The Rate of Air-Sea CO2 Exchange: Chemical Enhancement and Catalysis by Marine Microalgae.

Chapter 7: CO2 exchange without algae: Results and Discussion

7.1 Overview

The results reported in this chapter provide both a test of existing formulae used to calculate the uncatalysed chemical enhancement of the CO2 transfer velocity, and also the "control" experiments against which to compare the CO2 transfer velocity measured during blooms of algae, as reported in the next chapter. The principle variable factors are the speed of the water stirring paddle, the temperature, and the pH of the water (a function of pCO2 and alkalinity). The salinity is also a factor when comparing experiments in milliQ water and seawater. In addition, the effect of added bovine carbonic anhydrase and inhibitors are reported.

Except where otherwise indicated, only one factor was varied at a time. For both these results and those with algae presented in chapter 8, the other parameters were maintained constant as follows: the temperature was maintained at 15 ± 0.3 C and the water paddle speed at 13 ± 0.3 revs per minute (The variability of both was slightly greater while the control system was still evolving prior to June 1996, particularly during the second Dunaliella bloom, as noted in Section 8.3.2 ). The water pCO2 was typically in the range 370 ± 50 ppm for the "no-algae" data in seawater, and the pCO2 is indicated next to the datapoints for which it may be significant (as explained later). In MilliQ water and acidified seawater water pCO2 should not be a significant factor. Seawater was usually filtered (0.2 m m) before use. The lights were left on during all measurements.

All fitted regression curves shown on the figures are calculated by "least squares". For most of the data presented in this chapter the errors in the transfer velocity are expected to be similar for all measurements and can therefore be deduced by the scatter of the data. Therefore error bars are not included in most of the figures, to avoid unnecessary clutter. However, the measurement errors can be much greater when the air pCO2 was close to the water pCO2, and so maximum error ranges (as calculated in Section 6.5 ) are included in the figures illustrating the effect of varying pCO2.

7.2 Effect of water paddle speed.

The effect of varying the water paddle speed on the CO2 transfer velocity is shown in figure 7-1 . This also indicates the differences between seawater, acidified seawater, and MilliQ water.

7.2.1 Acidified Seawater and MilliQ water (diffusion only: effect of salinity)

The effect of chemical enhancement should be negligible in both the MilliQ (deionised) water and in the acidified seawater (pH<3), since in both cases the ratio of HCO3- to dissolved CO2 is very low. These two datasets clearly show a linear response of the gas exchange rate to increasing paddle speeds up to about 25 rpm. As there is some uncertainty as to which model (if any) best represents the actual physical process of gas exchange for low transfer velocities, it is not intuitively obvious that there should be such a linear response, but clearly it is so and many other workers have found likewise.

Linear regressions fitted to the data (below 25 rpm) are shown on figure 7-1 . When these are projected backwards, both lines predict a zero transfer velocity for a water paddle speed of about -3.9 rpm. This negative offset can be explained by the effect of the air-stirring paddles, which operate at a constant rate. For more discussion of the relative importance of air-stirring and water-stirring, see Section 4.7.3 . It was not possible to measure transfer velocities at lower paddle speeds because the steady-state method requires that the water is well mixed to ensure the homogeneity of the water pCO2, and also for low transfer velocities the time required to reach steady-state becomes very long.

The linear fit through the acidified seawater data has been used when correcting for slight variations in paddle speed when calculating the diffusion-only transfer velocity for other datasets. For a paddle speed of 13 rpm (the "standard" values used for investigating other parameters), the diffusion-only transfer velocity (acidified seawater) is about 2.8 cm hr-1.

Below 25 rpm, the water surface was flat, although horizontal eddies and vertical overturning had been observed when dye was added to the water (see Section 4.7.1 ). Above 25 rpm, the surface began to undulate regularly from one corner of each headspace to the other. This coincides with a more rapid increase in the CO2 transfer velocities. At about 34 rpm, this regular "sloshing" became much more vigorous, with waves reaching the roof of the tank in the corners of the headspaces, and much higher transfer velocities up to 33 cm hr-1 were measured. This paddle speed presumably coincides with the resonant frequency of waves constrained by the headspace walls. Slightly higher waves were seen in compartment D than in compartment A. D was the CO2 influx headspace for MilliQ water, but the CO2 efflux headspace for the acidified seawater, thus explaining the differences between influx and efflux data for this high paddle speed. Note that the resonance effect is likely to greatly multiply any slight physical difference between the two headspaces. The difference in surface area (<1%, see Section 4.6.1 ) has already been accounted for when calculating the transfer velocities.

The principle difference between the acidified seawater and the MilliQ water is the salinity, since the total alkalinity of both waters is effectively zero. Increasing the salinity of water decreases the solubility and diffusivity of CO2, but increases the density. The measured CO2 fluxes in and out of the acidified seawater were about 21% lower than the equivalent fluxes for the MilliQ water, but the calculated transfer velocities are only about 7% lower since the fluxes were divided by a lower solubility for CO2 in acidified seawater (see Section 6.5 for calculation method). Such a residual difference can be explained by the lower diffusivity of gases in seawater. This might be used to estimate the "Schmidt number relationship" as discussed later ( Section 7.4 ).

7.2.2 Seawater (effect of chemical enhancement)

The linear fit to the acidified water data has been used as a baseline with which to calculate the effective stagnant film thickness for diffusion-only CO2 transfer, as explained in Section 6.4 . This is then used to predict chemical enhancement using the formula of Hoover and Berkshire (1969) (this was introduced in Section 1.5.3 ). This calculation assumes that the total alkalinity is 2.45mM, and uses the reaction rate constants of Johnson (1982) (for more details see Section 6.4 ). The Hoover and Berkshire prediction is shown on figure 7-1 : the line is for pCO2=360ppm and the datapoints are for the same pCO2 as the corresponding seawater measurements.

It is clear from figure 7-1 that this prediction lies significantly below the measured transfer velocities in normal seawater. Since enhancement is expected to be greatest at lower transfer velocities, we would not expect a linear relationship with paddle speed for this data, so a 2nd order polynomial has been used (for paddle speeds below 25 rpm as before). At a paddle speed of 13 rpm (used for most other measurements), the fitted curve lies 22% above the acidified seawater baseline, whereas the Hoover and Berkshire equation predicts an increase due to chemical enhancement of only 13%. This discrepancy is also found in the seawater CO2 transfer velocities measured as a function of pCO2 and temperature, and will be discussed further in Section 7.7 .

We should also note that the measured enhancement factor seems to remain almost constant at higher paddle speeds. At 25rpm the enhancement is 20%, whereas the Hoover and Berkshire prediction gives only 5%, above a baseline of 4.6 cm hr-1 which corresponds to a 10m windspeed of about 4.8 ms-1 (using the parameterisation of Liss and Merlivat 1986). This may be due to the difference between a "surface renewal" system found in the tank, and the "stagnant film" model assumed by Hoover and Berkshire, which could be important for the global CO2 flux if such results also applied at sea. On the other hand, a closer look at the measured data shows that the MilliQ water transfer velocity begins to curve upwards as a function of paddle speed at about this point, earlier than the upward curve of the acidified seawater transfer velocities. So we cannot be certain that the onset of resonant waves in the normal seawater is not also slightly earlier in the seawater than in the acidified seawater baseline.

At very low paddle speeds the measured and predicted transfer velocities in seawater both suggest a residual transfer velocity between 1.9 and 1.7 cm hr-1 due to chemical reaction alone, as the flux due to diffusion approaches zero.

The large number of datapoints clustered around paddle-speed =13 rpm were mostly measured during the set of experiments in which the air pCO2 was varied, but for which the water pCO2 and temperature were fairly constant (near the standard values of 380ppm and 15C respectively). This cluster of datapoints also appears on most other graphs in this chapter. The scatter is partly indicative of the effect of air pCO2 on the microlayer pH, as discussed later in

7.3 Effect of temperature

7.3.1 Measurements and predictions

The effect of varying the temperature is shown in figure 7-2 and figure 7-3 .

