you suggest. It exists in many instruments used to measure climate phenomena.

[You have described the response of the system in discrete steps, which is OK even though the actual process would be continuous. In fact, making the process discrete helps minimize the algebra necessary to model it. So with your model in mind, consider at step 1 a slug of CO2, X, added to the atmosphere that had reached equilibrium, and that it caused some increase in surface temperature.

[Now at step 2, let the increase in CO2 outgassed from the ocean be a fraction, r, of the slug X. That is at step 2, the ocean emits rX, causing another temperature rise per your step 3.

[Step 4 takes us back through the steps, where now the added CO2 is not X but rX. So the second time through step 2, the ocean emits an additional r*rX, or r²X. And the next time at the 3rd step, it emits r³X, and so on.

[The original slug plus the ocean emission totals X + rX +r²X + r³X + … , which is equal to the original, X, times a gain factor of 1 + r + r² + r³ + … . This is equal to 1/(1-r), which you can verify by doing the long division. [1/23/09: The fraction is valid so long as r is less than 1, and infinite otherwise.] It is the gain of the system, and a lot can be said about it.

[However, from the standpoint of your model, the high temperature is not, as you call it, the norm. The temperature requires the slug input to upset the equilibrium, your trigger. And we presume an equilibrium does or can exist.

[The IPCC reckons that the feedback doubles the warming (4AR, FAQ 1.3, p. 116), making the factor r equal to one half. (As an aside, the IPCC has not come to grips with your step 2. Its feedback gain is due to water vapor, a more powerful and temperature dependent greenhouse gas, added when the CO2 triggered its release.) So suppose the slug of CO2 contained 6 GtC, the approximate annual anthropogenic emissions today, and that it would cause a temperature rise of, say, 0.01 ºC. In closed loop with r = 0.5, the temperature rise would be 0.02 ºC. Do this for a century, and the temperature rise might be a disastrous 2 ºC.

[Now the steps in your model are not instantaneous. If the slug is the annual output, the interval between the steps should be one year. If r is one half, the feedback is 99% complete in 7 years. The time to complete is simple to compute. It is 1-rk in k years.

[The IPCC adds a step not in your model. It calculates that about 50% of the Anthropogenic CO2 is absorbed by the ocean each year. (Aside: This is the tip of a bizarre iceberg. The IPCC reports that of 597 GtC of natural CO2 in the atmosphere, 70 Gt is absorbed by the ocean each year. That's 11.7%. At the same time, it reports that of 165 GtC of ACO2 in the atmosphere, the ocean absorbs 22.2 GtC. That's 13.5%. But the physics of solubility of CO2 in water cannot discriminate between the natural and anthropogenic species of the gas. The IPCC created separate paths through the ocean for nCO2 and ACO2, so the ocean also outputs 20 GtC of ACO2 to the atmosphere. Net, the ocean absorbs 2.2 GtC per year. The IPCC makes the net nCO2 exchange with the atmosphere zero; for ACO2, its number is -3.2 GtC per year. 4AR, Figure 7.3, p. 515.) Because of the absorption and re-emission of ACO2, the IPCC model is slow to develop. Next instead of keeping the slug constant from year to year, the IPCC experiments with various scenarios for ACO2 emissions. These scenarios are variations on your theme, "if we were to end all human contribution."

[In summary, your model is correct but the temperature achieved and when depends on the duration of each step, the loop gain, and the scenario. The process continues to infinity in your model, but the contribution quickly becomes insignificant, especially at the gain level employed by the IPCC in its GCMs.

[All of this discussion is by way of a tutorial on feedback prompted by your query and certainly not an endorsement of the IPCC's model. The slow re-absorption of ACO2 used by the IPCC is the assumption that ACO2 accumulates in the atmosphere. It does not. The IPCC claims at several points that its GCMs employ radiative forcing, and that radiative forcing has water vapor feedback turned off. At the same time, the IPCC makes clear that its models adjust warming caused by ACO2 through water vapor feedback. 4AR, FAQ 1.3, p. 116.

[The GCMs compute the total cloud cover from equations which depended on specific humidity in their derivation. See 4AR, ¶8.2.1, pp. 602-3, citing Bony, S., and K.A. Emanuel, 2001: A parameterization of the cloudiness associated with cumulus convection: Evaluation using TOGA COARE data. J. Atmos. Sci., 58, 3158-3183. The IPCC recognizes in its reports that warming increases specific humidity (4AR, FAQ 1.3, p. 116), but it gives no indication that it might compute cloud cover based on temperature. Consequently, the IPCC accounts for a water vapor feedback for CO2 warming, but does not model the strong, negative feedback of the cloud albedo caused by warming.

[The GCM models for the carbon cycle and for the hydrological cycle are incorrect. Consequently, the IPCC conclusions about AGW are false.]

yonason wrote wrote:

"RSJ: Watch this spot for a detailed answer."

I eagerly await it.

NOTE: I realize that the CO2/Ocean PChem dynamic you describe would preclude this possibility, BUT, that is not a factor that the advocates of anthropogenic GW admit to, at least as far as I know.

Anyway, I can't wait to hear what you have to say.

Thanks in advance!

ianric.ivarsson@spray.se wrote wrote:

"Solubility depends on the partial pressure difference of the gas and water temperature. It is not known to depend on ionic concentrations in the liquid (including the pH (see Climate Change 2001, p. 185)), nor on carbonate or any other chemistry."

This is incorrect. Solubility of CO2 in water is also dependant of pH and salinity. In particular the concentration of Ca2+ is important. But the temperature is of course most important. Beside this little error I find your paper superb.

[RSJ: 10/6/07. I stand by my observation on multiple grounds.

[First, it is accurate as stated. Given the partial pressure difference and the water temperature, the solubility is known regardless of salinity, S, or the alkalinity or acidity index, pH. This may be a scientific cop-out, but it is accurate, and accuracy rules the day in science. The reason is that the partial pressure of CO2 in water, CO2(aq), depends on S, so the salinity effect is already taken into account in the solubility expression. The pH may also be significant, but only at this sub-level, because pH and the partial pressure are correlated, although the cause and effect relationship has yet to be modeled. QED.

[Second, venerable handbooks are reliable sources for solubility data in graphs with best fit curves and formula, all of which depend on just two parameters: temperature and pressure. No one has produced such a formula depending on temperature and pressure plus either salinity or pH, or both.

[Third, the comment offered is in the context of posing a baseline from physics by which, in part, to expose the revisionist physics contained in the following statement by the Consensus on Climate:


[The solubility of ACO2 is the same as that of nCO2. Some plants are known to have an isotopic preference for the uptake of CO2, but that is not sufficient, nor does the Consensus claim it is sufficient, alone or in combination with the molecular weight differences, for natural processes to separate physically the two species of gases. This leaves the Consensus' model that the Mauna Loa CO2 concentration increase since 1957 is of anthropogenic origin, notwithstanding the isotopic claims, without a physical cause. This alone reduces the AGW theory to a conjecture.

[This is not the end of the errors in the Consensus model for CO2 uptake. For example, the carbonate chemistry does not interact with atmospheric CO2 as implied in the passage. This error is also suggested by the Consensus' diagram called "Carbon cycling in the ocean". Climate Change 2001, p. 188, Figure 3.1c. In the Fourth Assessment Report, the Consensus augments this diagram with another diagram depicting three parallel ocean carbon pumps that regulate "natural atmospheric CO2". Climate Change 2007, p. 530, Figure 7.10. The caption adds, "The oceanic uptake of anthropogenic CO2 is dominated by inorganic carbon uptake at the ocean surface and physical transport of anthropogenic carbon from the surface to deeper layers." Bold added. That sentence appears to be true, but it is equally valid for natural CO2. The implied distinction is false. The sentence is also inaccurate because dominated implies that other mechanisms participate in the uptake. They don't:

[Carbon dioxide molecules react chemically with water to form bicarbonate (HCO3 -) and carbonate (CO3 =) ions, neither of which communicate with the overlying air. Only about 0.5% of the total CO2 molecules dissolved in seawater communicate with air via gas exchange across the sea surface. Takahashi, T., S.C. Sutherland, and A. Kozyr. 2007. Bold added. Global Ocean Surface Water Partial Pressure of CO2 Database: Measurements Performed During 1968 - 2006 (Version 1.0). ORNL/CDIAC-152, NDP-088. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tennessee, 20 pp.

[The two diagrams need to be corrected to show a pool of CO2(aq) interacting above with atmospheric CO2, CO2(atm), and below with the biological pumps. (Also the calcium carbonate counter pump needs to be redrawn to make the CO2 flow consistent.)

[Once the Consensus adds the missing CO2(aq) reservoir, it needs to recognize that it may never be in equilibrium with the ocean chemical processes. That equilibrium is an essential assumption underlying perhaps every study or analysis of the partial pressure of oceanic CO2, pCO2(aq). In those works, the concentration of CO2(aq) is identical to pCO2(aq).

[The Consensus has the ocean chemistry and the sluggish vertical mixing tightly coupled to the atmosphere. This error, along with the assumption the physics of ACO2 is unique, is necessary to show ACO2 accumulating in the atmosphere for the Global Catastrophe Model. Instead, to the extent that the chemistry and vertical mixing proceed at rates different than that of the dissolution process (solubility), the pool of CO2(aq) will be in disequilibrium.

[Solubility can proceed apace, essentially instantaneous compared to the ocean mixing and chemistry processes, and dependent on the partial pressure difference and water temperature.]

PaddikJ wrote wrote:


Looks like there is some good info on this blog, but as I'm always busy-but-trying-to-keep-abreast-of-recent-AGW-developments, I must pass over for now. Visually, it's a mess & very hard to read and I don't have the patience to wade through it.

I have BMK'd and will check back occasionally, however.

Good luck on your layout!

[RSJ: Thanks. Some small format changes are in progress. Hope it helps. Please let me know if it doesn't.]

Jim McKinlay BSc MBA wrote wrote:


I was wondering what would be the position if all known reserves of petrochemicals were released into the biosphere, does it mean the end of the world? This led to a review of where the world's carbon is. I could not find a comprehensive list anywhere though somebody more capable must have tried before me. The IPCC figures never seem to give a full account. In any case this is the result of my research. I have converted all measures to Pg's (10 to the power 12 times kg's) of carbon. There is no doubt that these figures are only approximate and in a number of cases I have taken what seems the most recent and or most believable. I would be interested to know if you think any numbers are significantly in error. To me they were useful to give a perspective on the issues. Pg's of carbon Natural gas - (known world reserves) 90 Oil - (known world reserves) 128 Coal - (known worlds reserves) 836

World petrochemical reserves 1,054

Atmosphere 543 Living organisms 664 Soil 2,000 Oceans - dissolved organic carbon 3,000 - dissolved inorganic carbon above thermocline 7,000 - dissolved inorganic carbon below thermocline 28,000 Carbon in biosphere 41,207

Calcite deposited over the last 500m years in limestone 6,132,000

Total world carbon 6,174,261

Natural circulation of CO2 within Biosphere say 500 Pg's per annum Anthropogenic CO2 say 5 - 10 Pg's per annum

Having seen this I was no longer concerned about the biosphere being able to cope with anthropogenic CO2. More of an issue is how long the carbon will last us.

[RSJ:10/4/07. First, but for the IPCC, the voice of the Consensus on Climate, no climate crisis would exist. Therefore, the Rocket Scientist's Journal currently is dedicated to exposing Consensus' errors. It is not dedicated to creating an alternative climate theory. To the extent that it might shine scientific light on climate problems, that is a bonus. Your suggestion that the natural CO2 exchange and the anthropogenic CO2 addition are negligible when compared to the total reservoirs, whether correct or not, is such an alternative model.

[Regardless, your reservoir numbers add a bit and conflict a little with the data in the IPCC Third Assessment Report. See Figure 3.1a, p. 188. The Consensus puts the natural circulation with land at 119 up and 120 down (Figure 3.1d), and with the ocean at 88 up and 90 down (Figure 3.1c). In addition, the Consensus reports a balanced leaf water exchange of 270 (¶, p. 191, a figure which the Consensus seems to have neglected everywhere else. (All numbers in PgC/yr.) The combined numbers are about 480, and close to your 500 PgC/yr. Do you have a source for the 500 PgC/yr?

[The Consensus' reliance on your data is minimal. The GCMs are an attempt to represent the small signal, anthropogenic effects on top of a large signal, natural climate background. The models assume that the natural climate is variously between marginally stable and unstable, and has a constant temperature. The Consensus all but ignores that natural variations sometimes swamp the anthropogenic forcings. It does not model the stability of the climate. It ignores that the natural climate is always either warming or cooling, hence charging anthropogenic effects with the natural warming.

[On page 185, the Consensus quantifies the global gradient of CO2 concentration, but in 93 other places relies on CO2 being well-mixed. It seems to ignore the natural flow of CO2 from the oceans at the Equator and back to the oceans at the poles. The GCMs do not represent the natural dependence of CO2 concentration on global temperature. This flow must produce a background gradient. The GCMs do not model the effects of oceanic outgassing, the resulting CO2 gradient, and atmospheric circulation patterns to interpret Keeling's Mauna Loa data. In the Fourth Assessment Report, the Consensus now reckons different rates of exchange for natural and anthropogenic CO2. See Figure 7.3, p. 515. The Consensus has no mechanism by which this could happen, such as a difference in solubility for nCO2 and ACO2, not does it reconcile this difference with its well-mixed assumption.

[In short, a large number of inconsistencies and omissions plague the models of the Consensus on Climate related just to your CO2 reservoir and exchange data. The models are fatally flawed. Facetiously, they are not ready for prime time. Seriously, for a scientist to exploit these models for public policy is unethical.

[We can't reach the question you raise - whether the carbon exchanges with the atmosphere are significant compared to the total of all nearby carbon.]

Murray Duffin wrote wrote:

Hello Dr. Glassman,

Re: lack of high peaks of CO2 in ice cores (very low probability due to sampling resolution as you note) see:


"These data are CO2 concentration of the air occulded in Siple Dome ice core, Antarctica. The study was conducted between January 2001 and March 2003 on a deep ice core from Siple Dome Core A, located at 81.66 S, 148.82 W. The data covers up to the Termination II (around 140,000 years ago). The parameters are depth in meters and carbon dioxide (CO2) concentration in part per million (ppm). The deepest depth (>995 m) show CO2 values of more than 390 ppm, suggesting reaction and mixing near the bottom with a till ice layer (>1001.8 m), and the intrusions of different ice flows that were laterally located near bed rock. Although deep CO2 values cannot be dated in any way, two of the deepest CO2 results (~ 200 ppm) indicate ages of early Termination II or the penultimate glacial period."

So even when there is high CO2 associated with the penultimate warm maximum, by magic it comes from some other cause. Now where did those "different ice flows" (at great depth) get the elevated CO2 concentration? Hmmm.

Also note that it takes from 70 to 120 years for the Antarctic ice to close, and firn ice closes at a depth of about 60 to 120 m depending on the rate of snowfall at the surface. Therefore any sample taken is a 70 to 120 year moving average result, not a peak that may last less than 50 years. We simply do not know what prior peak concentrations were, but Siple strongly suggests that they were considerably higher than now. Fossil leaf stomata also suggest ACO2 concentration >340 ppm for the brief warming just before the Younger Dryas.

