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**Atmospheric Chemistry and Physics**
An interactive open-access journal of the European Geosciences Union

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**Research article**
11 Feb 2019

**Research article** | 11 Feb 2019

The influence of transformed Reynolds number suppression on gas transfer parameterizations and global DMS and CO_{2} fluxes

^{1}independent researcher, Kiel, Germany^{2}GEOMAR Helmholtz Centre for Ocean Research, Kiel, Germany

^{1}independent researcher, Kiel, Germany^{2}GEOMAR Helmholtz Centre for Ocean Research, Kiel, Germany

**Correspondence**: Alexander Zavarsky (alexz@mailbox.org)

**Correspondence**: Alexander Zavarsky (alexz@mailbox.org)

Abstract

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Eddy covariance measurements show gas transfer velocity suppression at medium to high wind speed. A
wind–wave interaction described by the transformed Reynolds number is used to
characterize environmental conditions favoring this suppression. We take the transformed
Reynolds number parameterization to review the two most cited wind speed gas transfer
velocity parameterizations: Nightingale et al. (2000) and Wanninkhof (1992, 2014). We propose an algorithm
to adjust *k* values for the effect of gas transfer suppression and validate it with two
directly measured dimethyl sulfide (DMS) gas transfer velocity data sets that experienced
gas transfer suppression. We also show that the data set used in the Nightingale 2000
parameterization experienced gas transfer suppression. A compensation of the suppression
effect leads to an average increase of 22 % in the *k* vs. *u* relationship. Performing
the same correction for Wanninkhof 2014 leads to an increase of 9.85 %. Additionally,
we applied our gas transfer suppression algorithm to global air–sea flux climatologies
of CO_{2} and DMS. The global application of gas transfer suppression leads to a
decrease of 11 % in DMS outgassing. We expect the magnitude of Reynolds suppression on
any global air–sea gas exchange to be about 10 %.

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Zavarsky, A. and Marandino, C. A.: The influence of transformed Reynolds number suppression on gas transfer parameterizations and global DMS and CO_{2} fluxes, Atmos. Chem. Phys., 19, 1819–1834, https://doi.org/10.5194/acp-19-1819-2019, 2019.

1 Introduction

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Gas flux *F* between the ocean and the atmosphere is commonly described as the
product of the concentration difference Δ*C* between the liquid phase (seawater)
and the gas phase (atmosphere) and the total gas transfer velocity *k*_{total}.
Δ*C* acts as the forcing potential difference and *k* as the conductance, which
includes all processes promoting and suppressing gas transfer. *c*_{air} and
*c*_{water} are the respective air-side and water-side concentrations. *H* is the
dimensionless form of the Henry's law constant.

$$\begin{array}{}\text{(1)}& {\displaystyle}F={k}_{\mathrm{total}}\cdot \mathrm{\Delta}C={k}_{\mathrm{total}}\cdot \left({c}_{\mathrm{water}}-{c}_{\mathrm{air}}\cdot H\right)\end{array}$$

Δ*C* is typically measured with established techniques, although the distance of
the measurements from the interface introduces uncertainties in the flux calculation.
Parameterizations of *k* are another source of uncertainty in calculating fluxes. The
flux *F* can be directly measured, e.g., with the eddy covariance technique, together
with Δ*C* in order to derive *k* and estimate a *k* parameterization
(Eq. 2).

$$\begin{array}{}\text{(2)}& {\displaystyle}{\displaystyle}{k}_{\mathrm{total}}={\displaystyle \frac{F}{\mathrm{\Delta}C}}={\displaystyle \frac{F}{{c}_{\mathrm{water}}-{c}_{\mathrm{air}}\cdot H}}\end{array}$$

It is very common that *k*_{total} is parameterized with wind speed and all wind
speed parameterizations have in common that *k*_{total} increases monotonically
with increasing wind speed. This assumption is sensible, as higher wind speed increases
turbulence both on the air side and the water side and hence the flux. Additional
processes like bubble generation can additionally enhance gas transfer. The total gas
transfer velocity *k*_{total}, which is measured by eddy covariance or other
direct flux methods, can split into the water-side gas transfer
velocity *k*_{water} and the air-side gas transfer velocity *k*_{air}
(Eq. 3).

$$\begin{array}{}\text{(3)}& {\displaystyle}{\displaystyle \frac{\mathrm{1}}{{k}_{\mathrm{total}}}}={\displaystyle \frac{\mathrm{1}}{{k}_{\mathrm{water}}}}+{\displaystyle \frac{H}{{k}_{\mathrm{air}}}}\end{array}$$

We focus, in this work, on *k*_{water}, which is the sum of the interfacial gas
transfer *k*_{o} and the bubble-mediated gas transfer *k*_{b}
(Eq. 4).

$$\begin{array}{}\text{(4)}& {\displaystyle}{\displaystyle}{k}_{\mathrm{water}}={k}_{\mathrm{o}}+{k}_{\mathrm{b}}\end{array}$$

Schmidt number (*S**c*) scaling (Eq. 5) is used to compare gas transfer
velocities of different gases. *S**c* scaling only applies to *k*_{o}
and *k*_{air}. *S**c* is the ratio of the viscosity *ν* to the diffusivity *D* of the
respective gas in seawater.

$$\begin{array}{}\text{(5)}& {\displaystyle}& {\displaystyle}Sc={\displaystyle \frac{\mathit{\nu}}{D}}\text{(6)}& {\displaystyle}& {\displaystyle \frac{{k}_{\mathrm{o},\mathrm{Sc}}}{{k}_{\mathrm{o},\mathrm{660}}}}={\left({\displaystyle \frac{Sc}{\mathrm{660}}}\right)}^{n}\end{array}$$

The exponent *n* is chosen depending on the surface properties. For smooth surfaces
$n=-\frac{\mathrm{2}}{\mathrm{3}}$ and for rough wavy surfaces $n=-\frac{\mathrm{1}}{\mathrm{2}}$ (Komori et al., 2011). In this
study $n=-\frac{\mathrm{1}}{\mathrm{2}}$ is used.

