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On the exchange of gases between the atmosphere and the sea
Deep-Sea Research, 1963, Vol. 10, pp. 195 to 207. Pergamon Press Ltd. Printed in Great Britain.
On the exchange of gases between the atmosphere and the sea* JOHN KANWISHER W o o d s Hole Oceanographic Institution, W o o d s Hole, Massachusetts
(Received 17 November 1962)
INTRODUCTION
THE exchange between the gases of the atmosphere and those dissolved in the oceans is pertinent to various geochemical, biological and physical problems. These two reservoirs are intermixed by a two-way flux through the water surface. It will be shown here that the rate of this exchange depends largely on molecular diffusion through a thin laminar surface layer of the water. The thickness of this layer is influenced by the turbulent structure of the underlying water. Since the wind is ultimately responsible for most of this turbulence through the shearing stress it exerts on the water surface, we shall not be surprised to find that this exchange flux depends critically on the wind velocity. The full range of conditions in nature varies from glassy calms to violent storms (FIt~. 1). In the latter case, the intermingling of air and water can impart three dimensional characteristics to the sea 'surface.' We can expect the rates of gas exchange to vary by correspondingly large amounts. In addition to the physical conditions at the surface, an understanding of the movement of these gases in nature requires consideration of their unique chemical and biological properties. Oxygen and carbon dioxide are involved in animal and plant respiration and photosynthesis. The behaviour of carbon dioxide is additionally complicated by its chemical reactivity. This links it to the carbonate system. The other important constituents of air, nitrogen and argon, can probably be treated as inert substances. But it should be kept in mind that nitrogen is involved in the metabolism of many unicellular marine plants and bacteria, and even argon is enriched in the swim bladder of some fishes. Our attention here, however, will be mainly directed towards the physical processes of gas exchange at the sea-air interface. All dissolved gases are held in solution by their respective partial pressures or tensions in the associated gas phase (Henry's Law). On a long time average the amounts of the various gases in solution in natural waters must be in diffusion equilibrium with their respective partial pressures in the atmosphere. At any given time however, the partial pressure in the water at a particular spot may be above or below that of the overlying air. There will then be a net flux one way or the other across the interface in the direction which brings the two towards equilibrium. To a fair approximation the atmosphere can be considered of constant composition and nearly constant pressure. Thus, the direction of net movement of these gases across a water surface will depend mostly on the factors that change their partial *Contribution No. 1373 from the W o o d s Hole Oceanographic Institution.
195
196
JOHNKANWISHER
pressure in surface water. Seasonal water temperature variations force the movement of gas into or out of the water to adjust for the changing solubility. Likewise biologicaJ photosynthesis and respiration account for complimentary changes of the amounts of oxygen and carbon dioxide in solution. Once a partial pressure difference bet~eei1 the sea and air exists, the net flux into o1" out of the water will depend on both the magnitude of the gradient and also the physical state of the sea surface. We will here be concerned only \~ith the latter factoJ. It should be kept in mind that there is always a two way dynamic exchange across the surface even when no gradient of partial pressure exists. This is of concern ont'~ if a given gas in the t,~o reservoirs differs in some measureable parameter~ ( a r b o n dioxide is such a case. its (?~'~content in air is different from that in variou~ ~urfac~ waters. This difference forms the basis of hypothesis concerning the rate:, of mixing and exchange of this gas between different natural reservoirs. It is the tw~ way c:, change that is pertinent in such problems and not the net flux. The latter is rciativel~ unimportant since the flux due to the difference in partial pressure rarely accounts for more than 10 per cent of the total. Oxygen and nitrogen may haze isotope differences that can be treated in the same manner. Workers in such diverse fields as stream pollution, animal respiration, petroleum chemistry, and limnology have contributed to our knowledge of the transfer oi gases across air-liquid boundaries. The transport of gases within the atmosphere and the oceans or other natural waters takes place mainly by turbulent mixing processes. But movement across the interface is usually considered a~ being by molecular diffusion through a thin unstirred surface layer (DAVIS and (RANDALl. 1930; Ee,IRSSON. 1959, etc.). The main body of liquid below and the gas above suci~ a film are assumed to be completely mixed. BouN (1960) has reviewed this poim. The thickness of these films in laboratory experiments can be readily computed from the measured diffusivity if gases through them. Values range from 0.04 to 0.001 cm. Whether these films are important on the sea, particularly under violent storm conditions, is not clear. But in any case they provide a convenient index/'or expressing gas exchange rates. In addition one must consider the potential role of bubbles formed by breaking waves. It will be shown here that these bubbles cannot bc considered merely as separated parts of the surface. Like most natural situations the actual sea surface is much too complicated t~ allow anything like an exact analysis of the events involved in gas exchange (FIG. I i But by combining available laboratory and filed data with the physical laws tha~ govern the behaviour of gases we can better appreciate the important physical para-~ meters in nature. For example, gas transfer across the surface appears to vary as the square (or higher power) of the wind velocity. This indicates that cataclysmic events such as severe storms may account for a large fraction of the exchange even though they are only of short duration, Unfortunately, much of the discussion that follows will be largely qualitative.
!.
SURFACE
LAYERS
There is multiple evidence for laminar surface layers which, if they exist, would act as a diffusion barrier to gas exchange. First, they are readily visible (RouGr~TON and BOOTH, 1946). The random flow pattern of a stirred liquid can be readily seen
On the exchange o f gases between the atmosphere and the sea
197
if the water contains many fine particles. When one looks at the surface with a microscope he will see a layer in which particles, and therefore water, are only slowly exchanged with those in the main volume of the liquid below. The only way a dissolved gas can cross such a film is by diffusion. The observed thickness of such films agree well with those computed from the measured diffusion rates. Such films also almost certainly exist in nature. From the dock at Woods Hole one can frequently see a surface layer (visible because of dust particles) apparently moving independently of the water underneath. A dye particle dropped into the water from close to the surface leaves a clean vertical dye trail that shows pronounced current shear in the upper millimetre of water. Drift envelopes which float fiat on the surface follow different courses from drift bottles which extend down into the water. It is clear from light reflection at the surface and the absence of capillary wave suppression that organic surface films are not responsible. The observed film thicknesses are of the order of 100/z This is 105 molecular diameters so the film is clearly not of a monolayer type phenomenon. It seems more likely to look for the causes in the turbulent structure of the water. Boundary conditions dictate that there be no motion of turbulent wa~ter elements transverse to the surface. Thus water in the surface layer can only be moved out of it by gentle shearing forces exerted from below. Simple dye marking experiments of the surface (sprinkling powdered fluorescene), indicate that the lifetime of this quasi-permanent film may be several seconds or longer, depending on the intensity of mixing. Since dissolved gas molecules diffuse through the film in a time shorter than this, such films can be considered permanent from the gases point of view. This is obviously an idealized model since there can hardly be a sharp separation between a laminar surface layer and a turbulent under body. But it has proved useful in analysing the exchange problem. Recently EWING et al. (1960) has shown by radiation thermometry that a surface film exists which has a temperature lower than the main body of water due to evaporative cooling. This film can be destroyed by forcing a jet of water up at the surface from underneath. This apparently tears the surface film away faster than evaporation can renew it. Strong turbulence such as in a breaking wave may do the same thing naturally. In the gas exchange problem this would amount to a renewal of the surface film in a time short compared to that for a gas molecule to diffuse through it. The rate of gas exchange would then be determined largely by the rate of renewal of the partially equilibrated film and the rate of penetration of gas molecules through the surface. It should be kept in mind that an equivalent surface film thickness computed from measured gas exchange rates, when applied to such a situation, has no physical reality. We lack the fundamental kinetic data, such as the fractional penetration of gas molecules striking the surface, to compute theoretical maximum exchange rates, (BOLIN, 1960). 2.
DIFFUSION
THROUGH
A LAMINAR
SURFACE
LAYER
We shall now consider the problem of diffusion through a surface layer between well mixed reservoirs of gas above and water below. FIG. 2 is a schematic representation of such a film. The partial pressure difference between the water and air for a particular gas can be considered the driving force of the diffusion through the film.
JOHN PARTIAL
K’I?IWISHER
PRESSURF I
DEPTH
)
!
SURFACE _A_ UNSTIRRED LAYER DIF FwwE\ : TRANSFER!
;,
WATEP
FIG.
2.
