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Definition of the Subject

Gaseous and volatile chemical species reside not only in the atmosphere. Because they dissolve in water, they are also distributed in the hydrosphere. The by far largest part of the hydrosphere is the ocean. Therefore, the exchange between atmosphere and oceans is the most important process for the fate of gaseous and volatile chemical species (Table 8.1).

Table 8.1 Comparison of size (as depth in m over entire earth surface) and mass of atmosphere and global water storage
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For long-lived species, that is, life time by reaction larger than residence times in either the atmosphere or the ocean, two basic factors determine the fate of these species. For time scales longer than the turnover time of ocean mixing, which is much slower than the same process in the atmosphere, the solubility of the species determines where it ends up. On much shorter time scales, the speed by which the species are exchanged between atmosphere and ocean and the concentration difference determines the flux between these two compartments.

While turbulent mixing is quite fast within the ocean and the atmosphere, it becomes more and more inefficient, the closer a species is transported to the surface. The final step toward the interface must be overcome by molecular diffusion, which is a slow process, especially in water. Therefore, very thin mass boundary layers at both sides of the water surface, in which turbulent transport is slower than molecular transport, are the bottleneck of the exchange between atmosphere and ocean.

In this way, tiny layers only about 20–200 μm thick in the water and 200–2,000 μm thick in the air control the exchange process. In consequence, the crucial question is which processes determine the thickness of these layers.

Introduction

Research in air–water gas exchange dates back more than a century. Bohr [1], for example, was one of the first to study the exchange of carbon dioxide in a stirred bottle. With the early observation of increasing carbon dioxide concentration in the atmosphere interest in air-sea gas exchange rose considerably, triggered by the question how much of the excess carbon dioxide would go into the ocean [2, 3]. Since then significant and continuous research work was devoted for a better understanding of air–water mass exchange, but the mechanisms of the exchange processes are still not fully understood even today.

This entry is divided into three major parts and partly based on previous reviews of the author on the same subject [4–6]. Section “Mechanisms of Atmosphere–Water Exchange” describes the basic mechanisms of air–water exchange and the many parameters influencing it. Focusing on field data, section “Experimental Techniques and Results” summarizes the various experimental techniques and gives a synthesis of the available experimental data. Using the information collected in the previous two sections, section “Empiric Parametrization” tries to give the best possible empirical parametrization of the exchange rate and section “Future Directions” points to future directions of research.

Mechanisms of Atmosphere–Water Exchange

Turbulent and Molecular Transport

The transfer of gases and volatile chemical species between the atmosphere and oceans is driven by a concentration difference and the transport by molecular and turbulent motion. Both types of transport processes can be characterized by diffusion coefficients, denoted by D and K c , respectively. The resulting flux area density j c is proportional to the diffusion coefficient and the concentration gradient:

$$ {j_c} = - {(D + }{{K}_c}{(z})){\nabla_c}. $$
(8.1)

In a stationary homogeneous case and without sinks and sources by chemical reactions, the flux density j is in vertical direction and constant. Then integration of Eq. 8.1 yields vertical concentration profiles:

$$ C({z_r}) - C(0) = {j_c}\int\limits_0^{{z_r}} {\frac{1}{{D + {K_c}(z)}}dz.} $$
(8.2)

The molecular diffusion coefficient is proportional to the velocity of the molecules and the free length between collisions. The same concept can be applied to turbulent diffusion coefficients. Far away from the interface, the free length (called mixing length) is set proportional to the distance from the interface and the turbulent diffusion coefficient K c for mass transfer is:

$$ {K_c} = \frac{k}{{S{c_t}}}{u_*}z, $$
(8.3)

where κ = 0.41 is the von Kármán constant, u *, the friction velocity, a measure for the velocity fluctuations in a turbulent flow, and Sc t = K m /K c the turbulent Schmidt number. Closer to the interface, the turbulent diffusion coefficients are decreasing even faster. Once a critical length scale l is reached, the Reynolds number Re = u * l/ν (ν is the kinematic viscosity, the molecular diffusion coefficient for momentum) becomes small enough so that turbulent motion is attenuated by viscosity. The degree of attenuation depends on the properties of the interface. At a smooth solid wall, \( {K_c} \propto {z^3} \), at a free water interface it could be in the range between \( {K_c} \propto {z^3} \) and \( {K_c} \propto {z^2} \) depending on surface conditions.

Viscous and Mass Boundary Layers

Boundary layers are formed on both sides of the interface (Fig. 8.1).

