Calculation of fCO₂ Results

The calculation of final fCO₂ values from the raw voltage readings of an NDIR analyzer involves a number of steps that are only briefly described here. More detail of the calculation procedure can be found in Appendix A and in the reprints of the pertinent literature section (Appendix B) in hard copy.

The NDIR detector signal depends on the number of CO₂ molecules in the optical path which, in turn, is mainly a function of pressure and temperature for a given CO₂ mixing ratio. The calculation procedure, therefore, requires temperature and pressure corrections to account for any fluctuations in these parameters as well as a calibration function. First the raw voltage readings are corrected to a standard pressure of one atmosphere (p^o) to account for fluctuations of the NDIR cell pressure. This requires continuous monitoring of the pressure in the cell. It has been found empirically (Welles and Eckles 1991) that pressure p affects the voltage signal v of NDIR analyzers in a linear fashion:

v'=v(p^o/p)

NDIR instruments are calibrated using standard gases with known CO₂ mixing ratios in dry air. The mixing ratio of a component gas (like CO₂) in a mixture of gases (like air) is equivalent to its mole fraction (xCO₂), assuming ideal behavior. The CO₂ mixing ratio of the standard gases should closely bracket the expected range of the sample xCO₂. Although the response of NDIR analyzers is considerably nonlinear, the use of a simple linear calibration function is generally justified over a small concentration range of 100-200 ppmv. The error incurred by this approximation is typically on the order of a few tenths of a ppmv. Furthermore any deviation of the NDIR cell temperature T from the calibration temperature T^o has to be accounted for. Welles and Eckles (1991) have shown that the mole fraction xCO₂* is scaled linearly with the inverse of the absolute temperature:

xCO₂=xCO₂^*(T/T^o)

The resulting CO₂ mole fraction xCO₂ in dry air is temperature and pressure corrected. The latter because the sample gas is either measured dry (i.e., after full removal of water vapor) or has been arithmetically corrected for the diluting and pressure-broadening effects of water vapor based on simultaneous wet xCO₂ and xH₂O measurements. As the air at the air-sea interface can be assumed to be at 100% humidity, a correction has to be applied to account for the increase of the CO₂ mole fraction that is the result of the (actual or arithmetical) removal of water vapor prior to the infrared measurement. Here the saturation water vapor pressure of seawater at equilibrator temperature was calculated using an equation by Weiss and Price (1980), which is valid over the temperature range 273-313 K and the salinity range 0-40 (see Appendix A, Part 1).

For very accurate interpretations the non-ideal behavior of CO₂ should be taken into account (i.e., fugacity has to be used instead of partial pressure). As the results are to be used later for consistency checks, together with other parameters of the CO₂ system in seawater, we decided to use fCO₂. The calculation of the fCO₂ at equilibrator temperature from the measured mole fraction (xCO₂) in dry air is described in detail in Appendix A (Part 2). The fugacity coefficient (i.e., the ratio between fugacity and partial pressure of CO₂), is on the order 0.996 to 0.997 under typical conditions (p = 1µatm, T = 270-300 K, pCO₂ = 350 µatm). Barometric pressure readings from the shipborne meteorological sensor were used for all calculations of final fCO₂ data.

Because the fCO₂ in seawater strongly varies with temperature, the final step in the calculation of fCO₂ (in situ) requires a correction to compensate for any difference between the equilibration temperature and the in situ seawater temperature. Different equations have been proposed for the temperature dependence of CO₂ partial pressure/fugacity in seawater (e.g., Gordon and Jones 1973; Weiss et al. 1982; Copin-Montegut 1988, 1989; Goyet et al. 1993; Takahashi et al. 1993). Because temperature deviations were typically on the order of a few tenths of a degree for all systems during the exercise, the correction is rather small and the choice from the above suite of equations is not critical. We have chosen the equation based on temperature and salinity given by Weiss et al. (1982), which is valid for ranges of 0 to 36°C in temperature, 30 to 38 in salinity, and 80 to 2000 µatm in fCO₂ (see Appendix A, Part 3.). All temperature corrections of the fCO₂ measurements during this exercise are based on this equation.