Variability of air-sea gas transfer velocities in the Baltic Sea

Heat transfer velocities measured during three different campaigns in the Baltic Sea using the Active Controlled Flux Technique (ACFT) with wind speeds ranging from 5.3 to 14.8 m s−1 are presented. Careful scaling of the heat transfer velocities to gas transfer velocities using Schmidt number exponents measured in a laboratory study allows to compare the measured transfer velocities to existing gas transfer velocity parameterizations, which use wind speed as the controlling parameter. The measured data and other field data clearly show that some gas transfer velocities are much lower than the empirical wind speed 5 parametrizations. This indicates that the dependencies of the transfer velocity on the fetch, i. e., the history of the wind and the age of the wind wave field, and the effects of surface active material need to be taken into account.


Introduction
The transfer of a trace gas across the air sea interface is commonly characterized by the gas transfer velocity k, which links the gas flux j with the concentration difference across the interface, ∆c, j = k∆c. (1) Traditionally, k is parameterized with the wind speed measured in 10 m height, u 10 .Different authors proposed different functional dependencies between k and u 10 , for example a gradual transition from a smooth to a wavy regime (Jähne, 1982), piecewise linear (Liss and Merlivat, 1986), linear and quadratic terms (Nightingale et al., 2000), quadratic (Wanninkhof, 1992) or cubic (Wanninkhof and McGillis, 1999).
In the last decades, the dual-tracer technique, especially with the tracer pair 3 He/SF 6 , has become state of the art of measuring the gas transfer velocity in situ.A recent review by Ho et al. (2011) proposed as the best fit to all available 3 He/SF 6 dual tracer data points.
However, mass balance techniques such as the dual tracer method have a large time constant of up to weeks and large spatial scales of a few tens of kilometers, smoothing away varying micrometeorological and surface conditions (e. g. the degree of surface contamination by surface active material).
In contrast, the eddy covariance method provides measurements of the gas transfer velocity on time scales below 1h and spatial scales of a few kilometers.However, bin averaging over wind speed intervals is frequently necessary, since even under idealized conditions, not all realizations of the turbulent field can me measured, so that each single flux measurement obtained during a 30 min time period is still uncertain (Garbe et al., 2014).
In this study, a thermographic technique is presented, which is capable of measuring the heat transfer velocity with a temporal resolution of about 20 minutes, which can then be scaled to gas transfer velocities.The active controlled flux technique was deployed during three cruises in the Baltic Sea to investigate the variability of the transfer velocities under field conditions.
Since the method discussed in this paper is insensitive to bubble contributions and can only be used to measure the interfacial part of the air sea gas transfer, and no measurements were performed in rain conditions, only the influence of surface active material and fetch will be discussed here.

Surfactants
One factor contributing to the disagreement between gas transfer velocities measured at the same wind speed 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 mono-molecular surfactant layer at the water surface (Frew et al., 1990), 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 visco-elastic properties of the surfactant (McKenna and Bock, 2006).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 (McKenna and McGillis, 2004).
Surfactants are enriched in the sea surface microlayer in the worlds oceans (Wurl et al., 2011) over a wide range of wind speeds as high as u 10 = 13 m s −1 (Sabbaghzadeh et al., 2017).ln the Baltic sea, high surface activities were measured (Schmidt and Schneider, 2011), with a seasonal dependency in a near-shore position.The reduction of 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 (Mesarchaki et al., 2015;Krall, 2013;Lee and Saylor, 2010;Frew et al., 1995), in water sampled from the ocean (Pereira et al., 2016;Schmidt and Schneider, 2011;Frew et al., 1990;Goldman et al., 1988), during field studies (Frew et al., 2004), as well as during field studies where artificial surfactants were released on the ocean surface (Salter et al 2011;Brockmann et al., 1982).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, with the momentum transfer resistance parameter β and the Schmidt number exponent n (Deacon, 1977;Jähne et al., 1979;Coantic, 1986;Jähne et al., 1989;Csanady, 1990).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 n = 1/2 is found to be smooth, rather than sudden (Jähne, 1987;Richter and Jähne, 2011).In addition, this change in the Schmidt number exponent depends also 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 (Krall, 2013).

