indirect and depend on a number of assumptions. This
inevitably produces significant uncertainties. In addition, the
low residence time of carbon in the ocean-atmosphere system (200,000 years) is an inherent cause of scattering of data
points. Temporal resolution for the geological past very
rarely reaches this level of precision. It follows that two
points, attributed to the same geological moment, may have
very different values.
An excellent overview was carried out by Royer et al.
(2001) using several reconstruction methods. For the very
distant past, the counting of the stomata of the fossil leaves is
commonly used. For modern species, there is a positive
correlation between the number of stomata and the ambient
CO 2 level. These correlations are applied to old geological
samples. This is probably the least precise method, but it has
the advantage of being able to go back very far in the past (as
far back as the Devonian) and does not encounter the problems experienced by isotopic systems, such as diagenesis.
A second method allows measurements to be traced back
to the Paleozoic. It involves measuring the d
13 C of pedogenic carbonates in paleosols and is based on the fact that the
level of CO 2 in modern soils results from a mixing of the
atmospheric CO 2 in the atmosphere and the CO 2 in the soil
through respiration. The d
13 C of this C
atm
2
mixture is registered in the pedogenic carbonates:
CO
atm
2 ¼ S z
ð Þ
d sample À 1:0044d resp À 4:4
d atm À d sample
ð7Þ
where d sample is the d
13
C of the pedogenic carbonate. The
method requires setting the d
13 C of the breathed CO 2 , d resp ,
at typical values. It therefore depends on the proportion of
C 4 plants to C 3 plants, for which the isotopic fractionations
are very different. In practice, it is not applicable after the
emergence of C 4 plants, 15 Ma ago. The method also
requires knowledge of the d
13 C of the atmosphere d atm and S
(z), the amount of breathed CO 2 at the estimated depth z of
the pedogenic carbonate in the paleosol. The d
13 C of the
atmosphere is estimated by measuring the d
13 C of marine
carbonates of the same age and by imposing the fractionation value between the carbonates and the atmospheric CO 2 .
As for the fraction of breathed CO 2 , it is calculated by
making major assumptions about soil temperature, porosity
and biological productivity. In fact, if CO 2 production in
soils is a function of productivity and temperature (which
partially controls the degradation of organic matter by bacteria), its diffusion to the atmosphere depends largely on the
physical structure of soils. The level of CO 2 at a given depth
is therefore dependent on the relative importance of the
production and loss by diffusion. This is by far the most
uncertain method. A recent recalibration of the method has
led to a considerable reduction in past reconstructed CO 2
pressures (Breecker et al. 2010; Foster et al. 2017). A similar
method consists of studying the trace d
13 C of pedogenic
carbonates contained in goethite, a mineral formed during
soil alteration reactions (Royer et al. 2001).
A third approach uses the measurement of isotopic fractionation of carbon by phytoplankton and its relationship
with the dissolved CO 2 content in seawater. Initially, the
difference between the d
13 C of carbonates and that of total
organic carbon was used. It was subsequently found to be
error-prone, in particular due to the presence of organic
matter of various origins in both continental and marine
sediments. This fractionation is now measured by directly
using biomarkers in the organic matter, such as alkenones
(Pagani et al. 2005). The link between isotopic fractionation
and the level of CO 2 dissolved in water is based on correlations established for the present. For example, this one is
based on a compilation of GEOSECS campaign data:
e P ¼ 12:03 CO 2aq
Â
à À 3:56
10
CO 2aq
Â
à 90 lM
ð8Þ
where e p is the photosynthetic fractionation of phytoplankton, and CO 2aq
Â
Ã
is the concentration of gaseous CO 2 dissolved in water.
The use of correlations established for current conditions
is the main weakness of this method, since they are
extrapolated to CO 2 ranges that are significantly higher than
the current level, using compounds made by organisms with
an unknown metabolism. In addition, isotopic fractionation
is also a function of the growth rate of these organisms,
which complicates reconstruction.
A final method is based on the measurement of the ratio
of boron isotopes
11 B/
10 B (d
11 B) in carbonate sediments
(Royer et al. 2001). The relative abundance of the two dissolved borate species (H 4 BO 4 and H 3 BO
À
4 ) depends on the
pH of the sea water. There is an isotopic fractionation of
about 19‰ between the two species. The carbonates are
mainly made up of the H 4 BO 4 species and the isotopic d
11 B
composition of the carbonates will therefore depend on the
pH. Nevertheless, the link with atmospheric CO 2 is not clear.
First, this requires assumptions that d
11 B of seawater
remains constant over time, that the isotopes are shared
between the two species and that the relative abundances of
11 B and
10 B remain the same. It was shown that this was
probably not the case and that d
11 B of total borate probably
changed in the past. Finally, we must make strong
assumptions about the alkalinity of seawater, to bring the pH
up to the pressure of atmospheric CO 2 .
The compilation of all these reconstructions inevitably
shows a large dispersion of points (Royer 2006; Foster et al.
2017) (Fig. 27.6). Nevertheless, some trends may emerge.