In contrast to commonly accepted gas transfer velocity parameterizations,
parameterizations based on direct flux measurements by eddy covariance systems have shown
a decrease or flattening of *k* with increasing wind speed at medium to high wind speeds
(Bell et al., 2013, 2015; Yang et al., 2016; Blomquist et al., 2017). We use the transformed Reynolds
number *R**e*_{tr} (Zavarsky et al., 2018) to identify instances of gas transfer
suppression.

$$\begin{array}{}\text{(7)}& {\displaystyle}{\displaystyle}R{e}_{\mathrm{tr}}={\displaystyle \frac{{u}_{\mathrm{tr}}\cdot {H}_{\mathrm{s}}}{{\mathit{\nu}}_{\mathrm{air}}}}\cdot \mathrm{cos}\left(\mathit{\theta}\right)\end{array}$$

*R**e*_{tr} is the Reynolds number transformed into the reference system of the
moving wave. *u*_{tr} is the wind speed transformed into the wave's reference
system, *H*_{s} the significant wave height, *ν*_{air} the kinematic
viscosity of air and *θ* the angle between the wave direction and direction
of *u*_{tr} in the wave's reference system. This parameterization is based on the
model of air flowing around a sphere (Singh and Mittal, 2004). The flow is laminar and attached
all around the sphere at low *R**e* (*R**e*_{tr}<10). However, this condition does
not occur in the oceanic environment as *u*_{tr} would have to be around
$\mathrm{3}\times {\mathrm{10}}^{-\mathrm{5}}$ m s^{−1} (using *H*_{s}=3 m and
${\mathit{\nu}}_{\mathrm{air}}={\mathrm{10}}^{-\mathrm{5}}$ m^{2} s^{−1}). At ${\mathrm{10}}^{\mathrm{1}}<R{e}_{\mathrm{tr}}<{\mathrm{10}}^{\mathrm{5}}$, vortexes form at the lee side of the
sphere and the flow separates. This is the state of gas transfer suppression and occurs
approximately at *u*_{tr} from $\mathrm{3}\times {\mathrm{10}}^{-\mathrm{5}}$ to 3 m s^{−1}. When
*u*_{tr}, and as a consequence *R**e*_{tr}, is further increased
(*R**e*_{tr}>10^{5}), turbulence in the boundary layer between the air and the
sphere counteracts the flow separation and reduces the surface area on which the
separation acts. This means that an increased relative wind speed *u*_{tr} favors
unsuppressed conditions.

A flux measurement at values of $\left|R{e}_{\mathrm{tr}}\right|\le \mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$ is gas transfer
suppressed (Zavarsky et al., 2018). The threshold presents a binary treatment of the problem. We
adopt this treatment since stall conditions, flow detachment and reattachment in
aerodynamics are also binary. Describing transition conditions is beyond the scope of the
first introduction of this model. The *R**e*_{tr} parameterization shows that the
suppression is primarily dependent on wind speed, wave speed, wave height and a
directional component.

It is noteworthy that, so far, only gas transfer velocities deduced by eddy covariance
have shown a gas transfer suppression. This may be due to the spatial (1 km) and
temporal (30 min) resolution of eddy covariance measurements, or to the types of gases
measured (e.g., CO_{2}; dimethyl sulfide, DMS; organic VOCs). The use of rather soluble gases (DMS, acetone,
methanol) means that the gas transfer velocity will not be greatly influenced by
bubble-mediated gas transfer. Gas transfer suppression only affects *k*_{o} (Zavarsky et al., 2018).
Another direct flux measurement technique, the dual-tracer method, utilizes sulfur
hexafluoride (SF_{6}) or ^{3}He. The dual-tracer measurement usually lasts
over a few days but could have a similar spatial resolution as eddy covariance.
SF_{6} and ^{3}He are both very insoluble and heavily influenced by the
bubble effect. Hence, if the gas transfer suppression only affects *k*_{o},
*k*_{b} could be the dominant process, masking the gas transfer suppression.
Additionally, the long measurement period could decrease the likelihood of detection of
gas transfer suppression as the conditions for suppression might not be persistent over a
few days.

There are two main goals of this study: (1) develop and use a simplistic algorithm to
adjust for gas transfer suppression; (2) illustrate that gas transfer suppression is
ubiquitous, showing up in our most used gas transfer parameterizations. To address
goal 1, we develop a gas transfer suppression model and apply it to two DMS eddy
covariance data sets. To address goal 2, we investigate the two most commonly used gas
parameterizations (both cited more than 1000 times each) for the occurrence of gas
transfer suppression. The Nightingale et al. (2000) parameterization (N00) contains data from the
North Sea, Florida Strait and Georges Bank between 1989 and 1996. The
N00 parameterization is derived from changes in the ratio of SF^{6} and
^{3}He (dual-tracer method). We also investigate the Wanninkhof (2014) gas transfer
parameterization (W14), which is an update to Wanninkhof (1992). They calculate the amount
of CO_{2} exchanged between the ocean and atmosphere using a global ocean
^{14}C inventory. This ^{14}C inventory is already influenced by gas
transfer suppression as it is globally averaged. They deduce a quadratic *k* vs. wind
speed parameterization using a wind speed climatology. Both *k* parameterizations (N00,
W14) are monotonically increasing with wind speed.

In addition, we use wind and wave data for the year 2014, calculate *R**e*_{tr} and perform an analysis of
the impact of gas transfer suppression on the yearly global air–sea exchange of DMS and
CO_{2}. So far global estimates of air–sea exchange of DMS have been based on
*k* parameterizations, which have not included a mechanism for gas transfer suppression.
We provide an iterative calculation of the effect of gas transfer suppression on existing
DMS climatologies. For global CO_{2} budgets, the widely used W14 and Tak09
(Takahashi et al., 2009) parameterizations already include a global average gas transfer
suppression. There, we calculate an estimate for the magnitude of gas transfer
suppression on a monthly local basis.