Fetch and wave age
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.Earliest indications that the fetch is an important parameter were seen by Broecker et al. (1978), 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 Liss (1973), who used a tank of only 4.5 m length.Wanninkhof (1992) 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 high as a few hundreds of kilometers offshore.Zhao et al. (2003) and Woolf (2005) developed parameterization for the transfer velocity based the breaking-wave parameter (Toba and Koga, 1986) 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.

Active thermography
The active controlled flux technique 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 an 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 Jähne et al. (1989) 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 a 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 in dependency of 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 (Jähne et al. (1987)) 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 Nagel (2014).

Scaling heat transfer velocities to gas transfer velocities
To compare the measured transfer velocities of heat to the transfer velocities of a gas like CO 2 , Schmidt number scaling is applied, where k gas and k heat are the transfer velocities for the gas and heat, respectively.The Schmidt number Sc = ν/D gas and the Prandtl number Pr = ν/D heat 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 (Jähne and Haußecker (1998), Richter and Jähne (2011), Krall (2013)).
However, using heat as a proxy for a gas tracer has one significant drawback.Diffusion of heat is about one hundred times faster than diffusion of a dissolved gas in water.Because of this, any uncertainty in the Schmidt number exponent n leads to a relative large uncertainty for the heat transfer velocity scaled to a gas transfer velocity.It is generally given by ∆k where ∆k and ∆n 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, ∆ n = ±0.083(Fig. 1) and Sc/Pr ≈ 600/9, the relative scaling error is ±35 %.This is quite a large uncertainty.
In the past decade, several studies (Asher et al., 2004;Atmane et al., 2004;Zappa et al., 2004;Jessup et al., 2009) found deviations between the Schmidt number scaled heat and the simultaneously measured gas transfer velocities.However, a more recent study by Nagel et al. (2015) showed that using a model independent analysis method, as proposed by Jähne et al. (1989) and the correct Schmidt number exponent results in a good agreement.(Krall, 2013) for the wind speeds encountered during this study.
Friction velocities measured in the Aeolotron were taken from Bopp (2011) and converted to the wind speed in 10 m height using the drag coefficient parameterization by Edson et al. (2013).To scale the heat transfer velocities measured in the present work, the mean values of the Schmidt number exponent were used.
For field measurements, the importance of using a Schmidt number exponent depending on the water surface condition is also highlighted in Esters et al. (2017), 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, see 1 (Krall, 2013), as opposed to Schimpf et al.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 ∆n from ±0.083 to < ±0.030 (Fig. 1).The resulting relative uncertainty of k is then ∆k/k < ±13%.
Another source of uncertainty lies in transferring the lab measurements of the Schmidt number exponent to the field conditions, since in the lab, the friction velocity u * is measured (Bopp, 2011) as opposed to the wind speed in 10 m height which is commonly measured in the field.To convert lab measurements to field conditions, the drag coefficient, C D = u 2 * /u 2 10 taken from Edson et al. (2013) was used.

Experimental setup on ship
To use the CFT method described in Sec.3.1, a CO 2 -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 synchronised by custom electronics.A water tight box, including the 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 used instruments is given in Nagel (2014).
Measurements were only conducted at stations, were the vessel was standing at 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 night time or on cloudy days.Nevertheless, reflections of thermal signature of the sky and the ship itself can not be avoided.However, the periodic forcing of the heat flux as described in Sect.3.1, suppresses these effects (lock-in technique).
Wind speed measured in 10 m height was provided by each vessels weather station.On FS Alkor, one minute mean wind speeds were stored only for the times during which measurements with the ACFT were performed.On RV Aranda, ten second 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.

Baltic Sea campaigns 2009 and 2010
Three ship campaigns were conducted in 2009 and 2010.