If memory serves Mauna Loa has been grafted on to Siple, not Vostok, but the result is much the same. To match the recent upslope of the Siple concentration to the Mauna Loa concentration, a decision was made that the age of the gas was current in 82 year old ice. Now how did surface CO2 concentration penetrate 60+ meters of snow and ice? No explanation. The likely conclusion is that atmospheric concentration of CO2 in ca 1870 was little different from 1958, which begs the question of why it has risen since 1958. Well 1958 global temperature was pretty similar to 1870. Hmmm. The problem here is that your Vostok Temp/CO2 correlation gives a 100 ppm change in concentration for a 10 degree C change in temp. Since we have had only about 0.7 degree C temp increase since 1958, why have we had a 75 PPM change in ACO2 concentration?

Regards, Murray

[RSJ: Your quotation says of a deep ice core, "deep CO2 values cannot be dated in any way". In the next paragraph, you speak of "high CO2 associated with the penultimate warm maximum". Are you correcting the quotation?

[Then you address the physics of deep ice formation with specific numbers. What is your source for these?

[What relationship do you see between the Vostok and Siple ice core data?

[The Consensus overlaid the Mauna Loa and South Pole data in Figure 3.2a, TAR, p. 201. The Consensus grafted Mauna Loa data on Law Dome, Adelle, Siple, and South Pole data in Figure 3.2d. As discussed in this response, the Consensus' unprecedented claims for the present CO2 concentration compares Mauna Loa with Vostok.

[The Consensus on Climate repeatedly claims,

[The present CO2 concentration has not been exceeded during the past 420,000 years and likely not during the past 20 million years. The current rate of increase is unprecedented during at least the past 20,000 years. TAR, p. 7, p. 39, p. 185.

[This is a reference to ice core data from Vostok. TAR, p. 137, citing Petit, J.R., J. Jouzel, D. Raynaud, N.I. Barkov, J.M. Barnola, I. Basile, M. Bender, J. Chappellaz, J. Davis, G. Delaygue, M. Delmotte, V.M. Kotyakov, M. Legrand, V.Y. Lipenkov, C. Lorius, L. Pepin, C. Ritz, E. Saltzman and M. Stievenard, 1999: Climate and Atmospheric History of the Past 420,000 years from the Vostok Ice Core, Antarctica. Nature, 399, 429-436. See also TAR, p. 102, last paragraph.

[Now if your data are correct, namely that the Vostok data are 70 to 120 year averages (whether moving or not), then the peaks during the 420,000 years worth of samples would be higher than measured. The Consensus claim of unprecedented levels would be weakened.

[Regardless, the 420,000 year set of samples comprise only 283 samples. Vostok Ice Core Deuterium Data for 420,000 Years, World Data Center for Paleoclimatology, Boulder. And NOAA Paleoclimatology Program, ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/deutnat.txt, ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/co2nat.txt. The average sample interval is 1,483 years. The maximum reading was 289.2 ppm CO2.

[The average CO2 concentration from Mauna Loa is 343.75 measured over 48.75 years (3/31/58 to 12/31/06). Calculated from data at http://www.cmdl.noaa.gov/projects/web/trends/co2_mm_mlo.dat. About 8,615 contiguous intervals of 48.75 years comprise 420,000 years. Suppose one such interval before the present existed in the 8,615 samples. What are the chances that it was included in the 283 taken? It's about 3.3% (283/8,615). Whether the Consensus was speaking about averages or peaks, its presumption that the present value of CO2 concentration is unprecedented during the past 420,000 years enjoys a 3% confidence level. I'd wager that that confidence level is unprecedented in scientific claims.

[The Consensus says reassuringly,


[If someone has a lot of time on his hands, he might want to solve this same problem taking into account that the Vostok samples are 70 to 120 year averages, and not 48.75 years. The result is not going to justify the Consensus claims for unprecedented CO2 levels.

[Murray Duffin alerts us to a new wrinkle. The Siple data analysis completed two years after the Third Assessment Report shows that the present levels were actually exceeded during the last 140,000 years, just one third of the first Vostok record. The Siple data disprove the Consensus unprecedented CO2 claim.

[The Siple data analysis was completed over three years before the IPCC Fourth Assessment Report (4AR). In that Report, the Consensus backtracked just a little from its unprecedented CO2 claim. It now says,

[The concentration of CO2 is now 379 parts per million (ppm) and methane is greater than 1,774 parts per billion (ppb), both very likely much higher than any time in at least 650 kyr (during which CO2 remained between 180 and 300 ppm and methane between 320 and 790 ppb). The recent rate of change is dramatic and unprecedented; increases in CO2 never exceeded 30 ppm in 1 kyr - yet now CO2 has risen by 30 ppm in just the last 17 years. 4AR, p. 510; see also 4AR, Frequently Asked Question 7.1, unpaginated.

[A favorite word of the Consensus, unprecedented (used 13 times in the TAR but now 28 times in the 4AR), no longer applies to the CO2 concentration. The modern concentration is "very likely much higher". The claim, formerly an exaggeration, is now false. The present level of 379 was exceeded in the Siple analysis, which measured 390 ppm.

[Do you remember in the History of the World, Part I, when Moses came down from the mountain lugging three tablets of 5 commandments each? He proclaimed, "The Lord, the Lord Jehovah has given unto you these fifteen … ". Whereupon he drops a stone, shattering it into unrecognizable bits. He announced something like, "Did I say 15? Ten; ten commandments for all to obey!"

[The Consensus cries, "Did I say unprecedented in 420,000 years? I mean, very unlikely in 650,000 years!" The Vostok record had indeed been extended by an unremarkable half, but the Siple record, ignored in the 4AR, showed the present level had been exceeded in the first sixth of the longer record.

[The Consensus also favors the word dramatic, an unscientific word at best, which it employs 18 times in the TAR and 42 times in the 4AR, now, with respect to CO2, coupled with unprecedented. It is subjective; a way to punch up what the data can't show.

[The Consensus by ignoring the Siple results and exaggerating the falsely alleged unprecedented time interval practices fear mongering. It is indeed drama. It goes beyond the unethical reliance on unvalidated models to urge a public policy.]

Murray duffin wrote wrote:

Since I posted this comment I went back to Vostok and found 2 references that it takes 4000 to 6000 yers for the ice to close, (Vostok is a very cold high desert with very low precipitation, orders of magnitude lower than Siple or Law Domes) and that modern air can be found in 4000 year old ice. That suggests to me that any relatively short peak in CO2, say a few hundred years, would be smeared out of recognition as part of a 4000 year moving average. Who knows how high the peaks might have been at previous interglacials? The concensus also ignores the fact that fossil leaf stomata from the warming prior to the Younger Dryas also suggest CO2 levels up to 340 ppm.

[RSJ: Comment repeated and answered at GAVIN SCHMIDT'S RESPONSE TO THE ACQUITTAL OF CO2 SHOULD SOUND THE DEATH KNELL FOR AGW for continuity in the thread.}

Heinz Kotzot wrote wrote:

I have question about the carbon content in the atmosphere, is this C from CO2 only or from hydrocarbons, primarily methane?

[RSJ: Do you have a reference where anyone has referred to the "carbon content of the atmosphere", meaning the total carbon content?

[The IPCC in its reports refers to the concentration of CO2 in parts per million (ppm), but also in petagrams (1015 grams) of carbon, where this carbon is from the CO2 molecule. It treats methane concentrations differently, first using parts per billion (ppb) and then uasing the weight of the total molecule, i.e., Tg(CH4), teragrams (1012 grams) of methane.]

[Should you come across a reference to the carbon content of the atmosphere without explanation, assume it be to the weight of the carbon in CO2 molecules. This would be safe because the concentration of CH4 is about 0.5% of that of CO2 in volume mixing ratio (molecular parts), a contribution small compared to the error in CO2 measurements.]

yonason wrote wrote:

Thank you for your detailed answer to my query above


You have given the scenario for how the temp allegedly would rise, but not how and why it would decrease, or did I miss that? And the overall point I wanted to make was that, given the very high CO2 and temps in the past, how is it that the Earth ever managed to cool down, according to their model?

[RSJ: Actually I didn't provide a scenario for warming. On 7/11/07, you asked why wouldn't Earth be at some maximum temperature assuming ACO2 caused some warming and that that warming released more CO2 from the ocean. I accepted your assumptions to answer the question why the temperature doesn't soar to some maximum. That is a question about feedback, in particular positive feedback. Positive feedback would cause runaway temperatures (i.e., going to the maximum) only if the gain at each step, whether infinitesimal or discrete, is greater than or equal to one. I've added a note to my previous comments to clarify my answer.

[Your model is not faithful to Earth's climate because it does not take into account the strong negative feedback against warming caused by albedo. That is the principal mistake IPCC makes in its modeling. Warming causes more water vapor, which causes more cloud cover, which irises down the Sun.

[Adding CO2 to the atmosphere would cause warming, but the temperature increase is too small to be measured. Even IPCC admits adding CO2 isn't sufficient (for its preconceived notion), so it makes the CO2 release water vapor throughout the warming cycle. However, the negative cloud albedo feedback, which, I repeat, IPCC omits, reduces the greenhouse effect by about an order of magnitude, that is, by a factor of 10. So, adding CO2 or adding water vapor causes warming, but it is a fraction of what IPCC says.]

Additionally, I am curious as to what sort of signature that would leave in terms of the simultaneous plots of temp and CO2. I would think that, in a continuous model, the CO2 would have to lead temp. As temp is not linearly related to [CO2], it would begin to level off as [CO2] increased until the CO2 level itself then leveled off (when would they expect that to happen? i.e., where would the respective peaks be?).

[RSJ: Your intuition is good – CO2 would have to lead temperature to have been a cause. IPCC doesn't agree, however. It disagrees because the paleo record shows that CO2 concentration lags the temperature increase, and IPCC operates from its wish that CO2 be shown to cause global warming.

[Elementary system models and even philosophical considerations show that cause must precede effect. It is not a consequence of a linear or nonlinear relationship, as you suggest. In system science it is a consequence of what is called realizability. Google for realizable filters or causal filters.

[IPCC rationalizes that CO2 amplifies the warming effect seen in the record. That is true, but without more is a smoke screen covering an admission that the CO2 didn't cause the warming.

[Rev. 1/24/09. If you want to visualize what happens to CO2 concentration and temperature, study the well-publicized Vostok record. See The Acquittal of CO2 in the Journal. IPCC says of it,

[Biogeochemical cycles interact closely with the climate system over a variety of temporal and spatial scales. On geological time scales, this interaction is illustrated by the Vostok ice core record, which provides dramatic evidence of the coupling between the carbon cycle and the climate system. AR4, ¶7.6, Concluding Remarks, p. 566.

[Note that by "the climate system", IPCC must mean global temperature. Note, too, that it links the Vostok record to other times and places. That evidence is indeed dramatic. Vostok ice core reduction shows that CO2 lags changes in the climate system, and it does so by a millennium. IPCC contradicts its core, AGW thesis. [End rev.]]

But, and this is what I really wanted answered, what subsequently drives the temp down? If temps force [CO2] up by degassing of oceans, then they would have to stay up until CO2 levels fall, which they can't while temps are high. Sure, you could say that plants would grow faster and absorb it, but what's the model for that, or any other CO2 depleting mechanism, and what are it's/their dynamics, and why can't they be invoked to prevent the uptick in CO2 in the first place?

[RSJ: You need to let go of the notion that CO2 is driving the climate. It never did, and won't in the future. IPCC shows CO2 has been 20 times the current level many times in the past few million years, and the oceans did not run dry. What drives Earth's temperature up and down is solar activity coupled with orbital mechanics. Solar activity takes two forms: variations in solar intensity and in solar wind. IPCC disputes the prevailing model for the latter, so it simply omits the solar wind from its GCMs despite the strong correlation. For more on orbital mechanics, read about the Milankovitch cycles.]

I suppose they could say that vegetative growth just can't keep up, but when CO2 and temps go up that vegetation growth kicks in and slowly depletes CO2, which would cause temps and CO2 to very slowly go down. And that is consistent with some (most) of the paleo data.


(note that the precipitous rise of both takes about 25K years, where the fall of both takes about 100K years.

[RSJ: The image is just another example of the 450 millennia Vostok record. But you can't rely on your eyeball to assess leads and lags. You need to do the math, or rely on someone who has. Both IPCC and its critics agree, however, CO2 lags temperature in the paleo record by about one millennium.]

Is there another explanation? I would expect so, and it probably has as much to do with reabsorption into the ocean as land based vegetation, but I haven't seen any material on that, which to me is as interesting as the initial rise.

[RSJ: IPCC reports the two major exchanges of atmospheric CO2 are about 90 GtC/yr with the ocean and about 120 GtC/yr with the terrestrial biosphere. Your concern relates to an ordinary mass flow analysis, which IPCC ignores. IPCC needs the MLO record to represent global concentration, so it proclaims that CO2 a well-mixed, long lived atmospheric gas. To do so, IPCC ignores the role of CO2 solubility in water. It needs ACO2 to build in the atmosphere for its warming model to be bad enough, so it proclaims that slow sequestration processes in the ocean keep the ocean from absorbing new CO2. To make this happen, IPCC models the top layer of the ocean as if it were in thermodynamic equilibrium. These assumptions are riddled with error, and even contradicted within IPCC reports.]

Aside - since the Temp is not linearly related to CO2, ...


... why do they appear to be nearly so in the paleo data? Is that some kind of artifact of assumptions made about the proxies? ... or am I misreading them?

[RSJ: Your source gets a few things wrong. It says, "CO2 does indeed absorb reflected sunlight returning to space from earth, having a warming effect." The greenhouse effect is about the absorption not of reflected sunlight, but of the radiation of the surface of Earth. Reflected sunlight comes from Earth's albedo and is spectrally similar to sunlight, specifically being visible. Earth's radiation is long wave radiation and invisible. This is quite a gaff, but not significant to the rest of the argument.

[A serious problem is that your source doesn't use climate sensitivity as it is defined and used by IPCC. The blog relies on a doubling of CO2 from the preindustrial level, about 285 ppm in 1750, to about 385 ppm today (2007), and 560 ppm to a doubling. IPCC uses a scenario of 1%/yr compounded growth from the present, say 2001. A doubling is achieved in 70 years. The blog growth rate is 0.1% initially. For IPCC, the doubling ends the growth, and the temperature continues to rise toward a steady state value of T2x, the defined climate sensitivity. See TAR, Figure 9.1, p. 534. The terms as defined and as used by the blog are not the same.

[The blog further uses climate sensitivity as a constant of proportionality between temperature rise and CO2 concentration. IPCC defines it as the ratio between the radiative forcing (from a doubling of CO2) and the "strength of the feedback processes in the system". TAR, ¶9.2.1, p. 533. To IPCC, the climate sensitivity is a measure of model response to a doubling of CO2. IPCC does not pretend that temperature rise has any particular shape, linear or otherwise. Yet the blog rationalizes the IPCC sensitivity of 1.2 [AR4, §, p. 631. Rev. 1/25/09] to mean something else.

[Rev. 1/25/09. To be as fair as possible, IPCC climate sensitivity seems to be a work in progress. It uses either 1/α (TAR, ¶9.2.1, p. 533) or λ (TAR, Ch. 6, Executive Summary, p. 351) as the model-dependent climate sensitivity parameter. It is careful to define climate sensitivity as the GCM equilibrium temperature rise, then introduces another, non-equilibrium climate sensitivity and the "effective climate sensitivity", Te with a different parameter, αe. Apparently α varies during a model run while λ is nearly invariant (id.) IPCC also uses the parameter TCR, the Transient Climate Response, to designate the GCM temperature rise at the moment of reaching the doubling of CO2. (Id., p. 933).

