Temperature dependence of CO₂ fugacity in seawater

Ideally, the correction of the measured CO₂ fugacity (fCO₂) at temperature T_m to fCO₂ at the in-situ temperature T_in should be made by using at least 2 known parameters (pH-A_T, C_T-A_T,...) and the reliable constants for carbonic acid. In practice however, a measured CO₂ property pair is not always available. When fCO₂ is measured alone, one must make an estimate of the effect of temperature on seawater fCO₂ from the accurate knowledge of seawater salinity and temperature and the approximate knowledge of the carbonate parameters. In this paper we present an empirical relationship that can be used to estimate the effect of temperature on fCO₂. The equation is of the form: f{hook}CO_2[t] - f{hook}CO_2[20]=A + Bt + Ct² + Dt³ + Et⁴ where fCO_2[t] and fCO_2[20] represent fCO₂ at temperatures t°C and 20°C, respectively; the parameters A, B, etc. are functions of the ratio X = C_T/A_T: A = (a₀ + a₂X +a₄X²) (1 + a₁X+ a₃X²) B = (b₀ + b₂X +b₄X²) (1 + b₁X+ b₃X²) C = (c₀ + c₂X +c₄X²) (1 + c₁X+ c₃X²) D = (d₀ + d₂X +d₄X²) (1 + d₁X+ d₃X²) E = e₀ + e₁X + e₂X²ln(X) + e₃exp(X) + e₄/ln(X) where the parameters a_i, b_i, etc. are functions of salinity. The 25-parameter equation is fitted by the values of fCO₂ calculated using the constants of Goyet and Poisson (1989), when X varies from 0.8 to 1.0, t varies from -1dgC to 40°C, and S varies from 30 to 40. For T_m - T_in within ± 10°C, direct measurements of fCO₂ as a function of the temperature (from -I to 30°C verify this equation within less than ±5 μatm.