Partitioning the \(\hbox {CO}_2\) Flux Mediated by Droplets Released from Breaking Waves

Abstract

The \(\hbox {CO}_2\) flux from spume droplets occurs in two steps. First, the initial droplet–air gas concentration gradient \(\nabla C\) is immediately removed with no change in the droplet solubility. Then, the solubility changes with droplet temperature T and radius r evolution, but the flux maintains the condition \(\nabla C=0\). The gas content of a droplet can be determined by \(\nabla C=0\) since the parameters T and r are known. Therefore, the net gas influx of a droplet depends on the values of T and r in its return to the sea. In the second step, the droplet temperature T evolves to an equilibrium temperature \(T_{eq}\), and the radius r is then reduced by evaporation at constant \(T_{eq}\). For the droplet spectrum, a cut-off radius \(r_{cut}\) is used to separate short-lived (\(r> r_{cut}\), returning to the sea before \(T=T_{eq}\)) and long-lived \(r\le r_{cut}\) conditions. The net influx is split into three contributions: the first (\(S_{2S}\)) is mediated by short-lived mechanisms, and the second and the third by long-lived (\(S_{2L}\)) mechanisms that are further separated into temperature-varying (\(S_{2L}^T\)) and radius-varying (\(S_{2L}^R\)) stages. The results show that, in the cases with large air–sea temperature differences, the first stage \(S_{2S}\) dominates the net gas input, but its importance decreases as the value of \(r_{cut}\) increases. The temperature-varying stage \(S_{2L}^T\) is dominant in cases with both large values of \(r_{cut}\) and large temperature differences, while the radius-varying stage \(S_{2L}^R\) increases as either the temperature difference decreases or as the value of \(r_{cut}\) increases.

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Acknowledgements

The authors are deeply grateful to Dr. David Richter for suggestions and constructive criticism, which significantly improved the discussions and the material presented. The participation of the second author in the present study has been supported by National Council for Scientific and Technological Development (CNPq)—Grant 429402/2016-3. All data employed in this study resulted from the equations described, whose numerical approaches are detailed in Gonçalves and Innocentini (2018, doi:10.1007/s10546-018-0369-z) and Andreas (2005, doi:10.1016/j.atmosres.2005.02.001).

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Correspondence to Iury Angelo Gonçalves.

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Innocentini, V., Gonçalves, I.A., Caetano, E. et al. Partitioning the \(\hbox {CO}_2\) Flux Mediated by Droplets Released from Breaking Waves. Boundary-Layer Meteorol (2020). https://doi.org/10.1007/s10546-020-00553-6

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Keywords

  • Air–sea \(\hbox {CO}_2\) exchange
  • \(\hbox {CO}_2\) sea-droplet flux
  • Droplet–air gas gradient
  • Droplet lifetime
  • Droplet solubility