Measurements in both seawater and acidified seawater are shown, the latter being used as a baseline to show the diffusion-only transfer, as for the paddle-speed variation in figure 7-1 . Three measurements with added bovine carbonic anhydrase are also shown, which will be discussed later in Section 7.6 .

The data is the same for both figures, but figure 7-2 shows the CO2 transfer velocity on the vertical axis, whereas figure 7-3 shows the transfer velocity multiplied by the solubility. The latter is included because many global carbon flux modellers do not include temperature as a parameter of air sea exchange, since the effect on the diffusivity of gases is approximately cancelled by the effect on the solubility (see introduction Section 1.2.2 ), and it is the product which is needed to calculate the flux. Figure 7-3 shows that this assumption is valid for non-reactive gases when transfer velocity is proportional to Sc-1/2 , but is not valid at high temperatures when there is chemical enhancement.

At the "standard" temperature of 15 C, the diffusion-only transfer velocity (acidified seawater) is 2.85 cm hr-1. This is almost as same as reported above in the paddle-speed variation dataset. The cluster of seawater datapoints at the standard temperature T=15 are also the same as shown in figure 7-1 and in figure 7-5 , figure 7-6 and figure 7-7 (to be discussed later).

Second order polynomials have been fitted to both the acidified and normal seawater data. The acidified seawater data (diffusion only) can be compared to the transfer velocity predicted using Schmidt number relationships of Sc-1/2 Sc-2/3 and Sc-1 , forced through k=2.85 at T=15. The Sc-1/2 line fits well, except at the highest temperatures where even that rises steeper than the measurements. The Schmidt number relationship is discussed further in Section 7.4 . The anomalously low value measured in seawater at 32.5C has been removed from the regression analysis. The higher water pCO2 may explain part but not all of this anomaly (for reasons explained later in Section 7.5.2 ).

It is possible that at the highest temperatures (>28C), the high water vapour content of the air flowing out of the tank headspace caused an slight error in the pCO2 measurement, since for these measurements a crude trap had to be installed in the gas pipe leaving the tank, to prevent damaging condensation inside the LiCOR analyser (see Section 5.5.5 ). This would not affect the measured flow rate (which is of air entering the tank), but removal of water vapour might increase the measured pCO2 in the gas leaving the tank by up to a few percent. However, this effect would decrease the influx measurement and increase the efflux measurement. Since there is no sign of any significant divergence, no correction was made.

Using the Sc-1/2 curve as a baseline, the prediction using the formula of Hoover and Berkshire (1969) is also shown (calculated as in Section 6.4 ). Again, as for the paddle-speed variation data, this falls clearly below the measured transfer velocities in seawater, particularly at high temperatures. One possible explanation for this is that the CO2 + OH- reaction rate constant used for the prediction is too low, since the OH- concentration is much higher at high temperatures for similar pCO2 and alkalinity. This is discussed further in Section 7.7 .

The water pCO2 is shown alongside the seawater datapoints. If seawater is heated without allowing CO2 exchange with the atmosphere, the pCO2 will rise dramatically, due to changes in both the solubility and the carbonic acid dissociation constants. For example, if the pCO2 is 170ppm at 0C, it would rise to 650ppm at 30 C (see table 7-1 ). Therefore, between each set of two or three measurements (which were mostly carried out in order of ascending temperature), scrubbed lab air was allowed to flow through the headspace overnight in order to facilitate degassing. Nevertheless, time did not permit a complete reequilibration for each measurement and therefore the water pCO2 was generally slightly greater at higher temperatures. This will decrease the measured transfer velocity slightly at higher temperatures, due to the lower [OH-] at higher pCO2. However the effect in this pCO2 range should be small compared to the observed trend, as shown by the data in Section 7.5 . The scale of this effect is also indicated by the deviation of the points showing the Hoover and Berkshire prediction calculated using the same pCO2 as the corresponding seawater, compared to the prediction line calculated using pCO2=380ppm.

7.3.2 Effect of temperature on thermodynamic and kinetic constants

In table 7-1, some figures are given to illustrate the effect of temperature on various equilibrium and rate constants, which are the underlying cause of the observed effects on the transfer velocity. Note, for instance, that Kw rises by almost a factor of 20 between 0 and 30C, although it is often thought of as constant! For sources and further explanation of these constants, see Section 6.2 and table 6-2 .

As explained in the introduction ( Section 1.1.3 ), a feature of the "solubility pump" of CO2 in the ocean is that pCO2 in equatorial waters (typically up to 500ppm) is generally much higher than pCO2 in polar waters (occasionally down to 200ppm). Based on this observation and assuming a constant total alkalinity in ocean water (see next chapter. Also this effect does not apply to 14C fluxes which are effectively one-way and little affected by water pCO2 (for reasons explained in Section 3.3.4 ). This discussion of the net effect on the global air-sea CO2 flux will be considered further in chapter 9.

7.4 Schmidt number relationship

Much discussion on air-sea gas exchange has focussed on the "Schmidt number relationship", as explained in the introduction ( Section 1.2.4 ). The measurements described above already provide two independent methods to estimate this in the tank, and the SF6 / O2 experiments reported below were intended to provide a third. However, since the "control" measurements for CO2 transfer velocity without chemical enhancement are provided by the acidified seawater, the Schmidt number relationship is not critical to interpreting these results, and serves only to indicate the type of process (stagnant film, boundary layer or surface renewal) controlling the gas exchange in this system.

7.4.1 Sulphurhexafluoride / Oxygen comparison

In early autumn 1995 four experiments were carried out to compare the transfer velocities of oxygen and SF6 in the tank. The results are given in table 7-2 , and they are represented graphically (SF6 vs O2) in figure 7-4 . At this time both the stirring motor speed and the water temperature changed significantly every few days, since the control systems were still being developed. Various different paddles were used to vary the water stirring, rather than a variable speed motor. Therefore, although conditions were generally consistent within one experiment, these results are not comparable with the CO2 gas exchange measurements reported elsewhere in this chapter. Water from various different sources was also used (see table 7-2 ). CO2 gas exchange was measured by the steady state method for each different water sample, usually the day before or after the SF6 / O2 measurements, but the temperature was sometimes slightly different (as noted in table 7-2 ).

The table also includes later SF6 and oxygen transfer velocity measurements which were made during algal blooms to investigate any possible film effects. These are discussed in chapter 8, but they are also included here because the three SF6 / O2 pairs of data have also been added to the figure 7-4 . Schmidt numbers for SF6 and Oxygen are not included in table 7-2 , because the calculated ratio Sc (SF6) / Sc (O2) was constant at 1.81, although the temperature and salinity varied. The Schmidt number for CO2 is only 13% higher than that for Oxygen (see Section 6.2 ), so any large difference between CO2 and O2 transfer velocities is presumably due to chemical enhancement .

The method for calculating the SF6 and oxygen transfer velocities has already been explained in Section 5.11 and Section 5.12 respectively. For each transfer velocity reported below, about 12 SF6 measurements were made (excluding calibration), and thousands of oxygen measurements were recorded automatically by the computer. Graphs of log (concentration) against time were plotted for each gas, which have already been shown in figure 5-8 and figure 5-9 . For most experiments, a new SF6 calibration curve was also calculated (as illustrated earlier by figure 5-7 ). The plots of measured concentrations generally showed quite good linear fits, but as explained in Section 5.11.5 , the error is large due to the uncertainty in the endpoint. In the table and graph, two SF6 transfer velocities are given for each set of measurements, one using the endpoint (equilibrium concentration of SF6 in the headspace) which was actually measured the next day, and one using the endpoint which was calculated from the amount of SF6 added in the spike. The endpoints themselves are indicated in brackets, in units of parts-per-billion. The error range in the oxygen measurement (see table 7-2 ) was estimated by eye from the plot of the recorded data, any large errors being caused by changes in the temperature or stirring rate, or by oxygen production by the algae. This range is indicated in figure 7-4 , but the main datapoint is placed using the transfer velocities calculated from the computed regression lines. These were all efflux measurements except for oxygen on 5/3/96. Transfer velocities are in cm hr-1 as usual.