Fig. 8.1
figure 1

Schematic graph of the mass boundary layers at a gas–liquid interface for a tracer with a solubility α = 3

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Fig. 8.2
figure 2

Schmidt number/solubility diagram including various volatile tracers, momentum, and heat for a temperature range (C) as indicated. Filled circles refer to only a temperature of 20°C. The regions for air-side, mixed, and water-side control of the transfer process between gas and liquid phase are marked. At the solid lines, the transfer resistance is equal in both phases. The following dimensional transfer resistances were used: r a = 31, r w = 12Sc 2/3 (smooth), r w = 6.5Sc 1/2 (wavy surface) with r a = R a u *a and r w = R w u *w (Adapted from Jähne and Haußecker [6])

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When the turbulent diffusivity becomes equal to the kinematic viscosity, the edge of the viscous boundary layer is reached. As the name implies, this layer is dominated by viscous dissipation and the velocity profile becomes linear because of a constant diffusivity. The edge of the mass boundary layer is reached when the turbulent diffusivity becomes equal to the molecular diffusivity. The relative thickness of both boundary layers depends on the dimensionless ratio Sc = ν/D (Schmidt number ).

The viscous and mass boundary layers are of about the same thickness in the air, because values of D for various gaseous species and momentum are about the same (Sc air is 0.56 for H2O, 0.63 for heat, and 0.83 for CO2). In the liquid phase, the situation is completely different. With Schmidt numbers in the range from 100 to 3,000 (Fig. 8.2, Table 8.3), molecular diffusion for a dissolved volatile chemical species is two to three orders of magnitude slower than diffusion of momentum (Table 8.2). Thus, the mass boundary layer is significantly thinner than the viscous boundary layer in the liquid phase. This means that the transfer of gases is much slower and almost entirely controlled by the tiny residual turbulence in the small top fraction of the viscous boundary layer. This basic fact makes it difficult to investigate the mechanism of air–water gas transfer both theoretically and experimentally. In addition, the transfer process depends strongly on the water temperature because the Schmidt number decreases by about a factor of 6 from 0°C to 35°C (Fig. 8.2, Table 8.3).

Table 8.2 Diffusion coefficients for various gases and volatile chemical species in deionized water and in some cases in sea water collected from Jähne et al. [18] and King et al. [20]. Die data for momentum (kinematic viscosity) are from Sündermann [22]. Column 3 and 4 contain the parameters for the fit of the diffusion coefficient: D = A exp[−E a /(RT)], the last four columns the diffusion coefficients for 5°C, 15°C, 25°C, and 35°C
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Table 8.3 Schmidt numbers of various gases and volatile species in the temperature range from 0°C to 40°C
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Description of Transport

The amount of species exchanged between the air and water across the interface can be described by a quantity with the units of a velocity. It represents the velocity with which a tracer is pushed by an imaginary piston across the surface. This quantity is known as the transfer velocity k (also known as the piston velocity, gas exchange rate or transfer coefficient ). It is defined as the flux density divided by the concentration difference between the surface and the bulk at some reference level z r :

$$ k = \frac{{{j_c}}}{{{C_s} - {C_b}}}. $$
(8.4)

The inverse of the transfer velocity is known as the transfer resistance R:

$$ R = \frac{{{C_s} - {C_b}}}{{{j_c}}}. $$
(8.5)

The indices s and b denote the surface and bulk. Both quantities can directly be related to vertical concentration profiles by introducing Eqs. 8.4 and 8.5 into Eq. 8.2:

$$ R = \frac{1}{k} = \int\limits_0^{{z_r}} {\frac{1}{{D + {K_e}(z)}}dz.} $$
(8.6)

Thus, the transfer resistances over several height intervals can be added in the same way as electrical resistances that are connected in series. Typical values of the transfer velocity across the water-side mass boundary layer are 10−6–10−5 m/s (1–10 m/day). With respect to typical mixed layer depths in the ocean of about 100 m, gas transfer is a very slow process. It takes a time constant τ = h/k = 10–100 days for the concentration of dissolved gases in the mixed layer to come into equilibrium with the atmosphere.

Boundary Layer Thickness

The boundary layer thickness \( \tilde{z} \) is defined as the thickness of a fictional layer in which the flux is maintained only by molecular transport: \( j = D({C_s} - {C_b})/\tilde{z} \). Then with Eq. 8.4 the boundary layer thickness is given by:

$$ \tilde{z} = \frac{D}{k}. $$
(8.7)

Geometrically, \( \tilde{z} \) is given as the intercept of the tangent to the concentration profile at the surface and the bulk (Fig. 8.1). With thicknesses between 20 and 200 μm, the mass boundary layer is extremely thin.

