Testing the proposed framework

To test the proposed framework outline in Section 4.2, a linear regression was performed with

the measured gas transfer velocities of CO2 and DMS and the right hand sides of Eq. 4.4

and Eq. 4.5 which will be referred to as Kε and Kb1χ, respectively. Note that the bubble

mediated transfer Kb1χ is solubility and gas dependent. The turbulent transfer component

is Schmidt number (diffusivity) dependent and in this case gas independent as the transfer velocities are all scaled to Sc = 660. Solving:

k = aKε+ bKb1χ (4.30)

gives a = 0.34 and b = 0.06. Results are shown in Figure 4.10a. Output of the COAREG algorithm for matching measurements are shown in Figure 4.10b allowing to evaluate the relative performance of the mechanistic model proposed by Eq. 4.1. Equation 4.30 is only able explain 45% of overall variability in the gas transfer velocities. The correlations to the

transfer velocities of CO2 and DMS individually are worse, particularly for DMS. In contrast

COAREG is able to reproduce 79% and 91% of the transfer velocities of CO2 and DMS,

respectively. Using the right hand side of Eq. 4.7, with the void fraction estimated based on

Eq. 4.24 instead of Kb1χ leads to very poor overall correlations (r

2 _{∼ 0.1) on account of the}

(a) (b)

Figure 4.10: The measured gas transfer velocities of CO2 (blue) and DMS (brick) measured during

HiWinGS, referenced to a Schmidt number of 660, plotted against (a) the model proposed in Eq. 4.1 and (b) the NOAA/COAREG.

4.5

Discussion

Several sources of uncertainties remain in the estimation of the breaking crest length distri- bution and the derived breaking statistics. As the cameras set up on the R/V Knorr were

set up looking at the breaking wave at an incidence angle of ∼65◦, the 3D nature of oceanic

waves may have led to parts of the breaking crest to be hidden from the cameras’ view. This was likely less of a problem in previous datasets as those acquired from the R/P Flip [Gemmrich et al., 2013; Sutherland and Melville, 2015] or from airborne imagery [Kleiss and Melville, 2010] in which camera were mounted to look straight down onto the ocean surface. The displacement of breaking waves with shorter wavelength than the underlying long waves is advected by than the orbital motion of long waves. In order to extract the phase speed of the breaking wave which is what Phillips [1985]’s spectral framework calls for, a Doppler correction has to be applied to the estimates derived from the imagery [see Gemmrich et al., 2013; Kleiss and Melville, 2010]. To do so requires knowledge of the long wave amplitude (a)

and frequency (ω) [Gemmrich et al., 2008]. Ideally, these should be measured locally such as by a Riegl altimeter located close or within the field of view of the camera. Such data was not available for the whole duration of the HiWinGS experiment, instead the correction was made based on spectral properties derived from the WAVEWATCH-III hindcast. It worth noting however, that the Doppler correction was shown to produce only modest changes to breaking crest length distribution [Gemmrich et al., 2013]. Another source of uncertainty arises from the limited field of view of the imagery which does not always allow to track the full life-cycle of a breaking wave. Estimation of the duration of a breaking event therefore relies on the assumption that it is proportional to the period of the breaking wave (see Eq. 4.21).

The formulations of the bubble air volume flux and void fraction contain several unknowns. The first unknown is the bubble cloud constant B was set to 0.1 in accordance to Deike et al. [2016, 2017]. B was determined from laboratory data from Duncan [1981], Lamarre and Melville [1991] and Deane and Stokes [2002] for time averaged volumes of air entrained

¯

V by a single breaking wave ranging several orders of magnitude (10−7 < ¯V < 10−1 m3).

The relationship however does not hold for ¯V < 10−5 m3 _{and it is unclear how these scale}

for open ocean conditions. The other unknown is the dissipation-weighted vertical mean

bubble plume rise velocity (Ub). A constant Ub of 10 cm s−1 was assumed in the analysis

presented above. It corresponds to the rise terminal rise velocity of clean bubble of radius of 450 µm according to Woolf and Thorpe [1991]. It is of the same order of magnitude as the rise velocity measured in a tank by [Asher et al., 1997] which average within the first 6

seconds around 8 cm s−1 in sea-water.