2 Methods

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We use wave data from the WWIII model hindcast run by the
Marine Modeling and Analysis Branch of the Environmental Modeling Center of the National
Centers for Environmental Prediction (NCEP; Tolman, 1997, 1999, 2009). The model
is calculated for the global ocean surface excluding ice-covered areas with a temporal
resolution of 3 h and a spatial resolution of 0.5^{∘} × 0.5^{∘}. The
data for the specific analysis of the N00, W14 parameterizations and the Knorr11 cruise
(Sect. 4.1–4.3) were obtained from the model for the specific
locations and times of the measurements. The data for the global analysis,
Sect. 4.4, were obtained for the total year 2014. The model also provides the
*u* (meridional) and *v* (zonal) wind vectors, assimilated from the Global Forecast
System, used in the model. We retrieved wind speed, wind direction, bathymetry, wave
direction, wave period and significant wave height. We converted the wave
period *T*_{p} to phase speed *c*_{p}, assuming deep water waves, using
Eq. (8) (Hanley et al., 2010).

$$\begin{array}{}\text{(8)}& {\displaystyle}{\displaystyle}{c}_{\mathrm{p}}={\displaystyle \frac{g\cdot {T}_{\mathrm{p}}}{\mathrm{2}\mathit{\pi}}}\end{array}$$

Surface air temperature *T*, air pressure *p*, sea surface temperature SST and sea ice
concentration were retrieved from the ERA-Interim reanalysis of the European Centre for
Medium-Range Weather Forecasts (Dee et al., 2011). It provides a 6-hourly time resolution
and a global 0.125^{∘} × 0.125^{∘} spatial resolution. Sea surface
salinity (SSS) was extracted from the Takahashi climatology (Takahashi et al., 2009).

Air–sea partial pressure difference (Δ*p*CO_{2}) was obtained from the
Takahashi climatology. Δ*p*CO_{2}, in the Takahashi climatology, is
calculated for the year 2000 CO_{2} air concentrations. Assuming an increase in
both the air concentration and the partial pressure in the water side, the partial
pressure difference remains constant. The data set has a monthly temporal resolution, a
4^{∘} latitudinal resolution and a 5^{∘} longitudinal resolution.

DMS water concentrations were taken from the Lana DMS climatology (Lana et al., 2011). These
are provided with a monthly resolution and a 1^{∘} × 1^{∘} spatial
resolution. The air mixing ratio of DMS was set to zero (${c}_{\mathrm{air},\mathrm{DMS}}=\mathrm{0}$). Taking
air mixing ratios into account, the global air–sea flux of DMS reduces by 17 %
(Lennartz et al., 2015). We think this approach is reasonable as we look at the relative flux
change due to gas transfer suppression only.

We linearly interpolated all data sets to the grid and times of the WWIII model.

The kinematic viscosity *ν* of air is dependent on air density *ρ* and
the dynamic viscosity *μ* of air, Eq. (9).

$$\begin{array}{}\text{(9)}& {\displaystyle}{\displaystyle}\mathit{\nu}(T,p)={\displaystyle \frac{\mathit{\mu}\left(T\right)}{\mathit{\rho}(T,p)}}\end{array}$$

The dynamic viscosity is dependent on temperature *T* and can be calculated
using Sutherland's law (White, 1991) (Eq. 10).

$$\begin{array}{}\text{(10)}& {\displaystyle}{\displaystyle}\mathit{\mu}={\mathit{\mu}}_{\mathrm{0}}\cdot {\left({\displaystyle \frac{T}{{T}_{\mathrm{0}}}}\right)}^{\frac{\mathrm{2}}{\mathrm{3}}}\end{array}$$

${\mathit{\mu}}_{\mathrm{0}}=\mathrm{1.716}\times {\mathrm{10}}^{-\mathrm{5}}$ N s m^{−2} at *T*_{0}=273 K (White, 1991). Air
density is dependent on temperature *T* and air pressure *p* and was calculated using the
ideal gas law.

The Reynolds number describes the balance of inertial forces and viscous forces. It is
the ratio of the typical length and velocity scale over the kinematic viscosity. The
transformed Reynolds number, in Eq. (11), uses the wind speed *u*_{tr}
transformed into the wave's reference system. The significant wave height *H*_{s}
is used as the typical length scale. The difference between wind direction and wave
direction is given by the angle *θ*. Between *θ*=0 and *θ*=90^{∘} the
air flowing over the wave experiences, due to the angle of attack, a differently shaped
and streamlined wave. The factor cos (*θ*) is multiplied by *H*_{s} to
account for directional dependencies and shape influences (Fig. A1).

$$\begin{array}{}\text{(11)}& {\displaystyle}{\displaystyle}R{e}_{\mathrm{tr}}={\displaystyle \frac{{u}_{\mathrm{tr}}\cdot {H}_{\mathrm{s}}}{\mathit{\nu}}}\cdot \mathrm{cos}\left(\mathit{\theta}\right)\end{array}$$

3 Gas transfer suppression model

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Below $\left|R{e}_{\mathrm{tr}}\right|\le \mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$ flow separation between the wind flowing
above the wave and the flow entering the trough suppresses gas transfer (Zavarsky et al., 2018).
As a result, common wind speed parameterizations of *k* are not applicable
(Eq. 1). To provide a magnitude for this suppression, we propose an alternative
wind speed *u*_{alt}, which is lower than *u*_{10}. This decrease accounts for the
effect of gas transfer suppression. *u*_{alt} represents the wind speed with the
maximum possible *k* in these conditions, hence an increase in *u*
beyond *u*_{alt} does not result in an increase in *k*. Thus, *u*_{alt} can
then be used with *k* parameterizations to calculate the gas flux.

