Methods to estimate anthropogenic carbon (C ant )

2 3 4 5 6 7

SF 6 mole fraction [ppt]

SF₆ CFC-12

Figure 1.5: CFC-12 and SF6 mixing ratios in the northern hemisphere. Data are taken from Bullister [2010]

convention has a GWP of 1. However, the overall contribution to global warming is rather low as the mixing ratio of SF6 is only about 7 ppt in the year 2010 compared to a mixing ratio of 390 ppm for CO₂. Thus no major restrictions for the SF₆ production have been released in the past and atmospheric concentration continue to increase linearly (Fig. 1.5). Like CO₂, both tracers enter the ocean via the air-sea interface in dependency of the atmospheric concentration and their water solubility. In contrast to CO2, CFC-12 and SF6 are inert in the water column and can therefore be used to estimate the waters age (see section 1.4.2).

1.4 Methods to estimate anthropogenic carbon (C

)

1.4.1 Overview

Anthropogenic carbon accounts for only a small fraction of the carbon reservoir in the ocean. By direct measurements it cannot be distinguished from the vast natural background but several methods have been developed to determine the ocean’s Cant inventory. The first estimates of C_ant used back-calculation techniques based on measurements of inorganic carbon, developed independently by Brewer [1978] and Chen and Millero [1979]. This approach did not find general acceptance [Shiller, 1981; Broecker et al., 1995] but was reintroduced by the concept of the ’quasi-conservative’ tracer ∆C^* Gruber et al.[1996]. Further variations of this approach and specific regional adjustments have been proposed since then [e.g.,Goyet et al., 1999;Perez et al., 2002; Lo Monaco et al., 2005; Touratier and Goyet, 2004; Touratier et al., 2007] and have been reviewed by e.g. Wallace [1995] andFriis [2006].

The ∆C^* method corrects the measured CT for all changes that have occurred since the water parcel lost contact with the atmosphere, which results in the preformed carbon (C_T⁰).

The changes are due to biological production and respiration (C_bio) and to calcium carbonate

dissolution (C_carb):

C_T⁰ =C_T−C_bio−C_carb (1.11)

The biological fraction is assessed via the apparent oxygen utilisation (AOU) because C and O₂ are combined via a constant stoichiometric ratio (R_C:O2):

C_bio=R_C:O2·(O₂−O^sat₂ ) (1.12) The carbonate dissolution process is assessed via the change in total alkalinity (A_T). As described earlier, total alkalinity is not only affected by the change in carbonate and bicarbonate ion concentration but also by the change in hydrogen ion concentration (see equation 1.8).

During oxidative decomposition of organic matter, hydrogen ions and nutrients are released and the change in hydrogen ion concentration is assumed to be proportional to the change in nitrate concentration, which in turn is proportional to the change in O₂ through a constant ratio (R_N:O2). Thus:

C_carb= 1

2·(AT−A⁰_T+RN:O2·(O2−O^sat₂ )). (1.13) The preformed alkalinity (A⁰_T) can be estimated by a (multiple) linear regression with salinity [Brewer, 1978; Chen and Millero, 1979; Gruber et al., 1996].

Assuming 100% CO2 saturation of surface water, the preindustrial preformed carbon concen-tration C_T^0/280 can be determined with the preindustrial pCO₂ of 280 ppm and the preformed alkalinity. The anthropogenic fraction of C_T can be estimated as:

C_ant=C_T−C_T^0/280−C_bio−C_carb. (1.14) A alternative method to estimate the excess carbon in the ocean is the ’time-series mul-tiparameter analysis’ introduced by Wallace [1995]. It is based upon repeat surveys of the carbon system parameters to determine the change in C_T over time, e.g. during the World Ocean Circulation Experiment (WOCE). Assumptions for this method show some similarities with those of the back-calculation techniques. The natural relationships between carbon and the alkalinity, oxygen and nutrient contents are assumed to stay constant, whereas the uptake of the excess CO₂ changes the C_T content of seawater in a way, which is assumed to be in-dependent of these natural correlations. Through multiple linear regressions (MLR) between C_T and predictors such as T, S, O₂, A_T and nutrients measured on the same water sample, an empirical predictive equation for C_T is established. This equation refers to one survey at a particular time, which is termed the ’baseline survey’. Applying the predictive equation to subsequent (or previous) surveys and comparing the residuals of observed minus predicted C_T, should result in an increase of the residuals in case an uptake of anthropogenic CO₂ has taken place. Integration over the residual changes could give an estimate for the inventory change during the period between the surveys. In order to eliminate the natural variability ofC_T,Friis et al.[2005] extended the MLR to the so called extended multiple linear regression (eMLR). The authors developed two predictive equations for two time-separated surveys and subtracted the two predictive equations from each other. The residual equation can then be used to estimate C_ant with either of the two datasets.

