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 us 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 those based on the empirical wind speed
parameterizations. 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, Δc:
j=kΔc.
Traditionally, k is parameterized with the wind speed measured at a height of 10 m, u10, since wind speed is the most readily available parameter.
Different authors proposed different functional dependencies between k and
u10, for example a gradual transition from a smooth to a wavy regime
or piecewise linear , linear and quadratic , quadratic , or
cubic terms .
gives an overview of the most commonly used techniques
to measure the gas transfer velocity. In the last decades, the dual-tracer
technique, especially with the tracer pair 3He-SF6, as well as eddy
covariance measurements of the gases CO2 and dimethylsulfide (DMS),
has become state of the art for measuring the gas transfer velocity in situ. A recent
review article by proposed
k600[cmh-1]=0.262±0.022u102[u10inms-1]
as the best fit to all available 3He-SF6 dual-tracer data points, where
k600 denotes the transfer velocity scaled to a CO2-equivalent
transfer velocity at 20 ∘C. 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 timescales below 1 h 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 be measured, so that each single flux measurement
obtained during a 30 min time period is still uncertain .
In this study, the active controlled flux technique (ACFT), a thermographic
technique, is used, which is capable of measuring the heat transfer velocity
with a temporal resolution of about 20 min, which can then be scaled to
gas transfer velocities. This technique is described in Sect. .
The ACFT was deployed during three cruises in the Baltic Sea to investigate
the variability of the transfer velocities under field conditions.
Earlier measurements of the gas transfer velocity in the Baltic Sea are
sparse. used the eddy covariance technique to measure the
transfer of CO2 in the Arkona Basin and used the
same technique in the Gotland Sea. Both studies found a very high variability
of the gas transfer velocity.
Factors influencing air–sea gas exchange
The common approach is to parameterize the gas transfer velocity with wind
speed alone. However, a wealth of studies have shown that a multitude of
factors influence gas transfer, for example the contamination of the water
surface with surface-active material (e.g., ),
bubble entrainment (e.g., ), fetch (e.g.,
), rain (e.g., ) and
convective mixing (e.g., ).
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 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
.
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. 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.
Measuring techniqueActive thermography
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 .
Scaling heat transfer velocities to gas transfer velocities
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=lnScPrΔn,
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.
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
for the wind speeds encountered during this study. Friction
velocities measured in the Aeolotron were taken from
and converted to the wind speed at 10 m height using the
drag coefficient parameterization by . To scale the heat
transfer velocities measured in the present work, the mean values of the
Schmidt number exponent were used.
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.
MeasurementsBaltic Sea campaigns 2009 and 2010
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.
Map of the Baltic Sea. The tracks of the three cruises are shown.
Experimental setup on ship
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.
ResultsMeasured transfer velocities
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. ).
Measured k600 transfer velocities plotted against the wind speed of the RV
Alkor spring 2009 cruise. For comparison the best fit of , Eq. (), is added.
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.
Measured k600 transfer velocities plotted against the wind speed of the RV
Alkor summer 2010 cruise. Conditions for which the measured transfer velocity
is likely overestimated are marked with open circles and will not be used for further analysis.
For comparison the wind speed parameterization taken from is added.
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.
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 is also shown.
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.
Comparison with other field and laboratory data
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.
Comparison of scaled heat transfer velocities measured in the Baltic
Sea and gas transfer velocities measured in the Heidelberg Aeolotron
wind-wave facility with a clean water surface (green shaded area). The
measurements on RV Aranda in 2010 which were made under open-ocean
conditions (i.e., with a virtually unlimited fetch) are marked with filled
circles, while the fetch limited measurements in the archipelago are marked
with open circles. Also shown is the lower limit for a smooth water surface; Eq. (). The region between the transfer velocities measured with
a clean water surface as the upper boundary and the values for a smooth water
surface as the lower boundary for possible transfer velocities is shaded in
magenta. Also shown are the data set from the North Atlantic of
(K&R1983) using the radon deficit method, DMS eddy
covariance measurements and the parameterization of
previous Baltic Sea gas transfer measurements by . The
individual data points in and
scatter too strongly to be shown here. Also shown is the parameterization by
.