Given a set wave field (constant *H*_{s}, wave direction and speed), if the
relative wind speed in the reference system of the wave *u*_{tr} is high enough
that $\left|R{e}_{\mathrm{tr}}\right|>\mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$, no suppression occurs. In the
“unsuppressed” case, *k* can be estimated by common gas transfer
parameterizations. If the wind speed *u*_{10}, in the earth's reference system, is
getting close to the wave's phase speed, *u*_{tr} in the wave's reference system
gets smaller and $\left|R{e}_{\mathrm{tr}}\right|$ drops below the threshold; thus, flow separation
happens and suppression occurs. We propose a stepwise (Δ*s*) reduction of *u*_{10}
to calculate when the wind–wave system changes from the flow separation regime
($\left|R{e}_{\mathrm{tr}}\right|<\mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$) to a normal flow regime
($\left|R{e}_{\mathrm{tr}}\right|>\mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$). This can be used to estimate the magnitude of the
suppression. We recalculate *R**e*_{tr} with a lower
${u}_{\mathrm{alt}}={u}_{\mathrm{10}}-i\cdot \mathrm{\Delta}s$ and iterate *i*=0, 1, 2, 3 … as long as
*R**e*_{tr} is below the threshold (flow separation). If *R**e*_{tr} crosses to
the non-suppressing regime, the iteration is stopped and the actual *u*_{alt} can
be used as an alternative wind speed. The iteration steps are
(1) calculate *R**e*_{tr} using ${u}_{\mathrm{alt}}={u}_{\mathrm{10}}-i\cdot \mathrm{\Delta}s$ and
(2) determine if $\left|R{e}_{\mathrm{tr}}\right|\le \mathrm{6.96}\times {\mathrm{10}}^{\mathrm{5}}$. (3) If yes, $i=i+\mathrm{1}$ and continue
with step (1). If no, break the loop. The step size in this model was 0.3 m s^{−1}.
We think this step size allows for a good balance between computing time and velocity
resolution. The minimum velocity for *u*_{alt} is 0 m s^{−1}.
Figure 1 shows a flowchart of the algorithm. This algorithm is applied to
every box at every time step.

A change in the parameters of the wave field is, in our opinion, not feasible as the wave field is influenced to a certain extent by swell that is externally prescribed. Swell travels long distances and does not necessarily have a direct relation to the wind conditions at the location of the gas transfer and measurement. Therefore, we change the wind speed only.

The difference between *u*_{alt} and *u*_{10} directly relates to the magnitude of
gas transfer suppression. *u*_{alt} can be used in two ways: (1) *u*_{10} can be
directly replaced by *u*_{alt}. This is only possible for parameterizations with a
negligible bubble contribution (like DMS), as we assume that the gas transfer suppression
only affects *k*_{o}. As a result, one gets a *k* estimation using the lower wind
speed *u*_{alt}. This is an estimate of the reduction of *k* by gas transfer
suppression. (2) For parameterizations of rather insoluble gases, like CO_{2},
SF_{6} and ^{3}He, one needs to subtract Δ*k* from the unsuppressed
*k* parameterization. This adjustment is done by inserting *u*_{10}−*u*_{alt} into a
*k*_{o} parameterization (Eq. 12) and subtracting Δ*k*. In this
paper, ZA18 from Zavarsky et al. (2018) is used as the parameterization of *k*_{o}. The
magnitude of the gas transfer suppression is given by Eq. (12).

$$\begin{array}{ll}{\displaystyle}\mathrm{\Delta}k& {\displaystyle}={k}_{\mathrm{o}}\left({u}_{\mathrm{10}}\right)-{k}_{\mathrm{o}}\left({u}_{\mathrm{alt}}\right)=\left(\mathrm{3.1}\cdot {u}_{\mathrm{10}}-\mathrm{5.7}\right)\\ \text{(12)}& {\displaystyle}& {\displaystyle}-\left(\mathrm{3.1}\cdot {u}_{\mathrm{alt}}-\mathrm{5.7}\right)=\mathrm{3.1}\cdot \left({u}_{\mathrm{10}}-{u}_{\mathrm{alt}}\right)\end{array}$$

For the global flux of DMS we use the bulk gas transfer formula (Eq. 1). The
global DMS gas flux calculations are based on the following *k* parameterizations:
ZA18 and the quadratic parameterization N00. For every grid box and every time step we
calculate *u*_{alt} according to the description in Sect. 3. If
*u*_{alt} is lower than *u*_{10} from the global reanalysis, then gas transfer
suppression occurs. Subsequently, *u*_{alt} together with Eq. (12) is
used in the specific bulk gas transfer formulas (Eqs. 13–14).
For ZA18, *u*_{alt} can be directly inserted into the ZA18 parameterization
(Eq. 13). However, other parameterizations, e.g., N00, which are based on
measurements with rather insoluble gases, have a significant bubble-mediated gas transfer
contribution. As a consequence, we subtract the linearly dependent Δ*k* using the
ZA18 parameterization, to account for the gas transfer suppression in *k*_{o}
(Eq. 14).

$$\begin{array}{ll}{\displaystyle}{F}_{\mathrm{lim},\mathrm{ZA}\mathrm{18}}& {\displaystyle}=\left[{k}_{\mathrm{ZA}\mathrm{18}}\left({u}_{\mathrm{10}}\right)-\mathrm{\Delta}k\right]\cdot \mathrm{\Delta}C\\ \text{(13)}& {\displaystyle}& {\displaystyle}=\left(\mathrm{3.1}\cdot {u}_{\mathrm{alt}}-\mathrm{5.37}\right)\cdot \mathrm{\Delta}C\end{array}$$

$$\begin{array}{ll}{\displaystyle}{F}_{\mathrm{lim},\mathrm{N}\mathrm{00}\mathrm{\&}\mathrm{other}}& {\displaystyle}=\left[{k}_{\mathrm{N}\mathrm{00}\mathrm{\&}\mathrm{other}}\left({u}_{\mathrm{10}}\right)-\mathrm{\Delta}k\right]\cdot \mathrm{\Delta}C\\ \text{(14)}& {\displaystyle}& {\displaystyle}=\left[{k}_{\mathrm{N}\mathrm{00}\mathrm{\&}\mathrm{other}}\left({u}_{\mathrm{10}}\right)-\mathrm{3.1}\cdot \left({u}_{\mathrm{10}}-{u}_{\mathrm{alt}}\right)\right]\cdot \mathrm{\Delta}C\end{array}$$

Sea ice concentration from the ERA-Interim reanalysis was included as a linear factor in the calculation. A sea ice concentration of 90 %, for example, results in a 90 % reduction of the flux. Each time step (3 h) of the WWIII model provided a global grid of air–sea fluxes with and without gas transfer suppression. These single time steps were summed up to get a yearly flux result.