It can be seen from figure 7-4 , that these experiments were not sufficiently accurate to provide any useful indication of the Schmidt number relationship. It should be noted, that even during sophisticated dual / triple tracer measurements at sea, using SF6 and 3He (see Section 1.2.7 ) where the transfer velocities are much higher than those in this laboratory tank, the uncertainty in the measurements is of the order of 5-10%. This leads to an error of about 33% in the "Schmidt number exponent" calculated from such data (Phil Nightingale, personal communication). If such measurements were combined with simultaneous measurements of CO2 transfer, they would probably not be sufficiently accurate to quantify the effect of uncatalysed chemical enhancement.

Measuring the SF6 transfer velocity by this method was also very labour intensive (each transfer velocity requiring about 2 full days work), whilst although oxygen measurements were easy, creating a disequilibrium in oxygen disturbed algae at the water surface (due to bubbling) and photosynthesis confused the interpretation. Therefore, these experiments were not continued, except occasionally during algal blooms to give some indication of the physical effect of surface films (see Section 8.3 ). Instead, the acidified seawater blanks (described above) were used to provide a "control" for CO2 gas exchange without reaction, and also to get an approximate idea of the Schmidt number relationship.

7.4.2 Derivation from salinity and temperature variation measurements.

The "Schmidt number" of CO2 in seawater has been estimated to be about 6% higher than that in deionised water (Wanninkhof 1992, see also Section 6.2 ). If the transfer velocity is proportional to the inverse square root of the Schmidt number, as predicted by the surface renewal model of gas exchange (see Section 1.2.4 ), then we should expect it to be about 3% lower in the seawater. Alternatively, the boundary layer model would predict a difference of 4%, and the stagnant film model would predict a difference of 6%. The measured difference (see figure 7-1 ) fits the film model best (i.e. n = -1), but this distinction is unreliable given the accuracy of the measurements compounded by any uncertainty in the solubility. Moreover, the two sets of measurements may not be directly comparable since, although the water density in the microlayer is taken into account in the "Schmidt number", the density may also affect the extent of turbulent mixing produced by rotating the paddle at a given speed.

A better distinction between the gas exchange regimes is given by the temperature-variation data already presented in figure 7-2 and figure 7-3 . Here, clearly only the Sc-1/2 curve fits the acidified seawater data, and at high temperatures the Schmidt number exponent would have to be even lower to match the measurements well. The Schmidt number decreases by a factor of five on increasing the temperature from 0C to 30C (see table 7-1 above), which is a much wider range than that caused by the salinity effect mentioned above. Consequently, in this case the error in the acidified seawater measurements is much smaller than the difference between predictions from the three Schmidt number regimes. From this we can therefore conclude that the surface renewal process is predominating. Early observations of the water circulation using dye support this conclusion, as it was clear that the headspace dividing walls caused regular overturning of the water surface (see Section 4.7.1 ).

The apparent transition between boundary-layer and surface renewal processes which occurs at the onset of capillary wave production is a well-known feature of wind-driven gas exchange tanks, but has not been observed in stirred tanks (see references in introduction Section 1.2.5 ). From my own observations on the open sea, there is usually some swell with associated vertical circulation within the waves, even if there is no wind to create capillary waves. Therefore stirred tanks with baffles to force overturning may actually represent such conditions better than wind-driven gas exchange tanks. In this case, it would not be unreasonable to find a surface renewal regime even at the low transfer velocities measured here, for which the parameterisation of Liss and Merlivat (1986) predicts a boundary layer regime. In any case, when calculating the CO2 transfer velocity from that of other inert gases at very low exchange rates, the enhanced transfer due to chemical reaction is much greater than the difference in the transfer due to diffusion, caused by switching between the Sc-1/2 and Sc-2/3 relationships.

7.5 Effect of pCO2 on the enhanced transfer velocity

7.5.1 Effect of water pCO2

Carbonic acid equilibria are such that, as the concentration of dissolved CO2 falls, the pH rises, assuming constant alkalinity (see introduction Section 1.1.2 ). Photosynthesis by the algal cultures sometimes took the pCO2 in the water down to very low levels, as reported in the next chapter, and the highest transfer velocities were measured in such low pCO2 conditions. To distinguish any effect of the algae from the effect of higher pH due the OH- reaction pathway (see Section 1.5.2 ), it was necessary to make "control" measurements over the full range of pCO2 without any algae. These results are summarised in figure 7-5 . Note the logarithmic scale for the pCO2 axis, and that the normal seawater pCO2 range is only a small portion of the right hand side of the figure. The use of a log (pCO2) scale is justified both by the distribution of the data, and by the seawater chemistry, since the [OH-] is more closely correlated to log (pCO2) than to pCO2. The figure combines a set of measurements made in January 1996 with further measurements over a wider range made in January 1997, and all other measurements without algae or enzyme, for which the temperature and rpm were 15 and 13 respectively. The cluster of measurements around pCO2=360ppm have already appeared in figure 7-1 , figure 7-2 and figure 7-3 .

Figure 7-5 also shows the enhanced transfer velocities predicted by the formula of Hoover and Berkshire (1969), using the reaction rate constants from Johnson (1982) and the baseline from acidified seawater as above, corrected for small variations in stirring speed and temperature (for more details see Section 6.4 ). It is clear that, as before, the prediction falls well below the measured transfer velocity, and that the discrepancy is greatest at low pCO2. This could be most easily resolved by using a higher OH- reaction rate constant in the prediction, which will be discussed later ( Section 6.5 . Generally, the error increases as the difference between the pCO2 in the air flowing in and out of the headspace decreases: consequently the error is greater for efflux then for influx measurements, and is also greater at lower water pCO2. It should be emphasised that the vertical bars in all of these plots do not indicate a statistical standard error, but a maximum error range calculated from a combination of the error ranges of the measured parameters (see Section 6.5 ). This maximum range is much greater than a statistical standard error, but the latter would be difficult to calculate since the transfer velocity formula involves the ratio of two non-independent parameters.

The horizontal bars do not represent an error range, as the measured pCO2 error should be only about 1ppm. Instead, the far end of the bar (without the datapoint) indicates the pCO2 of air in the headspace, on the same x-axis scale. Therefore the length of the horizontal bars (bearing in mind the logarithmic scale) indicates the D pCO2 between the top and bottom of the water surface microlayer, the thermodynamic driving force for gas exchange. For influx measurements the air pCO2 is obviously higher than the water pCO2, and so the bar extends to the right of the datapoint, and vice versa for efflux measurements.

To show the effect of [OH-] more clearly, the same data as in figure 7-5 has been plotted in figure 7-6 as a function of [OH-] rather than pCO2. The [OH-] is calculated from the water pCO2 assuming a constant alkalinity, as described in Section 6.3 . The other end of each horizontal bar indicates the [OH-] calculated using the air pCO2, as in figure 7-5 .

Here the order of the datapoints is reversed, and we can see that there is almost a straight line relationship, between the influx transfer velocity, and [OH-]. However, there is no particular reason to expect a straight line relationship between the transfer velocity and [OH-], because chemical enhancement is not a linear function of the total reaction rate, as is clear from the formula of Hoover and Berkshire (1969) (see Section 1.5.3 , and also Section 7.6.3 ). We should also remember that the ratio of HCO3- to CO2 will also be greater at higher pH, which is the driving force for CO2 transfer by all reaction pathways (this is represented by the factor "t " in the Hoover and Berkshire formula).