Bubble-mediated transfer
It is known that active thermography misses the contribution by bubbles to
the transfer; see Sect. . Because of the high solubility of
dimethylsulfide (DMS), this tracer's gas transfer has almost no
bubble-induced component, and the transfer velocities of DMS measured by
do indeed have values very similar to ours (Fig. ). Another observation, which supports this argument, are
the higher CO2 gas exchange values (CO2 has a significantly lower
solubility than DMS with a higher expected bubble-induced contribution)
measured in the Baltic Sea by and .
We only show the combined linear or quadratic parameterization by
, since does not give a
parameterization.
A very helpful indication comes, however, from laboratory experiments, which
suggest that this explanation is not correct. No evidence for a significant
bubble contribution to gas transfer was found in a laboratory study
up to the highest wind speed used in that study (≈12 m s-1), although tracers
with solubilities much lower than CO2
(dimensionless solubility α≈0.7) and DMS (α≈11.2)
were used, including N2O (α≈0.5), trifluoromethane
(α≈0.26) and pentafluoroethane (α≈0.07). In
another study, found no differences between gas transfer
velocities of N2O and heat transfer velocities for wind speeds as high as
12 m s-1, which indicates that bubble contribution for both the
transfer heat and that of N2O is not significant.
Fetch and wave-age effects
A second explanation would be the effect of fetch or, equivalently, quickly
varying wind conditions with young wave ages. This effect has almost not be
studied so far. Only recently, using active
thermography measurements in the Heidelberg Aeolotron, showed that, at very short
fetches and low wind speed, the gas transfer velocity is significantly higher
than at infinite fetch. This finding is supported by an old data set, which
constitutes the most diligently measured gas transfer velocities using the
radon deficit method . One part of this data
set was measured during the Joint Air Sea Interaction (JASIN) cruise in the North Atlantic with highly
varying wind speeds. The measured gas transfer velocities are higher or as
high as predicted by the empirical parameterization. However, the transfer
velocities measured during the First GARP (Global Atmospheric Research Program) Global Experiment
(FGGE) cruise with constantly blowing trade
winds are significantly lower. One value is 3 times lower than predicted
by the empirical parameterization of Ho. These measurements clearly indicate
that even on the open ocean (i. e. without fetch limitations), there will be
significant differences in the gas transfer velocity. The data suggest that
this effect may be as large as a factor of 5.
Surprisingly, the thermographic measurements in the Baltic Sea show just the
opposite dependency. In the shielded archipelago with fetches that are probably short,
the transfer velocities are lower and not higher. Thus fetch dependency does
not seem to be the correct explanation in this case at rather high wind
speeds, where the Aeolotron data by also show no significant
fetch dependency.
Surfactants
The third and most likely reason for the lower gas exchange rates during part
of the Aranda 2010 cruise is a reduction in the transfer velocity by surface
films. The reduction of about a factor of 2 is consistent with earlier
measurements discussed in Sect. .
At this point it is helpful to compare the field data with laboratory data
augmented by physical arguments about the mechanisms of air–sea gas transfer.
However, a direct comparison is physically not valid because the conditions
concerning the wave field and surface contamination will be different.
Despite that, laboratory data are suited to explore the possible upper and
lower limits of the gas transfer velocity at a given wind speed. The
Heidelberg Aeolotron laboratory has a virtually unlimited fetch due
to its annular shape, so it may resemble the ocean conditions in the best
possible way. 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. ). Those gas transfer velocities were measured with
the method described in and are published in
. In the green shaded area, the increase in the gas transfer
velocities at low wind speeds and short fetches observed by
is taken into account, too.
The lower limit for possible gas transfer velocities is given by the
prediction of (Eq. 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 or wave facility, when the water surface
was covered by surfactants . 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-1 corresponding to a smooth water surface
up to a wind speed of u10≈13 m s-1. This is supported by
the findings of , who measured surfactant enrichment
in the sea surface microlayer up to u10≈13 m s-1 as well.