4 Results

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We test the adjustment of *u*_{10}→*u*_{alt} with two data sets of
DMS gas transfer velocities, Knorr11 (Bell et al., 2017) and SO234-2/235
(Zavarsky et al., 2018). Both data sets experienced gas transfer suppression at high
wind speed. Using this proof of concept, we quantify the influence of gas
transfer suppression on N00 and W14 and provide unsuppressed estimates.
Finally, we apply the wind speed adjustment to global flux estimates of DMS.
For CO_{2}, we estimate the magnitude of gas transfer suppression.

Figures 2 and 3 show the unsuppressed DMS gas transfer
velocities for the SO234-2/235 and the Knorr11 cruises. We shift the measured datapoints,
which are gas transfer suppressed, along the *x* axis by replacing *u*_{10}
with *u*_{alt}. The shift along the *x* axis is equivalent to an addition
of Δ*k*, for a given *k* vs. *u* relationship, to balance gas transfer suppression
(see Appendix). The black circles indicate the original data set at *u*_{10}. The colored
circles are *k* values plotted at the adjusted wind speed *u*_{alt}. If a black
circle and a colored circle are concentric, the datapoint was not suppressed and
therefore no adjustment was applied. For comparison, the parameterization ZA18 is plotted
in both figures. Both figures show the significant wave height with the color bar.

Figure 2 illustrates the linear fits to the data set before (dotted) and
after (dashed) the adjustment. The suppressed datapoints from 14 to 16 m s^{−1} moved
closer to the linear fit after an adjustment with *u*_{alt}. The high gas transfer
velocity values at around 13 m s^{−1} and above 35 cm h^{−1} were moved to
11 m^{−1}. This means a worsening of the *k* estimate by the linear fit. These
datapoints have very low ΔC values (Zavarsky et al., 2018), therefore we expect a large
scatter as a result from Eq. (2).

Figure 3 also shows an improvement of the linear fit estimates. The gas
transfer suppressed datapoints were assigned the new wind speed *u*_{alt},
resulting in better agreement to ZA18. The change of the linear fit to the unsuppressed
and suppressed data set can be seen in the dotted (before) and dashed (after) line. The
adjusted datapoints at 12–16 m s^{−1} are still, relative to the linear estimates,
heavily gas transfer suppressed. A reason could be that the significant wave height of
these points is larger than 3.5 m and they experienced high wind speed. A shielding of
wind by the large wave or an influence of water droplets on the momentum transfer is
suggested as another reason (Yang et al., 2016; Bell et al., 2013). In principle, we agree that these
processes may be occurring, but only during exceptional cases of high winds and wave
heights. The Reynolds gas transfer suppression (Zavarsky et al., 2018) occurs over a wider range
of wind speeds and wave heights, but obviously does not capture all the flux suppression.
Therefore, it appears that several processes, including shielding and influence of
droplets, may be responsible for gas transfer suppression and they are not all considered
in our model. This marks the upper boundary for environmental conditions for our model.

Table 1 shows the average offset between every datapoint and the linear fit ZA18. A reduction of the average offset can be seen for all data combinations. The last two columns of Table 1 show the mean absolute error. The absolute error also decreases with the application of our adjustments. The linear fits to the two data sets, before and after the adjustments, are given in Table 2.

The slopes for the two altered data sets show a good agreement. However, we do not account for the suppression entirely. The adjusted slopes are both in the range of the linear function ZA18 ${k}_{\mathrm{660}}=\mathrm{3.1}\pm \mathrm{0.37}\cdot {u}_{\mathrm{10}}-\mathrm{5.37}\pm \mathrm{2.35}$ (Zavarsky et al., 2018), but the slopes barely overlap within the 95 % confidence interval.

The N00 parameterization is a quadratic wind-speed-dependent parameterization of *k*. It
is widely used, especially for regional bulk CO_{2} gas flux calculations as well
as for DMS flux calculations in Lana et al. (2011). The parameterization is based on
dual-tracer measurements in the water performed in the North Sea (Watson et al., 1991; Nightingale et al., 2000)
as well as data from the Florida Strait (FS; Wanninkhof et al., 1997) and Georges Bank (GB;
Wanninkhof, 1992).

We analyzed each individual measurement that was used in the parameterization to assess
the amount of gas transfer suppressing instances that are within the
N00 parameterization. The single measurements, which are used for fitting the quadratic
function of the N00 parametrization, are shown together with N00 in
Fig. 4a. As the measurement time of the dual-tracer technique is on the
order of days, we interpolated the wind and wave data, obtained from the WWIII model for
the specific time and location, to 1 h time steps and calculated the number of gas
transfer suppressing and gas transfer non-suppressing instances. Fig. 4b
shows the suppression index, which is the ratio of gas suppressing instances to the
number of datapoints (*x* axis). The value 1 indicates that all of the interpolated 1 h
steps were gas transfer suppressed. The *y* axis of Fig. 4 depicts the
relation of the individual measurements to the N00 parameterization. A ratio (*y* axis)
of 1 indicates that the measurement point is exactly the same as the
N00 parameterization. A value of 1.1 would indicate that the value was 10 % higher than
predicted by the N00 parameterization.

