William Bruch
email: william.bruch@mio.osupytheas.fr

Jacques Piazzola
email: jacques.piazzola@mio.osupytheas.fr

Hubert Branger

Alexander M J Van Eijk

Christopher Luneau

Denis Bourras

Gilles Tedeschi

Sea Spray Generation Dependence on Wind and Wave Combinations : A Laboratory Study

Keywords: Sea spray generation, Air-sea interaction, Wave slope variance, Friction velocity cubed

This paper investigates the effect of interacting winds and waves on the surface sea spray generation flux. To this end, the Marine Aerosol Tunnel Experiment (MATE2019) was conducted at the OSU-Pytheas large wind-wave tunnel facility at Luminy, Marseille (France), in June-July 2019.

A unique range of air-sea boundary conditions was generated by configuring the laboratory with four types of wave forcing and five wind speeds ranging from 8 to 20 m s -1 . The configurations included both young and developed

waves spanning a wave age (defined in terms of phase speed and friction velocity) range between 1.3 and 9.5. Sea spray concentrations were measured over the 0.1-47.5 µm radius range at different heights above water, and a fluxprofile method using [START_REF] Monin | Basic laws of turbulent mixing in the surface layer of the atmosphere[END_REF] theory allowed to estimate the sea spray generation flux from concentration profiles. Results show that the flux increases for increased wind-induced wave breaking, and the highest flux is found for steep and heavily-breaking wind-forced waves. Scaling analysis shows that the sea spray generation is best correlated with the wave slope variance (< S 2 >) for larger droplets (20 µm and above, assumed predominantly spume droplets generated by surface tearing). For smaller droplets (7-20 µm, presumed predominantly jet droplets generated by bubble bursting) highest correlation is found with a non-dimensional number combining < S 2 > and the friction velocity cubed u 3 1 Introduction Sea spray aerosols formed by the interaction between air and water represent a major component of the natural aerosol mass [START_REF] Jaenicke | Physical aspects of atmospheric aerosol in aerosols and their climatic effects;(eds) he gerbard and a deepak Jähne B, Riemer KS (1990) Two-dimensional wave number spectra of small-scale water surface waves[END_REF]Yoon et al., 2007) with a major role in the Earth radiation budget [START_REF] Mallet | Microphysical and optical properties of aerosol particles in urban zone during escompte[END_REF][START_REF] Mulcahy | Significant enhancement of aerosol optical depth in marine air under high wind conditions[END_REF]. In turn, the light scattering by sea spray aerosols is an important factor in the context of climate change [START_REF] Lewis | Sea salt aerosol production: mechanisms, methods, measurements, and models[END_REF]. Sea spray also has a significant impact on air quality, particularly in coastal regions where anthropogenic emissions are high [START_REF] Piazzola | Characterization of aerosols above the northern adriatic sea: Case studies of offshore and onshore wind conditions[END_REF][START_REF] Johansson | Global transport of perfluoroalkyl acids via sea spray aerosol[END_REF].

However, it remains difficult to numerically model these effects. Significant predictive uncertainties remain for sea spray aerosol in numerical models with significant biases observed for commonly used emission schemes (Tsyro et al., 2011;[START_REF] Chen | Sea salt emission, transport and influence on size-segregated nitrate simulation: a case study in northwestern europe by wrf-chem[END_REF][START_REF] Neumann | A comparison of sea salt emission parameterizations in northwestern europe using a chemistry transport model setup[END_REF]. Therefore, sea spray aerosol generation and subsequent transport in the atmosphere models need to be improved [START_REF] Canepa | Thoughts on earth system modeling: From global to regional scale[END_REF].

Sea spray can be produced both directly and indirectly from the water surface. Indirect generation is associated with the relatively small bubblemediated jet and film droplets produced by wave breaking, effective for wind speeds around 4 m s -1 and above [START_REF] Blanchard | The electrification of the atmosphere by particles from bubbles in the sea[END_REF][START_REF] Spiel | The sizes of the jet drops produced by air bubbles bursting on sea-and fresh-water surfaces[END_REF]. The transition from film to jet droplet dominance is thought to occur at radii 2 -4 µm [START_REF] Cipriano | Bubble and aerosol spectra produced by a laboratory breaking wave[END_REF]Woolf, 1997) with jet droplets dominating over the 2 -20 µm range and sometimes reaching 50 µm or more [START_REF] Newitt | Liquid entrainment 1. the mechanism of drop formation from gas vapour bubbles[END_REF][START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF]. The direct sea spray generation mechanisms activated at wind speeds higher than 10 -12 m s -1 [START_REF] Monahan | A model of marine aerosol generation via whitecaps and wave disruption[END_REF][START_REF] Jones | Production velocity of sea spray droplets[END_REF] consist of surface-tearing of larger (radius r > 20 µm) spume droplets that are directly ejected into the air flow.