[IPCC notes that "for CO2, RF increases logarithmically with mixing ratio." AR4, ¶2.3.1, p. 140. The author at coyoteblog uses undefined "simple math" and "a truer form of the curve" to arrive at logarithmic-like curves for his relation between concentration and warming. To that extent, coyoteblog results might be rationalized. He believes he has "derived a climate sensitivity of 1.2 from empirical data". Actually, he merely arrived at that figure.

[Coyoteblog is correct, however, in focusing on IPCC errors in feedback modeling. IPCC errs, overstating climate sensitivity because it doesn't model major feedbacks, especially albedo, in Earth's climate. IPCC errs philosophically to model Earth in an unstable state instead of in unending transitions between hot and cold stable states. End rev 1/25/09.]

Note that CO2 solubility vs temp ...


... IS consistent with paleo observation if CO2 rise is driven by rising temp, whereas temp rise driven by increased [CO2] would not be (remember that in the paleo data humans make NO contribution, so it's all natural, (presumable mostly oceanic?).

[RSJ: Why are you asking the question? The relationship between the CO2 concentration and the temperature inferred in the Vostok record is thoroughly analyzed for you again in The Acquittal of CO2. As shown there, that relationship follows the solubility curve for CO2 in water. See Figure 7. It is decidedly not linear, but has a well-known, non-linear physical cause based on measurements.

[Your link to solubility.png is to the same graph in Figure 6 of The Acquittal. What did wattsupwiththat have to say about it?]

btw, why do the temps go up so precipitously anyway, and at such apparently regular intervals? And, no, I don't believe it's due to any physical/chemical oscillation. Intuitively I would wager that it's not thermodynamically viable.

[RSJ: Always turn to IPCC for the official version first. Whatever it admits as fact can be used against it, the source now of the global warming scare. For a discussion of the rapid rise in paleo temperatures, see TAR, ¶2.4, How Rapidly did Climate Change in the Distant Past?, pp. 136-143. Climate changed as rapidly as 0.2ºC/yr. P. 140. At the end of the last four glacial epochs (450, 230, and 130 millennia past), temperature was 1º to 3º hotter than the present, which is still part of the end of the last glacial epoch (20 millennia ago). Figure 2.22, p. 137. All of these were due to natural causes.

[For glacial epoch causes, see AR4, Ch. 6, FAQ 6.1, What Caused the Ice Ages and Other Important Climate Changes Before the Industrial Era?, pp. 449-450.

[So here are some questions for IPCC relevant to your concerns. (1) How do your models account for the previous glacial cycles? (2) What were the causes and effects? (3) Do you not expect the current temperature to continue to rise another 1º to 3º due to natural causes? (4) Do you not assume that the climate was in equilibrium at the beginning of the industrial era? (5) How do your models cancel out the natural effects to show that the current warming is manmade?

[Since IPCC doesn't take questions, I'll supply the answers. (1) They don't. IPCC says its models are used to investigate ice ages, but provides no evidence of fit between GCMs and the paleo record. (2) IPCC says the Milankovitch theory is implicated, and not much more. (3) IPCC is silent on the possibility that a few more degrees of warming is still due to natural causes. (4) IPCC models assume equilibrium, plus some noise, and not that Earth is in the midst of a natural warming trend at the point of initializing its GCMs. (5) GCMs do not cancel out natural warming, but chalk up any natural warming to anthropogenic CO2 emissions. IPCC admits natural warming has been as high as 0.2ºC/yr, and without accounting for that possibility, predicts that man can cause about 3.5ºC warming over about the next 200 years, 0.0175ºC/yr, or about one tenth of natural causes with unknown variability.]

Oh, I almost forgot. How would an ice age end? There are fewer plants, and CO2 dissolves more readily in the cold water, so with the CO2 theoretically depleted, where does the heat come from?

[RSJ: [Rev. 1/24/09.] As you noted, abruptly. When Earth is a snow ball, its albedo is close to one. The surface of the ocean is frozen and white. The THC uptake and venting have ended. Earth is quite insensitive to solar activity, but as solar radiation increases the ice thins. When the edge of the ice retreats, dark ocean begins to appear and the albedo drops. The climate is still dry as humidity is condensed onto the remaining ice, so the greenhouse effect is for awhile minimal. Soon though the rapid transition begins to a liquid, absorbent ocean surface, and a moist climate. Total albedo would have become quite small but for the formation of cloud cover. Earth has moved from the cold stable state, latched by ice albedo, to the warm stable state, regulated by cloud albedo. Then Earth moves away from the sun and slowly begins to cool, first drawing heat stored in the ocean. We need to put numbers to this model to see if we can effect the slow cooling and rapid warming.]

Thanks again, and regards.

P.S., of course there is reason to believe that the "greenhouse effect" may be more theoretical than real.


I would like to see that repeated with some additional controls.

[RSJ: Rest assured that the greenhouse effect is well-founded and real, though perhaps misnamed. It might be better called the blanket effect. The greenhouse gases are a thermal resistance to heat from Earth's surface to space. Like the blanket on your bed or the insulation in your walls, the material supports a temperature drop through the media as heat passes through it.

[The main problem with the greenhouse effect and the global warming scare is that clouds, not greenhouse gases, control Earth's surface temperature. That is not modeled by the IPCC, who instead has the greenhouse effect in effect open loop.]

john wrote wrote:

Hello Dr G

Below are some links (which contain links to some other alleged refutations) relating to the accumulation (or not) of CO2 that you may or may not have seen. Your readers might like to hear your comments on the arguments presented, those both for and against the motion.




[RSJ: The first article John suggests for review is posted on Climate Realists, Formerly CO2sceptics, entitled "Alan Siddons: Proof that anthropogenic CO2 is not accumulating". Siddons' opening paragraph reads,

By current estimates, man is pumping about 4 ppm of CO2 into the air every year. But the atmospheric level is rising only 2 ppm every year. Theory has it, then, that half of human emissions are presently getting absorbed by so-called carbon sinks, thereby cutting the net emission in half every year.

[Airborne Fraction Definitions. Siddons does not refer to the IPCC, even though it is the source and owner of the alleged CO2 crisis. His model is related to IPCC's parameter called the airborne fraction. IPCC defines this as the ratio of the total anthropogenic emissions to the CO2 increase in the atmosphere, although IPCC also uses it, as does Siddons, with respect to fossil fuel CO2 emissions. As of 2005, IPCC put the fraction at 0.55, and varying little since 1958. AR4, Figure 7.4, p. 516. One of Siddons commenters, eadler2, calls Siddons' model arbitrary and a silly straw man, citing three non-IPCC articles, and thus omitting the only source worth critiquing. Eadler2 overlooks the consistency between Siddons' model and IPCC's position.

[IPCC calculates its airborne fraction with ACO2 concentration in parts per million per year (ppm/yr) in AR4, Figure 7.4, id. It computes its ACO2 cumulative emissions in gigatons of carbon per year (GtC/yr) in TAR, Figure 2.3, p. 138. These prove to be the same data by an unmentioned linear transformation. (GtC/yr = 2.2 ppm/yr -0.31, sigma = 0.10). IPCC says:

[Definition 1.] The 'airborne fraction of total emissions' is thus defined as the atmospheric CO2 increase as a fraction of total anthropogenic CO2 emissions, including the net land use fluxes. AR4, ¶ Perturbations of the Natural Carbon Cycle from Human Activities, p. 515.


[Definition 2.] The relationship between increases in atmospheric CO2 mixing ratios and emissions has been tracked using a scaling factor known as the apparent 'airborne fraction', defined as the ratio of the annual increase in atmospheric CO2 to the CO2 emissions from annual fossil fuel and cement manufacture combined (Keeling et al., 1995). AR4, ¶2.3.1 Atmospheric Carbon Dioxide, p. 139.

[Only by implication are these the same as saying that the airborne fraction is the portion of ACO2 that remains in the atmosphere. The word apparent would be superfluous in the second version if this were a simple empirical relationship. IPCC identifies Figure 7.4(b), id., as

[Definition 3.] Fraction of fossil fuel emissions remaining in the atmosphere ('airborne fraction') each year (bars), and five-year means (solid black line) (Scripps data) (mean since 1958 is 0.55). AR4, Figure 7.4, p. 516.

[So by Definition 1, the airborne fraction is a simple empirical ratio of the atmospheric CO2 rise of any species to the calculation of all CO2 emissions including land use fluxes. In Definition 2, it is an apparent parameter where the denominator does not include land use fluxes. In Definition 3, the numerator is the fossil fuel emissions remaining in the atmosphere instead of the total CO2 increase, and the denominator includes neither cement manufacture nor land use flux. IPCC finessed its definition to presume that the atmospheric increase is all fossil fuel emissions. Its implication is reinforced by the following:

[T]he increases in atmospheric carbon dioxide (CO2) and other greenhouse gases during the industrial era are caused by human activities. In fact, the observed increase in atmospheric CO2 concentrations does not reveal the full extent of human emissions in that it accounts for only 55% of the CO2 released by human activity since 1959. …

The increase in atmospheric CO2 concentration is known to be caused by human activities because the character of CO2 in the atmosphere, in particular the ratio of its heavy to light carbon atoms, has changed in a way that can be attributed to addition of fossil fuel carbon. AR4, FAQ 7.1 Are the Increases in Atmospheric Carbon Dioxide and Other Greenhouse Gases During the Industrial Era Caused by Human Activities? p. 512.

[Henry's Law of Solubility. To be clear, in some model ACO2 emissions might be fully absorbed to the extent that natural CO2 is absorbed, while at the same time causing an increase in outgassing of natural or aged CO2 by some mechanism like ocean heating. IPCC strongly implies, especially by its isotopic argument, that the increase in atmospheric CO2 is in fact residual ACO2 in the amount of 55%. This is absorption in which Henry's Coefficient is greater for natural CO2 than it is for ACO2. This is novel physics, and without more, unjustified.

[Now one might make a reasonable case for Henry's Coefficient to be different for differing isotopes. After all, dissolution is diffusion at the microscopic level, a kinetic process that should be mass dependent. However, the differences due to mass are small and complex to measure. Moreover, the difference between natural CO2 and ACO2 is not an integer atomic weight but a slight difference in the mix of two or three isotopes, 12C, 13C, and 14C. Moreover, natural CO2 and ACO2 combine in the atmosphere in some complex and unknown global pattern of mix ratios. The solubility preferences for 14C vs. 13C vs. 12 C would be even less discernable for the varying mixes of natural CO2 blended with ACO2. This is the best argument that can be made for this aspect of the IPCC carbon cycle and for IPCC's conjecture that the ACO2 accumulates in the atmosphere while natural CO2 remains in some kind of equilibrium. It is not adequate support for IPCC's implication that the solubility of the two species of CO2 differ.

[Siddons' model fits Definition 3, the silly definition. That model is not in accord with physics. It is a refinement on the CO2 content of the atmosphere, which most certainly would have a warming effect on the surface temperature, but as shown elsewhere would be unmeasurable regardless of the species of CO2. It would cause less warming than the total greenhouse effect, which too must cause warming, but as also shown elsewhere at an order of magnitude less than predicted by IPCC. The problem IPCC has failed to discover and implement is that the hydrological cycle regulates Earth's climate, not the carbon cycle. Cloud and surface albedo are dynamic feedbacks, the first negative and the second positive, and have no effect in GCMs which are not even dynamic. Consequently, enthusiasm over perfecting the CO2 model is hard to muster.

[Siddons Arithmetic. Siddons presents three arrays showing the computation of the growth of CO2. The first table might be improved by justifying the rows right instead of left, eliminating the redundant Total column, and providing just the grand total under the last column for 2008. Regardless, the table is no more than the computation of the simple algebraic relation that A*(1+x+x2+x3+… ) –> A/(1-x) for x = 0.5, A=2, for 9 terms. The third table is a single column version of the same relationship for x=0.95 and A=1.54, but with the data column inexplicably reversed, top to bottom.

[The second table, labeled ".09 increase" is a different animal altogether. It has the form b + m*(Δyear) where b = -177.31 and m = 0.0887, which is the sequence {m, 2m, 3m, … 9m}. The baffling arithmetic invalidates Siddons' conclusions. For any of his three different models, the total accumulation is easily computed, rather than requiring one to "fiddle with the parameters" or "drastically reducing" anything.

[Exponential Models. Putting aside the arithmetic problems, the model derived by IPCC in Definition 3 and analyzed by Siddons in Table 1 is a decaying exponential expression for atmospheric ACO2. A formula of the form A(1+x+x2 +x3+…) is equivalent to A(1+ek+e2k+e3k+…) where k = ln(x), and ln(0.55), IPCC's number, is -0.5988 and ln(0.5), Siddons' number, is -0.6931. Siddons adds a constant ACO2 each year, and IPCC follows a scenario, and both rely on a total residue, but neither changes the fact that the underlying model is an exponential decay.

[Whether growing or decaying, an exponential model represents a process whose variable changes at a rate that depends on the bulk of the variable. It arises in radioactive decay, in population growth, and in diffusion. The greater the radioactive mass, the more frequently are decay particles ejected. The greater the population, the more frequent are births or deaths. The greater the mass of a soluble gas in contact with a liquid, the more frequent do molecules enter the liquid. The latter is a model for the microscopics of dissolution, and may include the depth of penetration as it depends on the kinetic energy of the molecule entering the liquid.

[Thermohaline Circulation. However, the rate at which CO2 molecules dissolve in seawater is for all practical purposes instantaneous compared to other climatic processes. Outgassing from the thermohaline circulation should be as quick as seen when opening a soda pop due to the pressure release. In the THC, the release is caused by the rise to the surface, with continued bubbling as the pop goes stale at the ambient temperature on the surface. The water that outgases at the surface had been at maximum saturation perhaps centuries past, tending to have equilibrated with atmospheric CO2 in seawater at the temperature of an ice bath. Exhausted, light–weight seawater, newly exposed on the surface, circulates around the planet according to the prevailing currents, occasionally diverted by gyres, but on average heading poleward and cooling. The path is slow, requiring on the order of a year, but fully absorbing atmospheric CO2 all along the way. IPCC reckons that the absorption is dependent on the largely unknown, but wind-speed dependent, gas transfer coefficient. That variation is local. What counts is the final absorption at the poles and not the particulars of the paths by which the water arrived.

[According to IPCC, the thermohaline circulation (THC) is driven by a density gradient caused by low temperatures (thermo) and high salinity (haline). TAR, Technical Summary, ¶D.2 The Coupled Systems, p. 53; TAR, ¶1.1.2 The Climate System, p. 88; TAR, Glossary, p. 797. In the Fourth Assessment Report, it introduced the substitute name, "Meridional Overturning Circulation (MOC; often loosely referred to as the 'thermohaline circulation'…)". AR4, ¶1.4.6 Ocean and Coupled Ocean-Atmosphere Dynamics, p. 111. In a new definition, it said,

Thermohaline circulation (THC) … The THC is driven by high densities at or near the surface, caused by cold temperatures and/or high salinities, but despite its suggestive though common name, is also driven by mechanical forces such as wind and tides. Frequently, the name THC has been used synonymously with Meridional Overturning Circulation. AR4, Glossary, p. 953.

[hedging its and with a superfluous or, but still recognizing neither that the density has a positive driving component due to the dissolution of CO2, nor that the salinity effect is at best null, or worse, contrary to its model of the THC.

