The exchange of gases between the atmosphere and the oceans may occur directly through the sea surface and indirectly through the mediation of additional transient reservoirs: the bubbles injected into the upper ocean by breaking waves. These bubbles both will increase the gross rate of exchange between air and sea and will tend to force a supersaturation of the upper ocean. These two effects are made explicit by writing the equation for the net air-sea flux of a gas as F = (K0 + K(b))[C - SP(1 + DELTA)], where K(b) is the contribution of bubbles to the transfer velocity (gross exchange rate) and DELTA denotes the supersaturation effect. Significant supersaturations can be attributed to the small (less-than-or-equal-to 150-mum radius) bubbles, which are commonly advected several metres below the sea surface (Woolf and Thorpe, 1991). The values of K(b) attributable to this deep flux of bubbles are negligible for most gases, but much greater values are predicted by considering the total flux of bubbles through the sea surface.
The contribution of bubbles to the transfer velocity, K(b), is approximately proportional to the whitecap coverage. Transfer velocities are a complex function of the diffusivity and solubility of the dissolved gas. This function depends on the distribution of the bubbles. Transfer velocities of relatively soluble gases (and particularly the contribution of small bubbles) are limited by the volume flux of the bubbles, V, through the inequality K(b) less-than-or-equal-to V/beta where beta is the Bunsen solubility of the gas. Values of K(b) can be calculated using measurements of the bubbles in a simulated whitecap (Cipriano and Blanchard, 1981). Large (>150-mum radius) bubbles are the main contributors to the air-sea transfer velocity. Transfer velocities are less for more soluble gases. The global average value of K(b) for carbon dioxide is probably between 2 and 10 cm h-1; the best estimate is 8.5 cm h-1.