The direct generation mechanisms have proven to be elusive. [START_REF] Anguelova | Spume drops produced by the wind tearing of wave crests[END_REF] noted the tearing of spume drops at the wave crests by the wind, and found spume droplet generation to be strongly related to the whitecap coverage. On a microphysical scale the bag breakup of small canopies of water produced by wind surface friction at the wave crests is a potential mechanism for spume droplet generation [START_REF] Mueller | A sea state-dependent spume generation function[END_REF]Veron et al., 2012;Troitskaya et al., 2018). All in all, little is known about the generation of particles of radii > 20 µm (Veron et al., 2012;Veron, 2015). A better pa-rameterization of the droplet generation flux and transport over this range is urgently needed, since a major portion of the total volume of sea spray droplets is thought to be within the 10-200 µm radius range, as stressed by authors such as Andreas (1992).

The sea spray flux or sea spray generation function (SSGF) is known to depend on numerous environmental parameters such as the wind and wave fields (De Leeuw, 1986;[START_REF] Iida | A new expression for the production rate of sea water droplets on the sea surface[END_REF][START_REF] Smith | Marine aerosol concentrations and estimated fluxes over the sea[END_REF], the sea surface temperature [START_REF] Mårtensson | Laboratory simulations and parameterization of the primary marine aerosol production[END_REF], and the composition and salinity of the seawater [START_REF] Sellegri | Surfactants and submicron sea spray generation[END_REF][START_REF] Mehta | A laboratory investigation of spume generation in high winds for fresh and seawater[END_REF]. Although wind speed alone was traditionally used to parameterize the aerosol generation -cf. the SSGFs of [START_REF] Monahan | A model of marine aerosol generation via whitecaps and wave disruption[END_REF]; [START_REF] Smith | Marine aerosol concentrations and estimated fluxes over the sea[END_REF]; Andreas (1998) -there is increasing evidence that this is not sufficiently accurate, and additional environmental conditions have to be taken into account, wave parameters especially. Various authors have also considered scaling droplet generation with non-dimensional numbers such as wave age [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF][START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF], or the windsea Reynolds number R B [START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF][START_REF] Ovadnevaite | A sea spray aerosol flux parameterization encapsulating wave state[END_REF]Troitskaya et al., 2018). The wave age is defined as the ratio between the wave phase velocity c p and a wind parameter (for example the wind friction velocity u * ), and is generally used to describe wave-field developement and wave-wind equilibrium. R B , first introduced by [START_REF] Toba | A parameter describing overall conditions of wave breaking, whitecapping, sea-spray production and wind stress[END_REF] as u 2 * /(ν a ω p ) with the air kinetic viscosity ν a and the windsea spectrum peak angular frequency ω p , thus describing turblence at the wind-wave boundary. The role of wave breaking mechanisms on generation has also been a focus of study with the use of whitecap coverage to scale film, jet [START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF] and spume droplet generation [START_REF] Anguelova | Spume drops produced by the wind tearing of wave crests[END_REF]. In a similar fashion, wave energy dissipation -considered proportional to u 3 * (the third power of the friction velocity u * ) by several authors -has also been considered for the study of droplet and bubble generation [START_REF] Newell | Rough sea foam[END_REF]Zhao and Toba, 2001;[START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF][START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF][START_REF]A review of the sea spray generation function for the open ocean[END_REF][START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF].