Boundary Layer Time Constant

The time constant \( \tilde{t} \) for the transport across the mass boundary layer is given by:

$$ \tilde{t} = \frac{{\tilde{z}}}{k} = \frac{D}{{{k^2}}}. $$
(8.8)

Typical values for \( \tilde{t} \) are 0.04–4 s. Any chemical reaction with a time constant larger than \( \tilde{t} \) does not significantly affect the transfer process. Therefore, CO2 can be regarded as an inert gas, but not fast hydrating acid gases such as SO2.

The definitions of the three parameters k, \( \tilde{z} \), \( \tilde{t} \) are generally valid and do not depend on any models of the boundary layer turbulence. According to Eqs. 8.7 and 8.8, they are coupled via the molecular diffusion coefficient. Therefore, only one of them needs to be measured to get knowledge of all three parameters provided the molecular diffusion coefficient of the species is known.

Partitioning of Transfer Between Air and Water

Because a mass boundary layer exists on both sides, it is important to determine which one controls the transfer, that is, exhibits the largest transfer resistance (or lowest transfer velocity). At the surface itself, the thermodynamic solubility equilibrium is assumed to be established between the tracer concentrations c a in the gas phase and c w in the liquid phase:

$$ {C_{ws}} = \alpha {C_{as}}, $$
(8.9)

where α is the dimensionless solubility (partition coefficient). A solubility α ≠ 1 causes a concentration jump at the surface (Fig. 8.1). Thus, the resulting total transfer velocity k t or transfer resistance R t can either be viewed from the gas phase or the liquid phase. Adding them up, the factor α must be considered to conserve the continuity of the concentration profile:

$$ {\text{air\;side: }}\frac{1}{{{k_{at}}}} = \frac{1}{{{k_a}}} + \frac{1}{{\alpha {k_w}}},\quad {R_{at}} = {R_a} + {R_w}/\alpha, $$
(8.10)
$$ {\text{water\;side: }}\frac{1}{{{k_{wt}}}} = \frac{\alpha }{{{k_a}}} + \frac{1}{{{k_w}}},\quad {R_{wt}} = \alpha {R_a} + {R_w}. $$

The total transfer velocities in air and water differ by the factor α: k at = αk wt . The ratio αk w /k a determines which boundary layer controls the transfer process. A high solubility shifts control of the transfer process to the gas-phase boundary layer, and a low solubility to the aqueous layer. The solubility value for a transition from air-sided to water-sided control depends on the ratio of the transfer velocities. Typically k w is about 100–1,000 times smaller than k a . Thus, the transfer of even moderately soluble volatile chemical species with solubilities up to 30 is controlled by the water side. Some environmentally important species lie in a transition zone where it is required to consider both transport processes (Fig. 8.2). The transfer of highly soluble volatile and/or chemically reactive gas is controlled by the air-side transfer process and thus analogous to the transfer of water vapor. The following considerations concentrate on the water-side transfer process.

Gas Exchange at Smooth Water Surfaces

At smooth water surfaces, the theory of mass transfer is well established because it is equivalent to mass transfer to a smooth solid wall. The turbulent diffusivity can be described by the classic approach of Reichardt [7] with an initial z 3 increase that smoothly changes to a linear increase in the turbulent layer as in Eq. 8.3. Then integration of Eq. 8.6 yields the following approximation for Schmidt numbers higher than 100 [12, 16]:

$${k_w}={u_{*w}}\frac{1}{{12.2}}S{c^{- 2/3}}\quad Sc>60.$$
(8.11)

This equation establishes the basic analogy between momentum transfer and gas exchange. The transfer coefficients are proportional to the friction velocity in water, which describes the shear stress (tangential force per unit area) \( \tau = {\rho_w}u_{*w}^2 \) applied by the wind field at the water surface. Assuming stress continuity at the water surface, the friction velocity in water is related to the friction velocity in air by:

$$ {u_{*w}} = {u_{*a}}{\left( {\frac{{{\rho_a}}}{{{\rho_w}}}} \right)^{1/2}}. $$
(8.12)

The friction velocity in air, u *a , can further be linked via the drag coefficient to the wind speed U R at a reference height: c D = (u *a /U R )2. Depending on the roughness of the sea surface, the drag coefficient has values between 0.8 and 2.4 · 10−3. In this way, the gas exchange rate is directly linked to the wind speed. The gas exchange further depends on the chemical species and the water temperature via the Schmidt number.

