CHAPTER 1 • The Carbonate System in Marine Environments
35
As discussed earlier one can make an estimate of the changes in the TC02 due to the
oxidation of plant material and dissolution of CaC03 using equations discussed earlier.
If one uses the equations of Brewer (1978) and Chen and Millero (1979) to examine
the changes in TC02 in old deep waters and younger waters, it is possible to make an
estimate of the changes due to the increase of CO2 in the atmosphere due to the burning of fossil fuels. The estimated increase (260 ±20 ppm for preindustrial values) is in
reasonable agreement with the values obtained from ice cores (Fig. 1.1). As discussed
elsewhere (Gruber et al. 1996), these methods are subject to large uncertainties. The
method recently introduced by Gruber et al. (1996) has some improvements. The technique is based on the assumption that the natural carbon cycle is in steady state, meaning the carbon to oxygen and nitrate to oxygen ratios (rC/02 and rN/02) are constant.
They use the conservative tracer (~C') defined by
•
°
~C = TCOz- (TC02)eq(S, t, TA )]f C0 2= 280 - rC/02([02] - [02]sat)
-l/2[TA - TAO + rN/02([021- [02]sat)]
where TC02 is the measured total inorganic CO2, (TC02 )eq is the TC02 for the
preindustrial value at a fco 2 = 280 Ilatm, at the temperature (t), salinity (S) and performed total alkalinity (TAo) and [02]- [02]sat is the difference between the measured
and calculated oxygen (in situ t and S). The value of TA o is estimated from a multiple
regression of S and PO = [02]- r02/P04[P04] as independent variables. For the Indian Ocean, Sabine et al. (1999) have determined the values of TAo from the equation
TA O (Ilmol kg-I) = 357.6 + 55.98 S + 0.054 PO - 1.345 f:)
where PO (Ilmol kg-I) = [0 2 ] + 170 [P0 4 1 and f:) is the potential temperature (0C).
The ratios used for the organic carbon are PIN I C I O2 = 1 I 16 I 117 I -170 (Anderson and Sarmiento 1994). The value of ~C' reflects the uptake of anthropogenic CO2
(~CAnt) and the disequilibrium at the time the water left the surface and any uncertainties in the choice of the end members, etc. (~Cdiseq). This disequilibrium term is
related to
n
.
.
~Cdiseq = Lf' ~C:ii5eq
i=1
where t represents the relative contribution of the different end members (r/= 1).
They assume that the water is transported along constant density surfaces (isopycnals)
and the disequilibrium has stayed constant within an outcrop region of the isopycnal.
The value of ~C· should, thus, reveal the history of the CO2 uptake. The values of ~Cdiseq
are determined on a number of isopycnal surfaces.
The CO2 disequilibrium is determined by two methods. In the first, the variability
of ~C' in deep waters far away from the outcrop is assumed to contain no anthropogenic CO2. This method is used for all deep waters (>2000 m), except for the water
masses in the North Atlantic near Greenland and the Norwegian Seas. For shallow waters this method does not work because of the penetration of anthropogenic CO 2 • For
these density surfaces, the (TC02)eq in Eq. 1.37 is replaced by the value (TC02)eq(t)' which
35
As discussed earlier one can make an estimate of the changes in the TC02 due to the
oxidation of plant material and dissolution of CaC03 using equations discussed earlier.
If one uses the equations of Brewer (1978) and Chen and Millero (1979) to examine
the changes in TC02 in old deep waters and younger waters, it is possible to make an
estimate of the changes due to the increase of CO2 in the atmosphere due to the burning of fossil fuels. The estimated increase (260 ±20 ppm for preindustrial values) is in
reasonable agreement with the values obtained from ice cores (Fig. 1.1). As discussed
elsewhere (Gruber et al. 1996), these methods are subject to large uncertainties. The
method recently introduced by Gruber et al. (1996) has some improvements. The technique is based on the assumption that the natural carbon cycle is in steady state, meaning the carbon to oxygen and nitrate to oxygen ratios (rC/02 and rN/02) are constant.
They use the conservative tracer (~C') defined by
•
°
~C = TCOz- (TC02)eq(S, t, TA )]f C0 2= 280 - rC/02([02] - [02]sat)
-l/2[TA - TAO + rN/02([021- [02]sat)]
where TC02 is the measured total inorganic CO2, (TC02 )eq is the TC02 for the
preindustrial value at a fco 2 = 280 Ilatm, at the temperature (t), salinity (S) and performed total alkalinity (TAo) and [02]- [02]sat is the difference between the measured
and calculated oxygen (in situ t and S). The value of TA o is estimated from a multiple
regression of S and PO = [02]- r02/P04[P04] as independent variables. For the Indian Ocean, Sabine et al. (1999) have determined the values of TAo from the equation
TA O (Ilmol kg-I) = 357.6 + 55.98 S + 0.054 PO - 1.345 f:)
where PO (Ilmol kg-I) = [0 2 ] + 170 [P0 4 1 and f:) is the potential temperature (0C).
The ratios used for the organic carbon are PIN I C I O2 = 1 I 16 I 117 I -170 (Anderson and Sarmiento 1994). The value of ~C' reflects the uptake of anthropogenic CO2
(~CAnt) and the disequilibrium at the time the water left the surface and any uncertainties in the choice of the end members, etc. (~Cdiseq). This disequilibrium term is
related to
n
.
.
~Cdiseq = Lf' ~C:ii5eq
i=1
where t represents the relative contribution of the different end members (r/= 1).
They assume that the water is transported along constant density surfaces (isopycnals)
and the disequilibrium has stayed constant within an outcrop region of the isopycnal.
The value of ~C· should, thus, reveal the history of the CO2 uptake. The values of ~Cdiseq
are determined on a number of isopycnal surfaces.
The CO2 disequilibrium is determined by two methods. In the first, the variability
of ~C' in deep waters far away from the outcrop is assumed to contain no anthropogenic CO2. This method is used for all deep waters (>2000 m), except for the water
masses in the North Atlantic near Greenland and the Norwegian Seas. For shallow waters this method does not work because of the penetration of anthropogenic CO 2 • For
these density surfaces, the (TC02)eq in Eq. 1.37 is replaced by the value (TC02)eq(t)' which