Carbon cycle modelling and
the residence time of natural and anthropogenic atmospheric CO2 - 2

Oeschger et al. (1985) postulated this "air younger than enclosing ice" thesis from an explanation that the upper 70 m of the ice sheets should be open to air circulation until the gas cavities were sealed. Jaworowski et al. (1992 b) rejected this postulate on the basis that air is constantly driven out of the snow, firn, and ice strata during the snow to ice compression and metamorphism, so that ice deeper than about 1,000 m will have lost all original air inclusions. Deep ice cores will fracture when they are taken to the surface, and ambient air will be trapped in new, secondary inclusions. Both argon-39 and krypton-85 isotopes show that large amounts of ambient air are indeed included in the air inclusions in deep ice cores, and air from the inclusions will not be representative of paleoatmospheres (Jaworowski et al., 1992 b).

Contamination from drilling fluids and more than twenty physical-chemical processes occurring in the ice before, during, and after drilling, make ice cores unsuitable for paleoatmospheric work (Jaworowski et al., 1992 b).

The most famous ice core, the Vostok (Antarctica) core, with air inclusions allegedly representing the global paleoatmospheres over the last 160,000 years, show CO2 levels below 200 ppmv for many tens of thousands of years spanning 30,000 to 110,000 years BP (Barnola et al., 1987). "Most geochemists were convinced that changes such as these could not occur", says Sarmiento (1991) about these low alleged paleoatmospheric CO2 levels. Such low atmospheric CO2 levels below approximately 250 ppmv (McKay et al., 1991) would have led to extinction of certain plant species. This has not been recorded by paleobotanists, showing clearly that the ice core CO2 results are not representative of paleoatmospheres (Jaworowski et al., 1992 b), hence the CO2-ice-core-method and its results must be rejected.

6. Justifying the dogma - carbon cycle modelling vs. reality

The Intergovernmental Panel on Climate Change (IPCC) uses "carbon cycle modelling" as part of one of their 3 evidences that the observed atmospheric CO2 increase is indeed anthropogenic (Houghton et al., 1990; page 14, Section 1.2.5 called "Evidence that the contemporary carbon dioxide increase in anthropogenic", last sentence: "qualitatively consistent with results from carbon cycle modelling").

The present chairman of IPCC, Bert Bolin, entered the "Greenhouse Effect Global Warming" scene with his Bolin & Eriksson (1959) paper. Here they expand on the belief of Callendar (1958) that his apparent atmospheric CO2 increase must be anthropogenic, and that the reason for this is that the ocean is not dissolving the atmospheric CO2 which the chemical laws (cf. Henry's Law) say it should.

Bolin & Eriksson (1959) correctly state: "First we see that if the partial pressure of CO2 varies and the hydrogen ion concentration were kept constant, the relative changes would be the same in the sea as in the atmosphere. As the total amount of CO2 in the sea is about 50 times that in the air, practically all excess CO2 delivered to the atmosphere would be taken up by the sea when equilibrium has been established." They further cite Revelle & Suess (1957) that: "most of the CO2 due to combustion has been transferred into the ocean and that a net increase of CO2 in the atmosphere of only a few percent has actually occurred. Callendar's deduction has therefore been rejected". They also accept an atmospheric lifetime of about 5 years. This is all in accordance with the laws of chemistry and the carbon isotope ratios of the atmospheric CO2 (Segalstad, 1996).

Such a situation would not fit the heavily criticized atmospheric CO2 level rise constructed by Callendar (1958) as characterized by Bolin & Eriksson (1959) as: "deduced from a careful survey of all available measurements". Bolin & Eriksson (1959) goes on to model an ocean without its primary chemical buffer agent calcium carbonate and without organic matter (like all later carbon cycle modellers also have done). They further cite from the discussion of Revelle & Suess (1957) that the sea could have a "buffer" factor: "a buffer mechanism acting in such a way that a 10% increase of the CO2-content of the atmosphere need merely be balanced by an increase of about 1% of the total CO2 content in sea water to reach a new equilibrium". . . . "The low buffering capacity of the sea mentioned by Revelle and Suess is due to a change in the dissociation equilibrium between CO2 and H2CO3 on one hand and HCO3[-] and CO3[2-] ions on the other."

They neglect, however, the conclusion from the discussion by Revelle & Suess (1957, page 25): "It seems therefore quite improbable that an increase in the atmospheric CO2 concentration of as much as 10% could have been caused by industrial fuel combustion during the past century, as Callendar's statistical analyses indicate."