The theoretical increase in chemical enhancement at higher pH or [OH-] has been considered by many authors (notably Emerson 1975a, and Keller 1994). However, there have been few systematic experimental studies of this phenomenon. Emerson (1975b) found that his laboratory tank and lake measurements of chemical enhancement at high pH matched the predictions from his iterative model quite well. However the enhancements measured in alkaline lakes by Wanninkhof and Knox (1996) were higher than predicted Goldman and Dennet (1983) observed that the CO2 exchange rate measured in a tank of seawater at pH 9 was four times that at pH 8. Williams (1983) measured the reaction rate directly in alkaline lake water, and found that it was higher than predicted using previously published rate constants. For further details of these experiments, see Section 1.5.5 . The comparison between previously published measurements of chemical enhancement, and the results reported in this chapter, will be continued in Section 7.8

7.5.2 Influx and Efflux measurements: Effect of air pCO2?

As well as showing more scatter, the efflux measurements also lie significantly above the influx measurements. This difference is also apparent for the data from algal cultures (see figures in Section 8.4 , summarising all the data together in one plot). One possible explanation is that there is a significant influence of the air pCO2 on the microlayer pH. As the air boundary layer mixes much more rapidly than the water boundary layer, therefore the pCO2 gradient is mainly on the water side of the interface (see introduction Section 1.2.1 ). The average pCO2 in the surface microlayer would be lower than the water pCO2 for efflux measurements and higher than the water pCO2 for influx measurements. Although the microlayer pH will not be in equilibrium with the microlayer pCO2, because the reaction of CO2 with water is slow, nevertheless the pH at the air-water interface will be slightly higher than the bulk pH for efflux measurements, and slightly lower for influx measurements. Consequently the chemical enhancement of the CO2 transfer velocity due to the OH- reaction pathway should be slightly higher for efflux than for influx measurements, as observed.

It is difficult to confirm or deny an air-pCO2 effect from a simple inspection of the data shown in figure 7-5 and figure 7-6 , because although the data includes measurements over a wide range of both air and water pCO2, these two factors are intercorrelated. To illustrate this, Figure 7-7 (a) shows the same transfer velocity measurements as in figure 7-5 , but plotted vertically as a function of both air and water pCO2, both on log scales. The positions of the individual data points are also indicated. A 3-dimensional interpolated surface has been fitted to the data points and this is also indicated as a contour plot in Figure 7-7 (b), on which it is easier to see the exact positions of the datapoints.

Note the lack of data in the corners with high water pCO2 and low air pCO2 or vice versa, and also along the line where air and water pCO2 are equal (i.e. no gas exchange). This is because the ratio (pCO2 of air entering headspace - pCO2 of air in headspace) / (pCO2 of air in headspace - water pCO2) was normally kept fairly close to unity to minimise the error in the transfer velocity (see Section 5.8 and 6.5). One exception is the set of 15 points at constant water pCO2 = 380 ppm, which were measured specifically to investigate the effect of air pCO2. Although there is a slight trend within this set towards higher transfer velocity at lower air pCO2, the trend is less than the scatter amongst the points

We should also consider the possibility that the difference between the influx and efflux transfer velocities is due to an experimental artefact. For instance, the two transfer velocities were usually measured concurrently in two different headspaces, which were sometimes switched around for various reasons. Such changes were recorded, so the difference in surface area (<1%) has been corrected for in the calculation of the transfer velocity (see also Section 4.6.1 ). The measurements at high paddle speeds (see Section 7.2 ) showed that a slight difference in physical dimensions of the two headspaces could be greatly magnified when resonant waves were formed, but this was not apparent at lower speeds. An error in one of the flowmeters (about 2%) has been corrected for all the 1997 data, but it was not possible to correct for this in some of the earlier pairs of measurements.

A systematic error could also be caused by a non-linear output from the LiCOR analyser. One advantage of the steady-state method is that small errors in both the zero and the span of the analyser cancel in the transfer velocity calculation, so long as the response is linear. However, the output from the infra-red sensor within the analyser is not intrinsically a linear function of pCO2: the linear output is only achieved by applying a polynomial response curve based on calibration carried out for each instrument by the manufacturers. Therefore, the linearity was checked from time to time using CO2 standards at 0 (Nitrogen), 272, 438 and 2010 ppm (see Section 5.5.3 ). Although each standard could be a percent or two out, no systematic curve was ever apparent.

Another more intriguing explanation could be that we are observing a real intrinsic difference between influx and efflux transfer velocities, which is caused by the non-equilibrium thermodynamics of air-water gas exchange. Phillips (1991a and many subsequent references, see Section 1.4.4 ) has argued persistently that the simple parameterisation of gas exchange into independent thermodynamic and kinetic components is inherently incorrect, due to the coupling of heat and matter fluxes. This might cause an intrinsic difference between the influx and efflux transfer rates, but the direction and magnitude of such an effect is a matter of controversy (see papers of Doney, referred to in Section 1.4.4 ). Furthermore, the heat gradient across the air-water interface is probably very small in my tank as it is well insulated and maintained at a constant temperature during each measurement, so this is unlikely to be an explanation for the observed difference. Net evaporation or condensation at the water surface can also influence gas exchange (see Liss et al 1981 and other references in Section 1.4.3 ), but this should not be significant in the small headspace of the insulated laboratory tank, except possibly at high temperatures as already noted in Section 7.3.1 .

So the effect of air pCO2 on the microlayer pH remains the most plausible explanation for the difference between influx and efflux measurements. This effect deserves further theoretical study using an iterative reaction - diffusion computer model, as comparison with measured data might provide insights into the mechanism of the gas exchange process. However, the actual variation due to this effect is unlikely to be significant in the real sea, because the variation of air pCO2 over the oceans is much smaller than in my tank.

Nevertheless, the effect should be borne in mind when extrapolating from experimental measurements in which the air pCO2 is not close to atmospheric levels, or when proposing formulae for predicting the chemical enhancement of gas exchange. For instance, the CO2 transfer velocities measured by Wanninkhof and Knox (1996) are based on the efflux of CO2 from a natural water body into a headspace, through which air with a very low pCO2 flowed (see also Section 1.5.5 ). In this case the effect of the air pCO2 might be to increase the transfer velocity slightly above that which would be measured if the air pCO2 were 360ppm.

Although an iterative reaction-diffusion computer model of gas exchange should be able to predict the effect of varying air pCO2, no such model has been applied specifically to this problem, since it is usually assumed that the air pCO2 remains fairly constant over the ocean, at the current average level of 360ppm. The derivation of the formula of Hoover and Berkshire (1969), on the other hand, assumes a constant pH in the microlayer, equal to that of the bulk water, and consequently is independent of the air pCO2. Quinn and Otto (1971) pointed out that this constant pH assumption violated electroneutrality, and derived an iterative model which was constrained instead by electroneutrality, as did Emerson (1975) (see also Section 1.5.4 ). However, these iterative models are not as convenient as an algebraic formula. A formula which assumes constant pH within the microlayer at any one location, could slightly overestimate the chemical enhancement in regions where the net flux of CO2 is into the ocean (i.e. when air pCO2 is about 360ppm but water pCO2 is lower), but could underestimate the chemical enhancement for high CO2 regions. The overall effect of the relatively constant air pCO2 is therefore to reduce the bias of chemical enhancement towards lower water pCO2. This systematic error is probably smaller, however, than many others inherent in such simple chemical enhancement formulae.

Recently, Kirk and Rachipalsingh (1992) derived a complex iterative computer model describing the pH profiles in the water boundary layer at the surface of a rice-paddy, which considered the effects of both invasion of CO2 and evasion of NH3. The interaction between CO2 and NH4, helped to propogate the pH changes more rapidly through the solution. Increasing the CO2 reaction rate by adding carbonic anhydrase was found to reduce the microlayer pH during CO2 evasion, and increase it during CO2 invasion. This can be explained by considering that catalysis by carbonic anhydrase reduces the chemical disequilibrium near the surface, and hence reduces the influence of the air pCO2 on the microlayer pH.