Deike et al. [2017] found the following relationship for the dissipation-weighted velocity Ub:

Ub ∼ h/τbr (4.31)

where h is the height of the wave at the time of breaking. While h is not measured directly it

factor has however yet to be established. Since

Hsws

is on the order of 0.1-8 m and τbr on the order of 1-10 s, a proportionality coefficient equal to

1, as suggested by Deike et al. [2017], would lead to rise velocities ranging from a couple of centimeters a second to over a meter a second which is clearly too high. Equation 4.31 allows to re-write Eq. 4.20 as:

Fa ∝ bef fB Hswsg 2 Z Λ(c)c5dc (4.32)

This form, however, offers no advantage over Eq. 4.20 in terms of uncertainties as the

proportionality coefficient remains unknown and leads to more scattered estimates of Kb1χ.

The functional form of the proposed model for k (Eq. 4.1) is a linear combination of parameterizations of transfer velocities arising from different processes. As such, it follows the form adopted by previous studies outlined in section 4.4.3. Unlike in COAREG, it does not take into account the air-side transfer and may therefore only be applicable to sparingly soluble gases. This could also explain its poorer performance for DMS. No distinction is made between the turbulence mediated transfer due to wave breaking and other processes as is done in Asher and Wanninkhof [1998]. This is because computing the dissipation using the effective breaking strength gives an integrated estimate of the turbulence in the upper

ocean at the given whitecap coverage. Indeed, bef f was determined from the combination of

breaking crest length distribution estimates and measures of the upper ocean turbulence that include both the wave breaking turbulence injection and the background turbulence [Zappa et al., 2016]. The form of the bubble mediated transfer used in Asher and Wanninkhof [1998] could not be used for this study because 1) a wider variety of solubility have to be considered to estimate the coefficients and there are more unknowns than gases available, and 2) accounts for wave breaking only via W . Asher and Wanninkhof [1998] developed their model using laboratory W which may have led to unrealistic estimates of both the bubble

and the wave breaking turbulence mediate transfers (W kb and W kT in Eq. 4.27) . However,

one could easily use Eq. 4.28 with the coefficients determined by Asher and Wanninkhof

[1998] to estimate Kb1χ in Eq. 4.30.

Both Woolf [1997], Woolf et al. [2007] and Goddijn-Murphy et al. [2016] assumed that the left and right hand side terms of eq. 4.5 are equal rather than proportional. In the NOAA-

COAREG algorithm [Fairall et al., 2011] the proportionality constant (BCOARE) was originally

tuned to the SO GasEx data and set to 1.8. Note that there are two tunable parameters in the NOAA-COAREG algorithm’s formulation of the water-side transfer coefficient: one for the bubble mediated and another for the turbulent molecular component. These empirical adjustement factors cannot be set independently and further depend on the choice of the W

parameterization used. The original value of BCOARE was determined using the Monahan and

O’Muircheartaigh [1980] W parameterization which we have shown to highly over estimate W at high wind speeds. Based on the HiWinGS data set, Blomquist et al. [2017] updated both

tuning parameters and found BCOARE = 3.8 provides better model results. The proportional

factor b found through regression in Section 4.4.4 is 0.06 is consistent with BCOARE given

that the bubble air volume flux estimated from the breaking crest length distribution is

56.74 times bigger than that assumed in COAREG. Indeed, 56.74 × 0.09 = 5 ∼ BCOARE

(BCOARE× 2450 W ∼ 0.06 Fa).

The proportionality coefficient a that multiplies Kε to give kε is very close to that

determined in previous studies. The study by Zappa et al. [2007] which is based data collected in a large tidal river, a macro-tidal estuary and from a coastal ocean site as well as in a “model” saltwater ocean at Biosphere 2 (Oracle, AZ USA) suggested a = 0.4. The first open

ocean verification of the functional form of kε suggest a = 0.12-1.46 depending on the depth

at which the turbulent kinetic dissipation rate measurements were taken and the approach used to extrapolate these measurements to the surface [Esters et al., 2017]. Note that in

this study different values of a were determined for CO2 and DMS as the transfer velocities

While fitting the transfer velocities separately may have led to improved fir statistics, it would defeat the goal of finding an unified model for both gases.

Although the assumed functional form follows the typical approach used in other process based models, it may not be entirely correct. Indeed, it is not the gas transfer velocities that should be combined linearly, but rather the bubble and turbulence mediated fluxes

(Fg = Fε+ Fb). The partial pressure of a gas within a bubble is higher than that in the

atmosphere due to the pressure caused by the surface tension of the bubble skin, which can be estimated from the Young–Laplace equation and hydrostatic pressure of the surrounding water. Estimation of this excess pressure a bubble requires knowledge of the bubble size distribution as a function of depth and time.