Idealized representation
of the partial pressure variation in an unstirred surf&c film
The actual flux through the film will depend both on the concentration difference of the dissolved gas between the bottom and top of the film and the diffusibit) i\t that gas. 1 concentration ,: diffusibility FlllX thickness where concentration
partial
pressure
solubility.
Since the diffusibility varies as Ii \/ !mol. ibt.) we can neglect the small diEerence\ for the common gases in air. The value at 20 C is equal to 2 i IO- “cmjsec. However the concentration of a gas equals the partial pressure times the solubility and till, latter varies considerably for different gase.s. The ratio for N,, O,, and CO, is about 1 : 2 : 70. Thu.s for a given partial pressure difference across the film the fltt,w. But the amount in solution at saturatlclr! of different gases will vary as their solubilities. varies as the solubility also. so although the rate is faster for a more yoluble gab the amount that must flow to create saturation is also greater. This means that I; we expose a gas free sample of distilled water to a mixture of gases, they ~111 attain equilibrium at the same rate if surface film diffusion is the controlling process. The partial pressure distribution in the idealized surface layer under conditiori,. of dynamically equilibrated gas flow is shown in FIG. 2. It varies linearly betueeit the value in the air above and that in the water below. This follows ii’ we assume there are no sources or sinks within the film and if we also require that at every point there be the same flux normal to the surface. The average partial pressure in the filni then is midway between that of the two bordering phases. I have attempted to check this by directly sampling the surface layer in a container of undersaturated weaki! stirred &ater. The flux was such that a surface film of 1.59p would be expected. A 0.5 mm dia. sampling tube was inserted into the film from underneath (within I m of the surface) and held in this vertical position by a ring float. A motor-drivel! syringe drew a sample through this tube gently at a rate of 112 ml/min. Dye labelline (fluorescene dust) of the surface water showed that it was preferentially being \-viti+ drawn. The samples were analysed gasometrically for 0, and N, (SC‘HOLANDM ~1 af.. 1955). Additional determinations were made on samples withdrawn from 3 mm and lcm below the surface. The values are expressed as per cent difference from the
On the exchange of gases between the atmosphere and the sea
199
gas concentration well removed from the surface. The final value, when the water would have been entirely equilibrated, represents 100 per cent. Surface values (tip in the upper millimeter), ranged from 20 to 45 per cent, i.e. they were thus much more nearly equilibrated than deep samples. The 3 mm samples were 0-15 per cent while the 10 mm samples did not differ significantly from more deeply drawn samples. Even at 3 mm streaming at the sampling tip indicated that some true surface water was being withdrawn. Although the technique was not equal to the problem, it is clear from these values that a surface film of a millimeter or less dimensions exists which is more nearly equilibrated with the overlying gas phase. The values were the same for both oxygen and nitrogen. The surface film analysis has also been checked by simultaneously following the diffusion of oxygen, nitrogen and carbon dioxide into or out of a stirred container of distilled water. The relative partial pressures of the three dissolved gases were made different from air by boiling the gases out or bubbling a non air gas through the water. The exponential time curve of re-equilibration for all three was then measured. Nitrogen and oxygen were determined gasometrically on 1 ml samples withdrawn at intervals by a syringe. Oxygen was also continuously recorded with a polarographic electrode (CARRITT and KANWISHER, 1960). Carbon dioxide was indicated by the electrical conductivity of the water. The stirring was done magnetically and could be varied in intensity. Some representative data expressed as
Table 1. Diffusion film thickness (in microns)
Nitrogen Oxygen Carbon dioxide
Strong stirring
Weak stirring
41 50 47
110 118 127
the computed equivalent surface film thicknesses is given in TABLE I. The thickness differences between the gases is not considered significant: We can conclude that the simultaneous diffusion of different gases across a water-air interface behaves as though a surface film is the controlling factor. WYMAN et aL 0952) have studied the rate of solution of bubbles and found that an analogous surface film treatment explains their results. They followed simultaneously the time course of oxygen and nitrogen in dissolving bubbles. This appears to be the only such simultaneous experiment in the literature which is applicable to the present argument. 3.
CHEMICAL
REACTIVITY
OF
CARBON
DIOXIDE
Carbon dioxide behaves differently from inert gases such as 02 and Nz because it reacts with water to form carbonic acid, H2COa. This then singly and-doubly ionizes to form bicarbonate and carbonate ions, HCO~ and CO~. This can be represented as : CO2 --J-I--+ CO~
H20 ~
H~CO3 ~
HCO~ ~
CO~ ~ complexes
We will consider the consequences these reactions might have on the diffusion of CO~ through a surface film.
200
JOHN K:A.NWISHER
The solubility of COz is such that a partial pressure of one atmosphere would hold about 1 1. of the gas in solution in 1 I. of water. Since COs normally comprises 0.03 per cent of air the concentration of the dissolved gas in natural waters will be 0-3 ml/1. But the total CO2 in the carbonate system in sea water (obtained by acidifying and vacuum extracting), is 45 ml/l., which means that only 0.7 per cent is in physical solution. There is negligible undissociated carbonic acid, about 1/1000 the amount of free CO2. Thus in sea water more than 99 per cent is in ionic form. The situation in other natural waters will depend on their alkalinity; i.e. the concen~ tration of excess cations. In the extreme case of distilled water this is essentially zero and one is then only concerned with the dissolved COs. For this reason CO~ could be treated the same as O~ and N2 in the simultaneous gas exchange experiment~ described above. Any change in pCO2 will cause a displacement of all these reactions to form a new series of equilibria (BOUN and ERIKSSON, 1959). The amount of these shifts will determine thepCO2 buffering capacity of a given water type for changes in total CO2. Fro. 3 illustrates the experimentally determined situation for sea water and distilled water (IC~NWISI~R, 1960). 4000~
P
VS
TOTAL
7%
% .w: v)
5 )OOk
O I S T I L L E D ,qA'"", SEA WATER
RATIO F'OR
A
CCz
.P..
."t-'O0~-
~qr
II. k
L"
--
2 ' ~,~
_L?e
-.'7~k_
,) rC~ W , 4
TE,q'
FIo. 3. Partial pressure variation with changes in total COz in sea and fresh water.
In the region of the equilibrium point with the 0-03 per cent COs in the atmosphere the introduction or withdrawal of COs, i.e. respiration and photosynthesis, produces about 1/13 the change in the partial pressure that would occur in distilled water. The situation in other natural waters will depend primarily on their alkalinity. Low
On the exchange of gases between the atmosphere and the sea
201
alkalinity lakes will thus show many times greater changes in pCOs than sea water for an equal increment of total COs. Conversely, brine lakes should have greater buffering capacity. BoLm and ERIKSSON (1959) have computed that if the sea water were in equilibrium with solid CaCO3 (shell, coral) its buffering capacity would be increased another four times. It is important to know if the chemical reactivity of CO2 will effect its diffusion rate through the surface film of a natural water with appreciable alkalinity. Must we consider all of the carbonate system in the surface film or only the dissolved COs which is less than 1 per cent of the total ? The former will be important only if there is an appreciable chance of the COs molecule reacting with water during the time of its passage through the film. Removal of COs molecules in this way would lower the local partial pressure within the film and so we would expect a diffusion rate faster then predicted by our previous analysis. The average time of transit for a dissolved COs molecule diffusing through a 40 tz surface layer is less than 1 see. The half time for the reaction of COs and H20 at 20°C. is about 50 sec (ROUGttTON and BOOTH, 1946). For the thickness of surface films that are common in nature we can apparently neglect the effect of COs reactivity on its diffusion rate. Under very quiescent conditions when these layers may be as thick as 1000/~ there should be an effect. Under very alkaline conditions, which are only very rarely met in nature (above pH 9), COs will react directly with O H - ions at an appreciable rate and so enhance diffusion. BOLIN(1960) has just given an involved theoretical treatment of this point. He shows that the reaction rate is only of concern in layers thicker than about 150 tL. Some experimental verification can be given to the unimportance of COs reactivity in normal surface film diffusion. Carbonic anhydrase is an enzyme that catalyses the reaction of COs and water. Efficient COs transport in biological systems requires that this slow reaction be accelerated. The enzyme prepared from beef blood, can be purchased in a relatively pure form. I have used it to accelerate the reaction of COz with H~O in an experimental gas diffusion set-up. Intitial attempts to use the crystalline enzyme in sea water indicated that it was not active. It seems reasonable to assume the enzyme is rapidly denatured, probably by metal ions. Further experiments were done with 3.5 per cent NaClsolutions made alkaline to the same extent as sea water. The solution was made CO2 undersaturated and the exponential recovery was recorded. Part way through the enzyme was introduced. A kink in the curve indicated a change in the gas diffusion rate. Doubling the reaction velocity had no observable effect on the CO2 exchange rate. Not until the reaction velocity was increased nearly 10-fold was there a significant increase in the COs invasion rate. These experiments were performed on a stirred solution in which the laminar surface film was 50-70 tz thick. It seems additionally clear from this that COs reactivity does not alter the exchange rate of this gas across the sea surface.
