foraminiferal tests (Elderfield et al. 2006; Mathien-Blard and
Bassinot 2009; Hönisch et al. 2013). Another issue is the
observed offsets in both culture and field studies between
Mg/Ca ratios among individual species, that indicate the
need for single-species calibrations. In addition, the geographical extension of genotypes must be assessed when
choosing to develop calibrations (Vázquez Riveiros et al.
2016). Recent studies try to simultaneously assess the relationship between foraminiferal Mg/Ca, and temperature,
salinity, and the carbonate system using statistical approaches (Khider et al. 2015; Gray et al. 2018).
Mg/Ca in foraminifera has been cited here as a main
example of a geochemical temperature tracer. Other ratios,
such as Sr/Ca or Li/Mg in corals, are also used as tracers of
temperature (Corrège 2006; Montagna et al. 2014).
Isotopic Tracers
As presented in this chapter’s introduction, the first isotopic
approach developed was the relationship between temperature, the isotopic composition of seawater and the isotopic
composition of the biocarbonate that developed within that
water. Traditionally, isotopic compositions are expressed
using the notation d, which is the relative difference (expressed in parts per thousand) between the isotope ratio R of
the sample and that of a reference standard:
d ¼ ½ R sample =R st
À
Á À 1 Â 1000
The d
18 O of the water is denoted d w , that of a carbonate,
d c , and the relationship between temperature T, d w and d c is
known as the ‘paleotemperature equation’. This relationship
was experimentally determined by Urey’s group in the
1950s and improved by Shackleton (1974) in the form
below:
T ¼ 16:9 À 4:38 Â ðd c À d w Þ þ 0:10 Â ðd c À d w Þ
2 ð21:1Þ
In this empirical formula, d c represents the d
18
O of the
CO 2 extracted from the carbonate through dissolution with
phosphoric acid, and d w is the d
18
O of the CO 2 obtained by
equilibration with the seawater to be analyzed. d c and d w are
measured by mass spectrometry using the same CO 2 laboratory standard. Other d
18 O—temperature relationships
defined in the last decades (Bemis et al. 1998; Mulitza et al.
2003; Marchitto et al. 2014) use the same terminology.
Box 1. Practical Application of the Paleotemperature Formula
Nowadays, isotopic geochemistry laboratories have
adopted the convention of expressing the d c isotopic
compositions against the PDB (Pee-Dee Belemnite)
international standard and d w against the SMOW
(Standard Mean Ocean Water) international standard.
These standards are distributed by international agencies for laboratory calibration. To properly apply the
paleotemperature formula, which presumes that all
isotopic compositions are expressed relative to the
same standard, it is necessary to compare the isotopic
ratio of the CO 2 extracted from the PDB standard by
controlled phosphoric acid attack with the isotopic
ratio of the CO 2 isotopically equilibrated with the
SMOW standard. The latter is lower in
18 O content by
0.27‰ than the CO 2 extracted from PDB, so that for
every water sample:
d w vs:PDB À CO 2
ð
Þ ¼ d w vs:SMOW À CO 2
ð
Þ À 0:27:
ð21:2Þ
If, as in the paleotemperature formula, PDB is used
as the standard for carbonates and SMOW as the
standard for waters, then Shackleton’s equation
becomes:
T ¼ 16:9À4:38 Â ðd c À d w þ 0:27Þ
þ 0:10 Â ðd c À d w þ 0:27Þ
2 :
One major disadvantage of the paleotemperature formula
is that temperatures can only be determined if the isotopic
composition of the water is known, which is almost never
the case for geological samples.
A more recent isotopic method, still under development,
is expected to overcome this constraint (Ghosh et al. 2006;
Schauble et al. 2006). The crystal lattice of a carbonate
consists of CO
2À
3 groups and of cations (Ca
2+ , for example).
Among the CO
2À
3 ions in a sample, the heavy isotopes
13 C
and
18 O do not spread out randomly. Their relative abundance will depend on the isotopic equilibrium reaction:
13
C
16
O
ð2ÀÞ
3
þ
12
C
18
O
16
O
ð2ÀÞ
2
,
13
C
18
O
16
O
ð2ÀÞ
2
þ
12
C
16
O
ð2ÀÞ
3
so that the distribution of these four isotopic species depends
on their own binding energy, itself a function of temperature.
The abundance of the various isotopic species is assessed
by dissolving the carbonate with phosphoric acid and measuring the abundance of
13 C
18 O
16 O molecules (with a mass
of 47) in the extracted CO 2 , and comparing this to the
abundances of other isotopic species with masses 45 and 46.
The ‘stochastic’ state is taken as a reference and is defined
by a random distribution of the isotopes of C and O within
the molecules.