The region between these upper and lower bounds for gas transfer is shaded in
a magenta color in Fig. . 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 field data shown and based on mass balance methods, eddy covariance and
active thermography are compatible with this shaded region of possible gas
transfer velocities. The parameterization of CO2 measured with the eddy
covariance technique in the Baltic Sea according to is
slightly higher than the upper limit resulting from laboratory measurements.
Because of the high scatter of these data, some individual measurements are
even much higher. This means that we still see discrepancies between
measurements based on mass balance (now including also active thermography)
and eddy covariance measurements, although they are not as bad as in the
early days of eddy covariance measurements .
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.
It is new that, even at high wind speeds in the range of 8 to
15 m s-1, significantly lower gas transfer velocities were measured, which were about a
factor of 2 lower than the average transfer velocities measured by the dual-tracer technique and parameterized by the relation of . Based
on arguments from several lab studies, the influence of surfactants is the
most likely reason for variability of the gas transfer velocity under the
environmental conditions for the thermographic measurements in the Baltic Sea. But a possible influence of fetch and bubbles on these measurements
cannot completely be ruled out.
Therefore this study clearly indicates that a better understanding of air–sea
gas transfer urgently requires more systematic measurements of the effects of
bubbles, 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 in the gas transfer rate can be measured. This has recently been
demonstrated by 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 1 min using conventional mass balance techniques.
A very promising technique for fast measurements of gas transfer is the
recently developed mass boundary layer imaging technique
. 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.
Data availability
Data have been uploaded to https://pangaea.de/. All
third-party data sets used are cited in the text.
Numerical values of the measured transfer velocities
Tables , and give the
numerical values of the measurements conducted during the cruises in the
Baltic Sea.
Measured heat transfer velocities
kheat depending on time, position, wind speed, and water and air
temperature for the measurements on RV Alkor in 2009. Furthermore
the Prandtl number Pr, the Schmidt number exponent n and the
scaled transfer velocity k600 are given. The times given are
approximate starting times in UTC. Each measurement lasted about
20min.
NumberDateTimePosition u10TwaterTairkheatPrnk600hh:mmNE(m s-1)(∘C)(∘C)(cm h-1)(cm h-1)A128 April 200919:5555.00213.1698.47±0.177.310.8158.6±74.810.380.534±0.01218.2±8.6A230 April 200902:3055.12213.10312.4±0.337.48.2195.9±40.410.380.505±0.00125.2±5.2A31 May 200920:0556.38917.5915.29±0.315.76.4109.8±25.611.00.6±0.02910.0±2.6A42 May 200920:2057.33720.0166.81±0.236.28.0117.3±24.810.810.563±0.02312.2±2.8A53 May 200920:4557.36619.9047.62±0.476.57.9179.8±16.810.70.547±0.01719.9±2.3
Measured heat transfer velocities kheat depending on
time, position, wind speed, and water and air temperature for the measurements
on RV Alkor in 2010. Furthermore the Prandtl number Pr, the Schmidt
number exponent n and the scaled transfer velocity k600 are given. The
times given are approximate starting times in UTC. Each measurement lasted
about 20min.
NumberDateTimePosition u10TwaterTairkheatPrnk600hh:mmNE(m s-1)(∘C)(∘C)(cm h-1)(cm h-1)B1*2 July 201000:0554.95119.2334.0±0.317.015.8217.4±103.37.630.63±0.02413.9±6.8B2*2 July 201000:3555.06419.1753.9±0.316.615.8139.6±20.97.740.632±0.0238.9±1.6B3*3 July 201006:0557.38319.4901.6±0.217.917.7146.9±17.27.30.664±0.0037.9±0.9B4*3 July 201023:0557.65821.6533.6±0.218.418.5130.2±17.67.30.639±0.027.8±1.3B5*4 July 201022:0557.90322.5944.0±0.519.520.1103.2±16.77.090.63±0.0246.3±1.2B65 July 201020:3059.85719.6436.7±0.115.216.4154.9±16.38.10.566±0.02413.6±2.0B78 July 201018:5065.21522.6388.4±0.314.516.2168.7±46.18.230.535±0.01217.0±4.7B8*10 July 201022:3558.56118.2442.6±0.318.920.9249.4±35.77.190.655±0.0113.8±2.1B9*10 July 201023:0558.56718.2461.6±0.318.920.4227.3±59.27.190.664±0.00312.1±3.1B1011 July 201019:1558.56716.2409.7±0.119.622.5225.3±37.66.990.52±0.00622.3±3.8B1111 July 201019:4558.84716.2069.3±0.319.922.4198.2±23.06.990.524±0.00819.2±2.3
Measurements marked with an asterisk (*) are
considered unreliable; see Sect. .
