Figure 1. Vostok Correlation between Carbon Dioxide Concentration and Temperature.
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Geological climate records have been recovered from a number of ice cores. The best known is the Vostok ice core drilled by the Russians through Antarctic ice. The ice has been laid down over millions of years. The older ice is deeper than the younger ice. The Vostok data is available on the web site of the US National Climatic Data Center (www.ncdc.noaa.gov). The site also gives a comprehensive bibliography of the sources of the data (primarily from a French-Russian collaboration). This data has been extensively referred to as proof-positive of the relationship between atmospheric carbon dioxide concentrations and global temperature. For example, it is referred to in the Club of Rome book “Factor Four: Doubling Wealth, Halving Resource Use” by E von Weizsacher, A B Lovins and L H Lovins, Earthscan publications, London 1997. The relationship is referred to in their Figure 27, under the title “The ‘Vostok’ sensation: a surprisingly strict correlation during the last 160,000 years”. The graph is replotted from the paper “Vostok Ice Core: A Continuous Isotope Temperature Record over the last Climatic Cycle (160,000 years)” by Jouzel J., C. Lorius, J. R. Petit, C. Genthon, N. I. Barkov, V. M. Kotlyakov, and V. M. Petrov, Nature, 329, 1987, 402-408. On publication of the correlation, the World Meteorological Association (WMO), the United Nations Environment Programme (UNEP), and the International Council of Scientific Unions (ICSU) called a meeting in Austria. Thus, the correlation is almost iconic in setting the political global warming agenda. Environmental pressure groups continue to refer to this data as a graphic illustration supporting the position that atmospheric carbon dioxide causes global warming.
We produce here an even more “sensational” correlation extending over the 410,000 years of the data on the NCDC website. Our graph is derived from two of the published data sets:
deutnat.txt: Based on Deuterium concentrations, this file gives estimated ages and temperatures at 1m depth intervals back to 422,000 years before present. (Near the surface, these depth intervals correspond to approximately 20-year time intervals; at depth, they correspond to about 600-year intervals).
CO2nat.txt: This file gives atmospheric CO2 concentrations at, on average, 1,500 year intervals back to 414,000 years before present. (As for the deuterium data, the time increments are smaller near the surface and larger at depth).
The uncertainties in the ages, temperatures and concentrations are given in the relevant publications.
For statistical analysis, it is preferable to have the concentrations and temperatures at exactly corresponding times. We have prepared a suitable data set as follows. For each carbon dioxide measurement, we have taken the temperature measurements at immediately adjacent times. We have then linearly interpolated temperatures to get the temperature to be expected at the time of the CO2 measurement. This operation eliminates over 90% of the temperature record, and replaces the remaining measurements with interpolated values. Consequently, there is a risk that the reduced data set does not encapsulate the temperature data adequately. We checked the extent of the distortion by calculating the means of the original temperature data set and the reduced data set. We also calculated the average spread about the mean (standard deviation from the mean). We obtained the following comparison:
Original: Mean -4.52 C below present mean. Deviation 2.9 C
Reduced: Mean -4.07 C below present mean. Deviation 3.1 C
With a standard deviation of about 3 C, the maximum spread of the temperature measurements is about 15 C. The two means differ by only 0.45 C. Hence, in view of the large amount of data rejected, it is concluded that the reduced data set captures the temperature history adequately.
We can now illustrate the correlation between the carbon dioxide data and the temperature estimated at exactly corresponding times. To show the two variables on the same scale, we have scaled each series by subtracting its mean from each data point and dividing the result by the corresponding standard deviation. For example, for temperature, we take the “reduced” values above and put
Thus, a temperature exactly on the mean, is given a scaled value of T’ = 0.0. A temperature differing from the mean by one standard deviation (3.1 C) is given a scaled value of –1.0 or +1.0.