It is appropriate as this point to add that if Bolin & Eriksson's conditions in the last paragraph were true, carbonated beer (Bohren, 1987) and soda "pop" as we know it would be an impossibility with their "buffer" factor (see below); rain and fresh water would not show the observed equilibrium pH of 5.7 (Krauskopf, 1979); and experiments would not have shown complete isotopic equilibrium between CO2 and water in just hours, which in turn is the prerequisite for routine stable isotope analysis involving CO2 (Gonfiantini, 1981).

Experimentally it has been found that CO2 and pure water at 25 degrees C reaches 99% isotopic equilibrium after 30 hours and 52 minutes; after shaking (like wave agitation) 99% equilibrium is reached after 4 hours and 37 minutes (Gonfiantini, 1981). At 350 ppmv CO2 in the air, the equilibrium concentration of carbonic acid in pure water will be about 0.00001 molal at 25 degrees C. This chemical equilibrium is reached within 20 seconds (Stumm & Morgan, 1970). At the same temperature, at pH-values between 7 and 9, CO2 reaches 99% chemical equilibrium with water and calcium carbonate in about 100 seconds (Dreybrodt et al., 1996).

Carbonated beer, soda "pop", and champagne are good analogues to the CO2 distribution between atmosphere and ocean. In both cases they manifest the equilibrium governed by Henry's Law: the partial pressure of CO2 in the air will be proportional to the concentration of CO2 dissolved in water. The proportional constant is the Henry's Law Constant, giving us a partition coefficient for CO2 between air and water of approximately 1:50 (Revelle & Suess, 1957; Skirrow, 1975; Jaworowski et al., 1992 a; Segalstad, 1996). We have all experienced that carbonated drinks contain much more (about 50 times higher concentration) CO2 than the air under the bottle cap above the carbonated water. This fact is in harsh contradiction to the Bolin & Eriksson's "buffer" factor claim that the air will contain much more CO2 than the carbonated water, when trying to increase the partial pressure of CO2 from the assumed pre-industrial level of 290 ppmv (pressure less than 0.0003 atmospheres) to a pressure of about 3 atmospheres in the CO2 above the carbonated water in the brewed drink bottle.

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).

From their untenable conditions Bolin & Eriksson state: "It is obvious that an addition of CO2 to the atmosphere will only slightly change the CO2 content of the sea but appreciably effect the CO2 content of the atmosphere." . . . "The decisive factor is instead the rate of overturning of the deep sea." From: "the fact that the top layer of the ocean only need to absorb a small amount of CO2 from the atmosphere", and a CO2 lifetime of 500 years for the deep ocean, Bolin & Eriksson (1959) reach the conclusion that: "an increase of the atmosphere's content of CO2 of about 10 percent would have occurred in 1954. This value compares very favourably with the value of 10% given by Callendar (1958) as the total increase until 1955 deduced from a careful survey of all available measurements." By over-simplifying the properties of the ocean the authors were able to construct a non-equilibrium model remote from observed reality and chemical laws, fitting the non-representative data of Callendar (1958).

At this point one should note that the ocean is composed of more than its 75 m thick top layer and its deep, and that it indeed contains organics. The residence time of suspended POC (particular organic carbon; carbon pool of about 1000 giga-tonnes; some 130% of the atmospheric carbon pool) in the deep sea is only 5-10 years. This alone would consume all possible man-made CO2 from the total fossil fuel reservoir (some 7200 giga-tonnes) if burned during the next 300 years, because this covers 6 to 15 turnovers of the upper-ocean pool of POC, based on radiocarbon (carbon-14) studies (Toggweiler, 1990; Druffel & Williams, 1990; see also Jaworowski et al., 1992 a). The alleged long lifetime of 500 years for carbon diffusing to the deep ocean is of no relevance to the debate on the fate of anthropogenic CO2 and the "Greenhouse Effect", because POC can sink to the bottom of the ocean in less than a year (Toggweiler, 1990).

7. Boost for the dogma - the evasion "buffer" factor

Bacastow & Keeling (1973) elaborate further on Bolin & Eriksson's ocean "buffer" factor, calling it an "evasion factor" (also called the "Revelle factor"; Keeling & Bacastow, 1977), because the "buffer" factor is not related to a buffer in the chemical sense. A real buffer can namely be defined as a reaction system which modifies or controls the value of an intensive (i.e. mass independent) thermodynamic variable (pressure, temperature, concentration, pH, etc.). The carbonate system in the sea will act as a pH buffer, by the presence of a weak acid (H2CO3) and a salt of the acid (CaCO3). The concentration of CO2 (g) in the atmosphere and of Ca2+ (aq) in the ocean will in the equilibrium Earth system also be buffered by the presence of CaCO3 at a given temperature (Segalstad, 1996).