4.
GAS
EXCHANGE
VS.
WIND
VELOCITY
We can proceed with an assurance that gas exchange across a liquid surface follows known laws of gas diffusion and solubility. The stirred water column laboratory experiments show that the thickness of the surface film was controlled by the
202
JOHN KANWISHER
intensity of turbulent mixing in the body of water below. On the actual sea surface we can reasonably expect the predominant influence to be the wind in the air abo~,e since it is responsible t\~r m o s t of the turbulence in the water by way of the shearing stress it exerts on the air water interface. F~o. 1 shows the varying influence that different wind velocities have on the sea surface. 1 have investigated the effect o~ wind velocity on gas exchange by means of tank experiments in the laborator~ This is admittedl) a crude approximation to nature. A tank (dimensions of 1 0-5 . 0.5 m) full of water was arranged so air could be blown across its surface at different ~,etocitics. A pitot type a n e m o m e t e r measured the air velocity lil cm abo~e the surface, t-1¢,. 4 shows the effect of ~ind ~.elocit) o n the gas exchange rate. .&t io,a ~eh)cities there is little effect until a ethical vahl< is reached. This. ntercstingly enough, is about the same velocity where capillar ~, ~A
T~NIK
0
XL '~NGE~ ~N * 5 ~ % m
SMOOTF~
SORFACi
~----~
,'
WAVES 3 Cm HIGH
/
\
{
/e •
'
!
;
i)[) i J
Wt,V£P "/ELOGt T~ IN M E T E R S / S E C L:' cm ABOVE 9URFACE
FtG, 4. Liquid air gas exchange variation with wind velocity. Waves accelerate exchange a! low velocities and decrease it at high wind speeds,
~ a v e s c o m m e n c e , The gas data indicates independently that at this unique ~eiocit!, the wind gets a better ""grip '" on the water surface. A b o v e this the exchange rate increases approximately as the square of the velocity. The experiment could not be carried beyond 15 m / s e c because the water was blown out of the tank. Very similm results were obtained by DOWNING and TRUESDALE (1955). It appears from these laboratory experiments that the rate of gas exchange acros, the ocean surface at any place will be proportional to the average o f the quantity (wind velocity) 2. We can use this to see what the relative flux of gases is through various areas o f the oceans surface. These results will be pertinent to such problems as carbon dating of surface waters and the latitude flux of CO2, (ERIKSSON, 1961) Because of vertical shear in the wind the value indicated by the pitot tube at 10 c m is less than that measured by meteorologists. DOWNINO and TRUESDALE (1955)
On the exchange of gases between the atmosphere and the sea
203
indicate that the values should be multiplied by two to conform to those at the standard height of 10 m. Unfortunately, meteorological wind velocity data is usually averaged arithmetically. If one desires the average of (wind) 2 it is necessary to know the degree of variability of the wind. In the trades where it is fairly constant, the two are not very different. In mid-latitudes however, where much of the gas exchange may be due to short periods of high velocities (storms) the errors may be great. With this shortcoming in mind I have taken maps in the meteorological atlas and found the relative weight for 20 degree sections of latitude of (average wind) 2 dA. This was done by contouring 5-knot intervals of the average wind and planimetering the included areas. The corresponding latitude curves for summer and winter are shown in FIG. 5. They show that in either season the southern oceans represent the areas where gases are mixing fastest across the ocean surface. The strong nearly non-seasonal westerlies plus the greater proportion of water to land both contribute to this. The seasonal variations in the northern oceans are very marked. RED~IELD(1948) followed seasonal changes of 02 in the Gulf of Maine. He found that the surface flux was five times greater in the winter than in the summer. No data was available for polar latitudes but the rapidly decreasing area with latitude, plus sea ice, would both indicate they are not important. DEC. FEB. • J U N E " AUG. X -
/X~
"R 60
I
40
1
20
NORTH
AREA UNDER CURVE (RELATI~)
FXG. 5.
1
I
0
20
LA~TUDE
DEC. JUNE
~RTH 124 67
I
I
40
60
SOUTH SOUTH 169 257
TOT&L 293 324
Relative values of gas exchange for 20° latitude belts of the oceans.
The nature of the data used for these curves weakens their significance but it is clear that latitudinally there is considerable variation in sea surface gas exchange. We can apply this to C a4 dating o f surface sea water. The activity found is presumed to result from a dynamic balance between old low-activity deep water entering the surface layer and higher-activity atmospheric CO2 exchanged at the surface. Most surface values up to now show an apparent age of 300-400 years. Those areas of most active exchange with the higher activity atmosphere might be expected to have a smaller apparent age, i.e. more nearly atmospheric activity. Since they don't appear to, we must conclude that old (less active) bottom water is upwelling at a greater rate to compensate (BROECKER, 1960). To some extent this may result from the increased vertical mixing to be expected from the stronger winds. It could also be related to an understandable bias for doing oceanographic work in calm weather. A surface
204
JoHn 1 ~ ~
sample taken after a prolonged storm could help one decide. If the activity really is everywhere the same we can at least preclude that more of the atmospheric CO:, enters the ocean in the southern hemisphere.
5
POSSIBLE
ROLE
OF
BUBBLES
Breaking waves, which become more frequent as the wind velocity increases, mix large amounts of air down into the water. The turbulence disperses this air intc~ bubbles. These then rise toward the surface at a rate depending on their size. The gas in the bubbles will equilibrate with the sea water through which they are passing. Because of hydrostatic pressure, their pressure, and therefore their gas tensions, will be increased by 0.1 atm for every metre of depth. If • l~mbble is swept very far into the water it will have a subsequent history ot considerable variation in pressure. The hydrostatic pressure at depth will tend to force it into solution. By this means the water at "~tferent depths down to that o ~, maximum bubble penetration will tend to becorr, supersaturated with respect to the surface equilibration value. The entire water column (down to the thermocline) is usually being mixed vertically by tur~ulew Thus, supersaturated water will tend to unload gas as it moves up in the "~ .~er ,oiumn and pick up more as it moves down° (to a depth of maximum bubble penetration). There can be no exact treatment of such a complex situation, but inspection will show that the process tends to always work on the side of supersaturation. This effect is well known in physiology where it i~ standard procedure to use gentle rotation without bubbles in accurately equilibrating a blood sample. In the cases we have been considering the atmosphere can be considered an infinite reservoir with respect to the dissolved gases in any surface water it is exchanging with. This means its composition is not appreciably altered by the small amounts of gas entering and leaving it, The opposite is the case with a rising bubble. It is now the liquid phase that exerts the controlling force on gas tensions. A bubble rising in water will come to the partial pressures of the dissolved gases in the water around it. Agail~ the reason is the difference in amounts of gases in the two reservoirs. It is first pertinent to inquire into the rate of gaseous equilibration of a rising bubble. So me early work of ADENYand BECKER(1920) is probably not relevant because they used a long cylindrical bubble rising inside a glass tube. Gas exchange through the ends ol the bubble was several times faster than through the sides. WYMANet al. (1952) worked with larger bubbles than are important in nature. I have determined rates using a large number of identically sized bubbles of known gas composition rising a measured distance up through a water column. The change in composition of the bubbles when they pass through the surface plus the determination of the gas lost or introduced to the water provide independent measures of the exchange. A small rising bubble is found to be a surprisingly rapid gas exchanger. The equivalent surface diffusion film is only 10-15/~ thick for the 500/z bubbles I used. Such bubbles will be more than 90 per cent equilibrated for CO2 in rising through only 5 cm of water (in 2-5 sec). Apparently the rising bubble creates considerable turbulence at its surface. BLANCHARDand WOODCOCK (1957) have shown that most of the bubbles in a breaking wave are between 100 and 1000/z diameter. Nearly all of the bubbles in this size range which are swept into the water will have reached
On the exchange of gases between the atmosphere and the sea
205