7.5.3 pCO2 effect in the real ocean

When reading that "influx" transfer velocities were slightly lower than "efflux" transfer velocities, the reader should beware that the comparison is being made between pairs of measurements with the same water pCO2, but varying air pCO2, due to the design of the steady-state tank, in which two separate headspaces are in contact with the same body of water. In the real ocean, on the other hand, "influx" and "efflux" usually refer to low and high water pCO2 respectively, whereas the air pCO2 is fairly constant. From this point of view, figure 7-5 shows that the transfer velocities in oceanic "influx" conditions, i.e. those to the left of 360 ppm in the figure, are markedly higher than those for oceanic "efflux" conditions, i.e. those to the right of 360 ppm. This asymmetry due to the water pCO2 is greater than that due to the air pCO2. Using the more reliable "influx" (into tank) measurements, and the unenhanced baseline (2.75 cm hr-1) derived from the acidified seawater data (see Section 7.3.2 ). This is discussed further in the global flux calculations in chapter 9.

Although pCO2 in the sea rarely falls below 200ppm, even small asymmetries between the rate of CO2 entering and leaving the ocean could become important in calculations of the net global air-sea CO2 flux, as already demonstrated in Section 3.3 and illustrated by the "thought experiment" of Keller (1994). The measurements shown in figure 7-5 and figure 7-6 provide the first systematic experimental confirmation of the expected asymmetry, which is therefore in itself a valuable step forward. They also suggest that the Hoover and Berkshire equation significantly underpredicts the asymmetry, in which case the effect on the net global air-sea CO2 flux would be correspondingly greater. This discrepancy will therefore be considered further in Section 7.7 .

7.6 Effect of adding bovine carbonic anhydrase

As early as 1963, Kanwisher demonstrated how the transfer velocity of CO2 in seawater could be greatly enhanced by catalysis due to added bovine carbonic anhydrase (see Section 2.1 ). The results of the similar experiments presented in this section confirm the potential for such catalysis, but also show that this catalytic activity has a relatively short lifetime (from hours to days). The effect on catalysed enhancement of varying the temperature and the enzyme concentration are also investigated, and the measured catalysis is compared with that predicted using the enzyme kinetic formula developed earlier in

7.6.1 Early measurements of catalyzed CO2 transfer

One of the first experiments carried out in the gas exchange tank (February 1995) was an investigation of the effect on the CO2 transfer velocity of added bovine carbonic anhydrase, which was purchased from Sigma Chemical company. CO2 and Oxygen transfer velocities were measured concurrently, before and after the addition of 38.5 mg of enzyme to the tank, which contained Norwich tapwater at 19C. This water has a higher alkalinity than seawater: the TCO2 was measured to be 3.0mM at the initial pCO2 of 1170ppm. As the gas flow system for the steady-state tank was not yet complete, the headspace was first flushed with Nitrogen to create a disequilibrium, and the system was then closed while the change in pCO2 in the headspace and oxygen in the water was measured as a function of time. Transfer velocities could be estimated from the rate of reequilibration. The CO2 transfer velocity measured 2 hours after addition of the enzyme had increased from 2.9 to 5.7 cm hr-1, but the oxygen transfer velocity, 2.3 cm hr-1, was not significantly affected.

In August 1995 a similar experiment was carried out, but this time measuring CO2 gas exchange by the steady state method, and using artificial seawater, made up with NaCl, MgSO4, CaCl, NaHCO3 and H3BO3 with a total alkalinity of 2.79mM (carbonate alkalinity 2.35mM). Bovine enzyme was added twice (37mg then 55mg), and the transfer velocities measured at intervals over 4 days to observe the decline in activity which was expected, recalling the results of experiments with dansyl-amide fluorescence (see Section 3.5 ). The temperature increased from 27.4 to 29.6 during the 4 days of the experiment (this was before the tank had a cooling system), and the water pCO2 increased correspondingly from 450 to 650ppm.

The results are shown in figure 7-8 . In this case the efflux measurements were more accurate than the influx measurements due to a large variability in the high-pCO2 air supply. It can be seen that the there is a rapid decline of enzyme activity, with a "half life" of about 15 hours, which supports the conclusion drawn from the Dansyl Amide fluorescence measurements (see Section 3.5.5 , and also the appendix) that carbonic anhydrase activity is unlikely to be observed in stored seawater samples. This is important, because it implies that lack of catalytic activity in the samples analysed by Goldman and Dennet (1983) and Williams (1983) (see Section 2.1 ), does not necessarily imply that there was no carbonic anhydrase in situ before sampling. We do not know the exact cause of the decline in activity: it may be due to physical denaturation, chemical inhibition, or consumption by opportunist bacteria, but all of these processes are likely to operate in the real sea-surface microlayer.

In both these early experiments, the water stirring paddle was smaller than the one used in later experiments, whilst the stirring rate was faster - the change was necessary due to problems with the motor. Therefore the results are not directly comparable with other measurements reported in this chapter.

7.6.2 Effect of temperature on enzyme activity and lifetime

To provide measurements in physical conditions similar to those of other measurements reported in this chapter, and also to investigate the effect of temperature variation and added enzyme inhibitor, a set of similar experiments was carried out in April 1997. In this case, the paddle speed was always 13rpm, and real filtered seawater was used. Measurements were made at three different temperatures, and the temperature control was more precise. The results are shown in figure 7-9 . This shows that the decline in activity is much more rapid at high temperatures than at low ones: at 29 C the "half life" is about 10 hours, whereas at 15C it is about 50 hours. These estimates are for comparison only as the decline does not seem to be exponential, but they should be borne in mind when considering the possible presence of carbonic anhydrase produced by algae in the ocean surface microlayer.

For comparison with the effect of temperature on uncatalysed enhancement, the transfer velocities immediately after adding the enzyme have also been included in figure 7-2 and figure 7-3 shown earlier. Although equal weights of enzyme were added in each case, it was later noted that they came from two different batches of enzyme with slightly different activities. The data provided by Sigma (see next section below) was used to make a correction for this (about 10%) in figure 7-2 and figure 7-3 .

Figure 7-2 shows that, although the total catalysed transfer velocity increases at higher temperatures, the relative increase of the portion of this attributable to catalysed reaction (i.e. the gap between the enzyme measurements and the curve through the no-enzyme seawater data) is not so great as the relative increase of the portion attributable to uncatalysed reaction (i.e. the gap between the curve through the seawater data and the curve through the acidified seawater data). This is as expected, because the effect of the enzyme is to lower the activation energy of the reaction to about 38.1 kJ mol-1, compared with 81.7 kJ mol-1 for the uncatalysed reaction (Sanyal and Maren 1981, data for Human CA). By applying the Arrhenius equation (see Section 2.7.2 ), we can calculate that, on increasing the temperature from 0 to 30C, the relative increase in the catalysed reaction rate should be only 1/7th as great as the relative increase in the uncatalysed reaction rate (although note that the effect on chemical enhancement is not a linear function of the reaction rate).

7.6.3 Effect of enzyme concentration, enzyme inhibitor, and pCO2

To complete the added enzyme experiments, a set of measurements was made in May 1997 with varying concentrations of enzyme, all in the same seawater, at constant temperature and paddle speed (standard conditions: 15C and 13rpm). The results are shown in figure 7-10 . The transfer velocities were measured as soon as possible after each enzyme addition, as usually about 2 or 3 hours were required to achieve steady-state in the headspace. The next addition was not made until the activity had declined completely, and to be certain of this the transfer velocity was also measured just before adding the enzyme. These blank measurements are also included in the figure vertically below the subsequent measurement with enzyme. The large number of points at zero enzyme concentration are the same cluster of "blanks" in standard conditions as already shown in several figures earlier in this chapter.