We expect a negative correlation between the suppression index and the relation of the
individual measurement vs. the N00 parameterization. The higher the suppression index,
the higher the gas transfer suppression and the lower the gas transfer velocity *k* with
respect to the average parameterization. The correlation (Spearman's rank) is −0.43
with a significance level (*p* value) of 0.11. This is not significant. However, we must
take a closer look at two specific points: (1) point 11, GB11 that shows low measurement
percentage despite a low suppression index, and (2) point 14, FS14 that shows high
measurement percentage despite a high suppression index. GB11 at the Georges Bank showed
an average significant wave height of 3.5 m, with a maximum of 6 m and wind speed
between 9 and 13 m s^{−1}. Transformed wind speeds *u*_{tr} are between 4 and
20 m s^{−1}. As already discussed in Sect. 4.1 using the Knorr11 data set,
wave heights above 3.5 m could lead to gas transfer suppression without being captured
by the Reynolds gas transfer suppression model (Zavarsky et al., 2018). High waves together with
the strong winds could mark an upper limit of the gas transfer suppression model
(Zavarsky et al., 2018). On the other hand, the FS14 datapoint showed an average wave height of
0.6 m and wind speed of 4.7 m s^{−1}. It is questionable if a flow separation and a
substantial wind–wave interaction can be established at this small wave height. This
could mark the lower boundary for the Reynolds gas transfer suppression model
(Zavarsky et al., 2018). Taking out either one or both of these measurements (GB11 or FS14)
changes the correlation (Spearman's rank) to −0.62 *p*=0.0233 (excluding GB11), −0.59 *p*=0.033 (excluding FS14)
and −0.79 *p*=0.0025 (excluding GB11 and FS14). All three are significant. The solid black
line in Fig. 4b is a fit to all points except GB11 and FS14, and based on
Eq. (15).

$$\begin{array}{}\text{(15)}& {\displaystyle}{\displaystyle}y\left(x\right)={a}_{\mathrm{1}}+{a}_{\mathrm{2}}\cdot {\displaystyle \frac{\mathrm{1}}{x-{a}_{\mathrm{3}}}}\end{array}$$

We choose this functional form and hypothesize that gas transfer suppression is not
linear, but
rather has a threshold (Zavarsky et al., 2018). This means that the influence of suppression on
gas transfer is relatively low with a small suppression ratio, but increases strongly.
The fit coefficients are *a*_{1}=1.52, *a*_{2}=0.14 and *a*_{3}=1.18.

Figure 5 shows the unsuppressed datapoints, according to the gas
transfer suppression model (Sect. 3). We do not adjust the individual
datapoints along the wind speed axis (*x* axis), as the parameterization has a
significant bubble contribution, but add Δ*k* (Eq. 12) to make up for the
suppressed part of total *k*.

A new quadratic fit was applied to the adjusted datapoints (Eq. 16, Fig. 5).

$$\begin{array}{}\text{(16)}& {\displaystyle}{\displaystyle}{k}_{\mathrm{660}}=\mathrm{0.359}\cdot {u}^{\mathrm{2}}\end{array}$$

On average, the new parameterization is 22 % higher than the original N00
parameterization. This increase is caused by the heavy gas transfer suppression of the
individual measurements. As we believe that this suppression only affects the interfacial
*k*_{o} gas exchange, it might not be easily visible (decreasing *k* vs. *u*
relationship) in parameterizations based on dual-tracer gas transfer measurements,
because of the potential of a large bubble influence.

The calculation of the unsuppressed N00 parameterization is an example application for
this adjustment algorithm. We advise using the unsuppressed parameterization
(N00 + 22 %) for flux calculations with very insoluble gases like SF_{6}or^{3}He. We hypothesize that the original N00 contains a large bubble component, as it is
based on SF_{6} and ^{3}He measurements, which is compensated by the gas
transfer suppression. Therefore, the original N00 has been widely used for regional
CO_{2} gas flux calculations.

The W14 parameterization estimates the gas transfer velocity using the natural
disequilibrium between ocean and atmosphere of ^{14}C and the bomb ^{14}C
inventories. The total global gas transfer over several years is estimated by the influx
of ^{14}C in the ocean (Naegler, 2009) and the global wind speed distribution over
several years. The parameterization from W14 is for winds averaged over several hours.
The WWIII model wind data, used here, are 3 hourly and therefore in the proposed range
(Wanninkhof, 2014). The W14 parameterization is given in Eq. (17).

$$\begin{array}{}\text{(17)}& {\displaystyle}{\displaystyle}{k}_{\mathrm{660},\mathrm{W}\mathrm{14}}=\mathrm{0.251}\cdot {\left({u}_{\mathrm{10}}\right)}^{\mathrm{2}}\end{array}$$

The interesting point about this parameterization is that it should already include a
global average gas transfer suppressing factor. The parametrization is independent of
local gas transfer suppression events. It utilizes a global, annual averaged, gas
transfer velocity of ^{14}C and relates it to remotely sensed wind speed. This
means that the average gas transfer velocity has experienced the average global
occurrence of gas transfer suppression and therefore is incorporated into the *k* vs. *u*
parameterization.

The quadratic coefficient, *a*, is calculated by dividing the averaged gas
transfer velocity *k*_{glob} by *u*^{2} and the wind distribution, distu, of *u*.

$$\begin{array}{}\text{(18)}& {\displaystyle}{\displaystyle}a={\displaystyle \frac{{k}_{\mathrm{glob}}}{\sum {u}^{\mathrm{2}}\cdot \mathrm{distu}}}\end{array}$$

The quadratic coefficient then defines the wind-speed-dependent gas transfer velocity *k*
(Eq. 19).

$$\begin{array}{}\text{(19)}& {\displaystyle}{\displaystyle}k=a\cdot {u}^{\mathrm{2}}\end{array}$$

The Fig. 6a shows the global wind speed distribution of the year 2014
taken from the WWIII model, which is based on the NCEP reanalysis. Additionally, we added
the distribution taking our wind speed adjustment into account. At the occurrence of gas
transfer suppression, we calculated *u*_{alt} as the representative wind speed for
the unsuppressed transfer, as described in Sect. 3. The distribution
of *u*_{alt} shifts higher wind speed (10–17 m s^{−1}) to lower wind speed
regimes (0–7 m s^{−1}). This alters the coefficient for the quadratic wind speed
parametrization. A global average gas transfer velocity of
*k*_{glob}=16.5 cm h^{−1} (Naegler, 2009) results in a coefficient *a*=0.2269,
using the NCEP wind speed distribution. The value for *a* becomes 0.2439 with the
*u*_{alt} distribution. This is a 9.85 % increase. Our calculated value of
*a*=0.2269 differs from the W14 value of *a*=0.251 because we use a different wind speed
distribution. The W14 uses a Rayleigh distribution with *σ*=5.83, our NCEP-derived
*σ*=6.04 and the adjusted NCEP *σ*=5.78. This means that the W14 uses a wind
speed distribution with a lower global average speed. However, for the estimation of a
suppression effect we calculate the difference between using the NCEP wind speed and the
adjusted wind speed distribution. For the calculation of *a*, we did not use a
fitted Rayleigh function but the adjusted wind speed distribution from
Fig. 6.