Of the different wave parameters used to scale sea spray generation, the wave slope has not yet been considered. Nevertheless, it is an interesting candidate because of its strong relation to wave breaking [START_REF] Stokes | Supplement to a paper on the theory of oscillatory waves[END_REF][START_REF] Duncan | An experimental investigation of breaking waves produced by a towed hydrofoil[END_REF][START_REF] Ramberg | Laboratory study of steep and breaking deep water waves[END_REF], whitecap production [START_REF] Banner | Multiscale measurements of ocean wave breaking probability[END_REF][START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF], and therefore to sea spray bubble-bursting and surfacetearing generation mechanisms. The wave slope, however, is also thought to modulate the air flow at the wave crest (Veron, 2015;[START_REF] Richter | Turbulent transport of spray droplets in the vicinity of moving surface waves[END_REF][START_REF] Husain | Boundary layer turbulence over surface waves in a strongly forced condition: Les and observation[END_REF], which is of crucial importance for air-sea momentum transfer and surface tearing mechanisms. Finally, the relationship between the wave slope variance and the wind speed at the wind-wave boundary is relatively well documented [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF][START_REF] Plant | A relationship between wind stress and wave slope[END_REF]Vandemark et al., 2004;[START_REF] Bringer | Revisiting the short-wave spectrum of the sea surface in the light of the weighted curvature approximation[END_REF][START_REF] Lenain | Airborne measurements of surface wind and slope statistics over the ocean[END_REF].

With the advantage of easier instrumentation and control over important environmental parameters compared to the complexity of the field, the laboratory has proven to be a valuable alternative to the field (open ocean) for the study of wave-wind boundary processes and sea spray generation [START_REF] Toba | A parameter describing overall conditions of wave breaking, whitecapping, sea-spray production and wind stress[END_REF][START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF][START_REF] Ortiz-Suslow | A laboratory study of spray generation in high winds[END_REF]Troitskaya et al., 2018). Therefore, we conducted a series of experiments in the wave-wind tunnel at the OSU Pytheas (Observatoire Sciences de L'Univers) Ocean-Atmosphere laboratory in Luminy, France. In the field, a wide range of wind and wave combinations can be encountered. To reproduce a similar range in environmental conditions the laboratory experiments also included a unique range of wind and wave conditions, which, to the knowledge of the authors, is the most extensive range ever used for studying the SSGF in a laboratory configuration. The aim is to develop a universal wind and sea state-dependent SSGF applicable for radii typical of jet and spume droplets. To this end, from June to July 2019, sea spray aerosol size concentrations were measured for a total of twenty wind and wave combinations as part of the Marine Aerosol Tunnel Experiment (MATE2019). The experiment is described in Sect. 2 Methods

The wind-wave tunnel

The UMS Pytheas ocean-atmosphere interactions facility at Luminy (Marseille, France), schematically represented in Fig. 1, consists of a water tank with a wind tunnel on top of it. The facility currently allows the use of fresh water only. The water tank is 40 meters long, 2.6 meters wide, and has a wave-dissipating beach at the downwinde end to avoid wave reflection. On the upwind end, the facility is equipped with a programable submerged pistonlike wavemaker located at the bottom of a cavity below the air tunnel and controlled by an electrohydraulic motor. Wave properties such as amplitude, frequency and slope can therefore be selected. Waves can attain amplitudes reaching 15 cm, approximately. The air channel ceiling is slightly inclined to the fetch to avoid the airflow acceleration and the related longitudinal pressure gradient generated by the thickening of the wall and water surface boundary layers [START_REF] Coantic | Windwater tunnel simulation of small-scale ocean-atmosphere interactions[END_REF]. To reduce turbulence as the air flow encounters the water surface, a thin buoyant sheet is placed at the surface of the water at the entrance of the tunnel. The wind speed in the facility is adjustable, with winds reaching 15 m s -1 , approximately. Glass walls on either side of the laboratory made it possible to monitor the experiment at the location of the instruments (given below). For the experiments in June-July 2019, the water depth was set to 90 cm, leaving 150 cm between the water surface and the ceiling of the wind tunnel.

As schematically represented in Fig. 1, instruments used for the measurements of air, water, wind and wave characteristics were placed at the 27.2 meter fetch mark. A sensor positioned 81 cm above the mean water level (MWL) was used to measure air relative humidity (RH) and temperature (T a ). Vertical profiles of horizontal wind speed and air temperature between 15 and 66 cm above MWL were obtained using sensors mounted on a telescopic arm. The water temperature was measured at both 20 and 60 cm depth beneath the MWL.

A camera with 60 Hz sampling frequency placed on the tunnel ceiling allowed estimating the whitecap coverage during the experiments from color images.

