On the coefficients of small eddy and surface divergence models for the air‐water gas transfer velocity

Recent studies suggested that under low to moderate wind conditions without bubble entraining wave breaking, the air‐water gas transfer velocity k + can be mechanistically parameterized by the near‐surface turbulence, following the small eddy model (SEM). Field measurements have supported this model in a variety of environmental forcing systems. Alternatively, surface divergence model (SDM) has also been shown to predict the gas transfer velocity across the air‐water interface in laboratory settings. However, the empirically determined model coefficients ( α in SEM and c 1 in SDM) scattered over a wide range. Here we present the first field measurement of the near‐surface turbulence with a novel floating PIV system on Lake Michigan, which allows us to evaluate the SEM and SDM in situ in the natural environment. k + was derived from the CO 2 flux that was measured simultaneously with a floating gas chamber. Measured results indicate that α and c 1 are not universal constants. Regression analysis showed that α ∼ l o g ( ε ) while the near‐surface turbulence dissipation rate ε is approximately greater than 10 −6 m 2 s −3 according to data measured for this study as well as from other published results measured in similar environments or in laboratory settings. It also showed that α scales linearly with the turbulent Reynolds number. Similarly, coefficient c 1 in the SDM was found to linearly scale with the Reynolds number. These findings suggest that larger eddies are also important parameters, and the dissipation rate in the SEM or the surface divergence β ′ in the SDM alone may not be adequate to determine k + completely.