Upper Ocean 1-D Seasonal Models
File last modified 16 November 1998
19.3b Adding Gases to the Model: Air Injection
An additional aspect of gas exchange between the ocean and the atmosphere is the formation and dissolution of bubbles by wave action. Because bubbles formed by waves (as typified by white-caps) are forced downward into the water column by wave motion and turbulence, they are subjected to increasing hydrostatic pressure, and will partially or completely dissolve. The net effect is a transfer of gases from the atmosphere to the ocean, and a concomitant generation of supersaturation. Actually, the process results in a two way exchange of gases because bubbles rising back toward the surface, if they are not dissolved, will exchange gases with surrounding water and act as vehicles of gas transport. To some extent the sharp upturn in the Liss-Merlivat curve presented in the last section takes this enhancement into account, for the curve is constructed from actual observations, and hence folds this process in.
What we will do, in our numerical experiment here, is add the Liss-Merlivat two-way exchange a one-way flux of gas into the mixed layer due to bubbles. We will use a simple formulation which relates the volume flux of air into the surface ocean as a function of the fractional white-cap coverage proposed by Keeling (1993)
where VA is the air entrainment velocity, estimated to be approximately 0.01 m/s, and WA is the fractional surface area covered by white-caps, estimated by Monahan and Torgersen (1990) to be
where U10 is the velocity in m/s at 10m height (the standard meteorological height for wind measurements and reporting) and that WA=0 for U10<2.27 m/s. Combining the two equations, we get that
In addition to the crudeness of the models (no reflection on the proponents, it's just that the actual physical processes are extraordinarily complex) the "constants" used in these relations are subject to considerable uncertainty. Our strategy will be to use the existing model as a point of departure, and to scale the net injection rate by a constant (initially 1) which we'll adjust to match the observations. This seems a bit of a tinny thing to do, but in its defense, since the effect of the injection is inversely proportional to solubility of the gases involved, and since He and Ne are many times less soluble than Ar and O2, we have a "very long lever" on the magnitude of the process. Further, the similarity in physical characteristics between Ar and O2 again works in our favor: if the model successfully emulates Ar, then it must do a pretty good job with O2.
However, we'll propose one more refinement, similar to that proposed by Spitzer and Jenkins (1989), and originally suggested by Jenkins (1988). We argue that some significant fraction of the air entrained as bubbles will escape due to buoyancy forces. While the complete dissolution of bubbles due to increased hydrostatic pressure is non-fractionating, the partial dissolution experienced by the bubbles rising toward the surface will be kinetically fractionating. Hydrodynamic calculations and experiments reported, for example, by Levich (1962) show that the gas fluxes are proportional to the 2/3 power of the molecular diffusivity. Believe us, this is a well studied problem, especially regarding aeration techniques in sanitary engineering. The process is extremely complicated, as discussed at great length by Keeling (op cit), but we will again opt for a simple parameterization: we will argue that there are two end-member air injection processes. One we call "complete trapping" where the bubble totally dissolves, and one we call "partial trapping" which involves a grazing incidence of a bubble, which loses only an infinitesimal amount of its gas. While we expect a "spectrum" of processes in between, we argue that the two end members, and a mixture of them, captures the essence of the activity. So we argue for an air injection mechanism embodied in
where we have introduced an empirical scaling factor, which should be order 1, and two fractions corresponding to complete (fc) and partial (fp) trapping, constrained by
and Di is the molecular diffusivity of the ith gas, and DHe is the molecular diffusivity of the reference gas, which we have arbitrarily chosen to be He. Clearly the value of Ainj will depend on this choice, but ultimately the net simulation should not.
Why go to this trouble, and aren't we introducing unconstrained, arbitrary parameterization into our model? The answer to the first is that the length of the solubility lever we have developed when we use He to constrain the air injection component for Ar also works against us if there is some uncertainty in the fractionation of the processes involved. This time not in the solubility, but in the large differences in molecular diffusivity. We need to be careful about this! In answer to the second, we do have an external constraint: Ne has a very different molecular diffusivity (about a factor of two smaller) than He, and very similar (within about 25%) solubility. Thus the He/Ne ratio will be a critical indicator of the relative sizes of fc and fp. This will become evident in our model runs.
GoTo Next Section