[Published data on salinity show scant difference between the headwaters of the THC and the outgassing in the Eastern Equatorial Pacific. See data supplied by National Oceanographic Data Center, http://www.nodc.noaa.gov/General/salinity.html. If anything, the salinity declines at the headwaters, tending to contradict the conventional model for the THC. Reading the data with the greatest care, at most it might show a difference of 34.5 vs. 35.5 g/kg in which the headwaters are less haline than the outgassing by 1 g/kg, a sign reversal from the conventional model.

[Takahashi Diagram. Evidence for the THC conveyance of CO2 is in IPCC's global flux data. It provides the uptake of CO2 and outgassing flux in a chart attributed to Takahashi. AR4, Figure 7.8, p. 523. That these points encompass the headwaters and the exhaust of the THC is an RSJ deduction, judging in part from a variety of cartoons published by climatologists for the location of the THC. This particular Takahashi diagram divides the ocean into 1759 cells of 13 colors. Eleven colors across the rainbow span a range of 0.5 mol CO2 m-2yr-1 each, 41 violet cells span -7.5 to -3.5 mol m-2yr-1 each, and 53 red cells span 2.0 to 5.5 mol m-2yr-1 each. The average cell is -0.54. The average flux of the greatest uptake cells (violet) at the headwaters is 10 times as great as Takahashi's global average cell flux, and the flux of the largest outgassing cells (red) are -7 times the magnitude of the average cell flux. In short, these regions associated with the THC dominate the atmosphere-ocean CO2 exchange. For an explanation of the Takahashi diagram and other versions, see the Carbon Dioxide Research Group at Columbia University. http://www.ldeo.columbia.edu/res/pi/CO2/carbondioxide/pages/air_sea_flux_2000.html

[The Takahashi diagram is beautiful, illustrative, but troubling. It represents but one of 10 climatology studies, each of which supports the model that global atmosphere-ocean CO2 flux ranges between -3 and -.04 (AR4, Figure 7.6, p. 519) or between -4 and 6 PgC/yr (AR4, Figure 7.7, p. 522), and that it is on average around 2.2 GtC/yr (AR4, ¶5.4.2 Carbon, p. 403). IPCC admits with perhaps some understatement that these studies might not be independent. AR4, ¶, p. 522. The reason is Takahashi's work may be a font for the others:

The air-sea CO2 fluxes consist of a superposition of natural and anthropogenic CO2 fluxes, with the former being globally nearly balanced (except for a small net outgassing associated with the input of carbon by rivers). Takahashi et al. (2002) present both surface ocean pCO2 and estimated atmosphere-ocean CO2 fluxes (used as prior knowledge in many atmospheric inversions) normalised to 1995 using National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) 41-year mean monthly winds. Bold added, AR4, ¶ The bottom-up view: land and ocean observations and models, p. 521.

[This troublesome paragraph points out another problem with the Takahashi model: the assumption that the natural CO2 fluxes are nearly balanced. IPCC admits that the natural ocean exchange comprises an outgassing of about 90 PgC/yr and an uptake of about 92 PgC/yr. AR4, Figure 7.3, p. 515. Even if these were exactly in balance, they are examples of "massive exchanges" (AR4, FAQ 7.1, p. 512) of CO2 neither reported nor, perhaps, discovered by Takahashi. As the model adopted here provides, and as IPCC admits,

Atmosphere and oceans also exchange, among other gases, carbon dioxide, maintaining a balance by dissolving it in cold polar water which sinks into the deep ocean and by outgassing in relatively warm upwelling water near the equator. TAR, ¶1.1.2, p. 89.

[That dissolving doesn't occur just at the poles, but everywhere that the ocean is cooling, which is all along the paths to the poles. By contrast, outgassing occurs where the deep upwelling and warming occurs, a localized and concentrated phenomenon. The statistics of the cells in the Takahashi graphs do confirm these physical considerations. The cell frequency is characteristic of not one but two probability distributions, a broad distribution of negative (uptake) cells, plus a sharp distribution of positive (outgassing) cells. Thus the Takahashi diagram supports the pattern for the atmospheric flow of CO2 promoted in the RSJ.

[However, IPCC errs to adopt superposition of natural and anthropogenic CO2 fluxes. The two species of CO2 mix irreversibly in the atmosphere. The uptake and outgassing are consequences of the theory of solubility of gas in water controlled by the mechanical flow of ocean currents and the distribution of sea surface temperature. The uptake in the flow of CO2 is linearly proportional to the total mass of CO2 in the atmosphere, but the outgassing is inversely proportional to that total mass and is not linear. Being nonlinear means that the phenomena cannot be added, or in other words, that superposition does not hold. The problem needs to be solved by a mass balance analysis for the total CO2. Even if the natural uptake equaled the natural outgassing, the two processes cannot be added.

[Furthermore, the Takahashi method, involving the measuring of atmospheric pCO2 and estimating the oceanic pCO2 to arrive at a CO2 flux, has no way to discriminate and measure the flow of ACO2 within the background of the natural CO2 flux. IPCC shows the Takahashi diagram in Figure 7.8 without specifying the area of the cells, making the task of determining the total flows up and down in PgC/yr speculative, given that the individual cell density values are in PgC/m2/yr. However, detailed information is now available on line from Lamont-Doherty Earth Observatory at Columbia University, id. See Takahashi, T. and S. C. Sutherland, CO2 Partial Pressure Data for Global Ocean Surface Waters (Version 1.0), Lamont-Doherty Earth Observatory, 10/20/06; Carbon Dioxide Research Group, http://www.ldeo.columbia.edu/res/pi/CO2/. The chart for which published data are available is quite similar to that of Figure 7.8, and bears the same attribution. The printed scales differ, but the cells are similar in size, location, magnitude, and probability distribution. The Lamont-Doherty website conveniently provides the total flux for each cell, called the "Box Flux", in 1012 gC/yr, or TgC/yr, for each of 1757 cells in the chart, just two less cells than found in Figure 7.8.

[The Takahashi model has a total flux of -1.4 PgC/yr, which supports one leg of IPCC's conjecture that ACO2 accumulates in the atmosphere. However, this total is the sum of an uptake of 2.4 PgC/yr and an outgas of 1.0 PgC/yr, a stark contradiction to IPCC's widely accepted, massive estimates of an uptake of 92 PgC/yr and an outgassing of 90 PgC/yr. Takahashi's model contains evidence that contradicts IPCC's model of the carbon cycle using its radiative forcing model. In the latter, IPCC has natural CO2 in silent, background equilibrium, and ACO2 causing an additive disequilibrium. Regardless of any presumed background equilibrium, the two processes are neither additive nor separable.

[Takahashi went wrong in the same place that IPCC did. See Takahashi, 10/20/06, id., p2. Unable to measure a partial pressure of CO2 in the ocean, he estimated it from equilibrium chemistry for the surface layer. He computes the pCO2 of seawater from its temperature, total DIC, and pH. This is known by equilibrium chemistry (see AR4, Box 7.3, p. 529), which is not applicable because the surface layer is never in equilibrium. He further shows his reliance on equilibrium chemistry in his statement about only 0.5% of total DIC being CO2 molecules, which is a result of equilibrium analysis, illustrated in the Bjerrum plot. (For citations, see re Bjerrum plot in discussion on The Acquittal of CO2, especially in RSJ response at 4/11/09.) The Takahashi diagrams remain a fortuitous and useful illustration of a model for the global flow of CO2, but they are not correct in the magnitude of the local cell fluxes nor in their underlying equilibrium physics.

[At the uptakes, the ocean tends to equilibrate with ice, so the temperature is about 0ºC. At this temperature, the solubility of CO2 is 3.346 g/kg. At the outgassing in the Pacific, the SST runs around 28ºC, at which point the solubility of CO2 is 1.327 g/kg. The difference is about 2.0 g/kg, a positive density difference tending to propel the THC, and equivalent to two points on the Practical Salinity Scale (PSS). This is a relatively large force, and sufficient to overcome substantial freshening of polar seawater. The salinity force appears not even to exist. IPCC, too, found the salinity effects inconclusive or even contradictory. AR4, Box 5.1: Has the Meridional Overturning Circulation [MOC = THC] in the Atlantic Changed, p. 397.

[The Meridional Overturning Circulation, aka the THC, is a dominating, essential element in the carbon cycle, a role not implemented in IPCC's GCMs.

[IPCC and Takahashi err to model CO2 flux as two processes, one natural and the other anthropogenic. Similarly, Siddons, by virtue of using an exponential model, makes the ACO2 flux proportional to the bulk ACO2 content, which does not exist as a detectable physical parameter to drive a process. None of these models comports with physics.

[CO2 Is Irrelevant. Having examined this problem in its most gory detail, let's look at it now in perspective. The greenhouse effect cannot cause a runaway global warming. This is because of the hydrological cycle and cloud albedo, which IPCC intentionally ignored in its Third Assessment Report. This strong negative feedback of clouds, determined in part by the parameter called cloudiness or cloud cover, and not the reflectivity per unit area as treated by the IPCC, regulates surface warming. IPCC's vaunted climate sensitivity parameter is calculated open loop with respect to cloud cover. Closed loop, the order of magnitude of its climate sensitivity is about one tenth the open loop value.

[Since the effect of CO2 is at most a quarter of the greenhouse effect, it's effect will be too small to measure. Perfecting the carbon cycle for climate models is an academic exercise, valuable in refuting the claims of IPCC and its consensus of 4,000 scientists. CO2 is a benign, beneficial gas, and an optimum effluent for energy consumption, for the economic well being of man, and for the greening of the planet.

[Conclusion on Siddons. Siddons is correct that ACO2 does not accumulate in the atmosphere, impliedly differently than natural CO2, but this conclusion is not supported by his analysis.

[Spencer: On Watts Up With That?, "UPDATED: Roy Spencer on how Oceans are Driving CO2".

[What Roy Spencer hypothesizes is an extension in space and time of what The Acquittal established for the paleo record: polar CO2 concentration follows the solubility curve for CO2 in water according to global temperature, and lags by about the one millennium as others have reported. Spencer suggests what Keeling and Revelle found in 1985, that El Niño/La Niña might be the cause of the increase in CO2 seen at Mauna Loa through modulating "fluctuations in the ocean upwelling areas off the coasts of the continents", noting that man's emissions amount to only about 3% of "natural fluxes in and out of the surface." Keeling, C. D. and R. Revelle, "Effects of El Niño/Southern Oscillation on the Atmospheric Content of Carbon Dioxide", 6/30/85.

[IPCC puts ACO2 emissions at 6.4 PgC/yr, emissions from land at about 120 PgC/yr, and from the ocean at about 90 PgC/yr. That puts ACO2 at 3% of the total from land and ocean combined, but 7% from the ocean, making the hypothesized sensitivity much greater when attributed to the ocean. However, Keeling and Revelle placed those coastal upwellings from depths of only 50 to 150 meters, and the volume flow there is not evident from the Takahashi diagrams. El Niño and the SOI may indeed be correlated with variations seen at MLO, but El Niño and SOI are regional variations in the distribution of heat, more likely affected by the same global climate processes that cause climate change as opposed to being ultimate causes themselves.

[Far more likely is that a primary source of CO2 at Mauna Loa is the plume from the outgassing in the Eastern Equatorial Pacific, supported by the Takahashi analysis, and as discussed at length here in the Journal. There in the Pacific, perhaps 60 of the 90 GtC/yr rise from the surface, split into Northern and Southern Hemispheres at altitude, where they are intercepted by the Hadley Cells, to be carried down to the surface and into the westerlies. The Northern branch lies on or near MLO. The seasonal winds in Hawaii are sufficient to cause the seasonal modulations in CO2 as the plume wanders over the islands. And as global temperature rises, the outgassing would increase according to the laws of solubility.

[If one is interested in perfecting the model of the carbon cycle, what should be investigated is how well temperature accounts for the MLO CO2 concentration using the curve for the solubility of CO2 in water. Spencer might want to investigate the THC emissions instead of El Niño and local, shallow upwellings.

[Spencer asks the questions, "'What is the empirical evidence that CO2 is driving surface temperature, and not the other way around?'" This is a question about lead and lag, which he does not answer. For this he needs to have investigated the cross-correlation between CO2 concentration and surface temperature.

[In his problem setup, he says, "In mathematical terms, we need to analyze the sources and sinks contributing to dCO2/dt, not dT/dt." Accordingly, he then proceeds to analyze the correlation between temperature anomalies from HADCRUT3 and CO2 yearly emissions from MLO. IPCC and Hadley Center, who provides HADCRUT3, report global temperature anomalies as the offset from T0 = 14ºC, ostensibly the 1961 to 1990 average. AR4, Figure 3.8, p. 250. These appear to be the same data as used by Spencer in his Figure 2. So these are samples of T – T0, not of dT/dt.

[Next the CO2 yearly emissions do indeed appear to be a ΔCO2/year, a coarse approximation to the dCO2/dt. According to the equation in Spencer's Figure 3, the slope is 4.7051, which he later cites as 4,700 MmtC/yr. (M is a better symbol for Mega reserving m for milli.) The line, however, inexplicably rises from 1542 to about 4200 in 48 years, a rate of 55 (ordinate units) per year. The ordinate in Figure 3 is unlabeled, but appears to be similar to Figure 4, where it is Anomalies in Mauna Loa-Derived Yearly Emissions (MmtC/yr). If the ordinates are the same, the best fit in Figure 3 is in units of MmtC/yr2.

[In Figure 4, Spencer provides a best fit equation with a slope of 5102.8, presumably MmtC/yr divided by ºC/yr, or MmtC/ºC. Accordingly, two paragraphs above Figure 4, he claims the regression line has a slope of 5,100 MmtC/ºC. However, he writes, "A comparison of the two slope relationships (5100 mmtC/yr for interannual variability, versus 4,700 mmtC/yr for the trends) shows, at least empirically, that whatever mechanism is causing El Nino and La Nina to modulate CO2 concentrations in the atmosphere is more than strong enough to explain the long-term increase in CO2 concentration at Mauna Loa." To make his comparison, he has transmuted MmtC/ºC into MmtC/yr. Spencer's case is not made.

[Not just Spencer's execution, but his method is faulty. A sure test of faulty analysis is the statistical analysis of differences, as in period-to-period anomalies (not offset anomalies), or of slopes, as in Spencer's attempt to compare dCO2/dt with dT/dt. This is routinely done in papers on economics. It is a common fault in the hard sciences where an analyst attempts to model empirical probability or power spectral densities instead of probability distributions and power spectra, respectively. Data representing densities are not guaranteed to converge to the underlying density, while the cumulative data will converge to the distribution function. Another way of looking at this technical problem is that by taking differences, one is "differentiating noise", where the noise is the inevitable variability in measurements. The result is a magnification of noise, a loss of signal to noise ratio, and a decorrelation of the signals.

[Spencer should have compared CO2 concentration with ºC in a scatter plot much like his Figure 4. He might have examined the results both detrended and not detrended. Had he run a cross-correlation to answer his lead/lag question, detrending would have been obligatory.

[Another red flag in Spencer's analysis is his acceptance of data such as the MLO CO2 record of Figure 1 and the Human Emissions curve in Figure 3 as if they were independent, unprocessed records. The MLO CO2 record is simply too pat, too smooth, and in other reports, too contiguous with other records. It has been smoothed, and possibly adjusted to remove disturbances like El Niño and volcanic events. MLO raw data, or a reasonably reduced data set, seem not to have been made available to the public in any useable format. Secondly, the Human Emissions curve may have been derived from the MLO data, using a technique IPCC calls "prior knowledge". Without confirming how the Human Emissions data were obtained, the only valid conclusion that can be drawn from a strong correlation between it and the MLO CO2 curve is that one data set was derived from the other.

