An "all-encompasing" air-sea gas exchange model would include interfacial physics (micrometeorology, sub-surface structure, waves, turbulence, and mixing on both sides of the interface), bubble-mediated processes (wave breaking, energy dissipation, void fractions, bubble distributions, and turbulent bubble dynamics), and biochemical influences (temporal and spatial variability resulting in local or regional sources and sinks of gases). While considerable work has been dedicated to advancing many of these processes, more still must be done in terms of quantifying all of these processes into one parameterization. As it turns out, one area where major advancements are need is the role of bubbles which can account for as much of 50% of the total air-sea gas flux.




Over the past quarter of a century substantial progress has been made in refining parameterizations relating the gas transfer velocity, k, to the 10 meter windspeed, U10, such that they inlcude most known interfacial processes (Liss and Merlivat, 1986; Wanninkhof, 1992; Jahne and HauBecker, 1998; Edson and Fairall, 1998; Fairall et al., 2000; Taylor, 2000; Fairall et al., 2003), although they often ofter mixed or conflicting results, likely due to the lack of open ocean data beyond low-to-moderate wind speed (Fairall et al., 2000).

The goal of this project is to model gas fluxes across the wavy air-sea interface by considering both vertical gradients of gases in the atmosphere and ocean, and bubble mediated fluxes resulting from breaking wave energy dissipation through a proposed bubble model.

Breaking waves act as a source of vorticity and turbulence within the ocean surface layer as they dissipate surface-wave energy, enhancing gas transfer by drawing turbulence closer to the boundary layer while entraining bubbles (Melville, 1996). Early studies shed some light role of bubbles and found a solubility dependence during high wind speeds in wind/wave tank experiements (Merlivat and Memery, 1983; Broecker and Siems, 1984) with the total impact of bubbles thought to increase the total transfer velocity by as much as 50% (Keeling, 1993). Modeling the gas flux using vertical concentration gradients will force the model to fall back toward a Fick's law representation of the flux while providing a Eulerian concentration profile to be used in the bubble model.

Since diffusive processes happen on time scales much slower than the turbulent counterpart, the strongest concentration gradients are found within the molecular sub-layers, directly against the interface.  Therefore the gas flux on the oceanic side is modeled using the surface renewal model (Liu et al., 1979) . On the atmospheric side, gradients are modeled following the “wavy wall law”  framework of Mueller  and Veron, (2010).  The modeled gas concentration profiles and fluxes are used to calculate the gas exchange coefficient and the transfer velocity. The bubble mediated transfer velocity is parameterized as a function of the whitecap, Wc, following the work of Woolf (1997). As a wave breaks the breaking wave front is physically sweeping out an area of ocean (the whitecap) at the phase speed of the wave for a given period of time. This active breaking phase (stage A) is Wc.  Shown are the wave model results (blue and red) along with frequently cited parameterizations.

The top figure shows the modeled Wc for 100km (blue) fetch as function of wind speed. Also plotted are Wc functions by Monahan and Muircheartaigh (1980), Zhao and Toba (2001), and Woolf (2005), overlayed upon a figure from Yuan et al. (2009) who presents an addition selection of whitecap paraeterizations (including thier model model envelop (dashed line)) along with satelitte observations (A and B stages) from Anguelova and Webster (2006).

The middle figure shows the gas flux model results for CO2 against recent DMS observations from across the globe.  The transfer velocities are all scaled to Schmidt number of 660 as a means of comparing “apples to apples.”   Using SO Gas EX observations, k660 is modeled for  two different fetches (blue and red lines). Also plotted are the interfacial (green) and bubble mediated (orange) components of k660, along with popular cubic and quadratic parameterizations. k660 in the SO and North Atlantic (the presumably colder regions; black and dark grey dots) show a more linear trend at higher winds speeds compared with the warmer observations. The plotted observations (Figure 2) and & k660 parameterizations (Figure 3) from Yang et al. (2011).

As the research progresses, a full bubble model will be developed. For an individual bubble, gas transport across the bubble-sea interface is a diffusive process. In reality, bubble motion in the water column is affected by waves, Langmuir circulations, buoyancy, and turbulence. As a “first guess,” a simple model was developed that assumes bubble rise velocity  result from a balance of drag and buoyancy forces (Memery and Merlivat, 1985). As a test case, bubbles of varying radii were placed at a depth of 1.0 meter with the oceanic concentrations equal to that of the atmosphere (i.e. the bubble overpressure arising from surface tension and hydrostatic pressure will drive the flux). With the bubble origin assumed to be the atmosphere, a bubble model must allows for the exchange of N2, O2, Ar, and CO2 which collectively account for 99% of atmospheric gases.

The bottom figure shows the total volume of N2, O2, Ar, and CO2 gas transferred as a bubble ascends in the water column.  The result for N2, O2, and Ar show a similar structure with increase radii however it is evident that large bubbles de-gas large quantities of CO2 . In reality bubble dynamics and motion below a wind-driven wave field are far from terminal rise velocity as turbulence plays a critical role. Developing a more detailed bubble model is the topic of on-going research.