essentially complete equilibration before they reach the surface. Thus the net flux of gas the bubbles produce is proportional to their total volume. The water can be considered an infinite reservoir during the lifetime o f a bubble, i.e. its pressure will not be affected by the small amounts of gas going into solution from the bubble. The relative amounts of different gases that will be transported by a bubble will thus be directly proportional to their differences in partial pressure from that of air. Consider the plausible situation of sea water in which biological respiration has produced I ml/1. excess of CO8 and an equal decrement of 08. The pCO2 in the water will be roughly 0.04 per cent of an atmosphere as compared to 0.03 per cent in the initial gas of the introduced bubble (KANwISHER,1960). Air is 21 per cent O8 while the pO8 in the water will be 17 per cent (solubility 5--6 ml/l.). Thus the bubble can carry off 4 per cent of its volume of 08 and only 0.01 per cent of CO8. To the extent that bubbles are responsible for gaseous equilibration at the sea surface we can expect O8 (and Ns) to proceed several hundred times more rapidly than CO8. I f surface film diffusion is predominant the situation is not as marked. We can not yet estimate the amount of bubbles under different conditions. But observations give some useful information on their relative occurrence and behaviour. Although the foregoing describes the gas exchanging properties to be expected of bubbles we cannot assess their total effect in nature without a quantitative :estimate of the rate of bubble production in nature. The curves of BLANCHARD wer• taken on waves breaking in shallow water on a beach. F r o m the order of magnitude difference in the two sets of data it would appear that such numbers can not be used confidently on deep water waves. I have looked at the underside of breaking waves directly from a port on the R. V. Atlantis that is sometimes beneath the surface when the ship is sailing. The bubbles formed by a curling crest are swept as much as 2-3 wave heights into the water by the turbulence. Under still more violent conditions of a winter North Atlantic storm an echo sounding head floating at a depth of 30 m and looking up showed foam being swept down to 20 m when an occasional wave broke over the instrument. There was considerable sound reflection as long as 20 sec afterwards. A depth of 20 m represents a hydrostatic pressure increase of 2 atm over that at the surface. From the solution rates of bubbles of WYMAN et al. (1952) as corrected for curvature effects by BLANCHARDand WOODCOCK(1957), we can expect that most of the bubles of 1000/z or under which are carried down to depths greater than a few meters will go into solution before they can rise to the surface. One can estimate from aerial photographs the fraction of the sea surface area covered by breaking waves at different wind velocities (suggestion of D. BLAr~CnARO). White areas are contoured on an overlaying grid. When this is done the per cent covered by foam increases as the square of the velocity in the region from 20 to 60 knots. FIG. 1 shows some of the photographs used. The point of 100 per cent coverage is reached at velocities of around 100 knots. Photographs show that the sea- air interface becomes very diffuse at such velocities. Since wave heights increase with wind velocity the depth of the bubble regions will also increase and we may surmize that the total volume of bubbles produced increases at some power of the velocity greater than 2. But we have as yet no way of reasonably estimating the volumes involved and can only conclude that bubbles from breaking waves may be significant gas exchanging devices
206
JOHN KANVClSHER
at the higher wind velocities. When one has been hove-to on a small ship for days in a winter North Atlantic storm he needs little convincing. DISCUSSION
The thickness of the diffusion limiting surface film is affected by two factors the turbulent structure of the water, and the strength of the wind at the surface, Of these, the latter is the more important. The strongest practical stirring, that which did not quite produce bubbles from vortex formation, resulted in an exchange rate equivalent to a surface film about 40/~ thick. A wind velocity of only 7 m/sec produced an equal rate. At 12 m/sec the exchange was nearly three times as rapid. Measurements at higher velocities were unfortunately impossible because the water was blown out of the tank. We can surmize then that the wind shear stress is the most effective manner of promoting gas exchange. This is perhaps not surprising since the stress is applied directly on the surface film. Turbulent mixing in the main body of the water, which is always present to some degree, is a volume phenomena and so is not concentrated at the surface. We might expect the small eddies, of dimensions comparable to the film. to be the most effective in penetrating into it. But most of the energy in a turbulent system is stored in the larger eddies. Experimental details of phenomena in the regior: of the interface (within 100 t~), are needed if one is to analyse more extensively the mechanics of gas exchange. The gas exchange rate without wind in the tank experiments was increased by the presence of waves. Surface waves are composed of orbital motions in the water, This can be expected to generate some turbulence which will erode the underside of the surface film. As wind is applied to a tank with mechanically generated waves a velocity is reached where the waves actually inhibit gas exchange. These results duplicate the earlier ones of DOWNING and TRUESDALE(1955). This is due to the locally lower winds on the lea side of the waves. Such a variation of local winds is cleart5 visible on large ocean swells. Under storm conditions their upwind side shows more violent effects of the wind; i.e. the blowing the tops off small waves. Birds are able to fly upwind, albeit slowly, in gale force winds by exploiting the lea of such swells. They are visibly blown back as they pass over the crest of the swell. An increasing amount of data on sea surface pCO2 shows that some areas are characterized by partial pressures considerably different from the atmosphere. Equatorial regions in both Atlantic and Pacific have high CO2 partial pressures. The importance of such areas in providing a net flux of this gas into or out of the sea is proportional to both the difference in tension and also the amount of gas exchange promoted by the wind. The curves in FIG. 4 should help in establishing the latter factor. Bubbles swept into the sea can be considered as fully equilibrated when they reach the surface. If we can find some way of measuring the volume flux of such bubbles under the variety of conditions indicated in FIG. 1 then we will know how important they are as gas exchange mechanisms. For reasons already cited bubbles are at least a hundred times less important in promoting COz exchange as they are for O~ and N~ REFERENCES ADENY, W. E. and BECKER,H. G. (1920) The determination of the rate of solution of atmospheric nitrogen and oxygen by water. Sci. Proc. R. Dublin 8o¢. 15, 609,
On the exchange of gases between the atmosphere and the sea
207
BLANCHARD,D. C. and WOODCOCK,A. H. (1957) Bubble formation and modification in the sea and its meteorological significance. Tellus. 9 (2), 145-158. BOLIN, B. (1960) On the exchange of carbon dioxide between the atmosphere and the sea. Tellus, 12 (3), 274-281. BOLIN, B. and ERIKSSON,E. (1959) Changes in the carbon dioxide content of the atmosphere and sea due to fossil fuel combustion. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, B. BOLIN, editor, 130-142. BROECKER, W. (1960) Personal communication. CgRmrr, D. E. and KANWlSX-mR,J. (1960) An electrode system for measuring dissolved oxygen. Analyt. Chem. 31, 5-9. DAVIS, D. S. and CRANDALL,G. S. (1930) The liquid stationary film in gas absorptions. J. Amer. Chem. Soc. 52, 3757. DOWNING, A. L. and TRUESDALE,G. A. (1955) Some factors affecting the rate of solution of 02 in water. J. Appl. Chem. 5, 570. ERIKSSON, E. (1959) The circulation of some atmospheric constituents. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, B. BOLIN, Editor, 147-157. ER1KSSON, E. (1961) The exchange of matter between atmosphere and sea. Oceanography, MARY SEARSeditor, Amer. Assoc. Adv. Sci. Publ. No. 67, 411-423. EWING, G. and MCALLISTER, E. D. (1960) On the thermal boundary layer of the ocean. Science, 131 (3410), 1374-1376. KANWISHER, J. (1960) pCO 2 in sea water and its effect on the movement of CO 2 in nature. Tellus, 12, 209-215. REDFIELD,A. C. (1948) The exchange of oxygen across the sea surface, d. Mar. Res. 7, 347-361. ROUGHTON, e. J. W. and B o o m , V. H. (1946)The manometric determination of the activity of carbonic anhydrose. Biochem. J. 40, 309. SCHOLANDER, P. F., VAN DAM, L., CLAFF, C. LLOYD and KANWISHER,J. (1955) Micro gasometric determination of dissolved oxygen and nitrogen. Biol. Bull. 109, 328-334. WYMAN, J., SCHOLANDER,P. F., EDWARDS, G. A. and IRVING, L. (1952) On the stability of gas bubbles in sea water. J. Mar. Res. 11, 47-62.
