Winds piston velocity

The piston velocity, or gas transfer velocity, is a function of wind speed. There are large differences in the relationships between piston velocity and wind speed, especially at liigher wind speeds (e.g., Liss and Merlivat, 1986 Wannin-khof, 1992). This is the limiting factor for these calculations. 

The effect of wind velocity on (a) thin-film thickness and (b) piston velocity. The solid line represents results obtained from measurements made in wind tunnels. In situ measurements were made from distributions of the naturally occurring radioisotopes of carbon and radon. Source From (a) Broecker, W. S., and T.-H. Peng (1982). Tracers in the Sea. Lamont-Doherty Geological Observatory, p. 128, and (b) Bigg, G. R. (1996). The Oceans and Climate. Cambridge University Press, p. 85. 

We can attempt to apply the same type of model to the H2S data, however there are two additional unknown factors involved. First, we do not have a measurement of the sea surface concentrations of H2S. Second, the piston velocity of H2S is enhanced by a chemical enrichment factor which, in laboratory studies, increases the transfer rate over that expected for the unionized species alone. Balls and Liss (5Q) demonstrated that at seawater pH the HS- present in solution contributes significantly to the total transport of H S across the interface. Since the degree of enrichment is not known under field conditions, we have assumed (as an upper limit) that the transfer occurs as if all of the labile sulfide (including HS ana weakly complexed sulfide) was present as H2S. In this case, the piston velocity of H2S would be the same as that of Radon for a given wind velocity, with a small correction (a factor of 1.14) for the estimated diffusivity difference. If we then specify the piston velocity and OH concentration we could calculate the concentration of H2S in the surface waters. Using the input conditions from model run B from Figure 4a (OH = 5 x 106 molecules/cm3, Vd = 3.1 m/day) yields a sea surface sulfide concentration of approximately 0.1 nM. Figure S illustrates the diurnal profile of atmospheric H2S which results from these calculations. 

Figure 4. Box model results compared to Caribbean transect data ((6), solid symbols). Units are m/day for Vp and 106 molecule/cm3 for midday maximum OH. (a) Runs using piston velocities obtained from the radon deficit (V Rn = 3.1) and SFg lake study (VpSF6 = 2.2) wind speed relationships. Midday maximum OH concentrations (shown on plot) were adjusted to give mean DMS levels in agreement with the shipboard data, (b) Model runs with lower piston velocities and lower OH showing less diurnal variation. Conditions used were (a) Vp = 1.7, OH = 8.0 (b) Vp = 1.1, OH = 5.0 (c) Vp = 0.6, OH = 3.0.

Next, we apply the same model to the equatorial Pacific DMS data of Andreae and Raemdonck (14). Here the average wind speed was slightly less than the last case, 6 m/s, giving considerably smaller piston velocities. The Rn piston velocities converge with the SFg estimates at low wind speeds, so in this case they yield similar results. The average sea surface DMS concentration was... 

Fluxes were either measured directly with a floating chamber or calculated using either a constant piston velocity (value indicated) or using various wind speed relationships W92 is Wanninkhof (1992) C95 and C96 is a combined relationship of Clark et al. (1994) and Carini et al. (1996) M and H93 and C95 is a combined relationship of Marino and Howarth (1993) and Clark et al. (1994). 

In view of the difficulties in determining gas transfer coefficients accurately, direct methods for CO2 flux measurements aboard the ship are desirable. Sea-air CO2 flux was measured directly by means of the shipboard eddy-covariance method over the North Atlantic Ocean by Wanninkhof and McGillis in 1999. The net flux of CO2 across the sea surface was determined by a covariance analysis of the tri-axial motion of air with CO2 concentrations in the moving air measured in short time intervals ( ms) as a ship moved over the ocean. The results obtained over awind speed range of 2-13.5 m s are consistent with eqn [3] within about +20%. If the data obtainedin wind speeds up to 15 m s are taken into consideration, they indicate that the gas transfer piston velocity tends to increase as a cubeof wind speed. However, because of a large scatter ( + 35%) ofthe flux values at high wind speeds, further work is needed to confirm the cubic dependence. 

For low wind speeds, one might ask, at what characteristic depth or distance from the interface is the rate of advective transfer of normal dissolved gases away from the interface equal to diffusive transfer To answer this question, we can use the dimensionless Peclet number, (dV/D), which expresses the relative importance of mass transfer by advection to transfer by diffusion. In the Peclet number, d can be taken as the thickness of the diffusive layer, V the velocity and D as the gas diffusivity in the water phase. If we take V as the piston velocity with an appropriately low value of about 1 cm h, and a typical diffusivity for gases in water of about 10" cm s the thickness of the boundary layer can be determined for a Peclet number, Pe= 1, i.e. at a distance from the interface where advective and diffusive transport are comparable. Under these conditions, d is... 

Figure 4 shows some of the results of measurements of gas exchange in fresh water lakes and in the surface ocean, expressed in terms of piston velocity as a function of wind speed, Uiq, i. e. wind speed measured at 10 m above the water surface. From measurements such as these, and results from wind tunnel experiments, empirical models of piston velocity as a function of wind speed have... 

Fig. 4. Some field measurements of piston velocity as a fimction of wind speed, U,o, the wind speed measm-ed at 10 m elevation above the water sm-face. Data are taken from [18, 26, 52] which have compiled results from the original som-ces...

A number of other functions have been proposed that relate piston velocity to wind speed. These are shown along with the Liss and Merlivat [59] relationship in Fig. 5. On the basis of TTO data from measurements in the Equatorial Atlantic using the radon deficiency method, Smethie et al. [62] proposed a linear relationship between wind speed and gas exchange. Wanninkhof [26] proposed a quadratic function and noted the effect of using an average wind speed when the dependence of exchange on wind speed is nonlinear. The relationship is for steady winds or short-term winds and was determined from the data for bomb 002 and the wind speed distribution around the global mean wind speed. The model predictions of Deacon [28], also shown in Fig. 5, are appropriate only to low wind speeds. 

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