Figure 6. (a) Sea surface (<30 m) oxygen versus total CO₂ normalized to a salinity of 35. (b) Density sections from the equator to 5 N. Data from the shaded region of (a) were from Survey II from 2 N to the equator: the shaded region of (b). Oxygen data serves as a tracer for the atmospheric exposure time of surface waters on the cold side of the front. Oxygen is plotted as apparent oxygen utilization (AOU), the deviation from saturation at 1 atm total pressure, with positive AOU denoting undersaturation. Subsurface waters in this region covary in their oxygen : total CO₂ concentrations in a ratio of -0.85:1, as indicated by the vector (the deviation from Redfield is due to the export of CaCO₃ and increasing solubility of CO₂ in colder waters; [Archer et al., 1996]). Upon exposure to the atmosphere, both oxygen and CO₂ will begin to equilibrate toward atmospheric saturation values. Given a gas exchange rate constant, k, the gas exchange rate of oxygen can be calculated as

Flux O₂ [mol m^-2 d^-1] = k [m d^-1] . O₂ [mol m^-3]

where k is an exchange coefficient, and O₂ is the deviation from oxygen saturation. For total CO₂, the exchanging species is CO_2(aq), which has a concentration very much smaller than the total dissolved CO₂ concentration (which includes HCO₃^- and CO₃⁼). Under conditions of constant temperature and alkalinity, the exchange flux of CO₂ can be calculated from the total CO₂ concentration as

Flux CO₂ [mol m^-2 d^-1] = k [m d^-1] ^{. .} CO₂ / CO_{2 ref} ^. [CO₂]_(aq)ref

where is the Revelle buffer factor, taken for the cold water to be 12 [Archer et al., 1996], CO₂ is the deviation of total CO₂ of the saturation value, CO_2ref (taken here to 1990 uM kg^-1), and [CO₂]_{(aq) ref} is the dissolved CO₂ gas concentration at atmospheric saturation, taken here to be 10.2 uM kg^-1. The mixed-layer depth varied diurnally between 15 and 40 m from the equator to 1 N, and increased to 10-70 m diurnally in the cold water just south of the front. For this calculation we assume an average of 60 m. The diagonal lines in the shaded region indicate the time evolution of the total CO₂ / oxygen signature of a suite of recently exposed surface waters. The initial ratio of total CO₂ / oxygen variability is labeled "Initial (Subsurface)". In the course of time, the faster equilibration of oxygen drives the covariation toward a flat ratio, as observed in the rest of the Survey I and II datasets. We conclude the surface exposure time was of the order of 10-20 days.