On the exchange of gases between the atmosphere and the sea* JOHN KANWISHER W o o d s Hole Oceanographic Institution, W o o d s Hole, Massachusetts
(Received 17 November 1962)
INTRODUCTION
THE exchange between the gases of the atmosphere and those dissolved in the oceans is pertinent to various geochemical, biological and physical problems. These two reservoirs are intermixed by a two-way flux through the water surface. It will be shown here that the rate of this exchange depends largely on molecular diffusion through a thin laminar surface layer of the water. The thickness of this layer is influenced by the turbulent structure of the underlying water. Since the wind is ultimately responsible for most of this turbulence through the shearing stress it exerts on the water surface, we shall not be surprised to find that this exchange flux depends critically on the wind velocity. The full range of conditions in nature varies from glassy calms to violent storms (FIt~. 1). In the latter case, the intermingling of air and water can impart three dimensional characteristics to the sea 'surface.' We can expect the rates of gas exchange to vary by correspondingly large amounts. In addition to the physical conditions at the surface, an understanding of the movement of these gases in nature requires consideration of their unique chemical and biological properties. Oxygen and carbon dioxide are involved in animal and plant respiration and photosynthesis. The behaviour of carbon dioxide is additionally complicated by its chemical reactivity. This links it to the carbonate system. The other important constituents of air, nitrogen and argon, can probably be treated as inert substances. But it should be kept in mind that nitrogen is involved in the metabolism of many unicellular marine plants and bacteria, and even argon is enriched in the swim bladder of some fishes. Our attention here, however, will be mainly directed towards the physical processes of gas exchange at the sea-air interface. All dissolved gases are held in solution by their respective partial pressures or tensions in the associated gas phase (Henry's Law). On a long time average the amounts of the various gases in solution in natural waters must be in diffusion equilibrium with their respective partial pressures in the atmosphere. At any given time however, the partial pressure in the water at a particular spot may be above or below that of the overlying air. There will then be a net flux one way or the other across the interface in the direction which brings the two towards equilibrium. To a fair approximation the atmosphere can be considered of constant composition and nearly constant pressure. Thus, the direction of net movement of these gases across a water surface will depend mostly on the factors that change their partial *Contribution No. 1373 from the W o o d s Hole Oceanographic Institution.
195
196
JOHNKANWISHER
pressure in surface water. Seasonal water temperature variations force the movement of gas into or out of the water to adjust for the changing solubility. Likewise biologicaJ photosynthesis and respiration account for complimentary changes of the amounts of oxygen and carbon dioxide in solution. Once a partial pressure difference bet~eei1 the sea and air exists, the net flux into o1" out of the water will depend on both the magnitude of the gradient and also the physical state of the sea surface. We will here be concerned only \~ith the latter factoJ. It should be kept in mind that there is always a two way dynamic exchange across the surface even when no gradient of partial pressure exists. This is of concern ont'~ if a given gas in the t,~o reservoirs differs in some measureable parameter~ ( a r b o n dioxide is such a case. its (?~'~content in air is different from that in variou~ ~urfac~ waters. This difference forms the basis of hypothesis concerning the rate:, of mixing and exchange of this gas between different natural reservoirs. It is the tw~ way c:, change that is pertinent in such problems and not the net flux. The latter is rciativel~ unimportant since the flux due to the difference in partial pressure rarely accounts for more than 10 per cent of the total. Oxygen and nitrogen may haze isotope differences that can be treated in the same manner. Workers in such diverse fields as stream pollution, animal respiration, petroleum chemistry, and limnology have contributed to our knowledge of the transfer oi gases across air-liquid boundaries. The transport of gases within the atmosphere and the oceans or other natural waters takes place mainly by turbulent mixing processes. But movement across the interface is usually considered a~ being by molecular diffusion through a thin unstirred surface layer (DAVIS and (RANDALl. 1930; Ee,IRSSON. 1959, etc.). The main body of liquid below and the gas above suci~ a film are assumed to be completely mixed. BouN (1960) has reviewed this poim. The thickness of these films in laboratory experiments can be readily computed from the measured diffusivity if gases through them. Values range from 0.04 to 0.001 cm. Whether these films are important on the sea, particularly under violent storm conditions, is not clear. But in any case they provide a convenient index/'or expressing gas exchange rates. In addition one must consider the potential role of bubbles formed by breaking waves. It will be shown here that these bubbles cannot bc considered merely as separated parts of the surface. Like most natural situations the actual sea surface is much too complicated t~ allow anything like an exact analysis of the events involved in gas exchange (FIG. I i But by combining available laboratory and filed data with the physical laws tha~ govern the behaviour of gases we can better appreciate the important physical para-~ meters in nature. For example, gas transfer across the surface appears to vary as the square (or higher power) of the wind velocity. This indicates that cataclysmic events such as severe storms may account for a large fraction of the exchange even though they are only of short duration, Unfortunately, much of the discussion that follows will be largely qualitative.
!.
SURFACE
LAYERS
There is multiple evidence for laminar surface layers which, if they exist, would act as a diffusion barrier to gas exchange. First, they are readily visible (RouGr~TON and BOOTH, 1946). The random flow pattern of a stirred liquid can be readily seen
On the exchange o f gases between the atmosphere and the sea
197
if the water contains many fine particles. When one looks at the surface with a microscope he will see a layer in which particles, and therefore water, are only slowly exchanged with those in the main volume of the liquid below. The only way a dissolved gas can cross such a film is by diffusion. The observed thickness of such films agree well with those computed from the measured diffusion rates. Such films also almost certainly exist in nature. From the dock at Woods Hole one can frequently see a surface layer (visible because of dust particles) apparently moving independently of the water underneath. A dye particle dropped into the water from close to the surface leaves a clean vertical dye trail that shows pronounced current shear in the upper millimetre of water. Drift envelopes which float fiat on the surface follow different courses from drift bottles which extend down into the water. It is clear from light reflection at the surface and the absence of capillary wave suppression that organic surface films are not responsible. The observed film thicknesses are of the order of 100/z This is 105 molecular diameters so the film is clearly not of a monolayer type phenomenon. It seems more likely to look for the causes in the turbulent structure of the water. Boundary conditions dictate that there be no motion of turbulent wa~ter elements transverse to the surface. Thus water in the surface layer can only be moved out of it by gentle shearing forces exerted from below. Simple dye marking experiments of the surface (sprinkling powdered fluorescene), indicate that the lifetime of this quasi-permanent film may be several seconds or longer, depending on the intensity of mixing. Since dissolved gas molecules diffuse through the film in a time shorter than this, such films can be considered permanent from the gases point of view. This is obviously an idealized model since there can hardly be a sharp separation between a laminar surface layer and a turbulent under body. But it has proved useful in analysing the exchange problem. Recently EWING et al. (1960) has shown by radiation thermometry that a surface film exists which has a temperature lower than the main body of water due to evaporative cooling. This film can be destroyed by forcing a jet of water up at the surface from underneath. This apparently tears the surface film away faster than evaporation can renew it. Strong turbulence such as in a breaking wave may do the same thing naturally. In the gas exchange problem this would amount to a renewal of the surface film in a time short compared to that for a gas molecule to diffuse through it. The rate of gas exchange would then be determined largely by the rate of renewal of the partially equilibrated film and the rate of penetration of gas molecules through the surface. It should be kept in mind that an equivalent surface film thickness computed from measured gas exchange rates, when applied to such a situation, has no physical reality. We lack the fundamental kinetic data, such as the fractional penetration of gas molecules striking the surface, to compute theoretical maximum exchange rates, (BOLIN, 1960). 2.
DIFFUSION
THROUGH
A LAMINAR
SURFACE
LAYER
We shall now consider the problem of diffusion through a surface layer between well mixed reservoirs of gas above and water below. FIG. 2 is a schematic representation of such a film. The partial pressure difference between the water and air for a particular gas can be considered the driving force of the diffusion through the film.
JOHN PARTIAL
K’I?IWISHER
PRESSURF I
DEPTH
)
!
SURFACE _A_ UNSTIRRED LAYER DIF FwwE\ : TRANSFER!
;,
WATEP
FIG.
2.