Bacastow & Keeling (1973) show their calculated evasion factors for average ocean surface water as a function of "the partial pressure of CO2 exerted by the ocean surface water, Pm, and the total inorganic carbon in the water", here designated Ctotal, relative to the respective values they assumed for preindustrial times. The evasion factor is constructed such that: "if industrial CO2 production continues to increase, however, the evasion factor will rise with Pm according to the relation shown in Fig. 3. At the same time the short-term capacity of the oceans to absorb CO2 from the atmosphere will diminish" (Bacastow & Keeling, 1973). The evasion "buffer" factor is defined as

[ ( Pm - Pm,o ) / Pm,o ] / [ ( Ctotal - Ctotal,o ) / Ctotal,o ]

at constant sea water alkalinity. Pm,o and Ctotal,o are "preindustrial values" of Pm and Ctotal, respectively (Bacastow & Keeling, 1973). Slightly different definitions are used in various contexts (Kohlmaier, 1979). We clearly see that this evasion "buffer" factor is ideologically defined from an assumed model (atmospheric anthropogenic CO2 increase) and an assumed pre-industrial value for the CO2 level. These assumed pre-industrial values are calculated by an iteration technique (Bacastow, 1981) from so-called "apparent dissociation constants", established from empiric measurements at sea, but showing considerable variation between different authors (Takahashi et al., 1976). "There continues to be considerable uncertainty as to the magnitude of the gas exchange coefficient in the ocean", says Sarmiento (1991). The ideologically constructed non-linear evasion "buffer" factor or "Revelle factor" is later referred to as if it was established as a law of nature: "known from thermodynamic data" (Keeling & Bacastow, 1977); a gross exaggeration, giving a false scientific credibility to the method and the results from carbon cycle modelling using this "buffer" factor.

This is a beautiful example of circular logic in action, when such a construction as the evasion factor is used in all carbon cycle models which the IPCC base their anthropogenic CO2-level-rise evidence on. Using the evasion "buffer" factor instead of the chemical Henry's Law will always explain any CO2 level rise as being anthropogenic, because that very idea was the basis for the construction of the evasion "buffer" correction factor.

The results of carbon cycle modelling using the evasion "buffer" factor is shown in Table 1. Some go even further: according to Revelle & Munk (1977) "the atmospheric carbon dioxide content could rise to about 5 times the preindustrial value in the early part of the twenty-second century", i.e. in slightly more than 100 years from now.

Table 1. Carbon contents in giga-tonnes (GT) for a four-reservoir non-linear non-equilibrium model during the assumed initial pre-industrial situation, after the introduction of 1,000 GT carbon, and after the introduction of 6,000 GT carbon in the form of CO2 to the atmosphere, using an ideological evasion "buffer" correction factor of about 9. The first introduction corresponds to the total input from fossil fuel up to about the year 2000; the second is roughly equal to the known accessible reserves of fossil carbon. After Rodhe (1992).

In linear systems the fluxes between the reservoirs are linearly related to the reservoir contents, like in chemical equilibrium systems. In non-linear modelling, non-equilibrium complex relations are assumed, like for "logistical growth" models. The results after introduction of carbon to the atmosphere in Table 1 is from a simplified non-linear (non-chemical-equilibrium) non-steady state carbon cycle model with no calcium carbonate and no sea organics. The ideological evasion "buffer" correction factor is set at about 9. As a consequence of this factor a substantial increase in atmospheric CO2 from introduction of a certain amount of fossil carbon is mathematically balanced by a small increase in carbon in the sea layers. We see that the non-linear relations introduced in these current carbon cycle models give rise to substantial calculated variations between the reservoirs. The atmospheric reservoir is in such simplified non-realistic models much more perturbed than any of the other reservoirs (Rodhe, 1992). If this mechanism were true, it would be impossible for breweries to put their CO2 in beer or soda "pop".

The non-linear modelling results in Table 1 have been made to explain the apparent rise in atmospheric CO2 today of 20% (vs. an assumed pre-industrial level) from fossil fuel burning by default, and predict a 170% increase in CO2 when we have burned all our fossil fuel. The sea would in these models only see a maximum rise in CO2 of 12%.

Holmén (1992) emphasizes that such "box models and box diffusion models have very few degrees of freedom and they must describe physical, chemical, and biological processes very crudely. They are based on empirical relations rather than on first principles."