The level of atmospheric CO 2 seems to have been high
before the Devonian (with values generally in excess of
2000 ppmv). This period is followed by a time interval
366
Y. Goddéris et al.
inevitably produces significant uncertainties. In addition, the
low residence time of carbon in the ocean-atmosphere system (200,000 years) is an inherent cause of scattering of data
points. Temporal resolution for the geological past very
rarely reaches this level of precision. It follows that two
points, attributed to the same geological moment, may have
very different values.
An excellent overview was carried out by Royer et al.
(2001) using several reconstruction methods. For the very
distant past, the counting of the stomata of the fossil leaves is
commonly used. For modern species, there is a positive
correlation between the number of stomata and the ambient
CO 2 level. These correlations are applied to old geological
samples. This is probably the least precise method, but it has
the advantage of being able to go back very far in the past (as
far back as the Devonian) and does not encounter the problems experienced by isotopic systems, such as diagenesis.
A second method allows measurements to be traced back
to the Paleozoic. It involves measuring the d
13 C of pedogenic carbonates in paleosols and is based on the fact that the
level of CO 2 in modern soils results from a mixing of the
atmospheric CO 2 in the atmosphere and the CO 2 in the soil
through respiration. The d
13 C of this C
atm
2
mixture is registered in the pedogenic carbonates:
CO
atm
2 ¼ S z
ð Þ
d sample À 1:0044d resp À 4:4
d atm À d sample
ð7Þ
where d sample is the d
13
C of the pedogenic carbonate. The
method requires setting the d
13 C of the breathed CO 2 , d resp ,
at typical values. It therefore depends on the proportion of
C 4 plants to C 3 plants, for which the isotopic fractionations
are very different. In practice, it is not applicable after the
emergence of C 4 plants, 15 Ma ago. The method also
requires knowledge of the d
13 C of the atmosphere d atm and S
(z), the amount of breathed CO 2 at the estimated depth z of
the pedogenic carbonate in the paleosol. The d
13 C of the
atmosphere is estimated by measuring the d
13 C of marine
carbonates of the same age and by imposing the fractionation value between the carbonates and the atmospheric CO 2 .
As for the fraction of breathed CO 2 , it is calculated by
making major assumptions about soil temperature, porosity
and biological productivity. In fact, if CO 2 production in
soils is a function of productivity and temperature (which
partially controls the degradation of organic matter by bacteria), its diffusion to the atmosphere depends largely on the
physical structure of soils. The level of CO 2 at a given depth
is therefore dependent on the relative importance of the
production and loss by diffusion. This is by far the most
uncertain method. A recent recalibration of the method has
led to a considerable reduction in past reconstructed CO 2
pressures (Breecker et al. 2010; Foster et al. 2017). A similar
method consists of studying the trace d
13 C of pedogenic
carbonates contained in goethite, a mineral formed during
soil alteration reactions (Royer et al. 2001).
A third approach uses the measurement of isotopic fractionation of carbon by phytoplankton and its relationship
with the dissolved CO 2 content in seawater. Initially, the
difference between the d
13 C of carbonates and that of total
organic carbon was used. It was subsequently found to be
error-prone, in particular due to the presence of organic
matter of various origins in both continental and marine
sediments. This fractionation is now measured by directly
using biomarkers in the organic matter, such as alkenones
(Pagani et al. 2005). The link between isotopic fractionation
and the level of CO 2 dissolved in water is based on correlations established for the present. For example, this one is
based on a compilation of GEOSECS campaign data:
e P ¼ 12:03 CO 2aq
Â
à À 3:56
10
CO 2aq
Â
à 90 lM
ð8Þ
where e p is the photosynthetic fractionation of phytoplankton, and CO 2aq
Â
Ã
is the concentration of gaseous CO 2 dissolved in water.
The use of correlations established for current conditions
is the main weakness of this method, since they are
extrapolated to CO 2 ranges that are significantly higher than
the current level, using compounds made by organisms with
an unknown metabolism. In addition, isotopic fractionation
is also a function of the growth rate of these organisms,
which complicates reconstruction.
A final method is based on the measurement of the ratio
of boron isotopes
11 B/
10 B (d
11 B) in carbonate sediments
(Royer et al. 2001). The relative abundance of the two dissolved borate species (H 4 BO 4 and H 3 BO
À
4 ) depends on the
pH of the sea water. There is an isotopic fractionation of
about 19‰ between the two species. The carbonates are
mainly made up of the H 4 BO 4 species and the isotopic d
11 B
composition of the carbonates will therefore depend on the
pH. Nevertheless, the link with atmospheric CO 2 is not clear.
First, this requires assumptions that d
11 B of seawater
remains constant over time, that the isotopes are shared
between the two species and that the relative abundances of
11 B and
10 B remain the same. It was shown that this was
probably not the case and that d
11 B of total borate probably
changed in the past. Finally, we must make strong
assumptions about the alkalinity of seawater, to bring the pH
up to the pressure of atmospheric CO 2 .
The compilation of all these reconstructions inevitably
shows a large dispersion of points (Royer 2006; Foster et al.
2017) (Fig. 27.6). Nevertheless, some trends may emerge.
The level of atmospheric CO 2 seems to have been high
before the Devonian (with values generally in excess of
2000 ppmv). This period is followed by a time interval
366
Y. Goddéris et al.