[Conclusion on Spencer. Spencer is correct that the MLO CO2 concentration is not caused by ACO2 emissions, but his conclusion is not supported by his analysis.

[D'Aleo. On D'Aleo, Watts Up With That?, "Warming Trend: PDO And Solar Correlate Better Than CO2".

[For an analysis with rigor of these effects, see the RSJ entry, Solar Wind, El Niño/Southern Oscillation, & Global Temperature: Events & Correlations that shows the solar wind has twice the global warming effect of El Niño, and that IPCC and its consensus of 4000 scientists mistakenly attribute solar wind warming to ACO2. The Southern Oscillation Index (SOI) is a continuous measure for the arbitrary El Niño event determination, and a less filtered, and hence superior, parameter to the Pacific Decadal Oscillation (PDO).

[The data shown from D'Aleo is highly problematic. First, to the extent that the author or critic shows correlation by coplotting data records, the method is subjective and quite faulty. The calculation of the corresponding correlation parameter called R-squared is curative, but a superior method is to construct a scatter plot of each pair of variables and compute and plot the pair of correlation lines, as shown in the Solar Wind paper.

[A larger problem and a red flag is the high values obtained for R-squared, i.e., 0.44, 0.57, 0.83. Such levels are rare in basic science, especially in climate measurements where so many variables contribute to the parameters. High values can be obtained by analysis of heavily filtered data. Filtering alone produces correlations where none exist in the raw data. Another way that high values arise accidentally is when one data set is derived from another, the process IPCC calls "prior knowledge".

[Sometimes correlation exists because of analytical fraud. An example is IPCC's plotting of the delta 13C ratio by adjusting its offset and scale factor to parallel global CO2 emissions, and then to conclude that a "strong linkage" exists. AR 4, Figure 2.3(b), p. 138; AR4, ¶2.3.1 Atmospheric Carbon Dioxide, p. 139. Another example is IPCC's use of "flux adjustments".

[Another example is here in the first D'Aleo graph showing CO2 from ice cores blending smoothly into the CO2 Mauna Loa record. This is not consistent with physics for the concentration of CO2 in the atmosphere, and is more likely due to what IPCC calls "calibration procedures within and between monitoring networks". For a full discussion, see RSJ response of 10/13/07 in the paper Gavin Schmidt's Response to the Acquittal of CO2 Should Sound the Death Knell for AGW. The blending is not consistent with physics because ice core data are collected inside a polar CO2 sink while MLO CO2 data are collected from the plume of CO2 outgassing in the Eastern Equatorial Pacific. Keeling himself warned against comparing regional data, or data collected near sinks or sources. id.

[Conclusion on D'Aleo. D'Aleo's conclusions that PDO and TSI correlate better than does CO2 with global temperature is not supported by the analysis summarized in Watts Up With That. A strong correlation of CO2 to global surface temperature is highly probable, especially when analyzed in conjunction with wind conditions.

[0 for 3. No paper of this trio is helpful to the cause in its present form. Each is terribly vulnerable to criticism. Far from being unpersuasive in a free and open debate with the IPCC and its supporters on the AGW model, each analysis weakens what can readily be shown with sound science: the IPCC model is incompetent and a fraud.]

[Fitzpatrick. On Watts Up With That?, "A look at human CO2 emissions – vs- ocean absorption".

[On 5/22/09 in another post on WUWT, Steve Fitzpatrick responds to the Spencer article. In this response, Fitzpatrick says,

An increase in average ocean surface temperature will cause more CO2 to be emitted from surface water, but this effect is limited to a very small volume fraction of the ocean.


… how quickly surface water is replaced by deeper water, and it should be a relatively small number, since ocean circulation and mixing are slow.

[Fitzpatrick omitted the THC. IPCC estimates the MOC (formerly THC) volume rate at 31 Sverdrup (Sv), where 1 Sv = 106m2 s-1. AR4, Box 5.1, p. 397. Another source puts it at 20 Sv. http://hope.simons-rock.edu/~geshel/geosci245/thermohal/thermohaline.html. For the surface of the ocean at 3.61 km2, this flow is massive, equivalent to replacing the surface layer to a depth of 1.75 to 2.7 m every year. It is equal to 6.31 to 9.78 Pg/yr of seawater. Using the solubility range of 3.346 gCO2/kgH2O at the poles to 1.327 gCO2/kgH2O in the tropics, a loss of 2.0 kgCO2/kgH2O, if applied to the full circulation, means the THC could outgas between 344 and 533 PgC/yr.

[The uptake of CO2 in the RSJ model for the THC is at a constant temperature of about 0ºC as long as Earth has ice caps. If the global surface temperature changes, it would affect only the outgassing. A 1ºC change at 28ºC changes the solubility about 0.037 gCO2/kgH2O. This translates to a range of 0.64 to 0.99 PgC/y/ºC, or about 0.43 to 0.59 ppm/yr/ºC using IPCC's implied conversion formula, above. The range in Estimated Emissions in Fitzpatrick's Annual Increase chart is 1.25 to 4.3 ppm from about 1957 to 2008, a rate of 0.06 ppm/yr. This is equivalent to an average global temperature change over the period of about 0.10 to 0.14 ºC.

[Pending confirmation of these calculations, consideration of the THC appears to upset Fitzpatrick's model and conclusions.]

paul wrote wrote:

Dr Glassman

Some measurements can be seen here, for example - the monthly CO2 data and the ocean temperatures.



It seems the CO2 is highest in April/May, despite temperatures being highest in August/September. I understand that this annual cycle is consistent. How does your theory fit in with the seasonal variation in the Mauna Loa CO2 data?

[RSJ: To say I have a model is a bit of a stretch. What I have so far is too incomplete to rank even as a conjecture. However, pieces of a model are emerging as I discover more holes in IPCC's story. Proving the AGW model invalid is sufficient, so I leave it to legitimate climatologists to develop a valid climate model. Let's extinguish the panic; the science can wait. Nevertheless, some features for a realistic simulation can be cited with confidence.

[As shown by the Vostok record, Earth vacillates between a warm state and a cold state. The causes probably are changes in solar radiation amplified by the Milankovitch cycles, what I will call the net solar radiation, in a combination yet to be characterized.

[The climate is quick to cool, and slow to warm. This observation suggests differing mechanisms. And in combination with other considerations, the mechanisms are likely linked to the processes that stabilize Earth's two states: high surface albedo in the cold state, and high cloud albedo in the warm state. In the cold state, insolation and net radiation are the same, and relatively ineffective because of the high surface albedo. Clouds are gone and the greenhouse effect is nil. When the net radiation rises, the climate warms slowly, paced by the retreat of the ice toward the poles. As the climate warms, humidity rises, the greenhouse effect develops, and clouds begin to form. Because of cloud growth, insolation rises less than the net solar radiation. It rises continuously to a maximum in fully developed warm state when cloud albedo forms a powerful negative feedback that stabilizes the surface temperature. In cooling, net radiation decreases, humidity decreases, and clouds decrease. However, in the cooling direction, the clouds and hence their albedo instantaneously retreat, while in the warming direction, the surface albedo lags.

[So the greenhouse effect is important, but never controlling. CO2 is never significant to warming, either in the warm, moist atmosphere nor in the cold, dry atmosphere. Compared to water vapor, CO2 is insignificant to the greenhouse effect in the warm climate, and in the cold climate, while CO2 dominates the greenhouse effect compared to water vapor, the greenhouse effect itself is impotent because absorbed incoming SWR and outgoing LWR are weak.

[In today's warm state, CO2 circulates dominantly between the atmosphere and the land and ocean reservoirs, making man's emissions from fossil fuels all but negligible. IPCC shows 360 GtC, about half the atmosphere reservoir of 730 GtC, taken up by leaf water and the oceans every year. IPCC does not calculate with the leaf water, and instead uses Gross Primary Production of 120 GtC/yr. In this latter case, 210 GtC per year, or a little over a quarter of the atmosphere reservoir is circulated annually. This is a range of about 30 to 50 times man's fossil fuel emissions. In the geological record, IPCC shows that by proxy estimators, atmospheric CO2 levels were usually higher than it is at present, and several times ranged as high as 20 times the current level. The reasons are unknown.

[In the more recent record from ice cores, CO2 levels rise in proportion to surface temperature according to the laws of solubility, of which a large part exhibits a lag of about one millennia. The surface temperature estimate is based on oxygen isotopic ratios, so considering the low solubility of oxygen in water, the temperature is likely global. However, CO2 is highly soluble in water, so the ice core data, having been collected internal to a CO2 sink at ice water temperatures, should be at a minimum globally. Conversely, Mauna Loa sits in the plume of the Eastern Equatorial Pacific focus of outgassing from the ocean. MLO provides data from the most intense, large CO2 source on Earth, and the record should be little affected by terrestrial processes.

[Scripps collects the MLO data from some place on a ridge of air maximally rich in CO2. Regardless of whether MLO sits on the peak or the side of the ridge, its position shifts with the prevailing winds on Hawaii. While those winds are well-known to contain a seasonal variation in strength, what is needed is the seasonal pattern of the wind vector, or better, CO2 data collected with coincidental wind vector data. The wind vector needs to be resolved to extract the component perpendicular to the crown of the ridge. With these data, a model could be developed for the invisible CO2 plume, its position with respect to MLO, and its seasonal effect on MLO CO2 concentration, a prediction to be compared with the measured seasonal effects.]

Ken Griffith wrote wrote:


CO2 solubility in seawater falls as water temperature rises.


Given average ocean temp of 3.9C, what change in average ocean temperature (dT) is required to off-gas enough CO2 to raise atmospheric concentration by 100 ppm?

[RSJ: Answer: 1ºC.

[My answer is empirical. I compared the latest global sea surface temperature record from


[to the latest MLO de-trended CO2 record from

ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_mlo.txt .

[The best fit straight line of CO2 as a function of temperature has a slope of 108 ppm/ºC (r2 = 0.73, rms error over the 50 years of just 11 ppm.) This does not require knowledge of the average ocean temperature. I discounted the 108 ppm/ºC figure somewhat as a place keeper for the anthropogenic CO2 added during the period.

[The average ocean temperature would be needed if you wanted to test the solubility model. You might want to repeat the exercise, optimally placing the solubility curve through the data instead of a straight line. See The Acquittal of CO2, below. You may find that to answer the question analytically that you need to construct a mass flow model, maybe a climate model, and add a few more boundary conditions.

[Your opening assumption is Henry's Law, and requires no justification.

[Good question. IPCC should answer it. And the answer is rather satisfying, especially since we outside IPCC know CO2 is not causing global warming. What is also satisfying is to plot the MLO CO2 concentration on top of the history of sea surface temperature. Remember, this kind of plotting exercise proves nothing beyond observing that nothing appeared in either record to invalidate the hypothesis that the rise in sea surface temperature caused the rise in CO2 concentration at MLO.]

jt wrote wrote:


Will you comment upon this study which claims that the rate of ocean uptake of A-CO2 is/may be declining?


[RSJ: I'd be happy to comply, but the study is not available to the public. This is science for sale, and the price is $32. If you have a copy of the article, you may post it freely for critiquing without violating copyright laws.

[I am quite reluctant to comment on a press release, but am more likely to rely on quotations or images from the article. I will comment occasionally on abstracts where, as here, the article is not freely available. Here's the abstract of your article:

[The release of fossil fuel CO2 to the atmosphere by human activity has been implicated as the predominant cause of recent global climate change. The ocean plays a crucial role in mitigating the effects of this perturbation to the climate system, sequestering 20 to 35 per cent of anthropogenic CO2 emissions. Although much progress has been made in recent years in understanding and quantifying this sink, considerable uncertainties remain as to the distribution of anthropogenic CO2 in the ocean, its rate of uptake over the industrial era, and the relative roles of the ocean and terrestrial biosphere in anthropogenic CO2 sequestration. Here we address these questions by presenting an observationally based reconstruction of the spatially resolved, time-dependent history of anthropogenic carbon in the ocean over the industrial era. Our approach is based on the recognition that the transport of tracers in the ocean can be described by a Green's function, which we estimate from tracer data using a maximum entropy deconvolution technique. Our results indicate that ocean uptake of anthropogenic CO2 has increased sharply since the 1950s, with a small decline in the rate of increase in the last few decades. We estimate the inventory and uptake rate of anthropogenic CO2 in 2008 at 140 ± 25 Pg C and 2.3 ± 0.6 Pg C yr-1, respectively. We find that the Southern Ocean is the primary conduit by which this CO2 enters the ocean (contributing over 40 per cent of the anthropogenic CO2 inventory in the ocean in 2008). Our results also suggest that the terrestrial biosphere was a source of CO2 until the 1940s, subsequently turning into a sink. Taken over the entire industrial period, and accounting for uncertainties, we estimate that the terrestrial biosphere has been anywhere from neutral to a net source of CO2, contributing up to half as much CO2 as has been taken up by the ocean over the same period. Footnotes omitted, Khatiwala, S., F. Pimeau, & T. Hall, "Reconstruction of the history of anthropogenic CO2 concentrations in the ocean", Nature, 462, pp. 346-349, 11/19/09

[The article amplifies the urgency claimed for political action to cut back CO2 emissions, and for that alone it is publishable. Otherwise and technically, it doesn't pass the sniff tests.

[At the outset, how did the authors measure anthropogenic CO2 and not the total circulation or accumulation of CO2? IPCC observes the increase in atmospheric CO2 and attributes it to man by a pair of signatures. TAR, Figure 2.3, p. 138. These are a fraud. It claims that the decline in CO2 in the atmosphere parallels the increase in atmospheric CO2, implying that the increase in CO2 is from burning carbon in the atmosphere. Secondly, it claims that the isotopic lightening of atmospheric CO2 parallels global emissions. Neither of these is a quantified conclusion, but instead is based on artful, subjective, and fraudulent graphing to make dissimilar traces appear parallel.

[One of the analyses needed in climate modeling is a mass flow calculation. IPCC claims to have performed such an analysis, but it is nowhere to be found. If I had a copy of the full article, I'd look for that calculation or how the authors' might have relied on one.

[Sequestering is the wrong word and should be avoided because of IPCC error. It implies some form of secure storage, in particular photosynthesis, a.k.a. CO2 fertilization, and the production of oceanic calcareous shells. IPCC claims that the surface ocean is in equilibrium, applies the chemical equations for equilibrium, and so concludes the ocean's uptake of CO2 is paced by the rate of sequestration. See AR4, Box 7.3, p. 529; AR4, ¶ "Overview of the Ocean Carbon Cycle", pp. 528 ff, esp. Figure 7.10 (the three pumps), p. 530. This model violates Henry's Law for solubility, and is clearly false in light of the thermodynamic definition of equilibrium, or any reasonable substitute definition, and on the slightest consideration of the multitude of processes in the surface layer. The surface layer should be modeled as a separate, dynamic reservoir for molecular CO2, a source for the ocean to satisfy Henry's Law with respect to the atmosphere, and for ions to satisfy the various oceanic processes.

[The conclusion that oceanic "uptake of anthropogenic CO2 has increased sharply since the 1950s, with a small decline in the rate of increase in the last few decades" conflicts with Henry's Law and the recognition of global warming, including in SST, over the first four decades or so of that period. As specified with respect to observational-based anthropogenic CO2 implies a significant difference in Henry's constant for nCO2 compared with ACO2. Hypothetically the difference should exist because dissolution is a mechanical process and would be dependent on molecular weight. However, the molecular weight difference, which is the only hypothesized difference between the species, is minute, and not likely observable among the interfering processes and in the noise of the measurements. It would give the ocean the novel ability to fractionate CO2. Besides, IPCC doesn't use Henry's Law at all (it attributes the phenomena to its peculiar model of the Revelle Factor), much less make measurements that could show tiny differences in Henry's constant.