The x-axis scale on figure 7-10 shows enzyme concentration in Wilbur-Anderson units per litre, rather than mg per litre. This was necessary because three different bottles of enzyme were used, and they were not identical although all were purchased from the same supplier (Sigma). On each bottle, the number of "Wilbur Anderson units" (a measure of carbonic anhydrase activity - see Section 2.6.1 ) per mg protein was given (this was either 4500 or 5800), and also the percentage of protein (this was either 97% or 91%, composition of remainder unknown). The enzyme is provided as dried and lyophilized crystals extracted from bovine erythrocytes, so the difference could either be in the purification or in the cows themselves.

After the final enzyme addition, the activity was reduced rapidly by addition of the enzyme inhibitor "acetazolamide", 110mg in 50 litres, or about 1 m M. This is 50 times the mid-range enzyme concentration of approximately 20nM (assuming a molecular weight of 33000Da). Since the I50 values (see Section 2.7.3 ) for sulphonamide inhibitors of carbonic anhydrase are typically in the nanomolar range (Bundy 1986), this should be more than sufficient to completely inhibit all the enzyme. The flow of pCO2 out of the headspaces began to change immediately after addition of the inhibitor, although the steady state transfer velocity measurement which is shown in figure 7-10 could not be made until six hours later. It shows a complete inhibition of the enzyme activity, as expected. The same inhibitor was also used at the end of some of the algal blooms, as mentioned in the next chapter (e.g. Section 8.3.2 ).

As expected, the transfer velocity increases smoothly with added enzyme concentration, but begins to levels off at higher concentrations. This levelling off cannot be explained by saturation of the enzyme-kinetic process, because the ratio of enzyme to substrate molecules is still very low (approximately 1:1000). However, it is consistent with the shape of the theoretical curve of transfer velocity as a function of carbonic anhydrase concentration shown earlier in figure 3-3 , which was predicted using the enhancement formula of Hoover and Berkshire (1969). Note that it is the square-root of the total CO2 hydration rate ktot which appears in the key component of this formula β =Ö ( ktot τ / D) (see Section 1.5.3 ). Conceptually, this levelling off might be explained by competition between the reaction and diffusion processes of air-sea exchange.

A second order polynomial curve has been fitted through the data. One pair of measurements seems to lie above this curve, and another below. However, this can be easily explained by noting that for the points lying above the curve, the pCO2 in the water was lower than usual, whereas for the points lying below, the pCO2 in the water was higher than usual. Since most of the measured flux in this case is due to reaction rather than diffusion, such differences in pCO2 differences and corresponding differences in [OH-], should be expected to have a proportionally larger effect on the transfer velocity in the presence of the enzyme.

7.6.4 Comparison of measured and predicted catalysis

It would be useful to compare the measured enhancement due to enzyme catalysis, with a theoretical prediction based on the enhancement formula of Hoover and Berkshire (1960) combined with the steady-state enzyme kinetic formula developed in Section 2.5.4 . However, to apply this formula we need appropriate enzyme kinetic constants, and kcat in particular (see Section 2.5.2 ) varies considerably between different sources of carbonic anhydrase (see Section 2.7.1 ). In the absence of reported values specifically for bovine CA, we might expect that bovine CA is closer to human CA "C" than to others in table 2-2 . However, in human blood other CA types can also be isolated with much lower CO2 hydration activity (see Section 2.2.2 ), and the enzyme which we purchased, extracted from bovine erythrocytes, may actually be a similar mixture of such enzymes. Purified single isozomes of bovine CA are also commercially available, but not at an affordable price for the quantities required in air-water gas exchange experiments.

The catalytic activity of the bovine CA which we purchased from Sigma was defined in arbitrary "Wilbur-Anderson units" per mg (see Section 2.6.1 ). The Sigma catalogue tells us that one WA unit is sufficient to cause the pH of a 0.02M Trizma buffer to fall from 8.3 to 6.3 in one minute at 0 oC. We can assume that this pH change is caused by an addition of CO2 saturated water, as in the original experiment of Wilbur and Anderson (1948), but the exact mixing ratios are not known and it is not clear whether the WA unit includes the uncatalysed reaction. I wrote a computer program (in QBASIC) to attempt to model this system and hence deconvolute the data to determine genuine enzyme kinetic constants (using thermodynamic and kinetic data as in chapter 6), but found that even when the CO2 - saturated water makes up only 40% of the final mixture, the pH should fall from 8.3 to 6.3 in one minute without any enzyme.

The Fluka catalogue states that carbonic anhydrase extracted from bovine erythrocytes (i.e., a similar product to Sigma's) has an activity of 200,000 U /mg, where one U is the amount of enzyme which catalyses the hydration of 1 mmol CO2 per minute at pH 8.3 and 25 oC. We can assume that this also refers to a Wilbur-Anderson type experiment using CO2 saturated water. Initially at least, [CO2] is much higher than [HCO3-], and the catalysed reaction dominates the uncatalysed reaction. In these conditions we can apply the formula for an "initial velocity experiment" (for explanation of this term and derivation of the formula, see Section 2.5.2 ):

V = Vmax A0 / (Km + A0),

where: V is the reaction rate, Vmax = kcat Eo , kcat is the "turnover number" and E0 is the total enzyme concentration , Km is about 12mM (see figure for Bovine CA from Kernohan 1965 in table 2-2 ), and A0 is [CO2] in CO2 saturated water at 25C, which is about 25mM.

From this we can work out a value for E0 kcat , which is about 0.0049 s-1, when E0 is 1 mg l-1, at 25C. For comparison, the value for CA from Chlamydomonas Reinhardii measured by Bundy (1986), adjusted for temperature as in Section 2.7.2 , comes to be 0.0053 s-1 when E0 is 1 mg l-1 (assuming the molecular weight is 35,000). This remarkably close match is probably a coincidence, given the range of values of kcat in table 2-2 .

We now need to know E0 kcat for the amount of enzyme in the tank, at 15C. The measurement in the middle of the range shown in figure 7-10 used 3200 WA l-1, which corresponds to about 0.67 mg l-1 CA. Using the Arrhenius equation and the activation energy for human CA from

Sanyal and Maren (1981), we can calculate that kcat at 15C is 0.58 * kcat at 25C. Combining these figures, we get a value for E0 kcat in the tank, which is 0.0019 s-1.

We can now apply the formula for enzyme catalysis in steady-state reaction-diffusion conditions in the tank, as derived in Section 2.5.4 . This is:

ktot = E0 kcat / ([CO2] + [HCO3-] Km / Km + Km) + kCO2 + kOHKw / [H+]

Assuming that (the exact value is not critical), Km = 12mM as above (this does not vary significantly with temperature), Km / Km is about 1/4, [CO2], [HCO3-], and [H+] are 1x10-5, 2x10-3 and 8x10-9 mol l-1 respectively (the exact values are not critical) kCO2 =0.0142, kOHKw = 2.21x10-11, (at 15C as calculated in Section 6.2 ), and E0 kcat = 0.0019 s-1, we can calculate that ktot = 0.169 (about 10 times the total uncatalysed hydration rate).

We can now use this to calculate the enhanced catalysed transfer velocity by applying the Hoover and Berkshire formula (for details see Section 1.5.3 and Section 6.4 ), assuming a "stagnant film thickness" derived from an uncatalysed transfer velocity of 2.75 cm hr-1, as usual. The predicted enhanced transfer velocity comes to be 5.8 cm hr-1 (of which catalysis is 2.3 cm hr-1). By comparison, the measured transfer velocity was about 7.5 cm hr-1 (of which catalysis is 4.0 cm hr-1).

