Appendix A

Calculations

A.1 Calculation of the Water Vapor Pressure

The water vapor pressure of seawater is generally calculated from seawater temperature and salinity. We used the method given by Weiss and Price (1980) in which the authors provide an equation to assess the saturation water vapor pressure of seawater over the temperature range 273 to 313 K and the salinity range 0 to 40:

,

where p_sw is the water vapor pressure (in atm), T is the temperature (in K), and S is the salinity on the Practical Salinity Scale.

A.2 Calculation of fCO₂ for Moist Air Conditions

The first step in the calculation procedure for final fCO₂ values, either for the atmosphere or for surface seawater, is the calculation of the fCO₂ for moist air from the measured mole fraction (xCO₂) in dry air. Weiss and Price (1980) give the theoretical basis for this calculation based on equations given by Guggenheim (1967) for calculating fugacities in binary mixtures:

,

where x₁ is the mole fraction of pure gas 1, x₂ is the mole fraction of pure gas 2, P is the total pressure, R is the gas constant, T is the absolute temperature, and d ₁₂ is defined by

,

where B₁₁ is the virial coefficient for interaction between pure gas 1 molecules, B₂₂ is the virial coefficient for interaction between pure gas 2 molecules, and B₁₂ is the virial coefficient for interaction between molecules of gas 1 and 2. For calculating fCO₂, gas 1 is here considered as the analyte gas (CO₂) and gas 2 as dry air. The mole fraction x₂ of dry air in this mixture is approximately equal to 1 for the analyte concentrations considered here. To calculate the fCO₂ for moist air conditions at the equilibrator temperature (fCO₂ of seawater) or the air/sea interface (fCO₂ of air), the mole fraction of CO₂ in dry air x₁ must be corrected to the mole fraction of CO₂ in moist air x^'₁. If the

gas/water interface can be regarded as being saturated with water vapor at the water temperature, the following equation holds:

.

In this equation p_sw is the saturated water vapor pressure of seawater at the given temperature and p_atm is the total barometric pressure. Because of the thermal skin effect, the temperature at the interface is usually not the same as the mixed-layer bulk temperature (Schluessel et al. 1990). This effect, which typically accounts for an interface temperature of a few tenths of a degree below the bulk temperature, has significant implications for the effective fCO₂ difference at the air/sea interface (Robertson and Watson 1992). As the exact skin temperature is rarely known, the bulk temperature is used instead. The fCO₂ for moist air conditions can therefore be calculated according to

.

The virial coefficient B (in cm³/mol) of CO₂ can be calculated for the temperature range 265 to 320 K using a power series given by Weiss (1974):

.

Weiss (1974) gives the following equation for the cross virial coefficient d of CO₂ in air as a function of temperature (273 < T < 313 K):

.

A.3 Correction of fCO₂ to In Situ Temperature

To account for the slight warming of the seawater between the seawater intake and the equilibrator, the measured fCO₂ values have to be corrected back to in situ temperature. Different equations (for pCO₂ and fCO₂) have been published in the literature (e.g., Gordon and Jones 1973; Weiss et al. 1982; Copin-Montegut 1988, 1989; Goyet et al. 1993; Takahashi et al. 1993). As the temperature changes are of the order of a few tenths of a degree only, the choice among these equations is not critical. We have used the following equation given by Weiss et al. (1982), which describes the temperature dependence of the solubility of CO₂ and the carbonic acid equilibria:

,

where t is the seawater temperature (in °C). The equation gives the change in the logarithm of the fugacity of CO₂ in moist air for an incremental increase of the temperature between in situ and measurement temperature.