A comparison of W14, N00 and the unsuppressed parameterizations is shown in
Fig. 6b. N00 shows the lowest relationship between *u* and *k*. W14 shows
a parameterization with a global-averaged gas transfer suppression influence and is
therefore slightly higher than N00. It appears that the gas transfer suppression is
overcompensating the smaller bubble-mediated gas transfer of CO_{2} (W14). The
unsuppressed N00 is significantly higher than the W14 + 9.85 %. We hypothesize that
this difference is based on the different bubble-mediated gas transfer of He,
SF_{6}, and CO_{2}.

We used the native global grid (0.5^{∘} × 0.5^{∘}) from the WWIII for
the global analysis. The datapoints from the DMS and CO_{2} climatologies as well
as all auxiliary variables were interpolated to this grid.

Figure 7 shows the percentage of gas-transfer-suppressed datapoints with respect to the total datapoints for every month in the year 2014. The average yearly global percentage is 18.6 %. The minimum is 15 % in March and April and the maximum is 22 % in June–August. Coastal areas and marginal seas seem to be more influenced than open oceans. The reason could be that gas transfer suppression is likely to occur at developed wind seas when the wind speed is in the same direction and magnitude as the wave's phase speed. At coastal areas and marginal seas, the sea state is less influenced by swell and waves that were generated at a remote location. Landmasses block swell from the open ocean to marginal seas. The intra-annual variability of gas transfer suppression is shown in Fig. 8. Additionally, we plotted the occurrences split into ocean basins and northern and southern hemispheres. Two trends are visible. There is a higher percentage of gas transfer suppression in the Northern Hemisphere and, on the time axis, the peak is in the respective (boreal and austral) summer season. The Southern Hemisphere has a water-to-landmass ratio of 81 %, the Northern Hemisphere's ratio is 61 %. The area of free open water is therefore greater in the Southern Hemisphere. Gas transfer suppression is favored by fully developed seas without remote swell influence. In the Southern Hemisphere, the large open ocean areas, where swell can travel longer distances, provide an environment with less gas transfer suppression. The peak in summer and minimum in winter can be associated with the respective sea ice extent on the Northern Hemisphere and Southern Hemisphere. Figure 7 shows that seas, which are usually ice-covered in winter, have a high ratio of gas transfer suppression.

The global reduction of the CO_{2} and DMS flux is calculated using
Eqs. (13)–(14) and shown for every month in
Figs. 9 and 10. These magnitudes represent the
reduction of interfacial gas transfer due to gas transfer suppression. Most areas with a
reduced influx of CO_{2} into the ocean are in the Northern Hemisphere. The only
reduced CO_{2} influx areas of the Southern Hemisphere are in the South Atlantic
and west of Australia and New Zealand. Significantly reduced CO_{2} efflux areas
are found in the northern tropical Atlantic, especially in the boreal summer months, the
northern Indian Ocean and the Southern Ocean. The maximum monthly reduction of influx
(oceanic uptake) is 18.7 mmol m^{−2} day^{−1}. The maximum monthly reduction of
efflux (oceanic outgassing) is 12.9 mmol m^{−2} day^{−1}.

The absolute values of DMS flux reduction (Fig. 9), due to gas
transfer suppression, coincide with the summer maximum of DMS concentration and therefore
large air–sea fluxes (Lana et al., 2011; Simó and Pedrós-Alió, 1999). The northern Indian Ocean during boreal
winter also shows a high level (10 µmol m^{2} day^{−1}) of reduction. The
highest water concentrations and fluxes in the Indian Ocean are found in boreal summer
(Lana et al., 2011), which is less influenced by gas transfer suppression.

The DMS emissions from the ocean to the atmosphere are shown in Table 3. The
calculated total emission from the original N00 parameterization is
50.72 Tg DMS yr^{−1} for the year 2014. We use our estimations of *u*_{alt}
and Eq. (14) to subtract gas transfer suppression from the original
N00 parameterization. The resulting reduced total emission is 45.47 Tg DMS yr^{−1},
which is a reduction of 11 %. The linear parameterization ZA18 estimates an emission of
56.22 Tg DMS yr^{−1}. Using the gas transfer suppression algorithm and
Eq. (13), the global amount is reduced to 51.07 Tg DMS yr^{−1}, which is
a reduction of 11 %. Global estimates are 54.39 Tg DMS yr^{−1} (Lana et al., 2011) and
45.5 Tg DMS yr^{−1} (Lennartz et al., 2015). As stated above, a difference in wind speed or
sea ice coverage could be the reason for the difference in the global emission estimated
between the Lana climatology and our calculations with the N00 parameterization.
Lennartz et al. (2015) use the water concentrations from the Lana climatology, but include
air-side DMS concentrations, which reduces the flux by 17 %. We do not include air-side
DMS concentrations but gas transfer suppression, which reduces the flux by 11 %. We can
expect a reduction of 20 %–30 % when including both processes.

5 Conclusions

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We provide a first approach to adjust *k* values for the gas transfer suppression due to
wind–wave interaction (Zavarsky et al., 2018) and therefore to account for the effect of this
suppression. *R**e*_{tr} and the resulting alternative wind speed *u*_{alt}
can be calculated from standard meteorological and oceanographic variables. Additionally,
the condition (period, height, direction) of the ocean waves have to be known or
retrieved from wave models. The calculation is iterative and can be easily implemented.
The effect of this adjustment is shown with two data sets from the Knorr11
(Bell et al., 2017) and the SO234-2/235 cruises (Zavarsky et al., 2018). Both data sets show, after
the adjustment, a better agreement with the linear ZA18 parameterizations
(Tables 1 and 2), which only contains unsuppressed gas
transfer velocity measurements from the SO 234-2/235 cruise. Generally, the adjustments
may be only applied to the interfacial gas transfer velocity *k*_{o}.