The corresponding scaling is undertaken for the carbon dioxide concentrations. The results are illustrated in Figure 1. We see that the correlation noted in “Factor Four” extends over 410,000 years and is even better than in the Club of Rome illustration. (It is probable that our use of corresponding times, rather than corresponding depths improves the correlation. The gas bubbles, containing carbon dioxide, are generally younger than the ice at any given depth).
Figure
1. Vostok Correlation between Carbon Dioxide Concentration and
Temperature.
The correlation is striking but does not prove that increasing carbon dioxide causes increasing temperatures. A-priori, it is equally possible that increasing temperatures cause increased carbon dioxide concentrations. Over 95% of the accessible environmental carbon dioxide is dissolved in the oceans (mostly as bicarbonate ions). It is well known that all gas solubilities in liquids are temperature dependent. Gas solubilities are higher at low temperatures and lower at high temperatures. The effect has been known for centuries and, for low gas concentrations, is correlated by a version of the Clausius-Clapeyron equation. The equation was initially derived during the 1830’s. It was one of the early successes for the science of chemical thermodynamics. It has been extensively tested for thousands of liquid/gas combinations. It is also well known that the effect applies in the oceans. Carbon dioxide dissolves in the cold polar seas from where it is carried down by deep ocean currents. As the currents rise towards the equator, the seas warm, the solubility becomes less, and the carbon dioxide is discharged into the atmosphere. This mechanism transports gigatonnes of carbon dioxide per annum. Thus, it is possible that the correlation simply results from the fact that when the global temperatures are low, carbon dioxide dissolves in the oceans and its concentration in the atmosphere is correspondingly reduced. Similarly, when global temperatures rise, the solubility decreases and carbon dioxide is discharged to the atmosphere. We explore the extent to which the correlation of Figure 1 can be explained by such vapour-liquid equilibrium effects.
The vapour pressure of gases over liquids in which they have a low concentration is given by the Clausius-Clapeyron equation:
p = x.C.exp{-L/(RT)} (V2)
In this equation
p is the partial pressure
x is the concentration in the liquid phase
C is a constant
L is the heat change in moving from the gas phase to the liquid phase
R is the universal gas constant
T is the absolute temperature of the liquid.
The atmospheric concentration of carbon dioxide is given by
y = p/P (V3)
P is the total atmospheric pressure and, on average, remains constant at about 1 bar.
The constant C depends on the affinity of the gas molecules to the liquid in which they are dissolved and on the other species present in the solution. The constant L can be looked upon as the heat of solution. It depends on the form that the gas takes when it dissolves because there may be heat changes as the gas changes from its pure dissolved form to various species in the solution. For example, both in pure water and in seawater, carbon dioxide is present mainly as bicarbonate ions. Thus,
CO2(liq) + OH– = HCO3–
Note that equation (V2) can be used in two ways. When the concentration in the liquid (x) is fixed, it can be employed to predict gas partial pressure (p) over the liquid. When the gas-phase composition is fixed (y, p), it can be used to calculate the solubility of the gas in the liquid. Thus, the two constants C and L can be computed either from pressure data or from solubility data.
Figure 2. Clausius-Clapeyron Correlation of CO2 Solubility in the Oceans as derived Westerlund
Professor
Tapio Westerlund has shown that the build up of carbon dioxide in the
atmosphere (resulting from human activity) can be explained based on
equilibrium between the atmosphere and the oceans. (“On
modelling the Atmospheric Carbon Dioxide Change”, Westerlund T,
1990, Report 90-111-A, Aabo Akademi University, Finland, ISBN
951-649-827-2). He addresses the problem of the proportion of
human-activity carbon dioxide that is dissolved in the oceans and the
proportion of the increased atmospheric carbon dioxide resulting from
releases from the oceans. His model projected forward from data
measured in 1960 and predicted the measured values in 1990
accurately. The model has been left unmodified, and its projections
for 2007 are also consistent with measured values. Thus, it is a
well-validated model. He considers equilibrium between a range of
ionic species in the oceans and concludes that there is equilibrium
between the atmosphere and an upper layer of relatively well-mixed
ocean. The layer represents less than 10% of the volume of the
oceans. The deeper, relatively quiescent, ocean will take centuries
to equilibrate. (The time scales can be estimated using the methods
given in Johns W R and Lawn S J “Unsteady-state transfer
between a sphere and a surrounding stationary medium, with
applications to arrays of spheres”, Intl Jnl Heat and Mass
Transfer, 28, 1047-1053, 1985). The oceans are slightly alkaline (pH
8.1). Westerlund’s simulation includes allowance for
dependence of ocean pH on carbon dioxide concentrations. The effect
is a slightly reduced alkalinity (changes of order pH 0.01) resulting
from dissolution of carbon dioxide. The multi-species equilibrium
calculations can be summarized by our equation (V2). Thus, in Figure
2, we plot the results of Westerlund’s Table 4 according to
equation (V2). Even with the many equilibria considered by
Westerlund, equation (V2) correlates the solubility estimates well.
