One factor contributing to the disagreement between gas transfer velocities measured at the same wind speed even with the same measuring technique are surface-active materials (surfactants), which reduce the gas transfer velocity. This reduction in the gas transfer velocity in the presence of surfactants is not caused by the additional diffusion of the gas through the monomolecular surfactant layer at the water surface but by hydrodynamic effects in the mass boundary layer. Surfactant presence at the water surface inhibits eddy motion close to the surface and reduces fluid velocities. Upwelling at the surface is hindered by a reduction in the surface divergence due to the viscoelastic properties of the surfactant . Vertical velocity fluctuations near the interface are considered vital to gas transfer enhancement. Decreased vertical transport of fresh fluid towards the water surface results in a thicker boundary layer and thus a reduced transfer velocity .

Surfactants are enriched in the sea surface microlayer in the world's oceans over a wide range of wind speeds as high as u10=13 m s-1 . ln the Baltic Sea, high surface activities were measured , with a seasonal dependency at a near-shore location. The reduction in the gas transfer velocity due to surfactants has been observed in studies, where the gas transfer velocity was measured in laboratory setups in fresh water with added artificial surfactants , in water sampled from the ocean , during field studies and during field studies where artificial surfactants were released on the ocean surface . Gas transfer is found to be highly variable, with a reduction of up to 60 % under surfactant influence.

The gas transfer velocity k of sparingly soluble gases is commonly parameterized with the friction velocity u*, a measure for momentum input, k=1βu*Sc-n, with the momentum transfer resistance parameter β and the Schmidt number exponent n . Both the momentum transfer resistance β and the Schmidt number exponent n depend on the hydrodynamic properties of the water surface. For a hydrodynamically smooth water surface, e.g., at very low wind speeds or under surfactant influence, the Schmidt number exponent is found to be n=2/3, while for a wavy water surface, n=1/2. For increasing friction velocity, this change from n=2/3 to 1/2 is found to be smooth rather than sudden . In addition, this change in the Schmidt number exponent also depends on the contamination of the water surface with surface-active material, with the change starting at higher friction velocities and being steeper for a surfactant-covered water surface .

Another factor influencing the gas transfer velocity, which is disregarded in the widely used wind speed only parameterizations, is the dependency on fetch or the age of the wave field. The earliest indications that the fetch is an important parameter were seen by , who used an 18 m long wind-wave tank and found almost a doubling of the gas transfer velocity compared to the earlier work by , who used a tank of only 4.5 m length. pointed out that the differences observed between gas transfer measurements in lakes and the ocean might be caused by growing wave fields and thus increasing near-surface turbulence over distances as great as a few hundreds of kilometers offshore. and developed a parameterization for the transfer velocity based on the breaking-wave parameter and the whitecap coverage, both of which depend on the fetch. The considerations above indicate that there should be a dependency of the gas transfer velocity on the fetch. But unfortunately there is no solid knowledge because more detailed measurements and theories are lacking.

The active controlled flux technique (ACFT) can be used to measure gas transfer velocities under laboratory as well as under field conditions with a high temporal (minutes) and spatial (meters) resolution, using heat as a proxy tracer. A carbon dioxide laser with a scanning optic is used to deposit energy directly to the water surface. An infrared camera measures the resulting heating. For this study the system theory approach proposed in was used. In this approach, the laser is switched on and off with changing frequencies. At low laser forcing frequencies the water surface will reach the thermal equilibrium, resulting in constant heating. At higher forcing frequencies this equilibrium is not reached and the measured amplitude is damped. Using Fourier analysis to determine this amplitude damping depending on the laser forcing frequency, the time to reach the thermal equilibrium, which corresponds to the response time of the system, is calculated. It is linked to the transfer velocity by kheat=Dheatτorτ=Dheatkheat2 . This analysis technique is particularly suitable for field measurements as it requires no absolute calibration. A more detailed description of the analysis method, the necessary correction for the penetration depth of the infrared camera and the error estimation can be found in .