Measured transfer velocities
First results of the cruise in 2009 are already published in Schimpf et al. (2011).For this study a re-evaluation with slight differences in the correction of the penetration depth of the infrared camera was done.Also, the improved Schmidt number scaling described in section 3.2 was used, while Schimpf et al. (2011) used n=1/2 for all conditions.The obtained heat transfer velocities are given in Tab.A1. Figure 3 shows the measured transfer velocities, scaled to a Schmidt number of 600.To compare the results with other field measurements the parameterization by Ho et al. (2011), which parameterizes the transfer velocity with the wind speed is also shown.the system is very high, as it decreases with the square of the transfer velocity (Eq.4).The time a water parcel stays in the heated patch (residence time) is limited due to surface currents and the movement of the ship relatively to the water surface.
To be able to reach the thermal equilibrium, the residence time has to be longer than the response time of the water surface.
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 ms −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 time scales required for measurements are very long at low wind speeds, and sufficiently long periods of low winds are rarely encountered.parameterization.Because no other information is available, it is impossible to distinguish whether this is caused by the limited fetch or by surfactants or by a combination of both.

Comparison with other field and laboratory data
A very helpful hint comes, however, from an old data set which constitutes the most diligently measured gas transfer velocities using the Radon deficit method (Kromer and Roether, 1983;Roether and Kromer, 1984).One part of this data set was measured during the JASIN cruise in the North Atlantic with highly varying wind speeds.The measured gas transfer velocities there will be significant differences in the gas transfer velocity.The data suggests that this effect may be as large as a factor of five.
It is obvious that the deviations between the measurements shown here and the Ho parameterization cannot be explained by fetch or the age of the wave field alone, because both at a young wind wave field in the shielded archipelago and at very old wind wave fields (FGGE), significant reductions in the gas transfer velocities are observed.
At this point it is helpful, to compare the field data with laboratory data.A direct comparison is not useful, because the conditions concerning the wave field and surface contamination will be different.But laboratory data are very helpful to explore the upper and lower limits of the gas transfer velocity at a given wind speed.For the comparison, we used gas transfer velocities measured in the Heidelberg Aeolotron.This is an annular facility with virtually unlimited fetch and thus may resemble the ocean conditions in the best possible way.Those gas transfer velocities were measured with the method described in Mesarchaki et al. (2015) and are published in Krall (2013).
The gas transfer velocities measured when the water surface in the Aeolotron was carefully cleaned by skimming the top layer of the water before the start of each measurement to remove surface active material, can be considered to be the upper limit (green shaded area in Fig. 6).
The lower limit is constituted by the gas transfer velocities predicted by Deacon (1977) (eqn.3 with n=2/3 and β =12.1) for a smooth water surface.These values have been confirmed by measurements in a small annular wind/wave facility when the water surface was covered by surfactants (Jähne et al., 1979).The highest friction velocity in water at which the water surface remained smooth and without wind waves in this facility was 1.4 cm/s corresponding to a smooth water surface up to a wind speed of u 10 ≈ 13 m/s.This is supported by the findings of Sabbaghzadeh et al. (2017), who measured surfactant enrichment in the sea surface microlayer up to u 10 ≈ 13 m/s as well.
The region between these upper and lower bounds for gas transfer is shaded in a magenta color in Fig. 6.This difference between highest and lowest possible gas transfer velocities alone indicates that the gas transfer is highly variable and not only dependent on wind speed alone.All shown field data as well as the Ho parameterization are compatible with this shaded region of possible gas transfer rates.

Conclusions and outlook
Heat exchange measurements were conducted in the Baltic Sea during three different campaigns using the active controlled flux technique.The measured heat transfer velocities, scaled to gas transfer velocities using realistic Schmidt number exponents, show high variability even at the same wind speed.New is that even at high wind speeds in the range of 8 to 15 m/s significantly lower gas transfer velocities were measured, which were about a factor of two lower than the average transfer velocities measured by the dual tracer technique and parameterized by the relation of Ho et al. (2011).Based on the field data alone it is not possible to distinguish fetch effects from effects by surface films.This study clearly indicates that a better understanding of air-sea gas transfer requires more systematic measurements of the the effects of fetch (or the age of the wave field) and surfactants.In the field the most promising approach is eddy covariance measurements together with active thermography.
For laboratory measurements some serious limitations must be overcome.One is the fetch gap.In linear facilities only very short fetches can be studied, which are no longer than the maximum length of the water tunnel in the facility.Even at these short fetches, significant variations of the gas transfer rate can be measured.This has recently been demonstrated by Kunz and Jähne (2018) using active thermography.
In order to increase the fetch range available in the lab, gas exchange measurements could be performed in annular facilities under unsteady wind speed conditions.In the Heidelberg Aeolotron it is possible to switch on the wind in a few seconds, while it takes several minutes for the wave field to develop to a stationary state.Unfortunately, it is very hard to make gas exchange measurements with a temporal resolution of below a minute using conventional mass balance techniques.
A very promising technique for fast measurements of gas transfer is the recently developed mass boundary layer imaging technique (Kräuter et al., 2014;Kräuter, 2015).Using this technique will enable the measurement of the gas transfer velocity simultaneously and in the same footprint as the heat transfer velocity.This will allow a direct comparison as well as in-depth studies of the physical mechanisms governing air-sea gas and heat transfer.