[The uptake of CO2 is distributed over the entire ocean, but is highly focused in the Antarctic (part of the Southern Ocean) and in the Arctic waters. The distribution can be seen in the Takahashi diagrams. See for example AR4, Figure 7.8, p. 523. Note that the polar uptake cells have seven times the flow and the equatorial outgassing cells eight times the flow of the other cells. As the climate warms, so does the SST, and the outgassing increases while the uptake remains at 0ºC to 4ºC and relatively unaffected. Analysis of Takahashi diagrams shows a slow increase in uptake, corresponding to the surface layer poleward migration, and a sudden outgassing, principally in the Eastern Equatorial Pacific. These observations support the RSJ model in which the THC carries water from the poles to the EEP. However, Takahashi needs to be recalibrated so that his total flows in and out of the ocean jibe with IPCC's estimates of 92.2 and 90.6 GTC/yr, respectively. See AR4, Figure 7.3, p. 515. Takahashi, like Khatiwala et al., pretends somehow to have measured ACO2, not total CO2, and so calibrates the results to fit a preconceived notion.

[The Southern Ocean is not a primary collector of CO2. The currents that converge at the poles do the collecting. The SO is instead a primary sink, probably accounting for over half the headwaters of the total THC. The presence of this sink is one of a couple of reasons that the ice core CO2 concentrations, taken internal to such sinks, are not directly comparable to the MLO data, located in a branch of the outgassing plume from the EEP.]

Bart wrote wrote:


I can't take all of this in with a single read, but you have hit on a number of themes, though in much greater detail, which this fellow rocket scientist has been mulling and fretting over for some time. I can't count the number of times some simpleton has stated to me that A) the overwhelming natural fluxes don't matter because they cancel out and B) that the growth in CO2 is therefore observably half of what we have put in.

They have no inkling that the two are inextricably intertwined, that (A) forces limits on how (B) might come about. To get (B) given (A), you have to boost the marginal sensitivity so high for the additional anthropogenic forcing that increasingly erratic measurements would have to be immediately evident in the CO2 record. So far as I know, they aren't. I feel it likely that, if they were, the warmists would make sure we knew it.

[RSJ: Two scientific errors in IPCC's modeling, and so the AGW story, immediately come to mind as you state your problem, and more may be involved.

[The solubility of CO2 is proportional to its partial pressure in the atmosphere and the temperature of the sea water. The constant of proportionality is an empirical number. (A second order effect is salinity, and we might postulate third order effects like pH. For more discussion, see the main article, above.) Henry's Law applies at steady state, but for climate purposes we can safely assume steady state is achieved as quickly as gas escapes from a carbonated drink, which is to say, the dynamic effect is nil for our purposes. (Another high order effect would be the time to achieve steady state, and for that the isotopic weight should have an effect, but may be unmeasurable.) The important consideration here is that as far as the matter is known today, the solubility of CO2 depends on the total CO2 partial pressure, and not on the anthropogenic or natural gas considered alone. The two species of CO2 differ only as to their slight differences in isotopic ratios, and in fact the two are mixed in the atmosphere to create yet another species under the criteria assumed for species.

[In a mass flow model, the atmosphere and the surface layer are the usual nodes. The rate of transfer of CO2 is the flow variable, and the potential variable is the partial pressure. The partial pressure for the water is the partial pressure of the atmosphere at the time of dissolution. The rate of absorption is directly proportional to the atmospheric partial pressure, so the rate of absorption of ACO2 and nCO2 are linear with pressure and the model makes them additive. However, the rate of outgassing is inversely proportional to the atmospheric partial pressure. This is nonlinear, so the rate of outgassing of the two are not additive. The GCM model which assumes a natural background flux to which is added an anthropogenic flux is not correct. This is a root problem with the radiative forcing paradigm. The carbon cycle cannot be correctly partitioned with an additive part produced only by the anthropogenic CO2.

[The AGW model needs a mass flow analysis. IPCC says that it did one and relied on it, but it is nowhere to be found. The answer to your Part A is that the natural fluxes do not cancel out, but affect the manmade fluxes.

[For Part B, the growth rate of CO2 in the atmosphere is about half the rate of ACO2 emission. This does not mean that half those emissions remain in the atmosphere. IPCC claims to have discovered an isotopic signature to the atmosphere and a rate of decline in oxygen that accounts for the rate of burning of fossil fuel according to the stoichiometric ratio. Those claims are unsupported except by improper graphical tricks that make false signatures appear. Perhaps even more important is that IPCC makes the fraction of nCO2 absorbed each year different than that for ACO2. Henry's constant for CO2 is the same for both. IPCC would repeal what is known about solubility in order to have CO2 accumulate in the atmosphere and to satisfy its AGW model.

[By "marginal sensitivity", were you referring to solubility? Regardless, Part B is not true. An increase in atmospheric CO2 is required because the climate is warming. IPCC does not calculate that amount, so falsely attributes the growth in CO2 concentration from warming to be a residue from the emissions.

[Fossil fuel burning will increase the CO2 concentration in the ocean and in the atmosphere. This often makes discussion of the effects difficult. The increase is in the ratio of emissions to the concentration in the two reservoirs. It is about six parts in 730 or more in the atmosphere, much less in the ocean, and trivial in both cases. This simple physical relationship is analogous to the problem that CO2 does indeed cause warming. A little extra greenhouse gas always causes some warming. However the warming is regulated naturally, and from whatever cause. It is regulated by cloud albedo, the strongest negative feedback in the climate system, and not modeled by IPCC. The GCMs have a static cloud albedo, and because it is not dynamic, it exerts no feedback.

[Of course CO2 emissions accumulate in the atmosphere, and of course CO2 causes warming! It's just that neither effect is large enough to be measured, and meanwhile large scale, overwhelming warming and cooling effects are always in progress. The CO2 signals are well buried in the noise and competing signals.]

Charles Standley wrote wrote:


A suggested correction...

In your above text, you reference ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/deutnat.txt for CO2. I believe the correct file is ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/vostok/co2nat.txt

[RSJ: You are quite right. The paper has been revised. Thanks.]

Bart wrote wrote:


"However, the pdf paper incorrectly sets r equal to 8/220, the total emissions each by man and nature instead of the net emissions"

The net emissions are (Co-C)/tau + adot. That is what drives Cdot.

[RSJ: See next post by Bart.]

Bart wrote wrote:


Sorry, a little error - for the K0 term.


The equation is

Ċ = (C0-C)/τ + (1+K0)*ȧ

The net emissions are (C0-C)/τ + (1+K0)*ȧ, i.e., what drives Cdot. C0/τ + (1+K0)*ȧ is the total emissions from natural and anthropogenic sources. -C/τ is the total removed from the atmosphere.

[RSJ: Your paper provides the following: C0 = 280 ppmv, C0/τ = 220 GtC/yr, and C = 380 ppmv. So we can compute -C/τ = 299 Gt/yr. You have a net uptake of 220 -299 = 79 GtC/yr. In the discussion on IPCC AR4, Figure 7.3, in response to your 12/7/09 post, above, IPCC instead has a net outgas of 3.4 GtC/yr. This is the accumulation of CO2 in the atmosphere that is key to IPCC's conjecture that man is causing the observed warming. You are off in both sign and magnitude because you don't have enough variables in your equation to specify the problem without initializing with net numbers.

[My recommendation is that you construct a model that represents the fluxes between the reservoirs and follows the principles of your equation, eq. 5, above. Instead of starting with mathematical formulations, begin with a schematic. You need to account for all the initial conditions given by IPCC. This task may not be fruitful because, as discussed above, IPCC's Figure 7.3 doesn't make sense.]

Bart wrote wrote:


"IPCC gives no reason for Henry's Constant to be different for the two species of CO2."

They don't give it, but I think it has to do with this wrote:

Bolin & Eriksson's "buffer" factor would give about 10 times higher CO2 concentration in air vs. sea water at about 0.0003 atmospheres CO2 partial pressure, increasing dramatically to an air/water CO2 partition coefficient of about 50:1 at a CO2 partial pressure of about 0.003 atmospheres (10 times the assumed pre-industrial level; Bacastow & Keeling, 1973; see Section 7 below for more on the "buffer" factor).

[RSJ: IPCC mentions Bacastow & Keeling 1981 in a different context, and never relied on B&K 1973 in its Third or Fourth Assessment Reports. It refers to Bolin & Eriksson only once in its those Reports. It says,

[A more sluggish ocean circulation and increased density stratification, both expected in a warmer climate, would slow down the vertical transport of carbon, alkalinity and nutrients, and the replenishment of the ocean surface with water that has not yet been in contact with anthropogenic CO2. This narrowing of the 'bottleneck' for anthropogenic CO2 invasion into the ocean would provide a significant positive feedback to atmospheric greenhouse gas concentrations (Bolin and Eriksson, 1959; see also the carbon cycle climate model simulations by Cox et al., 2000; Friedlingstein et al., 2001, 2006). As long as the vertical transfer rates for marine biogenic particles remain unchanged, in a more sluggish ocean the biological carbon pump will be more efficient (Boyle, 1988; Heinze et al., 1991), thus inducing a negative feedback, which is expected to be smaller than the physical transport feedback (Broecker, 1991; Maier-Reimer et al., 1996; Plattner et al., 2001; see Figure 7.10). AR4, ¶ Carbon Cycle Feedbacks to Changes in Physical Forcing, p. 532.

[A buffer can have two meanings, to hold as in an accumulator or reservoir, and to bar or act as a barrier. A bottleneck is the latter. As discussed in Part 5 of the main article, above, IPCC called this buffer the Revelle factor. IPCC justified the factor based on equilibrium conditions in the surface layer, much as Revelle and Suess had done in 1957. The surface layer is plainly not in equilibrium. Secondly, as stated above, IPCC applies the bottleneck/buffer to ACO2, not to natural CO2. The implication that the two species of gas, differing only slightly in isotopic mix, have different coefficients of solubility is novel physics.

[A superior model is that the surface layer is a buffer in the sense of an accumulator of molecular CO2, distinctly not in thermodynamic equilibrium, and where the equilibrium chemistry does not apply. In this model, solubility can proceed apace, quite independent of deeper ocean chemistry or mixing.

[When IPCC tried to evaluate its Revelle factor, it turned out to have the characteristics of solubility. It suppressed the results in its reports. See discussion above.

[Remember that IPCC claims to have demonstrated that man has caused the recent global warming as shown in its Reports. To show that its conclusion is false we need to demonstrate the errors in its arguments. We have no choice. Trying to prove the truth or falsity of the conjecture by relying on different studies or data presents the difficult and unproductive problem of weighing contradictory reports to IPCC's. IPCC and its believers have suppressed opposing views, fudged the data, relied on fudged graphics for its results, made elementary scientific errors, and breached its ethics. While these errors would result in scientific disgrace, they are not quite decisive enough for AGW in the political arena.

[The best argument today is to concede for the sake of argument that IPCC's model as represented in its GCMs and AOGCMs is satisfactory, and to waive its abuses of science, but to show that this model omits the largest and dominating negative feedback in climate, cloud albedo. To be more specific, it omits cloud albedo in Earth's warm state, and surface albedo in its cold state. The climate is conditionally stable in these two states, and not unstable as IPCC models it. All the pieces of the albedo are in place and admitted by IPCC. This effect provides an argument on which reasonable people could quickly agree to defeat AGW.]

Bart wrote wrote:


By the way, what this "buffer factor" means is that, to reproduce their results, I can forget about the K0 factor and just focus on

Ċ = (Co-C)/τ + ȧ

I simply have to assume τ is not a constant, but is, in fact, a dramatically increasing function of C. In essence, the feedback bandwidth must decrease dramatically with increasing C until, in the limit, the system becomes a pure integrator.

I do not think this is reasonable, either.

[RSJ: Too much drama! I thought that the purpose of your derivation was precisely to compute the ACO2 gain factor, K0, but now you suggest dropping it. And by making τ some unknown function of C you have suggested an unlimited complexity. I agree with your last remark, though!]

Bart wrote wrote:


"You have a net uptake of 220 -299 = 79 GtC/yr..."

From natural, unstimulated sources alone.

"IPCC instead has a net outgas of 3.4 GtC/yr..."

So, we must have (1+K0)*ȧ = 79+3.4, or K0 = (79+3.4)/8-1 = 9.3. Had I used the nominal value of 3.6% anthropogenic forcing in my little note, I would have gotten K0 = (380/280-1.036)/0.036 = 9.9. Considering all the rounding we have done along the way, that much agreement is, frankly, surprising, but otherwise not so, because I calculated the 3.6% figure from that same figure. It all fits. As I stated, the K0 term would essentially be a stimulated emissions term, and a factor of ~10 for it would be absurd, in my view, hence the hypothesis of anthropogenic responsibility for the CO2 rise would be dubious at best.

[RSJ: You have demonstrated to yourself the nonsense in IPCC's model. I say to yourself because you need to show where your equation (5, above) is valid. Is it not based on an expansion around a point of equilibrium (better a point of stability) in the climate? At one point in the derivation you used IPCC's results that the other forcings (F) were negligible, but we know that to be false. What is negligible is man's emissions, and in fact, changes in the greenhouse effect are trivial in a properly closed model.

[Your equation also would need validating, should the AGW believers step up to any public challenge, because they already assert that the natural climate is in balance (they call it equilibrium). They give the natural environment a net of 0 change in atmospheric CO2 at t = 0 in their models. Your formula gives it -79 GtC/yr.]

"I thought that the purpose of your derivation was precisely to compute the ACO2 gain factor, K0..."

My purpose was to confirm to myself that their claims were absurd based on actual real-word physical dynamics - I knew their public explanations were absurd pablum for the technically illiterate. I just discovered this buffer business the other day and haven't really had time to process it. Sorry to have used up your time before I was fully aware of what cockamamie justifications they were using. I'm fairly sure that, if I go this route, I will find equally absurd requirements for the change in the time constant as for the conjectured stimulated emissions parameter K0. In my reading of what literature I have been able to dig up, it frankly appears they have completely uncoupled the dynamics between natural and anthropogenic CO2 and just chosen whichever parameters for each term they like, whether they are continuous and consistent with one another or not. I think that is what you are getting at in the discussion of Henry's law.

[RSJ: Pablum? You're too kind. They're dishing out poison.

[IPCC's GCMs are not dynamic models, and it does not pretend otherwise. The models compute successive points of "equilibrium" in long and costly computer time. Before these models could become dynamic they would need to have the heat capacity (called heat inertia in climatology jargon) for each node, an unused parameter in the radiative forcing paradigm. The models would also need to be three dimensional instead of vertical so that they could handle the dynamic transport of greenhouse gas across the moving surface, and the vertical transport across the dynamic atmosphere-ocean boundary layer, respecting Henry's Law.

[The idea that these models are at a state of development to guide public policy is, as the lawyers like to say, an outrage.]


I agree. But, it does rankle when people who aren't even technically oriented smugly spout this nonsense which, to borrow a phrase, is not even wrong, as though it were unassailable.

[RSJ: IPCC now uses the discoveries of collusion to adjust the data to fit its model and to suppress dissent as a smoke screen to hide the fact that man is not causing whatever warming might actually exist. It is using the argument that those revelations do not change the indisputable fact that ACO2 is causing global warming. This is a logical fallacy, perhaps one of the forms dealing with false hypotheses. It implies that because the fraud and deceit revealed do not deal with the source of the now alleged warming (previously we could concede the warming), then the hypothesis that it is manmade must be valid.