The value of L required for equation (V2) to fit the tabulated
points is 32.5 MJ/kmol. This value compares to about 20 MJ/kmol that
correlates the solubility of carbon dioxide in pure water.
Westerlund emphasizes that his calculations are based on a
pseudo-equilibrium. In the long term, the equilibrium will include
also the deep ocean and, in the very long term, will include
equilibrium between the dissolved species and the solid species
making up the ocean bed. This latter equilibrium will tend to
restore the alkalinity to a constant value. It will also influence
the value of L that correlates the solubility data.
Equilibrium with the deep ocean will be established over a few
centuries. Thus, over geological time scales, we can assume an
equilibrium between atmospheric carbon dioxide, carbon dioxide in its
various ionic forms in the oceans, and the minerals making up the sea
bed.
With the above information on carbon dioxide solubility in seawater, we can explore the extent to which the striking correlation of Figure 1 can be explained by simple phase equilibria. We adopt two approaches. In the first, we put in our best estimates of the parameters in equation (V2) based on independent observations. In the second, we find the values that best fit the observations to the theory. In both approaches, we hypothesize that the mean concentration of carbon dioxide in the oceans remains constant over geological periods. The mass of carbon dioxide in the atmosphere, and released by geological processes, is so small compared to the mass in the oceans, that the hypothesis seems to be reasonable. Without thermodynamic data on all the possible equilibrium reactions, it is impossible to compute the coefficient “C” from first principles. Hence, we compute it from a known value of “p” after an extended period at a near-constant temperature. After such a period, it would be expected that equilibrium would be achieved. We do not know the mean difference between atmospheric and ocean temperatures at that time. However, any error that we make is exactly compensated when we compute “C” from a known “p”. The strengths and weaknesses of the two approaches can be summarized as follows:
In taking our best estimates, we will take the value of L from figure 2, namely 32.5 MJ/kmol. We will take the pre-industrial mean global temperature as 13.5 C, which was the value in 1866 (the earliest reliable estimate). We will take the mean atmospheric carbon dioxide concentration as 270 ppm. This value is a rough mean of the more recent values from the Vostok record. It is claimed that global temperatures had been reasonably uniform for some millennia, so equilibrium may have been reached. The criticisms of this approach are as follows. When we take equilibrium with the ocean floor into account, the net heat of solution (L) will be altered. Our estimated one-off equilibrium carbon dioxide concentration of 270 ppm (2700 Pa), might be in error by several ppm. In view of the inevitable errors, a reasonably strong correlation between observed and calculated carbon dioxide concentrations would support the hypothesis that geologically, there is long-term equilibrium between ocean and atmosphere.
Making a best fit of the model to the data can be looked upon as cheating. Since there is a strong correlation between temperature and atmospheric carbon dioxide concentration, any 2-parameter model will necessarily give a good correlation. Thus, the test here is whether the computed values of L and p (at chosen temperature) are reasonably consistent with our knowledge of the equilibrium processes.