Influence of Waves

A free water surface is neither solid nor is it smooth as soon as short wind waves are generated. On a free water surface, velocity fluctuations are possible. Thus, there can be convergence or divergence zone at the surface; surface elements may be dilated or contracted. At a clean water surface, dilation or contraction of a surface element does not cause restoring forces, because surface tension only tries to minimize the total free surface area, which is not changed by this process. As a consequence of this hydrodynamic boundary condition, the turbulent diffusivity normal to the interface can now increase with the distance squared from the interface, \( {K_c} \propto {z^2} \). Then:

$$ {k_w} = {u_{*w}}\frac{1}{\beta }S{c^{ - 1/2}}, $$
(8.13)

where β is a dimensionless constant.

In comparison to the smooth case in Eq. 8.11, the exponent n of the Schmidt number drops from −2/3 to −1/2. This increases the transfer velocity for a Schmidt number of 600 by about a factor of 3. The total enhancement depends on the value of the constant β.

Fig. 8.3
figure 3

Transfer velocity of carbon dioxide plotted against the transfer velocity of water vapor. Measurements from a small annular wind/wave facility Jähne [15]

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Fig. 8.4
figure 4

Summary of gas exchange field data normalized to a Schmidt number of 600 and plotted versus wind speed together with the empirical relationships of Liss and Merlivat [11] and ? (After Jähne and Haußecker [6])

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Wind waves cannot be regarded as static roughness elements for the liquid flow because their characteristic particle velocity is of the same order of magnitude as the velocity in the shear layer at the surface. This fact causes a basic asymmetry between the turbulent processes on the air and on the water sides of the interface. Therefore, the wave effect on the turbulent transfer in the water is much stronger and of quite different character than in the air. This basic asymmetry can be seen if the transfer velocity for CO2 is plotted against the transfer velocity for water vapor (Fig. 8.3, [15]). At a smooth water surface, the points fall well on the theoretical curve predicted by the theory for a smooth rigid wall. However, as soon as waves occur at the water surface, the transfer velocity of CO2 increases significantly beyond the predictions.

Even at high wind speeds, the observed surface increase is well below 20% [24]. When waves are generated by wind, energy is not only transferred via shear stress into the water but a second energy cycle is established. The energy put by the turbulent wind into the wave field is transferred to other wave numbers by nonlinear wave–wave interaction and finally dissipated by wave breaking, viscous dissipation, and turbulence. The turbulent wave dissipation term is the least known term and of most importance for enhanced near-surface turbulence. Evidence for enhanced turbulence levels below wind waves has been reported from field and laboratory measurements. Experimental results also suggest that the gas transfer rate is better correlated with the mean square slope of the waves as an integral measure for the nonlinearity of the wind wave field than with the wind speed.

It is not yet clear, however, to what extent microscale wave breaking can account for the observed enhanced gas transfer rates. A gravity wave becomes instable and generates a steep train of capillary waves at its leeward face and has a turbulent wake. This phenomenon can be observed even at low wind speeds, as soon as wind waves are generated. At higher wind speeds, the frequency of microscale wave breaking increases.

At high wind speeds, wave breaking with the entrainment of bubbles may enhance gas transfer further. This phenomenon complicates the gas exchange between atmosphere and the oceans considerably [19, 26]. First, bubbles constitute an additional exchange surface. This surface is, however, only effective for gases with low solubility. For gases with high solubility, the gas bubbles quickly come into equilibrium so that a bubble takes place in the exchange only for a fraction of its life time. Thus bubble-mediated gas exchange depends – in contrast to the exchange at the free surface – on the solubility of the gas tracer. Second, bubble-mediated gas transfer shifts the equilibrium value to slight supersaturation due to the enhanced pressure in the bubbles by surface tension and hydrostatic pressure. Third, breaking waves also enhance near-surface turbulence during the breaking event and the resurfacing of submerged bubbles [17].

Experimental data are still too sparse for the size and depth distribution of bubbles and the flux of the bubbles through the interface under various sea states for a sufficiently accurate modeling of bubble-mediated air-sea gas transfer and thus a reliable estimate of the contribution of bubbles to the total gas transfer rate. Some experiments from wind/wave tunnels and the field suggest that significant enhancements can occur, other experiments could not observe a significant influence of bubbles.