[If Climategate simply destroyed the AGW notion, it would be deservedly to the economic good of the world. If in the process it put AGW and its leaders on trial, it could help rehabilitate science in the public eye.]

Bart wrote wrote:


Jeff, on what I said from above:


I didn't think of it at the time, but such a dynamic would produce positive feedback, and CO2 would have run out to its upper limit long ago. So, in the end, I think, FWIW, that the CO2 models relied on to attribute the current rise to humans are bunk.

[RSJ: If

[Ċ = (Co-C)/τ + ȧ

[and τ is a significant function of C, then the equation conveys nothing. It suggests that the rate of change of C is proportional to C, but then negates it. Every equation could be written in this form where the apparent constants are functions of the dependent or independent variables.

[Re the bunk: Most infamously, IPCC accepted Mann's Hockey Stick graph to demonstrate an unprecedented temperature rise since the industrial revolution. TAR, Summary for Policymakers, Figure 1(b), p. 3, also Figure 2.20, p. 134. In this reconstruction, the past record was the result of Mann heavily smoothing hand selected data to obscure real variability (the Hockey Stick handle), then, with no justification grafting the present instrument record smoothly onto the end (the Hockey Stick blade). IPCC also manufactured hockey stick graphs to show CO2, CH4, and N2O, along with temperature, were also unprecedented in the same time frame. See, for example, AR4, FAQ 2.1, Figure 1, p. 135. When McIntyre and McKitrick embarrassed IPCC by exposing the fraud in the Hockey Stick, IPCC responded by retaining Mann's reduction now obscured by a dozen other reductions, mean-shifted and variance-scaled to muddy the handle, but each blended with the unprecedented current thermometer record to match in the blade.

[Underlying this mess are two logical fallacies. The coincidences between T, CO2, CH4, and N2O would be correlation if they weren't manufactured, and even then would not be cause and effect. Correlation tells scientists where a promising cause and effect model might lie. In fact, the ice core record shows T and CO2 correlated alright, but also that T precedes CO2 and that the CO2 follows Henry's Law for its solubility in water. CO2 appears to come from a warming ocean rather causing any measurable warming.

[Second is the fallacy of excluded hypotheses. Unprecedented does not show a relationship unless every other hypothesis can be shown invalid. IPCC cannot account for the climate in the paleo or geological record. The causes were natural because man is properly eliminated from that side of the equation. That historical climate was coherent in time and magnitude with today's climate, but IPCC has no way to rule out the unknown natural causes today. The fact that natural causes for today's climate are unknown is no evidence that today's climate is manmade.

[IPCC linearly sums non-linear processes, redefines feedback and albedo to ignore natural feedbacks (especially with respect to CO2 and cloud albedo), and assumes equilibrium that does not exist in nature. IPCC disregards, or worse discards, data that confound its model (e.g., CRU discarded data; IPCC disregarded on-going, natural temperature and CO2 increases, and disregards disequilibrium). IPCC practices calibrating dissimilar records to look alike, low pass filtering records to look alike, and applying shifting and scaling in graphs to make records look alike. From this sophistry of things that look alike, it proclaims that CO2 is long lasting in the atmosphere, that it leaves a signature by which it is known to accumulate in the atmosphere, and therefore by coincidence and the elimination of other causes, that CO2 must be the cause of current warming. And much more. This could not be climatology if climatology is science.

[IPCC practices Hockey Stick Science.]

sunsettommy wrote:


Hello Dr. Glassman,

Here is a link to a blog post titled "CO2: Effect of temperature on the equilibrium pressure of the CO2 over the seawater."

Here is the excerpt by Frank Lansner,

"In addition, Dr Antti Roine has collected relevant info and illustrations on the subject, and a long row of links to thermodynamic information and utilities."

The internal link leads to Dr. Roine's presentation.

I thought it was interesting.

[RSJ: The link got lost. I found this:


[which is a chart of the complement of the solubility chart for CO2 in water, showing a datum of 383 ppm at 15ºC for the current concentration, about 255 ppm above the concentration graph. The text is brief:

[With an average global sea water temperature [of] 15 degrees Celsius, it appears that normally the CO2-concentrations by far exceed equilibrium with the ocean water. Thus, CO2 is taken up by the ocean, and there is nothing at present to suggest that oceans are almost saturated with CO2. [In addition, Dr Antti Roine has collected relevant info and illustrations on the subject, and a long row of links to thermodynamic information and utilities.

[Watch the animated sea water temperature at


[Assuming the scale is in ºC, you'll see the temperature around Hawaii varying in the vicinity of about 22ºC to perhaps 30ºC. More importantly, Hawaii is in the plume of outgassing from the Eastern Equatorial Pacific, a region that shifts seasonally but with a near maximum temperature of 32ºC. As outline in the Journal, that gas rises with convective currents, splits north and south, enters the Hadley cells, and is carried down and into the westerlies, in a plume that wallows across Hawaii.

[(1) The datum above at 383 ppm is from MLO, wrongly attributed to be global. (2) That datum is much closer to the curve if the local temperature is used to go with the local concentration. (3) The problem is dynamic, not static as suggested by equilibrium analyses and data. (4) Dissolution is governed by Henry's Law, an equilibrium model, to be sure, but a theory with as yet no dynamic component. My conjecture, or working model, is that for dynamics on a scale between weather and climate, the air/sea CO2 flux is for all practical purposes instantaneous.

[One could envision the SST animation recalibrated using the (equilibrium) solubility curve to show an animated mean CO2 concentration over the ocean. Then imagine the ocean and wind currents superimposed to create an average river of CO2 emerging mostly, but not exclusively, in the EEP, and then working its way poleward to feed the THC headwaters, heavily laden not with salt but CO2, which then runs deep to reemerge a millennium later.]

LunchBox wrote wrote:


Dr. Glassman, thank you for your detailed, yet easy to read breakdown of CO2. I am a 7th grade science teacher with only a BS in Enviro-Sci (for now), yet I was able to understand most of what you put forth. I noticed you stated a number of times a logical point that I have never been able to get an AGW advocate to really even discuss: you basically state there is no way to discriminate CO2 and (a)CO2. I have said for years, even with my layman's brain, that CO2 molecules do not have barcodes in which to discover their origins. I'm glad to see some common sense being injected back into science.

[RSJ: Glad to be of assistance.

[The story is not quite as pat as your note suggests. Anthropogenic CO2 (ACO2) and natural CO2 (nCO2) do differ, but as far as is known or speculated, only in their isotopic ratio of 12CO2:13CO2:14CO2 (and the 14CO2 is too small to be measurable in the background of the natural world). Because ACO2 is primarily from burning fossil fuels, an ancient source, and because 13CO2 decays to 12CO2, ACO2 should be slightly richer in 12CO2 and therefore slightly lighter than nCO2. That much is reasonable. IPCC then claims that the buildup of atmospheric CO2 is lighter by the appropriate amount to establish a fingerprint of human activity. The claim is false, and the evidence is shameful graphical trickery. For a full discussion, see SGW in the Journal, introduced at Figure 27 and investigated in full following Figure 30.

[IPCC's model implies much more. It has nCO2 in balance every year, as much absorbed from the atmosphere as emitted in return from the ocean and leaf water. But for ACO2, it has 50% of the total emissions for the past 100 to 250 years retained in the atmosphere until the present. While IPCC never mentions Henry's Law of solubility and shows no mass balance calculation for either species of gas, its model implies that ACO2 and nCO2 have a large difference in their coefficient of solubility, known as Henry's Coefficient, a fact unknown in physics and a conjecture with no physical basis.

[Even if Henry's Coefficient for 12CO2 and 13CO2 were significantly different, the surface waters would prefer one isotope over the other out of the mix in the atmosphere, a process known generally as fractionation. It would not absorb the species of ACO2 and nCO2 intact, as if each mix had, as you say, a barcode. The waters would dissolve not dominantly nCO2 from the atmosphere, but the isotopic mix in the atmosphere. IPCC's model operates as if nCO2 and ACO2 not only had different Henry's Coefficients, but as if they were in separate channels or pipes, or had barcodes.

[So even if the only known difference between ACO2 and nCO2 were measurable, it would not account for IPCC's model. The isotopic difference, a postulated third order solubility effect after the first order effects of temperature and pressure and the second order effects of salinity and wind, cannot support IPCC's global climate models in which nCO2 is in balance while ACO2 accumulates in the atmosphere.

[You are quite right, too, that AGW advocates won't defend their model in public on the merits of that model. No public action should be taken based on that model until they come forward to defend every point raised.]

David P wrote wrote:


Dear Dr Glassman,

Your work was briefly mentioned in readers' comments on an article by Willis Eschenbach on CO2:


Steve Hempell wrote:


Care to comment on this?


Just like to have your opinion. I get lost in the mathematics.'

Eschenbach replied:

'Yes. Like many others, he is conflating e-folding time and residence time.'

[RSJ: Eschenbach did not read the paper he criticized, specifically the lead entry above. In his guest paper posted on the What's Up With That blog, he lays down six rules for discussion. He personally seems to violate them all. He shoots from the hip, and maliciously quotes out of context. The details are below.

[Relative to Eschenbach's instant point, my paper never mentioned e-folding time to have conflated it with anything. This was a bad guess on his part.]

In his article Eschenbach writes:

"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."

Starting from emitted anthropogenic C, and assuming an e-folding time of 31 years, Eschenbach calculates how much C should stay in the atmosphere, shows that this matches the measured increase in C, and concludes that "humans are the main cause of the increase in atmospheric CO2."

Perhaps you would like to comment on the weaknesses in this argument.



[RSJ: Eschenbach goes out on a limb to make a distinction without out a difference, then uses his precarious perch as the basis for an article and a position from which to criticize legitimate works.

[Physics is noted for its "thought experiments". It is the foundation for models of the real world built on reasoning. This method and its models are called à priori. When models are built on experiment or experience the method and models are known as à posteriori. Probability theory does the same thing with the thought experiment becoming the definition of events for the assignment of probabilities from reasoning, like the fair die or fair coin models, while other probability models are built on experiment where the set-up defines the events. These ideas are the core of the scientific method, where success is measured by the ability of the models to predict experiments.

[Eschenbach reports on two different concepts, one which he calls the "residence time of CO2", a phenomena calculated as "about 6–8 years", and the other identified as the "e-folding time of CO2", calculated "somewhere between 90 and 200 years". He says these are both supported by measurements, which would make them experimental (à posteriori). However, he provides neither the data nor a citation. Worse, he provides no physical description by which one might understand his distinction for either kind of scientific model, or to accept his differing numerical results as a possiblity.

[His short duration numbers ("6–8 years") correspond to about two to five time constants from IPCC's formula for the characteristic time for CO2 being dissolved out of the atmosphere. AR4, Annex I, Glossary, Lifetime, Turnover time, p. 948. His long numbers ("90 and 200 years") correspond to between one half and one of the longer time constants in IPCC's CO2 response formula. AR4, Table 2.14, p. 213, fn. a. This latter formula is rationale for IPCC's essential claim for AGW that CO2 is a long lasting greenhouse gas, persisting in the atmosphere from "decades to centuries". TAR, Technical Summary, p. 25.

[The Turnover time and CO2 response formulas create a conflict. Some disciples of IPCC have attempted to rectify this contradiction by creating the false dichotomy that Eschenbach naively adopts. He construes the residence (turnover) time formula to apply in some inexplicable way to a single molecule of CO2, while the "decades to centuries" absorption time is based on buffering against of CO2 absorption by the ocean followed by stages of absorption and sequestration at various rates and depths. See AR4, ¶7.3.4 Ocean Carbon Cycle Processes and Feedbacks to Climate, and especially Figures 7.10 - 7.12.

[Eschenbach's concepts of an "average molecule" and of a single molecule statistical measurements are twaddle. The statistical behavior of molecules is known only from analysis of large numbers of molecules. With a dice, we can toss a thousand at one time, or we can toss one a thousand times and get the same result. But with molecules, we have no way to experiment sequentially on one molecule some multiple of Avogadro's number of times. The turnover time formula is mundane physics, applicable to any number of a plurality of molecules. We extrapolate it down to one molecule, always wary that we might be creating another Big Bang.

[Contrary to IPCC's model and Revelle's conjecture, the ocean does not buffer against CO2, holding off absorption until the slow, ocean processes can make room. Absorption of CO2 into the surface ocean is for all practical purposes instantaneous. At times, it is as explosive as opening a well-shaken bottle of pop, and as slow as the time it takes to go stale, but either way, far less than ocean transport times, and much, much less than any climate scale. The time for the surface layer to saturate with CO2 is on the order of a year because the process is governed by Henry's Law of solubility, and the time is that required for the surface layer to cool by current transport from tropical temperatures to ice water at the poles. IPCC's formula with multiple time constants is unfeasible. It depends on four processes, each with its own reservoir. Those reservoirs do not exist.

[Relations Between Characteristic Times in Decay. The calculations next show the essential assumption that leads to exponential behavior, the relationships between the characteristic constants of the exponential, and that all but one, the half-life, are identical, including turnover time.

[IPCC provides the following definitions:


[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. AR4, Glossary, p. 948.

[These definitions are doubly hedged. The main bodies of IPCC Third and Fourth Assessment Reports don't use the term "Turnover time", leaving the reader free to expand on it. The Reports do use "Mean Residence Time", regardless that IPCC seems to restrict it to soil carbon biology. Secondly, IPCC's glossary entry under "response time" is supposed to provide the climate relevant definitions, but it does not.

[IPCC's definition here of "Adjustment time or response time (Ta)" is ambiguous, lacking, as it does, a formula. The text might be implying that either half-life or decay constant may be used for Ta. They are not the same.

[Following are calculations as a tutorial for Eschenbach's readers, starting from first principles, buffed-up for WUWT, but not postable there.

[Turnover time is



[Recognizing that under the ordinary physics of many growth, hydraulic, and gas problems, these terms are time dependent, so equation (10) is better written as



[and in these situations,



[making Turnover time a constant:



[That is, the rate at which a plant or population grows depends on the size of the plant or population, and the rate of discharge from a reservoir of a liquid through a leak or of a gas through dissolution depends on the declining mass remaining in the reservoir, the so-called head. This equation for S(t) is the key assumption in the model.

[As can be seen, S(t) is the rate of change of M(t), and is positive for growth and negative for population death and for pressure-dependent discharge. So we observe the following relationships and conventions in notations:



[with k positive, so



[from which we write,



[First semester integral calculus develops the solution:



[where c is a constant of integration, and ln(·) is the natural logarithm (the logarithm to the Naperian base, also known as the base e, and e is the Euler constant). Raising both sides of this equation as a power of e, and evaluating the constant in the expected sense, it converts to



[Thus the mass, M, is a decaying exponential in time. The term k is the "decay constant".

[These functions of arguments, logarithms (ln(·)) and power relations (like e to a power), are typical of functions in mathematics in that they require the argument to be a number, a dimensionless thing. So where time, for example, appears in an exponent, it must be made dimensionless by a multiplier, for example, it must have the dimension of time, and be in the same units as desired for time. So if the decay constant is in the units of reciprocal years, years-1, then the formula applies to time in years.