The results are illustrated in figures 3 and 4. Figure 3 shows that the equilibrium model fits the observed carbon dioxide measurements well. The fit is achieved although we know that the parameter estimates are only approximate. Figure 4 shows the best fit. It is achieved with L = 23.15 MJ/kmol and p(at 13.5 C) = 267.23 ppm. Both these estimates are physically reasonable. The former is between the values for pure water and for partially equilibrated seawater as estimated from Westerlund’s calculations. The latter is close to our judged value.
Figure
3. Comparison of measured and calculated carbon dioxide
concentrations using parameters derived from Westerlund.
Figure
4. Best-fit Correlation of Vostok Carbon Dioxide Concentrations.
We show, in Chapter 2, that the measured Vostok carbon dioxide concentrations are probably smoothed values averaged over a number of centuries. Thus, carbon dioxide concentrations may well vary more widely than illustrated in Figures 1, 3 and 4. If that is the case, a larger value of “L” would be required to correlate the data. It follows that the true value of “L” is probably nearer to the theoretical value derived by Westerlund than it is to the best-fit value of Figure 4.
Despite the small uncertainty in the Vostok carbon dioxide concentrations, we conclude that the observed correlation is fully accounted for by ocean/atmosphere equilibrium. Thus, for geological time, increased atmospheric carbon dioxide has been caused by increased temperatures and decreased concentration by decreased temperature. This finding is now widely accepted by climate scientists. However, it does not preclude the possibility that increased atmospheric carbon dioxide also causes increased temperature. Indeed, this situation is supported by Professor Jeff Severinghaus (“What does the lag of CO2 behind temperatures in ice cores tell us about global warming?” www.realclimate.org). He explains that observed increases in carbon dioxide concentrations tend to lag temperature increases. (The converse also applies; temperature falls precede reductions in CO2 concentrations). Superficially, these time lags suggest that temperature changes drive carbon dioxide changes, not vice versa. Prof. Severinghaus notes that initially periods of global warming may be driven by events unrelated to carbon dioxide concentrations. However, once underway, the global warming causes carbon dioxide to be driven from the oceans, which then through the greenhouse gas effect drives further global warming. Neither does the observation preclude the possibility that global temperatures are determined primarily by atmospheric carbon dioxide concentrations. The ocean would still be in equilibrium with the atmosphere over a geological time scale. Thus, we would still have the observed equilibrium relationship between temperature and atmospheric carbon dioxide concentration. However, the results reported in the Appendix are now difficult to explain. The ice-core analysis in the Appendix shows that, during periods of global warming, carbon dioxide concentrations are consistently lower (at corresponding temperatures) than during periods of global cooling. Thus, superficially at least, it appears that low carbon dioxide concentrations drive global warming and high concentrations drive global cooling. This fact seems to conflict with the conventional theory of global warming. This apparent anomaly can be explained by climate models introduced in Chapter 4. In one of the models, carbon dioxide is a primary cause of global warming, but heat transfer by convection causes atmospheric carbon dioxide concentrations to lag temperature changes.
We conclude that the ice-core carbon-dioxide data prove conclusively that in geological time atmospheric carbon dioxide levels are determined by temperature. (Thus, in a sense, global warming causes increased atmospheric carbon dioxide concentrations). They neither support nor negate the hypothesis that global temperatures are determined by atmospheric carbon dioxide concentrations. Neither do they illuminate the current situation in which increased atmospheric carbon dioxide is man made. To this extent, at least, they are irrelevant to the debate on global warming. It is astonishing that not one of the august scientific bodies calling the Austria meeting in 1987 spotted the problem. Did not one of these bodies have someone who had studied undergraduate Chemical Thermodynamics? Such a person would have told them that the correlation was entirely expected. It is no more than a manifestation of atmosphere/ocean phase equilibrium.
Unfortunately, these iconic graphs are still quoted in the global warming debate by scientists who should know better. This correlation is just one example of the shaky science that partially props up the carbon hypothesis of global warming. As we will see below, some arguments for the carbon hypothesis stand. Nevertheless, (on both sides) there is too much spin passing for science in the global warming debate.
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