Chapter 5

Conclusion and Future work

5.1

Key Outcomes

The dependence of the whitecap coverage on wind and wave field characteristics was evaluated in Chapter 2 based on measurements acquired during the Southern Ocean Gas Exchange (SO GasEx) and the High Wind speed Gas exchange Study (HiWinGS) projects. High frequency ship-borne visible imagery were analyzed along side concurrent in situ eddy covariance flux

measurements and wave field observations complemented by a WAVEWATCH-III® hind

cast. The HiWinGS data set represents the first ship-borne measurements of W under

sustained wind speeds (U10N) of 25 m s−1, extending the validity range of wind and wave

dependent W parameterizations. Treating both datasets individually or as a combined dataset allowed critical assessment of the universality of the parameterizations obtained. A thorough literature review further provides a reference base for the results. There is remarkable inter-dataset agreement of the average dependence of W on wind speed alone and on wave-wind Reynolds numbers. The data further shows good agreement with two previous studies [Goddijn-Murphy et al., 2011; Salisbury et al., 2013] both for the wind-speed only and the wave-wind Reynolds number dependence of W . An important common trait of these studies is the use wind statistics that account for atmospheric stability effects.

While wind-speed-only models capture more of the observed W variability than Reynolds number parameterizations, the latter display is better inter-dataset agreement for both the current and the aforementioned previous studies. When expressing W in terms of wave field statistics only or wave age, larger scatter is observed and there is little agreement between SO GasEx, HiWinGS, and previously published data. The data also does not support the use of a multi-parameter model based on the combination of non-dimensional numbers that incorporate both wind and wave field variables. An interesting feature of the high wind

speed measurements is the apparent leveling off of W for wind speeds above 18 m s−1. The

data suggest that W does not exceed 10% when averaged over 20 minutes to 1 hour. Such a leveling off had been previously proposed based on a small data sample and more data is needed to corroborate these observations.

Having recognized the usefulness of wind and wave related Reynolds numbers for use in simple single parameter models of wave breaking related processes such as W , Chapter 3 explores their applicability to air-sea gas transfer. Four distinct open ocean data sets were analyzed: GasEx-98, SO GasEx, Knorr11, and HiWinGS. These data cover a wide range of

environmental conditions and the measured gas transfer velocity of CO2 differ considerably:

both SO GasEx and GasEx-98 display a cubic wind speed dependence, while the HiWinGS dataset displays a quadratic dependence. Expressing the gas transfer velocity, k as a function

of breaking and wave-wind Reynolds numbers, RB and RH, respectively, allowed to collapse

the three open ocean datasets. This is the first successful approach to reconcile diverging

CO2 gas transfer measurements. It highlights the necessity of taking into account sea state

when estimating the transfer of sparingly soluble gases such as CO2. In contrast, for DMS,

parameterizations based on wave-related Reynolds number or wind speed alone perform

comparably well. This is because DMS is more soluble than CO2 and bubble-mediated

exchange associated with wave breaking accounts for only a small fraction of the net air-sea transfer of DMS.

was put forward to model gas transfer in the open ocean in the presence of breaking waves. NOAA’s Coupled Ocean-Atmosphere Response Experiment Gas transfer algorithm was updated based on the whitecap coverage presented in Chapter 2 and the gas transfer

velocities of CO2 and DMS measured during HiWinGS. Shortcomings of other physically

based parameterizations were revealed. The proposed framework incorporates both the turbulence and bubble mediated transfer. It is based on various statistics determined from the breaking crest length distribution, such as the turbulent kinetic energy dissipation rate, the bubble volume flux and the void fraction. In the last decade multiple field campaigns have aimed to apply the spectral framework proposed by Phillips [1985] to quantify wave breaking properties. They have provided a robust link between the breaking crest length distribution to the turbulent kinetic energy dissipation rate. Only recently has a study extended the application of the Phillips [1985] framework allowing estimations of bubble cloud properties from the breaking crest length distribution. This study is based on DNS and laboratory observations and many sources of uncertainties remain. It was applied to the HiWinGS data but we currently lack the necessary field measurements to corroborate the results. Nevertheless, the novel mechanistic approach to model gas transfer shows promise and will be explored further.