This is a remarkably close match between the predicted and measure enhancement, given the myriad of assumptions used in the above calculation, in which enzyme kinetic constants from several different types of CA were all combined together. Moreover, we must recall that the transfer velocity measurements without enzyme all suggested that the Hoover and Berkshire formula appears to underpredict enhancement (this will be discussed further in the next section). We must also bear in mind that the enzyme concentration may be higher in the surface microlayer, which has not been considered in the prediction above. On the other, the potential reduction in catalytic activity due to the anions in seawater, has also not been considered in the prediction.

This result gives us some confidence in the enzyme kinetic formula developed in Section 2.5.4 , compared to the simpler formula used by Emerson (1995) which predicts much greater catalysis, and which I believe is incorrect (see Section 2.5.5 ). This is important, because this

formula is a critical component of the global flux CO2 calculations including enzyme catalysis, which are reported in chapter 3 and chapter 9. This result also gives some confidence in the combination of kinetic constants selected from various sources. Note, however, that the global flux calculations in chapter 3 and chapter 9 use a value of 3mM for Km taken from Bundy (1986) for CA extracted from Chlamydonomas, rather than 12mM for bovine CA as used above. This lower value of Km raises the steady-state catalysis. We might also expect extracellular CA produced by marine microalgae in the sea-surface microlayer, to be less inhibited by seawater anions, and more surface-active, than CA extracted from bovine erythrocytes.

We can also compare these catalysed enhancements with some other figures reported in the literature. Quinn and Otto (1971) used their iterative model to predict that adding about 3mg l-1 (10-7 M) CA would decrease the "equivalent stagnant film thickness" for CO2 from 300 μm to 30 μm, which corresponds to increasing the transfer velocity from about 2 cm hr-1 to about 20 cm hr-1. Goldman and Dennet (1983) reported that 0.5 mg l-1 bovine CA increased the CO2 exchange rate measured in their tank by 60%, and 2 mg l-1 CA increased it by a factor of 2, for an equivalent stagnant film thickness of 450μm. These figures seem consistent with the measured and predicted enhancements reported above. On the other hand, Berger and Libby (1969) reported that adding 0.5 mg l-1 CA increased their measured transfer velocity by a factor of 20 or more, but they did not report their baseline uncatalysed exchange rate, which may have been very low.

7.7 Difference between measured and predicted chemical enhancement.

Using the more reliable "influx" data (pCO2(air) > pCO2(water)), the measured chemical enhancement for the standard experimental conditions (no algae, temperature=15C, paddle speed =13rpm, pCO2=360ppm) is about 20% whereas the Hoover and Berkshire equation (using rate constants of Johnson 1982) predicts only 13%. This discrepancy increases at higher temperatures (see figure 7-2 ), at lower pCO2 (see figure 7-5 ) and possibly also at higher paddle speeds (relative to the predicted enhancement, see figure 7-1 ). All these measurements and predictions have been brought together in figure 7-11 , in which measured enhancement factors are plotted as a function of predicted enhancement factors. Note that the enhancement factor is the enhanced transfer velocity divided by that expected for diffusion only transfer, and therefore the order of the data points is reversed compared to the previous figures ( figure 7-1 and figure 7-5 ) showing the effect of varying paddle-speed and varying pCO2.

It is clear that the three different sets of measurements (varying paddle speed, varying temperature, and varying pCO2) show three different relationships between the predicted and measured enhancement, and therefore the discrepancy cannot be resolved just by scaling up the predicted enhancement factor by a constant factor. There may be several different processes involved. The calculation of the predicted enhancement includes the effect of temperature on the reaction rates and equilibrium constants, and also includes the OH- reaction pathway (dependent on [OH-] calculated from water pCO2). So, in addition to the small effect of air pCO2 on the microlayer pH, which has been discussed above, there are two principal reasons why the Hoover and Berkshire prediction may be too low. The first is the use of the stagnant film model, and the second is the uncertainty in the OH- reaction rate constant.

Keller (1994) discussed both of these issues in some detail. He set-up a reaction-diffusion surface-renewal computer model of CO2 air-water transfer, which predicted higher chemical enhancement than the stagnant film models of Hoover and Berkshire (1969) and Smith (1985) (see Section 1.5.3 ). This is to be expected, because the pCO2 disequilibrium at the water surface is greater for a fresh parcel of water, which has just been upwelled to the microlayer surface, than for a stagnant film. Consequently, in conditions which produce the same amount of diffusion, the potential for reaction is greater (this is also discussed in Section 1.5.4 ).

Studies of the Schmidt number relationship between different gases in wind-driven tanks (see Section 1.2.5 ) suggest a transition from a stagnant film to a turbulent boundary layer to a surface renewal system as transfer velocities increase. Since the Hoover and Berkshire equation is based on a stagnant film model, we might therefore expect it to be most accurate for low windspeeds or stirring rates, and then to increasingly underpredict the chemical enhancement as the windspeed (or stirring rate) increases and surface renewal becomes the more appropriate model. This might explain the slightly increased divergence at higher stirring speeds shown in figure 7-1 .

Keller (1994) also noted that OH- reaction rate constant measured by Miller and Berkshire (1971) was considerably higher than that of Johnson (1982), and so he took a value half way between these two. Increasing this reaction rate will have a greater effect at lower pCO2 (higher [OH-]). In figure 7-5 and figure 7-6 , the relative discrepancy between the measured data and the Hoover and Berkshire prediction is also much greater at lower pCO2 (higher [OH-]). This discrepancy could therefore be resolved by using a higher OH- reaction rate in the prediction, rather than a change in the assumptions behind the equation. I therefore recalculated the predicted transfer velocities keeping all factors unchanged, except the OH- reaction rate. To make the Hoover and Berkshire predictions match the "influx" measurements (which were more accurate than the "efflux" measurements as explained in Section 6.5 ), it was necessary to increase the OH- reaction rate by a factor of about six. This is shown in figure 7-12 , where the predictions now match the measurements reasonably well, compared to the equivalent figure 7-6 with the lower OH- reaction rate

Figure 7-13 then shows what happens when this same sixfold increase in the OH- reaction rate is applied to all the measurements of uncatalysed enhancement, plotted together as in figure 7-11 . This higher OH- reaction rate pulls all the datapoints towards the right of the plot, but has most effect on the datapoints corresponding to low pCO2 or high temperature, for which [OH-] is higher (recall the effect of temperature on Kw and hence [OH-]) and for which the discrepancy between predicted and measured enhancements is also higher. On the other hand, the set of measurements made at varying stirring speeds are affected much less by the higher OH- reaction rate. Consequently, the overall effect is to resolve the discrepancy for all three datasets, and to bring them into much better agreement in figure 7-13 , compared to figure 7-11 .

The reader may recall that Quinn and Otto (1971), using an iterative reaction-diffusion stagnant film model, predicted that the Hoover and Berkshire equation would overestimate chemical enhancement due to the constant pH assumption. However it should be noted that the sign of this effect depends upon the air pCO2 (influx or efflux), as already discussed in Section 7.5.2 , and also that the model of Quinn and Otto (1971) model did not include the OH- reaction at all.

There may be other explanations why the discrepancy between predicted and measured enhancements differs depending on the parameter being varied. However, the observation that all these different discrepancies can be resolved by changing just one factor, suggests that the possibility that the reported OH- reaction rates are too low, is at least worthy of further investigation.

7.8 Comparison with previous measurements of chemical enhancement

7.8.1 Measurements of chemical enhancement in published literature

There are only a few published papers reporting measurements of the chemical enhancement of the CO2 transfer velocity in seawater or solutions of similar alkalinity, and these experiments in tanks and wind tunnels have already been discussed individually in Section 1.5.5 . Here, all the previously published measurements of chemical enhancement, which are reported in sufficient detail to enable comparison of measured and predicted enhancement factors, are summarised together in figure 7-14 . This has the same format as figure 7-11 and figure 7-13 , i.e. it shows the measured chemical enhancement factor as a function of the enhancement factor predicted by the formula of Hoover and Berkshire (1969). The line shows where the two are equal. Note that the points towards the left hand end of the graph represent higher windspeeds or stirring rates, corresponding to lower enhancement factors, and vice versa. The various experimental methods, and the assumptions used here in order to calculate the predicted enhancements where the published predictions were not used, are summarised in the table 7-3 below (for more detail, see Section 1.5.5 ).

