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

Abstract

Recent studies suggested that under low to moderate wind conditions without bubble entraining wave breaking, the air-water gas transfer velocity k 1 can be mechanistically parameterized by the nearsurface 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 (a 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 1 was derived from the CO 2 flux that was measured simultaneously with a floating gas chamber. Measured results indicate that a and c 1 are not universal constants. Regression analysis showed that a $ logðeÞ while the near-surface turbulence dissipation rate e is approximately greater than 10 26 m 2 s 23 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 a 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 b 0 in the SDM alone may not be adequate to determine k 1 completely.

The FuGas 2.3 Framework for Atmosphere–Ocean Coupling: Comparing Algorithms for the Estimation of Solubilities and Gas Fluxes

“…This coupling agrees with observations that k w scales with the turbulent kinetic energy dissipation at the sea surface (ε), and that ε is better reflected by the sea state [54,56]. Accordingly, the COARE 3.0 included the wave state in the estimation of the roughness parameters essential for the transfer of mass, heat and momentum [69].…”

“…With the optional coupling of the sea state and wind velocity forcings (through the iWLP joint estimate of z0 and u*), the FuGas enables an enhanced representation of local conditions that was demonstrated to be fundamental for the estimation of transfer velocities in fetch-limited situations [50,55,57]. This coupling agrees with observations that kw scales with the turbulent kinetic energy dissipation at the sea surface (ε), and that ε is better reflected by the sea state [54,56]. Accordingly, the COARE 3.0 included the wave state in the estimation of the roughness parameters essential for the transfer of mass, heat and momentum [69].…”

“…There, the steeper waves, a consequence of shorter fetches, should extract more momentum from the atmosphere under similar u 10 conditions [54][55][56]58]. Thus, the rougher coastal ocean surfaces were expected to have relatively more turbulent layers through which gases were transferred at higher rates.…”

“…Such are the formulations proposed by Carini et al [30] or Raymond and Cole [31], accounting only for u 10 , or by Borges et al [32], adding current drag with the bottom. Meanwhile, new evidence emerged for the effects of the sea surface cool-skin and warm-layer [33][34][35][36][37][38], atmospheric stability [39,40], wave-breaking [41][42][43][44][45][46][47][48][49][50], water surface renewal [28,[51][52][53][54][55][56][57], surfactants [28,[58][59][60] and rain [61][62][63][64], just to mention a few examples from an extensive list of published works. In addition to their single influence, these factors also interact.…”

A Structure Function Model Recovers the Many Formulations for Air‐Water Gas Transfer Velocity

“…Equation appears to hold across a wide range of marine and coastal systems (Zappa et al, ) with α = 0.4, though variations reported in the literature are by no means small ( α = 0.17 − 0.63), as discussed elsewhere (Tokoro et al, ; Vachon et al, ). Some studies amended α with a multiplier or a Reynolds number dependency (Wang et al, ), while others suggested that these amendments may be due to changes in exponent n with surface wind conditions (Esters et al, ). When the most efficient waterside momentum transporting eddy scales with Kolmogorov variables (labeled as microeddies), then dimensional considerations alone recover equation for n = 1/2 without invoking complex transport schemes (Lorke & Peeters, ) such as surface renewal (Lamont & Scott, ; Soloviev, ).…”