A model of sea-foam thickness distribution for passive microwave remote sensing applications

[1] Foam formations at the sea surface significantly contribute to microwave brightness temperature signatures over the ocean for moderate to high wind speeds. The thickness of foam layers generated by breaking waves follows a specific distribution due to unsteadiness of breaking and the large range of wave scales involved in the phenomenon. Although the effect of a distributed thickness-parameter on the foam-induced microwave brightness temperature may be comparable to or larger than the fractional whitecap coverage, it is not yet included in brightness models. To fill this gap, we develop a dynamical model for the conditional fraction of sea-surface covered by whitecaps with given thickness, as a function of wind speed. It is an integrated function of the foam-layer lifetime and of the distribution of the total length of breaking fronts at given scale. The depth at which air bubbles are injected into the water column is scaled with breaking front velocity using reported dynamical properties of unsteady breaking regions. For wind speed less than 20 m/s, the model predicts that two thirds of the fractional whitecap coverage is due to layers on average thinner than 60 cm and 35 cm for crest- and static-foam formations, respectively. In unstable atmospheric conditions, an increase in wind speed from 7 to 20 m/s corresponds to a coverage-weighted foam-layer thickening of about 1 cm and 3.5 cm, respectively. In neutral conditions, the thickening is approximately 2 times lower. Still, this will induce doubling of foam emissivity at Ku and C bands.