Idealized representation
of the partial pressure variation in an unstirred surf&c film
The actual flux through the film will depend both on the concentration difference of the dissolved gas between the bottom and top of the film and the diffusibit) i\t that gas. 1 concentration ,: diffusibility FlllX thickness where concentration
partial
pressure
solubility.
Since the diffusibility varies as Ii \/ !mol. ibt.) we can neglect the small diEerence\ for the common gases in air. The value at 20 C is equal to 2 i IO- “cmjsec. However the concentration of a gas equals the partial pressure times the solubility and till, latter varies considerably for different gase.s. The ratio for N,, O,, and CO, is about 1 : 2 : 70. Thu.s for a given partial pressure difference across the film the fltt,w. But the amount in solution at saturatlclr! of different gases will vary as their solubilities. varies as the solubility also. so although the rate is faster for a more yoluble gab the amount that must flow to create saturation is also greater. This means that I; we expose a gas free sample of distilled water to a mixture of gases, they ~111 attain equilibrium at the same rate if surface film diffusion is the controlling process. The partial pressure distribution in the idealized surface layer under conditiori,. of dynamically equilibrated gas flow is shown in FIG. 2. It varies linearly betueeit the value in the air above and that in the water below. This follows ii’ we assume there are no sources or sinks within the film and if we also require that at every point there be the same flux normal to the surface. The average partial pressure in the filni then is midway between that of the two bordering phases. I have attempted to check this by directly sampling the surface layer in a container of undersaturated weaki! stirred &ater. The flux was such that a surface film of 1.59p would be expected. A 0.5 mm dia. sampling tube was inserted into the film from underneath (within I m of the surface) and held in this vertical position by a ring float. A motor-drivel! syringe drew a sample through this tube gently at a rate of 112 ml/min. Dye labelline (fluorescene dust) of the surface water showed that it was preferentially being \-viti+ drawn. The samples were analysed gasometrically for 0, and N, (SC‘HOLANDM ~1 af.. 1955). Additional determinations were made on samples withdrawn from 3 mm and lcm below the surface. The values are expressed as per cent difference from the
On the exchange of gases between the atmosphere and the sea
199
gas concentration well removed from the surface. The final value, when the water would have been entirely equilibrated, represents 100 per cent. Surface values (tip in the upper millimeter), ranged from 20 to 45 per cent, i.e. they were thus much more nearly equilibrated than deep samples. The 3 mm samples were 0-15 per cent while the 10 mm samples did not differ significantly from more deeply drawn samples. Even at 3 mm streaming at the sampling tip indicated that some true surface water was being withdrawn. Although the technique was not equal to the problem, it is clear from these values that a surface film of a millimeter or less dimensions exists which is more nearly equilibrated with the overlying gas phase. The values were the same for both oxygen and nitrogen. The surface film analysis has also been checked by simultaneously following the diffusion of oxygen, nitrogen and carbon dioxide into or out of a stirred container of distilled water. The relative partial pressures of the three dissolved gases were made different from air by boiling the gases out or bubbling a non air gas through the water. The exponential time curve of re-equilibration for all three was then measured. Nitrogen and oxygen were determined gasometrically on 1 ml samples withdrawn at intervals by a syringe. Oxygen was also continuously recorded with a polarographic electrode (CARRITT and KANWISHER, 1960). Carbon dioxide was indicated by the electrical conductivity of the water. The stirring was done magnetically and could be varied in intensity. Some representative data expressed as
Table 1. Diffusion film thickness (in microns)
Nitrogen Oxygen Carbon dioxide
Strong stirring
Weak stirring
41 50 47
110 118 127
the computed equivalent surface film thicknesses is given in TABLE I. The thickness differences between the gases is not considered significant: We can conclude that the simultaneous diffusion of different gases across a water-air interface behaves as though a surface film is the controlling factor. WYMAN et aL 0952) have studied the rate of solution of bubbles and found that an analogous surface film treatment explains their results. They followed simultaneously the time course of oxygen and nitrogen in dissolving bubbles. This appears to be the only such simultaneous experiment in the literature which is applicable to the present argument. 3.
CHEMICAL
REACTIVITY
OF
CARBON
DIOXIDE
Carbon dioxide behaves differently from inert gases such as 02 and Nz because it reacts with water to form carbonic acid, H2COa. This then singly and-doubly ionizes to form bicarbonate and carbonate ions, HCO~ and CO~. This can be represented as : CO2 --J-I--+ CO~
H20 ~
H~CO3 ~
HCO~ ~
CO~ ~ complexes
We will consider the consequences these reactions might have on the diffusion of CO~ through a surface film.
200
JOHN K:A.NWISHER
The solubility of COz is such that a partial pressure of one atmosphere would hold about 1 1. of the gas in solution in 1 I. of water. Since COs normally comprises 0.03 per cent of air the concentration of the dissolved gas in natural waters will be 0-3 ml/1. But the total CO2 in the carbonate system in sea water (obtained by acidifying and vacuum extracting), is 45 ml/l., which means that only 0.7 per cent is in physical solution. There is negligible undissociated carbonic acid, about 1/1000 the amount of free CO2. Thus in sea water more than 99 per cent is in ionic form. The situation in other natural waters will depend on their alkalinity; i.e. the concen~ tration of excess cations. In the extreme case of distilled water this is essentially zero and one is then only concerned with the dissolved COs. For this reason CO~ could be treated the same as O~ and N2 in the simultaneous gas exchange experiment~ described above. Any change in pCO2 will cause a displacement of all these reactions to form a new series of equilibria (BOUN and ERIKSSON, 1959). The amount of these shifts will determine thepCO2 buffering capacity of a given water type for changes in total CO2. Fro. 3 illustrates the experimentally determined situation for sea water and distilled water (IC~NWISI~R, 1960). 4000~
P
VS
TOTAL
7%
% .w: v)
5 )OOk
O I S T I L L E D ,qA'"", SEA WATER
RATIO F'OR
A
CCz
.P..
."t-'O0~-
~qr
II. k
L"
--
2 ' ~,~
_L?e
-.'7~k_
,) rC~ W , 4
TE,q'
FIo. 3. Partial pressure variation with changes in total COz in sea and fresh water.
In the region of the equilibrium point with the 0-03 per cent COs in the atmosphere the introduction or withdrawal of COs, i.e. respiration and photosynthesis, produces about 1/13 the change in the partial pressure that would occur in distilled water. The situation in other natural waters will depend primarily on their alkalinity. Low
On the exchange of gases between the atmosphere and the sea
201
alkalinity lakes will thus show many times greater changes in pCOs than sea water for an equal increment of total COs. Conversely, brine lakes should have greater buffering capacity. BoLm and ERIKSSON (1959) have computed that if the sea water were in equilibrium with solid CaCO3 (shell, coral) its buffering capacity would be increased another four times. It is important to know if the chemical reactivity of CO2 will effect its diffusion rate through the surface film of a natural water with appreciable alkalinity. Must we consider all of the carbonate system in the surface film or only the dissolved COs which is less than 1 per cent of the total ? The former will be important only if there is an appreciable chance of the COs molecule reacting with water during the time of its passage through the film. Removal of COs molecules in this way would lower the local partial pressure within the film and so we would expect a diffusion rate faster then predicted by our previous analysis. The average time of transit for a dissolved COs molecule diffusing through a 40 tz surface layer is less than 1 see. The half time for the reaction of COs and H20 at 20°C. is about 50 sec (ROUGttTON and BOOTH, 1946). For the thickness of surface films that are common in nature we can apparently neglect the effect of COs reactivity on its diffusion rate. Under very quiescent conditions when these layers may be as thick as 1000/~ there should be an effect. Under very alkaline conditions, which are only very rarely met in nature (above pH 9), COs will react directly with O H - ions at an appreciable rate and so enhance diffusion. BOLIN(1960) has just given an involved theoretical treatment of this point. He shows that the reaction rate is only of concern in layers thicker than about 150 tL. Some experimental verification can be given to the unimportance of COs reactivity in normal surface film diffusion. Carbonic anhydrase is an enzyme that catalyses the reaction of COs and water. Efficient COs transport in biological systems requires that this slow reaction be accelerated. The enzyme prepared from beef blood, can be purchased in a relatively pure form. I have used it to accelerate the reaction of COz with H~O in an experimental gas diffusion set-up. Intitial attempts to use the crystalline enzyme in sea water indicated that it was not active. It seems reasonable to assume the enzyme is rapidly denatured, probably by metal ions. Further experiments were done with 3.5 per cent NaClsolutions made alkaline to the same extent as sea water. The solution was made CO2 undersaturated and the exponential recovery was recorded. Part way through the enzyme was introduced. A kink in the curve indicated a change in the gas diffusion rate. Doubling the reaction velocity had no observable effect on the CO2 exchange rate. Not until the reaction velocity was increased nearly 10-fold was there a significant increase in the COs invasion rate. These experiments were performed on a stirred solution in which the laminar surface film was 50-70 tz thick. It seems additionally clear from this that COs reactivity does not alter the exchange rate of this gas across the sea surface.