Influence of Surface Films

A film on the water surface creates pressure that works against the contraction of surface elements. This is the point at which the physicochemical structure of the surface influences the structure of the near-surface turbulence as well as the generation of waves [13, 21]. As at a rigid wall, a strong film pressure at the surface maintains a two-dimensional continuity at the interface just as at a rigid wall. Therefore, Eq. 8.11 should be valid for a smooth film-covered water surface and has indeed been verified in wind/wave tunnel studies as the lower limit for the transfer velocity. As a consequence, both Eqs. 8.11 and 8.13 can only be regarded as limiting cases. A more general approach is required that has not yet been established. One possibility is a generalization of Eqs. 8.11 and 8.13 to:

$$ {k_w} = {u_{*w}}\frac{1}{{\beta (s)}}S{c^{ - n(s)}}, $$
(8.14)

where both β and n depend on dimensionless parameters describing the surface conditions s. Even films with low film pressure may easily decrease the gas transfer rate to half of its value at clean water surface conditions. But still too few measurements at sea are available to establish the influence of surfactants on gas transfer for oceanic conditions more quantitatively.

Experimental Techniques and Results

Laboratory Facilities

Laboratory facilities play an important role in the investigation of air-sea gas transfer. Only laboratory studies allow a systematic study of the mechanisms and are thus an indispensable complement to field experiments. Almost all basic knowledge about gas transfer has been gained by laboratory experiments in the past.

Geochemical Tracer Techniques

The first oceanic gas exchange measurements were performed using geochemical tracer methods such as the 14C [2], 3He/T [23], or 222Rn/226Ra [8, 9] methods. The volume and time-average flux density is given by mass balance of the tracer concentration in a volume of water V w :

$$ {V_w}{\dot{c}_w} = {F_w}j\quad or\quad j = {h_w}{\dot{c}_w}, $$
(8.15)

where F w , and h w are the surface area and the effective height V w /F w of a well-mixed water body, respectively. The time constant τ w = h w /k is in the order of days to weeks. It is evident that the transfer velocities obtained in this way provide only values integrated over a large horizontal length scales and time scales in the order of τ w . Thus a parametrization of the transfer velocity is only possible under steady state conditions over extended periods. Moreover, the mass balance contains many other sources and sinks besides air-sea gas exchange and thus may cause severe systematic errors in the estimation of the transfer velocity. Consequently, mass balance methods are only poorly suited for the study of the mechanisms of air–water gas transfer.

Tracer Injection

The pioneering lake studies for tracer injection used sulfur hexafluoride (SF6). However, the tracer concentration decreases not only by gas exchange across the interface but also by horizontal dispersion of the tracer. This problem can be overcome by the dual tracer technique [10] simultaneously releasing two tracers with different diffusivities (e.g., SF6 and 3He). When the ratio of the gas transfer velocities of the two tracers is known, the dilution effect by tracer dispersion can be corrected, making it possible to derive gas transfer velocities. But the basic problem of mass balance techniques, that is, their low temporal resolution, remains also with artificial tracer approaches.

Eddy Correlation Flux Measurements

Eddy correlation techniques are used on a routine basis in micrometeorology, that is, for tracers controlled by the boundary layer in air (momentum, heat, and water vapor fluxes). Direct measurements of the air-sea fluxes of gas tracers are very attractive because the flux densities are measured directly and have a much better temporal resolution than the mass balance based techniques. Unfortunately, large experimental difficulties arise when this technique is applied to gas tracers controlled by the aqueous boundary layer [Broecker 1986, 14]. The concentration difference in the air is only a small fraction of the concentration difference across the aqueous mass boundary layer. But after more than 20 years of research has this technique delivered useful results. Some successful measurements under favorable conditions have been reported and it appears that remaining problems can be overcome in the near future.

Passive and Active Thermography

The basic idea of this technique is to determine the concentration difference across the mass boundary layer when the flux density j of the tracer across the interface is known. The local transfer velocity can be determined by simply measuring the concentration difference Δc across the aqueous boundary layer (cold surface skin temperature) according to Eq. 8.4 with a time constant \( \tilde{t} \) for the transport across the boundary layer Eq. 8.8. This technique is known as the controlled flux technique (CFT).

Heat proves to be an ideal tracer for the CFT. The temperature at the water surface can then be measured with high spatial and temporal resolution using IR thermography. A known and controllable flux density can be applied by using infrared radiation. Infrared radiation is absorbed in the first few ten micrometers at the water surface. Thus a heat source is put right at top of the aqueous viscous boundary layer. Then the CFT directly measures the water-side heat transfer velocity.