We investigated the individual measurements leading to the N00 gas transfer
parameterization for the influence of gas transfer suppression. We think that the overall
parameterization is heavily influenced by gas transfer suppression, but the suppression
is likely masked by bubble-mediated gas transfer, due to the solubility of the
dual-tracer measurement gases. We show a significant negative correlation between the
occurrence of gas transfer suppression and the ratio of the individual measurements to
the N00 parameterization. We applied an adjustment due to gas transfer suppression and
fitted a new quadratic function to the adjusted data set. The new parameterization is on
average 22 % higher than the original N00 parameterization. This leads to the
conclusion that gas transfer suppression influences gas transfer parameterizations, even
if it is not directly visible, via a smaller slope. Asher and Wanninkhof (1998) state that
SF_{6}∕^{3}He gas transfer measurements could lead to a 23 % overestimation of CO_{2}
gas transfer velocities. After adjusting of N00 for gas transfer suppression, the
difference between gas transfer velocities of the original N00 and the adjusted version
closely matches this estimation.

For the W14 parameterization we used a global wind speed climatology for the year 2014
and applied the gas transfer suppression model *u*_{10}→*u*_{alt}. Using
the distribution function of *u*_{alt} we calculated an unsuppressed gas transfer
parameterization. The coefficient of the unsuppressed parameterization is 9.85 % higher
than the original one. W14 already includes the global average of gas transfer
suppression. Therefore the increase, due to the adjustment, is expected to be less than
the one for N00, which is strongly suppressed. The original N00 is lower than W14, but
after adjustment N00 is larger than the unsuppressed W14, which is expected due to the
larger bubble-mediated gas transfer of He and SF_{6} over CO_{2}.

We think that gas transfer suppression has a global influence on air–sea gas exchange of 10 %–11 %. These numbers are supported by the adjustment of the W14 parametrization as well as a global DMS gas transfer calculation. Local conditions may lead to much higher influences. Gas transfer velocity parameterizations from regional data sets might be heavily influenced by gas transfer suppression. We have shown this for the N00 parameterization. This should be considered with their use.

Using the *R**e*_{tr} parameter, one can evaluate if a flux measurement or flux
calculation is influenced by gas transfer suppression. For unsuppressed conditions and
rather soluble gases, such as DMS, we recommend the use of a linear parameterization
(e.g., ZA18). For gases with a similar solubility as CO_{2}, we recommend the use
of the adjusted W14 + 9.85 % parameterization. The adjusted N00 (N00 + 22 %)
parameterization is recommended for very insoluble gases. In case of gas transfer
suppression, we recommend the previous parameterizations together with our iterative
approach to adjust *u* to *u*_{alt} (Fig. 1) with the use of
Eqs. (13)–(14). For global calculations, we recommend the use
of the Wanninkhof parameterizations W14 (Wanninkhof, 2014), as it already has an average
global gas transfer suppression included.

Data availability

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Data availability.

The wave data are available at the website of the NOAA Environmental Modeling Center. The ERA-Interim data are available at the website of the ECMWF. The data are stored at the data portal of GEOMAR Kiel.

Appendix A: Directional dependencies

Back to toptop
Figure A1 shows the shape of the wave (half sphere) as experienced by the
wind flowing over it with a certain angle *θ*. The larger *θ*, the more
streamlined the wave (half sphere). The more streamlined the wave, the more difficult it
is to generate turbulence; this counteracts the flow detachment and as a consequence gas
transfer suppression occurs.

Wind at an angle of *θ*=90^{∘} does not experience a wave crest or trough, but
rather an along-wind corrugated surface. In this case there should be no gas transfer
suppression. Zavarsky et al. (2018) predict a unsuppressed condition around
*R**e*_{tr}=0, which coincides with *θ*≈90^{∘} or
*u*_{tr}→0. Both conditions rarely occur and must be investigated in the
future.

Adjustment of wind speed or adjustment of *k*

Back to toptop
A shift on the *x* axis from *u*_{10} to *u*_{alt} is equivalent to an increase
in *k* by Δ*k*, when related to a linear relationship. We use the
ZA18 parameterization as a reference (Eq. 12), which is a linear relationship
describing *k*_{o}, as gas transfer suppression only affects interfacial gas
transfer. Figure B1 illustrates the two different possibilities of
adjusting suppressed gas transfer values.

The adjustments of the two DMS data sets (SO234-2/235 and Knorr11) are done by
shifting *u*_{10} along the *x* axis to *u*_{alt}. We want to test whether
*u*_{10} can be directly replaced by *u*_{alt} for
*k*_{o} parameterizations. Gas transfer suppression adjustments for
bubble-influenced parameterizations are done by adding Δ*k*, which is directly
related to the difference $\mathrm{\Delta}u={u}_{\mathrm{10}}-{u}_{\mathrm{alt}}$.

Author contributions

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Author contributions.

AZ developed the model. AZ and CAM provided and collected the data. AZ prepared the manuscript with contributions from CAM.

Competing interests

Back to toptop
Competing interests.

The authors declare that they have no conflict of interest.

Acknowledgements

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Acknowledgements.

The authors thank Kirstin Krüger, the chief scientist of the R/V *Sonne*
cruise (SO234-2/235), as well as the captain and crew. We thank the Environmental
Modeling Center at the NOAA/National Weather Service for providing the
WAVEWATCH III^{®} data. We thank the European Centre for
Medium-Range Weather Forecasts for providing the ERA-Interim data. This work was carried
out under the Helmholtz Young Investigator Group of Christa A. Marandino,
TRASE-EC (VH-NG-819), from the Helmholtz Association. The cruise 234-2/235 was financed
by the BMBF, 03G0235A.

Edited by: Martin Heimann

Reviewed by: Christopher Fairall and Mingxi Yang

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Short summary

Wind–wave interaction can suppress gas transfer between the atmosphere and the ocean. Using a global wave model we investigate the impact of this interaction on the global gas transfer of CO_{2} and DMS. We also investigate the impact on of gas transfer limitation on two commonly used gas transfer velocity parameterizations.

Wind–wave interaction can suppress gas transfer between the atmosphere and the ocean. Using a...

Atmospheric Chemistry and Physics

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