To compare the measured transfer velocities of heat to the transfer velocities of a gas like CO2, Schmidt number scaling is applied: kgas=kheatScPr-n, where kgas and kheat are the transfer velocities for the gas and heat, respectively. The Schmidt number Sc=ν/Dgas and the Prandtl number Pr=ν/Dheat are given by the kinematic viscosity of the water divided by the diffusion coefficient of the gas and of heat in water, respectively. The Schmidt number exponent n varies between n=2/3 for a flat and n=1/2 for a wavy water surface . Schmidt number scaling is used to provide a value for the gas transfer velocity, which is independent of the specific measurement technique or tracer.

However, using heat as a proxy for a gas tracer has one significant drawback. Diffusion of heat is about 100 times faster than diffusion of a dissolved gas in water. Because of this, any uncertainty in the Schmidt number exponent n leads to a relatively large uncertainty for the heat transfer velocity scaled to a gas transfer velocity. It is generally given by Δkkgas=ln⁡ScPrΔn, where Δk and Δn are the absolute uncertainties for the transfer velocity and the Schmidt number exponent, respectively. For the whole expected range of n=2/3 to 1/2, Δn=±0.083 (Fig. ) and Sc/Pr≈600/9, the relative scaling error is ±35 %. This is quite a large uncertainty.

In the past decade, several studies found deviations between heat scaled by the Schmidt number and the simultaneously measured gas transfer velocities . However, a more recent study by showed that using a model independent analysis method, as proposed by and the correct Schmidt number exponent results in good agreement.

For field measurements, the importance of using a Schmidt number exponent, depending on the water surface condition, is also highlighted in , who relate the gas transfer velocity to the turbulent energy dissipation rate.

Currently, there are no measurement techniques available to measure the Schmidt number exponent in the field with the same temporal resolution as the heat transfer measurements. Therefore, the scaling in the present work was done using Schmidt number exponents measured in the Heidelberg Aeolotron wind-wave tank , as opposed to , who used a fixed Schmidt number exponent of 1/2. In , Schmidt number exponents were measured with different concentrations of the surface-active material (surfactant) Triton X-100. The mean of the Schmidt number exponent of the two extreme cases presented in , corresponding to clean water and water with 167 µg l-1 Triton X-100, respectively, was used to scale the heat transfer velocities to gas transfer velocities (see Fig. ) to account for possible contamination of the water surface with surface-active material. The difference between the mean and both extreme values of the Schmidt number exponent was used as the uncertainty of the Schmidt number exponent. Since the Aeolotron wind-wave tank is an annular facility, it has virtually unlimited fetch, comparable with open-ocean conditions. Due to the lack of simultaneously measured Schmidt number exponents in the field, this approach is more realistic than using n=1/2 for all encountered wind conditions disregarding a potentially smooth condition (n=2/3) of the water surface. The approach used here reduces the uncertainty of Δn from ±0.083 to <±0.030 (Fig. ). The resulting relative uncertainty of k is then Δk/k<±13 %. Another source of uncertainty lies in transferring the lab measurements of the Schmidt number exponent to the field conditions, since the friction velocity u* is measured in the lab as opposed to the wind speed at 10 m height, which is commonly measured in the field. To convert lab measurements to field conditions, the drag coefficient, CD=u*2u10-2, taken from was used.

Three ship campaigns were conducted in 2009 and 2010. Figure  show the tracks of these three cruises. The first one (Alkor Cruise 336, ) took place from 25 April until 7 May 2009 on the German RV Alkor. It included measurements northwest of Rügen and the Gotland Sea. The second cruise on the same vessel (Alkor Cruise 356, ) between 30 June and 13 July 2010 included measurement stations spread across the whole Baltic Sea. The third cruise took place on the Finnish research vessel RV Aranda from 14 until 19 September 2010. Due to the stormy weather conditions, most measurements were conducted in the Finnish archipelago and only two measurements were conducted under open-ocean conditions in the Gulf of Finland.