The thermodynamic variable, denoted as D47, which
describes the state of the carbon dioxide and from which we
deduce a paleotemperature, is defined by the relationship:
232
T. Caley et al.
Bassinot 2009; Hönisch et al. 2013). Another issue is the
observed offsets in both culture and field studies between
Mg/Ca ratios among individual species, that indicate the
need for single-species calibrations. In addition, the geographical extension of genotypes must be assessed when
choosing to develop calibrations (Vázquez Riveiros et al.
2016). Recent studies try to simultaneously assess the relationship between foraminiferal Mg/Ca, and temperature,
salinity, and the carbonate system using statistical approaches (Khider et al. 2015; Gray et al. 2018).
Mg/Ca in foraminifera has been cited here as a main
example of a geochemical temperature tracer. Other ratios,
such as Sr/Ca or Li/Mg in corals, are also used as tracers of
temperature (Corrège 2006; Montagna et al. 2014).
Isotopic Tracers
As presented in this chapter’s introduction, the first isotopic
approach developed was the relationship between temperature, the isotopic composition of seawater and the isotopic
composition of the biocarbonate that developed within that
water. Traditionally, isotopic compositions are expressed
using the notation d, which is the relative difference (expressed in parts per thousand) between the isotope ratio R of
the sample and that of a reference standard:
d ¼ ½ R sample =R st
À
Á À 1 Â 1000
The d
18 O of the water is denoted d w , that of a carbonate,
d c , and the relationship between temperature T, d w and d c is
known as the ‘paleotemperature equation’. This relationship
was experimentally determined by Urey’s group in the
1950s and improved by Shackleton (1974) in the form
below:
T ¼ 16:9 À 4:38 Â ðd c À d w Þ þ 0:10 Â ðd c À d w Þ
2 ð21:1Þ
In this empirical formula, d c represents the d
18
O of the
CO 2 extracted from the carbonate through dissolution with
phosphoric acid, and d w is the d
18
O of the CO 2 obtained by
equilibration with the seawater to be analyzed. d c and d w are
measured by mass spectrometry using the same CO 2 laboratory standard. Other d
18 O—temperature relationships
defined in the last decades (Bemis et al. 1998; Mulitza et al.
2003; Marchitto et al. 2014) use the same terminology.
Box 1. Practical Application of the Paleotemperature Formula
Nowadays, isotopic geochemistry laboratories have
adopted the convention of expressing the d c isotopic
compositions against the PDB (Pee-Dee Belemnite)
international standard and d w against the SMOW
(Standard Mean Ocean Water) international standard.
These standards are distributed by international agencies for laboratory calibration. To properly apply the
paleotemperature formula, which presumes that all
isotopic compositions are expressed relative to the
same standard, it is necessary to compare the isotopic
ratio of the CO 2 extracted from the PDB standard by
controlled phosphoric acid attack with the isotopic
ratio of the CO 2 isotopically equilibrated with the
SMOW standard. The latter is lower in
18 O content by
0.27‰ than the CO 2 extracted from PDB, so that for
every water sample:
d w vs:PDB À CO 2
ð
Þ ¼ d w vs:SMOW À CO 2
ð
Þ À 0:27:
ð21:2Þ
If, as in the paleotemperature formula, PDB is used
as the standard for carbonates and SMOW as the
standard for waters, then Shackleton’s equation
becomes:
T ¼ 16:9À4:38 Â ðd c À d w þ 0:27Þ
þ 0:10 Â ðd c À d w þ 0:27Þ
2 :
One major disadvantage of the paleotemperature formula
is that temperatures can only be determined if the isotopic
composition of the water is known, which is almost never
the case for geological samples.
A more recent isotopic method, still under development,
is expected to overcome this constraint (Ghosh et al. 2006;
Schauble et al. 2006). The crystal lattice of a carbonate
consists of CO
2À
3 groups and of cations (Ca
2+ , for example).
Among the CO
2À
3 ions in a sample, the heavy isotopes
13 C
and
18 O do not spread out randomly. Their relative abundance will depend on the isotopic equilibrium reaction:
13
C
16
O
ð2ÀÞ
3
þ
12
C
18
O
16
O
ð2ÀÞ
2
,
13
C
18
O
16
O
ð2ÀÞ
2
þ
12
C
16
O
ð2ÀÞ
3
so that the distribution of these four isotopic species depends
on their own binding energy, itself a function of temperature.
The abundance of the various isotopic species is assessed
by dissolving the carbonate with phosphoric acid and measuring the abundance of
13 C
18 O
16 O molecules (with a mass
of 47) in the extracted CO 2 , and comparing this to the
abundances of other isotopic species with masses 45 and 46.
The ‘stochastic’ state is taken as a reference and is defined
by a random distribution of the isotopes of C and O within
the molecules.
The thermodynamic variable, denoted as D47, which
describes the state of the carbon dioxide and from which we
deduce a paleotemperature, is defined by the relationship:
232
T. Caley et al.