4.
GAS
EXCHANGE
VS.
WIND
VELOCITY
We can proceed with an assurance that gas exchange across a liquid surface follows known laws of gas diffusion and solubility. The stirred water column laboratory experiments show that the thickness of the surface film was controlled by the
202
JOHN KANWISHER
intensity of turbulent mixing in the body of water below. On the actual sea surface we can reasonably expect the predominant influence to be the wind in the air abo~,e since it is responsible t\~r m o s t of the turbulence in the water by way of the shearing stress it exerts on the air water interface. F~o. 1 shows the varying influence that different wind velocities have on the sea surface. 1 have investigated the effect o~ wind velocity on gas exchange by means of tank experiments in the laborator~ This is admittedl) a crude approximation to nature. A tank (dimensions of 1 0-5 . 0.5 m) full of water was arranged so air could be blown across its surface at different ~,etocitics. A pitot type a n e m o m e t e r measured the air velocity lil cm abo~e the surface, t-1¢,. 4 shows the effect of ~ind ~.elocit) o n the gas exchange rate. .&t io,a ~eh)cities there is little effect until a ethical vahl< is reached. This. ntercstingly enough, is about the same velocity where capillar ~, ~A
T~NIK
0
XL '~NGE~ ~N * 5 ~ % m
SMOOTF~
SORFACi
~----~
,'
WAVES 3 Cm HIGH
/
\
{
/e •
'
!
;
i)[) i J
Wt,V£P "/ELOGt T~ IN M E T E R S / S E C L:' cm ABOVE 9URFACE
FtG, 4. Liquid air gas exchange variation with wind velocity. Waves accelerate exchange a! low velocities and decrease it at high wind speeds,
~ a v e s c o m m e n c e , The gas data indicates independently that at this unique ~eiocit!, the wind gets a better ""grip '" on the water surface. A b o v e this the exchange rate increases approximately as the square of the velocity. The experiment could not be carried beyond 15 m / s e c because the water was blown out of the tank. Very similm results were obtained by DOWNING and TRUESDALE (1955). It appears from these laboratory experiments that the rate of gas exchange acros, the ocean surface at any place will be proportional to the average o f the quantity (wind velocity) 2. We can use this to see what the relative flux of gases is through various areas o f the oceans surface. These results will be pertinent to such problems as carbon dating of surface waters and the latitude flux of CO2, (ERIKSSON, 1961) Because of vertical shear in the wind the value indicated by the pitot tube at 10 c m is less than that measured by meteorologists. DOWNINO and TRUESDALE (1955)
On the exchange of gases between the atmosphere and the sea
203
indicate that the values should be multiplied by two to conform to those at the standard height of 10 m. Unfortunately, meteorological wind velocity data is usually averaged arithmetically. If one desires the average of (wind) 2 it is necessary to know the degree of variability of the wind. In the trades where it is fairly constant, the two are not very different. In mid-latitudes however, where much of the gas exchange may be due to short periods of high velocities (storms) the errors may be great. With this shortcoming in mind I have taken maps in the meteorological atlas and found the relative weight for 20 degree sections of latitude of (average wind) 2 dA. This was done by contouring 5-knot intervals of the average wind and planimetering the included areas. The corresponding latitude curves for summer and winter are shown in FIG. 5. They show that in either season the southern oceans represent the areas where gases are mixing fastest across the ocean surface. The strong nearly non-seasonal westerlies plus the greater proportion of water to land both contribute to this. The seasonal variations in the northern oceans are very marked. RED~IELD(1948) followed seasonal changes of 02 in the Gulf of Maine. He found that the surface flux was five times greater in the winter than in the summer. No data was available for polar latitudes but the rapidly decreasing area with latitude, plus sea ice, would both indicate they are not important. DEC. FEB. • J U N E " AUG. X -
/X~
"R 60
I
40
1
20
NORTH
AREA UNDER CURVE (RELATI~)
FXG. 5.
1
I
0
20
LA~TUDE
DEC. JUNE
~RTH 124 67
I
I
40
60
SOUTH SOUTH 169 257
TOT&L 293 324
Relative values of gas exchange for 20° latitude belts of the oceans.
The nature of the data used for these curves weakens their significance but it is clear that latitudinally there is considerable variation in sea surface gas exchange. We can apply this to C a4 dating o f surface sea water. The activity found is presumed to result from a dynamic balance between old low-activity deep water entering the surface layer and higher-activity atmospheric CO2 exchanged at the surface. Most surface values up to now show an apparent age of 300-400 years. Those areas of most active exchange with the higher activity atmosphere might be expected to have a smaller apparent age, i.e. more nearly atmospheric activity. Since they don't appear to, we must conclude that old (less active) bottom water is upwelling at a greater rate to compensate (BROECKER, 1960). To some extent this may result from the increased vertical mixing to be expected from the stronger winds. It could also be related to an understandable bias for doing oceanographic work in calm weather. A surface
204
JoHn 1 ~ ~
sample taken after a prolonged storm could help one decide. If the activity really is everywhere the same we can at least preclude that more of the atmospheric CO:, enters the ocean in the southern hemisphere.
5
POSSIBLE
ROLE
OF
BUBBLES
Breaking waves, which become more frequent as the wind velocity increases, mix large amounts of air down into the water. The turbulence disperses this air intc~ bubbles. These then rise toward the surface at a rate depending on their size. The gas in the bubbles will equilibrate with the sea water through which they are passing. Because of hydrostatic pressure, their pressure, and therefore their gas tensions, will be increased by 0.1 atm for every metre of depth. If • l~mbble is swept very far into the water it will have a subsequent history ot considerable variation in pressure. The hydrostatic pressure at depth will tend to force it into solution. By this means the water at "~tferent depths down to that o ~, maximum bubble penetration will tend to becorr, supersaturated with respect to the surface equilibration value. The entire water column (down to the thermocline) is usually being mixed vertically by tur~ulew Thus, supersaturated water will tend to unload gas as it moves up in the "~ .~er ,oiumn and pick up more as it moves down° (to a depth of maximum bubble penetration). There can be no exact treatment of such a complex situation, but inspection will show that the process tends to always work on the side of supersaturation. This effect is well known in physiology where it i~ standard procedure to use gentle rotation without bubbles in accurately equilibrating a blood sample. In the cases we have been considering the atmosphere can be considered an infinite reservoir with respect to the dissolved gases in any surface water it is exchanging with. This means its composition is not appreciably altered by the small amounts of gas entering and leaving it, The opposite is the case with a rising bubble. It is now the liquid phase that exerts the controlling force on gas tensions. A bubble rising in water will come to the partial pressures of the dissolved gases in the water around it. Agail~ the reason is the difference in amounts of gases in the two reservoirs. It is first pertinent to inquire into the rate of gaseous equilibration of a rising bubble. So me early work of ADENYand BECKER(1920) is probably not relevant because they used a long cylindrical bubble rising inside a glass tube. Gas exchange through the ends ol the bubble was several times faster than through the sides. WYMANet al. (1952) worked with larger bubbles than are important in nature. I have determined rates using a large number of identically sized bubbles of known gas composition rising a measured distance up through a water column. The change in composition of the bubbles when they pass through the surface plus the determination of the gas lost or introduced to the water provide independent measures of the exchange. A small rising bubble is found to be a surprisingly rapid gas exchanger. The equivalent surface diffusion film is only 10-15/~ thick for the 500/z bubbles I used. Such bubbles will be more than 90 per cent equilibrated for CO2 in rising through only 5 cm of water (in 2-5 sec). Apparently the rising bubble creates considerable turbulence at its surface. BLANCHARDand WOODCOCK (1957) have shown that most of the bubbles in a breaking wave are between 100 and 1000/z diameter. Nearly all of the bubbles in this size range which are swept into the water will have reached
On the exchange of gases between the atmosphere and the sea