Note that measurements made in much more alkaline waters, such as those of Emerson (1975b) or the lake measurements of Wanninkhof and Knox (1996), are not included, because these are not comparable with seawater measurements.

As with my own measurements, this data falls into several different sets. The measurements of DeGrandpre et al (1995), along with the measurements of Broecker and Peng (1974), fall significantly above the Hoover and Berkshire prediction, whereas those of Liss (1971), Hoover and Berkshire (1969), and Wanninkhof and Knox (1996) agree with the prediction.

We should consider whether these differing discrepancies might also be explained by the OH- reaction rate constant being too low. Liss (1971) and Hoover and Berkshire (1969) used water of a much lower alkalinity (and therefore higher pH) than seawater, and so the OH- reaction would make a negligible contribution to the measured enhancement. The effect of OH- in the laboratory tank measurements of Wanninkhof and Knox (1996) is harder to predict, because the pCO2 of the air was very low (as discussed already in Section 7.5.2 ), but the pCO2 of the water was much higher than atmospheric levels (the exact levels are not reported). Probably, the effect of high water pCO2 dominates in controlling the microlayer pH, and consequently [OH-] in the microlayer would be low. Thus, in this collection of data from previously published measurement of enhancement in laboratory tanks and wind tunnels, the discrepancy between measured and predicted enhancements is again greater, in conditions when the concentration of OH- is probably higher.

We should also consider the effect of the stagnant-film assumption which is inherent in the formula of Hoover and Berkshire (1969) used for all the predictions above. At the lower pH of the buffered freshwater used in the experiments of Hoover and Berkshire (1969) and Liss (1973), the chemical potential for reaction is less. Consequently, the baseline transfer velocity due to diffusion only must have been considerably lower compared to the baseline transfer velocities corresponding to equivalent enhancement factors measured in seawater (i.e. the other three sets of measurements in figure 7-14 ). Therefore the conditions for these two experiments must have been closer to those of a stagnant film, in which case we might expect the formula of Hoover and Berkshire (1969) to predict the measured enhancement quite well. For the other three sets of measurements in figure 7-14 , it is possible that conditions were closer to those of a surface renewal system. Keller (1994) used an iterative reaction-diffusion model to show that enhancement is slightly greater for a surface-renewal system, than an equivalent stagnant film system, so in these conditions the formula of Hoover and Berkshire (1969) might be expected to underpredict the measured enhancement (see also Section 1.5.4 and Section 7.7 ). However, this effect is relatively small, and unlikely to explain all of the observed discrepancies.

Wanninkhof and Knox (1996) also reported measurements of chemical enhancement made in several lakes, using a floating helmet to enclose a headspace above the lake water. (see also Section 1.5.5 ). In this case, unlike the laboratory tank experiments discussed above, they found that the Hoover and Berkshire formula significantly underpredicted the measured enhancement. Since all but one of these lakes had a high alkalinity (with pH up to 9), this discrepancy would easily be explained by a higher OH- reaction rate, and the uncertainty in this rate constant is also discussed in this paper. Close examination of the data also suggests that the discrepancy is slightly greater during evasion experiments, which might be attributed to the effect of air pCO2 on [OH-] in the microlayer, since the headspace was flushed with N2 during evasion experiments. However, there are not enough measurements to be certain of this interpretation.

7.8.2 Data from measurements by Law, Frankignoulle, and Watson, PML 1993

There remains one set of unpublished data which may also be of interest in this context, the gas exchange measurements made by Cliff Law, Michel Frankignoulle, and Andy Watson in a tank in Plymouth Marine Laboratory in 1992 and 1993. Although the results could not be explained at the time, they helped to inspire further curiosity about this topic, which led to the research presented here in this thesis. The conclusions reached above may now in turn help to explain some of the PML data. I thank the investigators for permission to include their data here.

Simultaneous measurements were made of SF6 and CO2 air-water exchange rates, in a mechanically stirred tank containing various different water samples and over a range of stirring speeds. For one set of measurements bovine carbonic anhydrase enzyme was added, as in Section 7.6 . The temperature varied slightly (typically 20C), but the Schmidt number ratio SF6 / CO2 was always 1.6. I have summarised all the data in figure 7-15 , in which the CO2 transfer velocity is plotted as a function of the SF6 transfer velocity (similar to figure 7-4 ), thus making measurements at different temperatures and salinities comparable. Lines showing the Sc-1/2 and Sc-1 relationships have also been plotted. The temperatures and water sources are indicated in the figure legend. The figure is split into three plots on different scales since the measurements cover a wide range of transfer velocities.

Although from this dataset, as for figure 7-4 , it is not possible to distinguish the exact "Schmidt number relationship", at high stirring speeds in freshwater (right hand plot) it seems to favour the surface renewal model, as expected. At lower stirring speeds, chemical enhancement is clearly important in seawater, as the CO2 transfer velocities lie well above the Sc-1 line, the maximum diffusion-only transfer rate which would correspond to the SF6 measurements. At the lowest transfer velocities corresponding to zero agitation (left hand plot), the transfer velocities for CO2 measured in seawater are clearly higher than their equivalents measured in freshwater, and those measured at a higher temperature are also higher as expected.

Particularly interesting, however, are the measurements made with added enzyme, which in one case raised the CO2 transfer velocity to 27 cm hr-1 whilst the SF6 transfer velocity was only 5.5 cm hr-1. I also noticed that the original data suggested a slight decline in enzyme activity over time. Most intriguing is the difference between influx and efflux measurements with added enzyme (centre plot). The efflux transfer velocities are much higher, by a factor of three in the zero-agitation case (5 cm hr-1 influx, 15 cm hr-1 efflux). Presuming that the water pCO2 was fairly constant and therefore efflux measurements corresponded to low pCO2 in the air phase, then this might be explained by the effect of the air pCO2 on the OH- concentration, as suggested by my own measurements (see Section 7.5.2 ). However, there is no significant difference between influx and efflux measurements without added enzyme.

7.9 Conclusions

Altogether about 200 measurements of uncatalysed chemical enhancement of the CO2 transfer velocity have been reported in this chapter, about 5 times more than previously reported in the literature. This is also the first systematic set of experiments investigating all the major factors contributing to the chemical enhancement of CO2 air-sea transfer, including the first investigation over a wide range of temperatures and the first practical demonstration of the importance of not only the water pCO2, but also to a lesser extent the air pCO2, factors ignored by most previous investigators. Nevertheless, in the real ocean, temperature variation will dominate over this air pCO2 effect.

Generally, it was found that the formula of Hoover and Berkshire (1969) underpredicts chemical enhancement, although qualitatively the effects of each controlling factor - stirring speed, temperature, pCO2, and added enzyme - is much as expected from the model predictions. The discrepancy increases at lower pCO2 and higher temperatures (see figure 7-11 ), which suggests that the OH- reaction rate constant used in the prediction may be too low. The slight increase in the discrepancy at higher stirring rates might possibly be attributed to the shift towards a surface renewal system, rather than a stagnant film as assumed in the formula of Hoover and Berkshire (1969). A similar discrepancy was observed among the previous sets of measurements of chemical enhancement reported in the literature ( figure 7-14 ), and may be explained by the same factors.

A longer summary of the results in this chapter is provided in the concluding chapter, section 10.1.

Continue to Chapter 8:
CO2 exchange rates with algae: results and discussion

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