A further approach uses the ¹³C/¹²C isotopic anomaly to quantify the anthropogenic car-bon inventory [Quay et al., 1992; K¨ortzinger et al., 2003]. The CO₂ released during fossil fuel burning has a smaller ¹³C/¹²C ratio than the atmosphere. This is due to fractionation during

photosynthesis as terrestrial plants preferentially fix the lighter carbon isotope ¹²C. The ex-tensive use of fossil fuel has lead to an overall decrease of the ¹³C/¹²C ratio in the atmosphere, which in turn is exchanged with the surface ocean. The constructed mass balance for the anomaly contained terms that presented large uncertainties so that its application is limited.

An almost completely different category of observational methods to estimateCant is based on measurements of anthropogenic tracers such as the bomb-derived carbon (¹⁴C), CFCs and SF6. With the help of the atmospheric time histories of these compounds and the analytical investigation of their concentrations in the ocean, conclusions can be drawn about the water mass ages and, by inference, theC_antcontent. It should be mentioned that Friis [2006] showed that the ∆C^* technique is similar to a tracer technique. An extensive description of the transit time distribution (TTD) method based on CFC-12 and SF6 measurements is given in the next section 1.4.2.

1.4.2 The transit time distribution method

As described in section 1.3, the tracers CFC-12 and SF6 are supposed to be stable in ocean waters and thus their concentrations can be converted into ages. This age is the time elapsed between the year when the water left the mixed layer, which is assumed to be in equilibrium with the atmosphere mixing ratios, and the year when the subsurface tracer was measured [Haine and Richards, 1995]. A further assumption for this classical age calculation is the uniform origin of the sampled water parcel, which does not hold true in reality. The transit time distribution (TTD) method instead assumes that a water parcel consists of waters with varying time histories. So instead of a single age, each water parcel has an age or transit time distribution (Fig. 1.6). The TTD method has been developed for atmospheric transport by Hall and Plumb [1994] and its application to oceanic transport followed [e.g., Beining and Roether, 1996;Delhez et al., 1999;Deleersnijder et al., 2001;Haine and Hall, 2002]. It assumes steady-state water transport.

The shape described by the TTD can be approximated by an ’inverse Gaussian function’

(G(t)) with two free parameters that have to be estimated:

G(t) =

r Γ³

4π∆²t³ ·exp −Γ (t−Γ)² 4∆²t

!

, (1.15)

where Γ is the mean transit time (’mean age’) and ∆ defines the width of the TTD. The^∆/Γ

ratio is a measure for mixing. The higher the ratio the stronger the mixing. Knowledge of this ratio leaves only one remaining free parameter, the mean age Γ. For ocean interior waters a constant^∆/Γ ratio of 1 has shown to be reasonable [Waugh et al., 2004].

Further, the interior concentration c(r, t) of any tracer at location r and time t can be determined by [Hall and Plumb, 1994]:

c(r, t) = Z ∞

0

c₀(t−t⁰)·G(r, t⁰)dt⁰, (1.16) wheret⁰is the integration variable, representing all the apparent ages in the water parcel (from 0 to∞years). G(r, t⁰) is the TTD presented in equation 1.15 at locationr, giving the appropriate fraction for each water aget⁰, andc₀(t−t⁰) is the surface water tracer concentration in the year t−t⁰ to be multiplied by this fraction. The surface tracer concentration is assumed to be in equilibrium with the atmosphere. Given an interior tracer concentration and a ^∆/Γ ratio, the mean age of the water sample can now be constrained with equation 1.15 and 1.16.

The application of the TTD method to estimate the anthropogenic CO₂ of a water parcel considersC_ant as inert passive tracer, that fully equilibrates at the air-sea interface. According to equation 1.16 each interior Cant concentration is related to the concentration history in surface waters (C_ant,0) as:

C_ant(t) = Z ∞

0

C_ant,0(t−t⁰)·G(t⁰)dt⁰, (1.17) where tis the sampling year. The mean ages and the corresponding TTDs are determined using tracer measurements (e.g. CFC-12). The local variabler can be left out because for each discrete water sample a new TTD is determined. With the help of the atmospheric history of anthropogenic CO₂ and an empirical relation between surface salinity and alkalinity, the historicalC_ant concentrations in surface waters can be calculated, assuming that alkalinity has not changed since preindustrial times. A last assumption of the TTD method is a constant air-sea CO₂ disequilibrium over time, whilst it can change in space.

0 10 20 30 40 50 60 70 80

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Density [yr

]

Age [yrs]

∆/Γ = 0.1

∆/Γ = 0.3

∆/Γ = 1.5

∆/Γ = 1

Figure 1.6: Transit time distributions (TTDs) for different^∆/Γ ratios.

The uncertainty in the^∆/Γratio can be reduced with the help of a second tracer (e.g. SF6).

This is be done by initially calculating the mean age with the first tracer (CFC-12) and then, the concentration of the second tracer (SF₆) is calculated using that mean age and the same

∆/Γ ratio. If the calculated SF6 concentration matches the measured SF6 concentration, the assumed ^∆/Γratio is accurate or otherwise, the ^∆/Γ ratio is varied in order for the two tracer mean ages to match.