Figure 1 .
Figure 1.Possible ranges of Schmidt number exponents for a clean and surfactant covered water surface as a function of the wind speed as inferred from experiments in the Heidelberg Aeolotron wind-wave tank(Krall, 2013) for the wind speeds encountered during this study.

(
2011), who used a fixed Schmidt number exponent of 1/2.(Jähne et al. (1987),Richter and Jähne (2011),Krall (2013)).InKrall (2013), 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 inKrall (2013), corresponding to clean water and water with 167 µgl −1 Triton X-100, respectively, was used to scale the heat transfer velocities to gas transfer velocities to account for possible contamination of the water surface with surface active material.The difference between 10 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.Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 2 Figure 2 .Figure 3 .
Figure 2 show the tracks of these three cruises.The first one (Alkor Cruise 336, Schmidt (2009)) took place from 25 April 2009 until 7 March 2009 on the German research vessel FS Alkor.It included measurements north-west of Rügen and the Gotland Sea.The second cruise on the same vessel (Alkor Cruise 356, Schneider (2010)), between 30 June and 13 July 2010

Figure 4 Figure 4 .
Figure 4 shows the measured heat transfer velocities over the wind speed in comparison to the same parameterization as used for the measurements in 2009.Schmidt number scaling was done with the same method as for the Alkor 2009 data set.10

10 9Figure 5 .
Figure 5. Measured k600 transfer velocities plotted against the wind speed of the RV Aranda Fall 2010 cruise.The filled circles show the open ocean measurements, while the open circles are data from the archipelago.For comparison, the wind speed parameterization by Ho et al. (2011) is also shown.

Fig. 6 Figure 6 .
Fig.6shows a comparison between the measured transfer velocities with the empirical parameterization ofHo et al. (2011).The measurements from the Alkor 2009 and Alkor 2010 cruises coincide within the error margins with the empirical parameter-5

5
are higher or as high as predicted by the the empirical parameterization.However, the transfer velocities measured during the FGGE cruise with constantly blowing trade winds are significantly lower.One value is three times lower than predicted by the 11 Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.empirical parameterization.These measurements clearly indicate that even at the open ocean (i.e. without fetch limitations) Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.
Appendix A: Numerical values of the measured transfer velocitiesTables A1, A2 and A3 give the numerical values of the measurements conducted during the cruises in the Baltic Sea.

Table A1 .
Measured heat transfer velocities k heat in dependency of time, position, wind speed and water and air temperature for the measurements on FS Alkor in 2009.Furthermore the Prandtl number Pr, the Schmidt number exponent n and the scaled transfer velocity k600 are given.The given times are approximate starting times in UTC.Each measurements lasted about 20 min.Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.

Table A2 .
Measured heat transfer velocities k heat in dependency of time, position, wind speed and water and air temperature for the measurements on FS Alkor in 2010.Furthermore the Prandtl number Pr, the Schmidt number exponent n and the scaled transfer velocity k600 are given.The given times are approximate starting times in UTC.Each measurements lasted about 20 min.Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.

Table A3 .
Measured heat transfer velocities k heat in dependency of time, position, wind speed and water and air temperature for the measurements on RV Aranda in 2010.Furthermore the Prandtl number Pr, the Schmidt number exponent n and the scaled transfer velocity k600 are given.The given times are approximate starting times in UTC.Each measurements lasted about 20 min.All measurements were conducted in a fetch-limited position with the exception of the two conditions marked with an asterisk (*).Ocean Sci.Discuss., https://doi.org/10.5194/os-2018-108Manuscript under review for journal Ocean Sci. Discussion started: 5 October 2018 c Author(s) 2018.CC BY 4.0 License.