Analytical Quantification of Carbon Dioxide Exchange Mediated by Spume Droplets

The role of spume droplets in the air–sea exchange of CO_2 is investigated by applying simultaneous rate equations for the mass of dissolved CO_2 , radius, and temperature of a droplet. The life of a droplet can be divided into two phases, except when the air is saturated, and when the air and sea temperatures are the same. In the first phase, the CO_2 fluxes at the droplet surface and at the air–sea interface are in the same direction. In the second phase, the air–droplet CO_2 gradient vanishes, and the droplet loses water and CO_2 as long as there is evaporation. The largest sea–air CO_2 transfer by the droplets is in the case where the sea temperature is greater than the air temperature, and the air–sea CO_2 concentration gradient is towards the air. The net transfer of CO_2 for a droplet depends on its lifetime, which is longer for smaller droplets. The overall role of a droplet spectrum is assessed assuming a sea-spray generation function for radii from 30 to 500 m, whose formulation of its dependence on the surface-wave peak period and 10-m wind speed is currently accepted; for situations with an air–sea CO_2 concentration gradient towards the air and a warmer sea than the air, the overall transfer obtained is towards the sea. The effect of the turbulence is analyzed by increasing the droplet lifetime by a factor of 10, which increases the CO_2 flux towards the sea for droplet spectra composed mainly of small droplets (generated by waves with small peak period). However, the mean droplet size is larger for droplets generated by waves with a high peak period, and then the flux is towards the air because many large droplets reach the second phase.