A disadvantage of the CFT is that the transfer velocity of gases must be extrapolated from the transfer velocity of heat. The large difference in the Schmidt number (7 for heat, 600 for CO2) casts some doubt whether the extrapolation to so much higher Schmidt numbers is valid.

Two variants of the technique proved to be successful. Active thermography uses a CO2 laser to heat a spot of several centimeter in diameter on the water surface. The heat transfer rates are estimated from the temporal decay of the heated spot. Passive thermography uses the naturally occurring heat fluxes caused by latent heat flux j l , sensible heat flux j s and longwave emission of radiation j r . The net heat flux j n = j l + j s + j r results according to Eq. 8.4 in a temperature difference across the interface of ΔT = j h /(ρc p k h ). Because of the turbulent nature of the exchange process any mean temperature difference is associated with surface temperature fluctuations which can be observed in thermal images. With this technique, the horizontal structure of the boundary layer turbulence can be observed. Surface renewal is directly observable in the IR image sequences, which show patches of fluid being drawn away from the surface.

With some knowledge about the statistics of the temperature fluctuations, the temperature difference ΔT across the interface as well as the time constant \( \tilde{t} \) of heat transfer can be computed from the temperature distribution at the surface. Results obtained with this technique are shown in Fig. 8.4.

Summary of Field Data

A collection of field data is shown in Fig. 8.3. Although the data show a clear increase of the transfer velocity with wind speed, there is substantial scatter in the data that can only partly be attributed to uncertainties and systematic errors in the measurements. Thus, in addition, the field measurements reflect the fact that the gas transfer velocity is not simply a function of the wind speed but depends significantly on other parameters influencing near-surface turbulence, such as the wind-wave field and the viscoelastic properties of the surface film.

Empiric Parametrization

Given the lack of knowledge, all theories about the enhancement of gas transfer by waves are rather speculative and are not yet useful for practical application. Thus, it is still state of the art to use semiempiric or empiric parameterizations of the gas exchange rate with the wind speed. Most widely used is the parametrization of Liss and Merlivat [11]. It identifies three physically well-defined regimes (smooth, wave-influenced, bubble-influenced) and proposes a piece-wise linear relation between the wind speed U and the transfer velocity k:

$$ \begin{array}{l}k = {10^{ - 6}}\left\{\begin{array}{ll}{0.472U{{(Sc/600)}^{ - 2/3}}} & {U\le \ 3.6\;{\text{m/s}}} \\{7.971(U - 3.39){{(Sc/600)}^{ - 1.2}}} & {U> 3.6\;{\text{m/s \ and}}\;} \\{} & {U \le\ 13\;{\text{m/s}}} \\{16.39(U - 8.36){{(Sc/600)}}^{{ - 1/2}}} & {U> 13\;{\text{m/s}}} \end{array}\right. \end{array}$$
(8.16)

At the transition between the smooth and wavy regime, a sudden artificial jump in the Schmidt number exponent n from 2/3 to 1/2 occurs. This actually causes a discontinuity in the transfer rate for Schmidt number unequal to 600.

The empiric parametrization of Wanninkhof [25] simply assumes a quadratic increase of the gas transfer rate with the wind speed:

$$ k = 0.861 \cdot {10^{ - 6}}(s/m){U^2}{(Sc/600)^{ - 1/2}}. $$
(8.17)

Thus, this model has a constant Schmidt number exponent n = 1/2. The two parameterizations differ significantly (see Fig. 8.3). The Wanninkhof parametrization predicts significantly higher values. The discrepancy between the two parameterizations and many others proposed (up to a factor of two) mirrors the current uncertainty in estimating the air-sea gas transfer rate.

Future Directions

In the past, progress toward a better understanding of the mechanisms of air–water gas exchange was hindered by inadequate measuring technology. However, new techniques have become available and will continue to become available that will give a direct insight into the mechanisms under both laboratory and field conditions. This progress will be achieved by interdisciplinary research integrating such different research areas as oceanography, micrometeorology, hydrodynamics, physical chemistry, applied optics, and image processing.

Optical and image processing techniques will play a key role because only imaging techniques give direct insight to the processes in the viscous, heat, and mass boundary layers on both sides of the air–water interface. Eventually, all key parameters including flow fields, concentration fields, and waves will be captured by imaging techniques with sufficient spatial and temporal resolution. The experimental data gained with such techniques will stimulate new theoretical and modeling approaches.