To use the ACFT method described in Sect. , a CO2 laser (Firestar f200, Synrad, Inc.) was used to heat the water surface. A scanning system (Micro Max 671, Cambridge Technology, Inc.) was used to widen the laser to create a heated patch on the water surface. The temperature response of the water surface was recorded with an infrared camera (CMT 256, Thermosensorik). Laser, scanner and camera are synchronized by custom electronics. A watertight box, including the infrared (IR) laser, the IR camera and the electronics, was installed on rails on top of an aluminum cradle at the bow of the research vessels. During transit times the box was retracted and fixed over the vessel, while it was moved over the ocean during measurement times. A more detailed description of all instruments used is given in .

Measurements were only conducted at stations where the vessel was standing in one position. Nevertheless due to currents the water surface moved relative to the ship. As direct sun irradiation disturbs the infrared signals, most measurement were conducted during nighttime or on cloudy days. Nevertheless, reflections of the thermal signature of the sky and the ship itself cannot be avoided. However, the periodic forcing of the heat flux as described in Sect.  suppresses these effects (lock-in technique).

Wind speed measured at 10 m height was provided by the weather station of each vessel. On RV Alkor, 1 min mean wind speeds were stored only for the times during which measurements with the ACFT were performed. On RV Aranda, 10 s mean values were stored for the whole duration of the cruise. During data processing, averages of the stored values were calculated for the times during which the respective ACFT measurements were performed.

The first results of the cruise in 2009 are already published in . For this study a reevaluation with slight differences in the correction of the penetration depth of the infrared camera was done. Also, the improved Schmidt number scaling described in Sect.  was used, while used n=1/2 for all conditions. The obtained heat transfer velocities are given in Table . Figure  shows the measured transfer velocities, scaled to a Schmidt number of 600. To compare the results with other field measurements, the parameterization by , which parameterizes the transfer velocity with the wind speed is also shown. This parameterization was chosen for comparison, since it is one of the few in which a margin of uncertainty is included (gray band in Fig. ).

Figure  shows the measured heat transfer velocities against the wind speed for the Alkor campaign in 2010 in comparison with the parameterization by . Schmidt number scaling was done with the same method as for the Alkor 2009 data set. During most of the RV Alkor campaign in 2010 the wind speeds were rather low. At low wind speeds, the response time of the water surface is very long, as it increases with the square of the inverse transfer velocity (Eq. ). The time a water parcel stays in the heated patch (residence time) is limited due to surface currents and the movement of the ship relative to the water surface. In the thermal equilibrium, the heat energy deposited on the water surface by the laser equals the energy removed from the surface by processes driving heat transfer, which results in a constant water surface temperature. Only if the residence time is longer than the response time does the water surface reach the thermal equilibrium. Otherwise a lower temperature and therefore a higher amplitude damping will be observed, which leads to an overestimation of the measured transfer velocities. The residence times were estimated from the infrared images themselves by measuring the time a single structure stayed in the heated patch. All measurements with wind speeds of 4 m s-1 and below are not reliable because the estimated residence times were found to be too long. Therefore, they will be excluded from further analysis.

This highlights the difficulties of measuring gas transfer velocities at very low wind speeds. However, difficulties also exist with other approaches to measure the gas transfer velocity in the field, such as dual-tracer studies, where the timescales required for measurements are very long at low wind speeds and sufficiently long periods of low winds are rarely encountered.

The heat transfer velocities scaled to Sc=600 measured on RV Aranda in 2010 are shown in Fig. . The transfer velocities measured in the shielded archipelago are significantly lower than the ones measured under open-ocean conditions.

Figure  shows a comparison between the measured transfer velocities and the empirical parameterization of . The measurements from the Alkor 2009 and Alkor 2010 cruises coincide within the error margins with the empirical parameterization by Ho, except for the value at the highest wind speed, which is approx. 40 % lower. The two open-ocean measurements during the RV Aranda cruise 2010 are slightly lower than the empirical parameterization but still close to it.

This is, however, not the case for the RV Aranda cruise measurements in the shielded archipelago. The measured values are significantly lower. On average, the values are only about one half of the transfer velocities predicted by the empirical parameterization. There are three possible explanations for this finding: bubble-mediated transfer, fetch (or wave age) and surfactants. In the following sections, these possible explanations will be discussed in detail.