[The half life is the time required for the mass to decline by half. Thus,








[Thus the half life is a constant times the decay constant:



[Another popular term is the e-folding time, given by:






[The equation for M(t) enables calculation of the average lifetime of molecules. To do this, first convert M(t) to a probability density, pm, for the molecules in the mass. This is



[As a check, the normalization makes the probability distribution, Pm, run from 0 to 1 without decreasing:



[This is an equation for the probability that the lifetime of a molecule is at least as large as t. Probability is dimensionless, and thus the probability distribution is dimensionless. The probability density is the rate of change of probability with respect to a variable, so it has the dimensions and units of the reciprocal of the variable. Accordingly, pm, above has the same dimensions and units as k, the scale factor for time.

[With the probability density, the computation of the mean (which is the average) lifetime of a molecule is





[so the mean lifetime is 1/k, and is conventionally given the Greek symbol, τ, and often the mass is written



[So, as posted on WUWT, the e-folding time is 1/k. The average lifetime of a molecule in a slug is 1/k. The average lifetime of a hypothetical molecule in general is 1/k. The average lifetime of the slug itself is 1/k. The mean residence time is 1/k. And the Turnover time, T, is 1/k.

[IPCC's CO2 Response Function. IPCC's support equation for long-lived CO2 is contained in this footnote:

[The CO2 Response Function used in this report is based on the revised version of the Bern Carbon cycle model used in Chapter 10 of this report (Bern2.5CC; Joos et al. 2001) using a background CO2 concentration value of 378 ppm. The decay of a pulse of CO2 with time t is given by



[Where a0 = 0.217, a1 = 0.259, a2 = 0.338, a3 = 0.186, τ1 = 172.9 years, τ2 = 18.51 years, and τ3 = 1.186 years. AR4, Table 2.14, p. 213, fn. a.

[In more than a few places, IPCC seems to be discussing its CO2 Response Function, equation (30). See, for example, AR4, ¶, p. 404 ("Because of the limited rate of vertical transport …"); AR4, ¶, p. 405 ("The decrease in oceanic uptake … "); AR4, Ch. 7 Executive Summary, p. 501 ("Carbon dioxide cycles between the atmosphere … "); AR4, ¶, p. 515 ("The speed with which anthropogenic CO2 is taken up …"); AR4, ¶, p. 531 ("The ocean will become less alkaline … "); TAR, ¶, p. 199 ("Air-sea gas transfer allows older waters to … "). It relates the long transport times and long reaction times that occur in the ocean at the three layers of surface, intermediate and deep ocean. As much as any passage, the next links the ocean layers, their contribution to uptake time, and two of the three carbon pumps involved in the transport.

[Carbon dioxide is continuously exchanged between the atmosphere and the ocean. Carbon dioxide entering the surface ocean immediately reacts with water to form bicarbonate (HCO3–) and carbonate (CO32–) ions. Carbon dioxide, HCO3– and CO32– are collectively known as dissolved inorganic carbon (DIC). The residence time of CO2 (as DIC) in the surface ocean, relative to exchange with the atmosphere and physical exchange with the intermediate layers of the ocean below, is less than a decade. In winter, cold waters at high latitudes, heavy and enriched with CO2 (as DIC) because of their high solubility, sink from the surface layer to the depths of the ocean. This localised sinking, associated with the Meridional Overturning Circulation (MOC; Box 5.1) is termed the 'Solubility Pump'. Over time, it is roughly balanced by a distributed diffuse upward transport of DIC primarily into warm surface waters.

[Phytoplankton take up carbon through photosynthesis. Some of that sinks from the surface layer as dead organisms and particles (the 'biological pump'), or is transformed into dissolved organic carbon (DOC). Most of the carbon in sinking particles is respired (through the action of bacteria) in the surface and intermediate layers and is eventually recirculated to the surface as DIC. The remaining particle flux reaches abyssal depths and a small fraction reaches the deep ocean sediments, some of which is re-suspended and some of which is buried. Intermediate waters mix on a time scale of decades to centuries, while deep waters mix on millennial time scales. Several mixing times are required to bring the full buffering capacity of the ocean into effect (see Section 5.4 for long-term observations of the ocean carbon cycle and their consistency with ocean physics). Bold added, AR4, ¶ The Natural Carbon Cycle, p. 514.

[IPCC illustrates its carbon pump arrangement in the next figure.


Figure 7.10. Three main ocean carbon pumps govern the regulation of natural atmospheric CO2 changes by the ocean (Heinze et al., 1991): the Solubility Pump, the Organic Carbon Pump and the CaCO3 'counter pump'. The oceanic uptake of anthropogenic CO2 is dominated by inorganic carbon uptake at the ocean surface and physical transport of anthropogenic carbon from the surface to deeper layers. … Reprinted with permission, copyright 1991 American Geophysical Union. AR4, p. 530.


[This typewritten chart from the antiquities collection was not up to IPCC's fine graphical standards. Coupled with the poorly coordinated discussion, it gives the appearance of having been a last minute insertion. IPCC slicked it up for its online edition (http://www.ipcc.ch/publications_and_data/ar4/wg1/en/figure-7-10.html), while retaining the misprints and bogus physics. This says something about IPCC's priorities.

[This figure refers to the Solubility Pump as the "solution pump". It refers to the biological pumps to cover the Organic Carbon Pump plus the CaCO3 Counter Pump. IPCC's text of Chapter 7 does as well, but it also refers to the Organic Carbon Pump alone as the biological pump. The figure has the flux arrows on the CaCO3 Counter Pump reversed. These are trivial errors.

[The major error is that the two biological pumps have access to the atmosphere, where the CO2 is in gaseous form. Those pumps require CO2 to be ionized first. In the same chapter, IPCC says, "Carbon dioxide entering the surface ocean immediately reacts with water to form bicarbonate (HCO3-) and carbonate (CO32-) ions. Just on practical grounds, atmospheric CO2 would have to enter the surface layer first in all cases, where it might be ionized or conceivably reside partially in molecular form. For a realistic model, the biological pumps need ionized CO2, and should be connected to the surface layer.

[IPCC implies that three different time constants exist according to the three pumps, the Solubility Pump for the surface layer with τ3 = 1.186 years, the Organic Carbon Pump to reach the intermediate depths with τ2 = 18.51 years, and the CaCO3 Counter Pump to reach the deep ocean and sediment layers with τ1 = 172.9 years. Let us concede for the sake of argument that IPCC has support for these time constants. The problem with the CO2 Response Function is not quantitative, it is qualitative. It lies not in the optimization of the time constants, but in the model that provides separate reservoirs to feed the processes.

[Because the two biological pumps connect separately to the atmosphere, IPCC's carbon pumps figure begins to agree with its CO2 Response Function. All that is missing are four separate reservoirs at the top of diagram, one for each ai. No such partition exists in nature. Consequently, the fastest process, here the Solubility Pump, will drain the atmosphere of CO2 before the other biological pumps can produce much effect at all.

[A reasonable model that satisfies all the physics is to recognize that the surface layer is never in equilibrium, and that its stoichiometric equations are unbalanced. This surface layer permits Henry's Law to function with respect to the air-sea flux with a surplus of immediately available CO2, while it provides a reservoir of ions for the biological pumps.

[Conflation of an Artificial Division. To conflate means to merge two separate ideas into one. Eschenbach in his article and in his shot-from-the-hip, dismissive criticism of this paper accuses others of conflating what he has artificially divided.

[As IPCC wrongly divided the atmosphere into four reservoirs, the three above plus one inaccessible to the ocean, a0, Eschenbach relabeled the bulk model as the model for a single molecule, and then claimed that a true bulk model existed somewhere.

[He went wrong when he equated the average lifetime of a molecule with the lifetime of an "average molecule". A mental alarm should have gone off when he wrote about an average molecule. That makes no sense in general, unless he has a reference for his averaging. For example, he might talk about the average molecule in molecular weight of ACO2 or nCO2, which in theory are different. But the notion of a molecule of one of these species of CO2 makes no more sense than a molecule of air.

[Eschenbach goes wrong when he refers to snippets of other writings out of context, writings which he fails to cite. This is likely where he got the notion that the average lifetime of a molecule was different than the average lifetime of a slug of molecules. This appears to be an invention by IPCC disciples created to rehabilitate IPCC's model when faced with the recognition that its own lifetime formula did not support IPCC's "decades to centuries" persistence of CO2 in the atmosphere.

[Eschenbach proclaims IPCC's turnover time to be a model for the absorption a single molecule, but he provides no clue how that model might have come to pass, even if he were to treat CO2 as molecularly homogeneous. He provides neither a thought experiment for an à priori model, nor a practical experiment for an à posteriori model for his lifetime, resident time, or turnover time of a molecule.

[An à priori model might proceed by defining all possible trajectories of a single molecule throughout the atmosphere, and computing the probability that it collides with the ocean with an appropriate vector momentum to be absorbed. One approach might be to consider the atmosphere to be a reflecting enclosure, and then letting the enclosure expand without limits. If during the expansion, the probability converged, one difficulty might be overcome. How the probability of absorption might vary with temperature and grazing angle need to be quantified. And how one might represent and average the trajectories would have to be solved. If this analysis could produce a robust solution, it would make a great doctoral dissertation. For today, it is fanciful.

[One way to approach an experimental solution is to release a single molecule of CO2 into the atmosphere, and measure the time it remains there. Then the process would be repeated perhaps a thousand times so that the average lifetime could be calculated. How does one release a single molecule? How is it launched? How do we detect when that molecule reenters the ocean? How many detectors are required? How does one identify the specimen molecule? This is clearly impossible.

[An alternative is to release a large mass of molecules simultaneously and measure the size of the mass by some imaging technique until a trend and model can be developed from the measurements. At every instant we would know how many molecules were absorbed in the last little interval of time, and since they were all released together, we would know their age. How we might identify the released mass in the background of gases is a difficult problem, unless the released sample is extremely large. Regardless of the difficulty with this experiment, it is no more than an à posteriori approach to the conventional bulk model reflected by IPCC's turnover equation. And if that is to be the approach, one might as well use the à priori model.

[This little thought experiment shows the artificiality of Eschenbach's partitioning of the physics of decay.

[Eschenbach's conclusion that "humans are the main cause of the increase in atmospheric CO2" rests on his marginalization of the bulk absorption model to the molecular level, and his adoption of an arbitrary alternative bulk model. Humans are causing an increase in atmospheric CO2 in proportion to the sizes of the reservoirs, and relative to the emissions from all sources. It is on the order of a few percent, making his conclusion nonsense.

[Whatever contribution Eschenbach might make to the climate debate succumbs to his hip-shooting.]

[Reprint of the Response to Eschenbach on WUWT. For the record, here is my full response to Eschenbach on WUWT in four parts. It appears to be back referenced enough to provide a self-sufficient read.

Response to Eschenbach, Part 1 of 4, 6/12/10:

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,


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:


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.

Response to Eschenbach, Part 2 of 4, 6/16/10:

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.

Response to Eschenbach, Part 3 of 4, 6/19/10:

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.

Response to Eschenbach, Part 4 of 4, 6/21/10:

Willis Eschenbach on 6/19/10 at 1:40 pm said, shouting at the end,

>>Mean residence time is the time an average molecule stays in a reservoir. It is calculated as mass divided by throughput. IT DOES NOT HAVE A HALF-LIFE.  

He does not explain what he means by an "average molecule". The reader might think he's talking about the average in some sense of 12CO2, 13CO2, and 14CO2 molecules. What happened is that he conflated the average of time into the time of the average. These are interchangeable only in a special circumstance (linearity), which happens not to be applicable here. Then when he moved the average from time to the molecule, he was left with an expression of an average with respect to nothing real.

What he needed to do was average the life time of a bunch of molecules, then he would have had a target for the averaging. This might have kept him from conflating the average life of a molecule and the average lifetime in a slug of molecules.

When in his second sentence cited, Mr. Eschenbach says, "It is calculated …", the "it" pretty surely refers to "mean residence time". But that is not what "it" references in the third sentence. He might intend for the second "it" to refer to his "average molecule". This is the grammatical error of a faulty pronoun reference, and it contributes to his scientific and mathematical error.

In his opening piece on 6/7/10, Willis Eschenbach said,


We can excuse Mr. Eschenbach's use of the word equilibrium, even though IPCC seriously bungles the concept repeatedly, because Mr. E. says its "some kind of equilibrium". Out of kindness, we can read "some kind of equilibrium" to mean steady state. However, Mr. E. didn't even need the assumption to explain the decay of a pulse. He need not have introduced the state of the system. Later, Mr. E. says, "there is no half-life of a pulse when a system is at equilibrium." When a pulse is added to a system, it will, as described below, have a half life regardless of the state of the system. What counts is the mass of the pulse and its vanishing at a rate proportional to its remaining mass.

Mr. E. claims that "a certain percentage of the excess is removed each year." First, he doesn't mean the "excess". There is no excess in his problem, and he is left with a "certain percentage" of an uncertain thing. In many basic physical problems, the rate of increase or decrease is proportional to the instantaneous parameter value, whether mass, quantity, or size. Dissolution of a gas into a liquid and the emptying of a reservoir are relevant examples. This is known from physics and experiment, and is not a consequence of the problem as Mr. E. has described it. When the rate is proportional to the total remaining, the solution is unique and it is the exponential.

Mr. E. suggested I "Read the IPCC definition again." Here it is, again, for all to read:


IPCC goes on to equate T to mean residence time -- sometimes. Now IPCC never uses Turnover time in the main body of either its 3rd or 4th Assessment Report, so it doesn't matter to its writings that the definition is incomplete. In the case of CO2 being dissolved into water, the conventional model is that the rate of removal S is equal to a constant times the instantaneous mass remaining in the reservoir. So S = kM. This is the situation Mr. E. should have in mind, but can't express, when he says "a certain percentage … is removed". This has the effect of making T = 1/k.

Now S is the rate of change of the mass, M. So we use differential calculus to write, dM/dt = S = -kM, where k is positive and is called the decay constant. This equation is easily solved, but can't be written here within the html limits on this blog. We have the integral of dM/M dt equals the integral of k dt, and the solution is ln(M) = -kt + constant. Using the obvious value for the constant and obvious notation, the result is M(t)=M_0*exp(-kt).

We write that M(t_1/2) = M_0/2, so that exp(-kt_1/2) = ½, and thus t_1/2, the half-life, equals ln(2)/k. It doesn't matter how big the mass is, all the way down to one molecule.

Similarly, we write M(T_e folding) = M_0/e = M_0 exp(-kt_e folding). Thus e-folding = 1/k.

Now the remarkable thing is that the e folding time is equal to the mean residence time as defined by IPCC. This is true for one molecule or for Avogadro's number of molecules or for 800 PgC worth of CO2 in the atmosphere in some unknown isotopic mix. This is not an average molecule.

Just to be sure, we can compute the average lifetime of a molecule in the reservoir being dissolved. First we need the normalized number of molecules at time t, and that is kexp(-kt). So the average is the integral of kexp(-kt)t dt from 0 to ∞. It is demonstrated in first year calculus to be 1/k. It is the e folding time, the average life time of a molecule in a slug, the average life time of a hypothetical molecule in general, the average life time of the slug, the reciprocal of the decay constant (k), the mean residence time, and the (instantaneous) Turnover time, T, all at the same time.

I write a lot of words and provide a lot of references and cite a lot of sources because that's what it takes to untangle what you write.

Brian H wrote wrote:

1007191351 Why Me?

Let's hear it for 1/k! Can we call it "The Rule of (Dot) Sixty-Nine?" ;)

The more CO2 in contact with the ocean surface, the faster it dissolves.

[RSJ: Good idea, though at first I thought you were writing about k factorial.]

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