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essentially complete equilibration before they reach the surface. Thus the net flux of gas the bubbles produce is proportional to their total volume. The water can be considered an infinite reservoir during the lifetime o f a bubble, i.e. its pressure will not be affected by the small amounts of gas going into solution from the bubble. The relative amounts of different gases that will be transported by a bubble will thus be directly proportional to their differences in partial pressure from that of air. Consider the plausible situation of sea water in which biological respiration has produced I ml/1. excess of CO8 and an equal decrement of 08. The pCO2 in the water will be roughly 0.04 per cent of an atmosphere as compared to 0.03 per cent in the initial gas of the introduced bubble (KANwISHER,1960). Air is 21 per cent O8 while the pO8 in the water will be 17 per cent (solubility 5--6 ml/l.). Thus the bubble can carry off 4 per cent of its volume of 08 and only 0.01 per cent of CO8. To the extent that bubbles are responsible for gaseous equilibration at the sea surface we can expect O8 (and Ns) to proceed several hundred times more rapidly than CO8. I f surface film diffusion is predominant the situation is not as marked. We can not yet estimate the amount of bubbles under different conditions. But observations give some useful information on their relative occurrence and behaviour. Although the foregoing describes the gas exchanging properties to be expected of bubbles we cannot assess their total effect in nature without a quantitative :estimate of the rate of bubble production in nature. The curves of BLANCHARD wer• taken on waves breaking in shallow water on a beach. F r o m the order of magnitude difference in the two sets of data it would appear that such numbers can not be used confidently on deep water waves. I have looked at the underside of breaking waves directly from a port on the R. V. Atlantis that is sometimes beneath the surface when the ship is sailing. The bubbles formed by a curling crest are swept as much as 2-3 wave heights into the water by the turbulence. Under still more violent conditions of a winter North Atlantic storm an echo sounding head floating at a depth of 30 m and looking up showed foam being swept down to 20 m when an occasional wave broke over the instrument. There was considerable sound reflection as long as 20 sec afterwards. A depth of 20 m represents a hydrostatic pressure increase of 2 atm over that at the surface. From the solution rates of bubbles of WYMAN et al. (1952) as corrected for curvature effects by BLANCHARDand WOODCOCK(1957), we can expect that most of the bubles of 1000/z or under which are carried down to depths greater than a few meters will go into solution before they can rise to the surface. One can estimate from aerial photographs the fraction of the sea surface area covered by breaking waves at different wind velocities (suggestion of D. BLAr~CnARO). White areas are contoured on an overlaying grid. When this is done the per cent covered by foam increases as the square of the velocity in the region from 20 to 60 knots. FIG. 1 shows some of the photographs used. The point of 100 per cent coverage is reached at velocities of around 100 knots. Photographs show that the sea- air interface becomes very diffuse at such velocities. Since wave heights increase with wind velocity the depth of the bubble regions will also increase and we may surmize that the total volume of bubbles produced increases at some power of the velocity greater than 2. But we have as yet no way of reasonably estimating the volumes involved and can only conclude that bubbles from breaking waves may be significant gas exchanging devices
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at the higher wind velocities. When one has been hove-to on a small ship for days in a winter North Atlantic storm he needs little convincing. DISCUSSION
The thickness of the diffusion limiting surface film is affected by two factors the turbulent structure of the water, and the strength of the wind at the surface, Of these, the latter is the more important. The strongest practical stirring, that which did not quite produce bubbles from vortex formation, resulted in an exchange rate equivalent to a surface film about 40/~ thick. A wind velocity of only 7 m/sec produced an equal rate. At 12 m/sec the exchange was nearly three times as rapid. Measurements at higher velocities were unfortunately impossible because the water was blown out of the tank. We can surmize then that the wind shear stress is the most effective manner of promoting gas exchange. This is perhaps not surprising since the stress is applied directly on the surface film. Turbulent mixing in the main body of the water, which is always present to some degree, is a volume phenomena and so is not concentrated at the surface. We might expect the small eddies, of dimensions comparable to the film. to be the most effective in penetrating into it. But most of the energy in a turbulent system is stored in the larger eddies. Experimental details of phenomena in the regior: of the interface (within 100 t~), are needed if one is to analyse more extensively the mechanics of gas exchange. The gas exchange rate without wind in the tank experiments was increased by the presence of waves. Surface waves are composed of orbital motions in the water, This can be expected to generate some turbulence which will erode the underside of the surface film. As wind is applied to a tank with mechanically generated waves a velocity is reached where the waves actually inhibit gas exchange. These results duplicate the earlier ones of DOWNING and TRUESDALE(1955). This is due to the locally lower winds on the lea side of the waves. Such a variation of local winds is cleart5 visible on large ocean swells. Under storm conditions their upwind side shows more violent effects of the wind; i.e. the blowing the tops off small waves. Birds are able to fly upwind, albeit slowly, in gale force winds by exploiting the lea of such swells. They are visibly blown back as they pass over the crest of the swell. An increasing amount of data on sea surface pCO2 shows that some areas are characterized by partial pressures considerably different from the atmosphere. Equatorial regions in both Atlantic and Pacific have high CO2 partial pressures. The importance of such areas in providing a net flux of this gas into or out of the sea is proportional to both the difference in tension and also the amount of gas exchange promoted by the wind. The curves in FIG. 4 should help in establishing the latter factor. Bubbles swept into the sea can be considered as fully equilibrated when they reach the surface. If we can find some way of measuring the volume flux of such bubbles under the variety of conditions indicated in FIG. 1 then we will know how important they are as gas exchange mechanisms. For reasons already cited bubbles are at least a hundred times less important in promoting COz exchange as they are for O~ and N~ REFERENCES ADENY, W. E. and BECKER,H. G. (1920) The determination of the rate of solution of atmospheric nitrogen and oxygen by water. Sci. Proc. R. Dublin 8o¢. 15, 609,
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BLANCHARD,D. C. and WOODCOCK,A. H. (1957) Bubble formation and modification in the sea and its meteorological significance. Tellus. 9 (2), 145-158. BOLIN, B. (1960) On the exchange of carbon dioxide between the atmosphere and the sea. Tellus, 12 (3), 274-281. BOLIN, B. and ERIKSSON,E. (1959) Changes in the carbon dioxide content of the atmosphere and sea due to fossil fuel combustion. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, B. BOLIN, editor, 130-142. BROECKER, W. (1960) Personal communication. CgRmrr, D. E. and KANWlSX-mR,J. (1960) An electrode system for measuring dissolved oxygen. Analyt. Chem. 31, 5-9. DAVIS, D. S. and CRANDALL,G. S. (1930) The liquid stationary film in gas absorptions. J. Amer. Chem. Soc. 52, 3757. DOWNING, A. L. and TRUESDALE,G. A. (1955) Some factors affecting the rate of solution of 02 in water. J. Appl. Chem. 5, 570. ERIKSSON, E. (1959) The circulation of some atmospheric constituents. The Atmosphere and the Sea in Motion, Rossby Memorial Volume, B. BOLIN, Editor, 147-157. ER1KSSON, E. (1961) The exchange of matter between atmosphere and sea. Oceanography, MARY SEARSeditor, Amer. Assoc. Adv. Sci. Publ. No. 67, 411-423. EWING, G. and MCALLISTER, E. D. (1960) On the thermal boundary layer of the ocean. Science, 131 (3410), 1374-1376. KANWISHER, J. (1960) pCO 2 in sea water and its effect on the movement of CO 2 in nature. Tellus, 12, 209-215. REDFIELD,A. C. (1948) The exchange of oxygen across the sea surface, d. Mar. Res. 7, 347-361. ROUGHTON, e. J. W. and B o o m , V. H. (1946)The manometric determination of the activity of carbonic anhydrose. Biochem. J. 40, 309. SCHOLANDER, P. F., VAN DAM, L., CLAFF, C. LLOYD and KANWISHER,J. (1955) Micro gasometric determination of dissolved oxygen and nitrogen. Biol. Bull. 109, 328-334. WYMAN, J., SCHOLANDER,P. F., EDWARDS, G. A. and IRVING, L. (1952) On the stability of gas bubbles in sea water. J. Mar. Res. 11, 47-62.