Measured heat transfer velocities kheat depending on
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 times given are approximate starting times in UTC. Each measurement lasted about 20min. All measurements were conducted
in a fetch-limited position with the exception of the two conditions marked
with an asterisk (*).
NumberDateTimePosition u10TwaterTairkheatPrnk600hh:mmNE(m s-1)(∘C)(∘C)(cm h-1)(cm h-1)C115 September 201018:0559.89921.50210.4±0.614.913.3143.6±25.78.070.515±0.00415.6±2.8C215 September 201021:2559.89921.5029.2±0.814.813.8137.6±21.88.10.525±0.00814.4±2.3C316 September 201004:1559.89921.50213.6±0.714.914.1143.6±38.98.070.502±0.016.5±4.5C416 September 201005:3059.89921.50214.8±1.614.914.0201.0±30.78.070.5±0.023.3±3.5C516 September 201016:1059.89921.50213.5±1.514.913.9177.2±37.88.070.503±0.020.3±4.3C616 September 201017:1559.89921.50213.5±1.114.913.7179.5±70.58.070.502±0.020.6±8.1C716 September 201020:5559.89321.48610.0±1.014.813.6141.6±65.08.10.517±0.00515.3±7.0C816 September 201021:5059.89321.48610.1±0.614.714.0119.2±16.38.120.517±0.00512.9±1.8C917 September 201004:1559.89321.48610.7±0.814.513.7166.2±27.98.170.512±0.00418.4±3.1C1017 September 201005:2559.89321.48610.8±0.914.613.7145.9±24.08.140.512±0.00316.1±2.7C1117 September 201016:1559.89321.48611.3±0.814.613.4141.5±31.48.140.51±0.00315.8±3.5C1217 September 201019:1559.89321.4869.8±0.614.513.6121.6±34.88.170.519±0.00613.1±3.8C13*18 September 201013:0559.37821.44111.0±1.014.012.2268.5±49.28.290.511±0.00330.1±5.5C14*18 September 201013:3559.37821.44110.8±0.713.211.3209.9±29.48.490.512±0.00423.7±3.3Author contributions
LN was involved in designing the experiments, performed the experiments and calculated the heat transfer
velocities from the IR images. KEK calculated the k600 values, prepared
all figures and tables, and served as communicating author. BJ was involved in
designing the experiments and the analytical methods and outlined the main
conclusions. All authors contributed to writing the manuscript.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
We would like to thank Kimmo Kahma and Heidi Pettersson, Finish
Meteorological Institute, for the possibility of participating in the
Aranda CO2_WAVE10_CTD10/2010 cruise. We would also like to thank
Robert Schmidt and Bernd Schneider, Institut für Ostseeforschung,
Warnemünde, for their chief scientist work during the cruises
Alkor 336 and Alkor 356. We are grateful for the assistance
onboard by the captains and crews of RV Aranda and RV
Alkor. We would like to thank Uwe Schimpf and Günther Balschbach
for help with preparing and conducting the measurements as well as logistical
support. Financial support for this work by the German Federal Ministry of
Education and Research (BMBF) joint project “Surface Ocean Processes in the
Anthropocene” (SOPRAN, FKZ 03F0462F, 03F0611F and 03F0622F) within the
international SOLAS project is gratefully acknowledged. We acknowledge financial
support by Deutsche Forschungsgemeinschaft within the funding programme Open
Access Publishing, by the Baden-Württemberg Ministry of Science, Research
and the Arts and by Ruprecht-Karls-Universität Heidelberg. Edited by: Mario Hoppema Reviewed by: three
anonymous referees
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