8. Trouble for the dogma - the CO2 "missing sink"

The next problem is that the Mauna Loa atmospheric CO2 level increase only accounts for approximately 50% of the expected increase from looking at the amount of CO2 formed from production data for the burning of fossil fuels (e.g., Kerr, 1992). This annual discrepancy of some 3 giga-tonnes of carbon is in the literature called "the missing sink" (analogous to "the missing link"; Holmén, 1992). When trying to find this "missing sink" in the biosphere, carbon cycle modelling has shown that deforestation must have contributed a large amount of CO2 to the atmosphere. So instead of finding "the missing sink" in the terrestrial biosphere, they find another CO2 source! This makes "the missing sink" problem yet more severe.

Trabalka (1985) summarizes the status of carbon cycle modelling and its missing sinks (Trabalka et al., 1985) by: "As a first approximation in the validation of models, it should be possible to compute a balanced global carbon budget for the contemporary period; to date this has not been achievable and the reasons are still uncertain." . . . "These models produce estimates of past atmospheric CO2 levels that are inconsistent with the historical atmospheric CO2 increase. This inconsistency implies that significant errors in projections are possible using current carbon cycle models."

Bolin's (1986) conclusion regarding carbon cycle models is on the contrary: "We understand the basic features of the global carbon cycle quite well. It has been possible to construct quantitative models which can be used as a general guide for the projection of future CO2 concentrations in the atmosphere as a result of given emission scenarios". This is in high contrast to Holmén (1992), who concludes his book chapter on "The Global Carbon Cycle" with: "obviously our knowledge of the global cycle of carbon is inadequate to get ends to meet".

A 50% error, i.e. the enormous amount of about 3 giga-tonnes of carbon annually not explained by a model, would normally lead to complete rejection of the model and its hypothesis using the scientific method of natural sciences. Still the 50% inexplicable error in the IPCC argumentation has strangely enough not yet caused all governments to reject the IPCC model. This fact beautifully shows the result of the "scare-them-to-death" principle (Section 2 above).

9. Problems for the dogma - CO2 residence time

A number of lifetimes and timescales are being used in both scientific and policy context to describe the behavior of heat-absorbing gases in the atmosphere. These concepts are very important for the discussion on whether anthropogenic CO2 will be accumulated in the atmosphere and exert an additional global "Greenhouse Effect" warming. If each CO2 molecule in the atmosphere has a short lifetime, it means that the CO2 molecules will be removed fast from the atmosphere to be absorbed in another reservoir.

A number of definitions for lifetimes of atmospheric CO2 has been introduced, like "residence time", "transit time", "response time", "e-folding time", "turnover time", "adjustment time", and more varieties of these (e.g., Rodhe, 1992; O'Neill et al., 1994; Rodhe & Björkström, 1979), to try to explain why atmospheric CO2 allegedly cannot have the short lifetime of approximately 5 years which numerous measurements of different kinds show. It is being said that because we observe the atmospheric CO2 level increase, which apparently has not been dissolved by the sea, the turnover time of atmospheric CO2 "of the combined system" must be several hundred years (Rodhe, 1992).

IPCC defines lifetime for CO2 as the time required for the atmosphere to adjust to a future equilibrium state if emissions change abruptly, and gives a lifetime of 50-200 years in parentheses (Houghton et al., 1990). Their footnote No. 4 to their Table 1.1 explains: "For each gas in the table, except CO2, the "lifetime" is defined here as the ratio of the atmospheric content to the total rate of removal. This time scale also characterizes the rate of adjustment of the atmospheric concentrations if the emission rates are changed abruptly. CO2 is a special case since it has no real sinks, but is merely circulated between various reservoirs (atmosphere, ocean, biota). The "lifetime" of CO2 given in the table is a rough indication of the time it would take for the CO2 concentration to adjust to changes in the emissions . . .".

O'Neill et al. (1994) criticize the IPCC report (Houghton et al., 1990) because it "offers no rigorous definition of lifetime; for the purpose of defining Global Warming Potentials, it instead presents integrations of impulse-response functions over several finite time intervals. Each of these estimates has its own strengths and weaknesses. Taken together, however, they create confusion over what "lifetime" means, how to calculate it, and how it relates to other timescales." IPCC's assertion that CO2 has no real sinks, have been rejected elsewhere (Jaworowski et al., 1992 a; Segalstad, 1996).

Carbon cycle modelling and CO2 - 2 - 3 - 4

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