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We present an estimate of the total volume of entrained air by breaking waves in the open ocean, based on a model for a single breaking wave and the statistics of breaking waves measured in the field and described by the average length of breaking crests moving with speeds in the range (c,c + dc) per unit area of ocean surface, Lambda(c)dc, introduced by Phillips (1985). By extending the single breaking wave model to the open ocean, we show that the volume flux of air entrained by breaking waves, V-A (volume per unit ocean area per unit time, a velocity), is given by the third moment of Lambda(c), modulated by a function of the wave slope. Using field measurements of the distribution Lambda(c) and the wave spectrum, we obtain an estimate of the total volume flux of air entrained by breaking for a wide range of wind and wave conditions. These results pave the way for accurate remote sensing of the air entrained by breaking waves and subsequent estimates of the associated gas transfer.

Plain Language Summary Processes at the ocean-atmosphere interface control the transfer of gas and have a profound effect on weather and climate. Among these processes, breaking waves play an important role by entraining bubbles into the ocean. The dynamics and statistics of breaking waves in a particular location of the ocean are complex and depend mainly on the local sea state and not only the wind speed. However, current parameterizations of air-sea gas transfer rely solely on the wind speed, which leads to large uncertainties in the air-sea exchange budget of gases key to the climate system. In this paper, we present a theoretical model to estimate the volume of air entrained in the ocean by breaking waves. Using our model and field measurements of the wave and wave breaking statistics, we obtain an estimate of the total volume of air entrained by breaking for a wide range of wind and wave conditions. These results pave the way for accurate remote sensing of the air entrained by breaking waves and estimates of the associated gas transfer, which will lead to improvements in current climate models.