Though not schematically represented in Fig. 1 a higher-frequency 128 Hz camera was used to film through the glass wall of the tunnel for monitoring purposes only. Finally, at the 30 meter fetch mark, vertical profiles of the sea spray number concentration were measured using two particle probes mounted onto a vertically displaceable frame.

Wave generation and characterisation

The water surface elevation was measured by an array of two calibrated capacitance wave gauges placed at the 27.2 meter fetch mark. The sample frequency for the wave gauges was 256 Hz allowing to sample a wide range of wave surface elevation and slope frequency spectra. The sensors were aligned orthogonally to the general wave direction, and were placed 1 cm from each other to ensure accurate wave slope measurements.

In the present study, four types of waves were generated. Five different wind speeds between 8-20 m s -1 were applied over each wave type, in a total of 20 laboratory wind-wave configurations. A first type of waves was generated solely by the wind, resulting in pure wind waves. The other three types of waves were generated using the piston wavemaker and are referred to as short wave forcing (peak frequency f p = 1.3 Hz and wavelength λ = 0.92 m), intermediate wave forcing (f p = 1.1 Hz and λ = 1.29 m), and long wave forcing (f p = 0.8 Hz and λ = 2.4 m). These conditions were selected to ensure that near-equilibrium with the overlying wind field was either never met, or met at different wind speeds.

Deep water conditions are theoretically confirmed for all types of forcing except the long wave case. This is also the wave type that is least forced by the wind and can be considered representative of the wind over swell condition that can be found in the field. Together, the 20 tunnel wind and wave combinations span a range of wave ages cp u * between 1.3 and 9.6.

The wave sensor array provides several parameters that are useful to relate the wave properties measured at the 27.2 m fetch mark to the sea spray concentrations measured at the 30 m fetch mark. The significant wave height H S is determined using:

H s = 4σ η
where σ η is the standard deviation of the surface elevation (η) time series measured by the wave sensor array.

The wave slope variance < S 2 > is considered equal to the wave mean square slope (MSS). It is calculated from the time series of the wave slope S, for wavelengths λ > 1 cm (strong majority of waves dominated by gravity).

The use of classical Fourier analysis allows to determine the peak frequency f p from the wave elevation energy spectra. Finally, the wave phase speed c p is determined from the phase shift between the wave gauges as the waves propagated along the wave sensor array.

Whitecap measurements

To quantify the wave breaking, the whitecap coverage W(%) is estimated from video colour images taken by a camera mounted at the tunnel ceiling (cf. Fig. 1). The system takes images at 60 Hz frequency with dimensions 2704 × 2028.

These images are spatially referenced to allow to estimate the approximate surface area of each pixel. To identify the whitecaps, a separation method is used that applies a greyscale conversion and a subsequent intensity threshold to the image. The surface areas of the pixels above threshold are subsequently added and divided by the total image surface area for an estimate of the whitecap surface coverage W(%). Using a time series of images, it was found that W(%) estimates converge to an average value within approximately 120 frames. This method for whitecap estimation is commonly used (e.g. [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF]; [START_REF] Lenain | Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer[END_REF]; [START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF]), and although the selection of the intensity threshold may be subjective, we expect that our whitecap coverage estimates capture the relative amount of wave breaking induced by various wind and wave conditions.

Wind measurements

A hot film wind sensor (E+E Elektronik, Langwiesen, Austria) mounted onto a telescopic arm was used to measure vertical profiles of horizontal wind speed U at the 27.2 meter fetch mark (cf. Fig. 1). This sensor was calibrated against a reference sonic anemometer on several occasions during the experiments. Some subsets of wind data obtained at 15 cm of the MWL were eliminated from the dataset to avoid erroneous measurements caused by large droplets impacts on the hot film sensor. To ensure representative wind statistics, convergence of the wind speed time-averages was achieved for each height z along the U(z)

profiles, with averages spanning over 20 to 80 minutes in accordance with the sea spray aerosol sample durations.

The wind speed reference used in this study is U 10 , i.e. the wind speed at 10 meters above MWL. Assuming a logarithmic wind profile and neutral conditions, [START_REF] Monin | Basic laws of turbulent mixing in the surface layer of the atmosphere[END_REF] scaling allows evaluation of U 10 (m s -1 ) and the friction velocity u * (m s -1 ) from the measured U (z) profile values U(z):

U (z) = u * k ln( z z 0 ) (1)
where k = 0.4 the von Kármán constant, z is the measurement height above MWL, and z 0 the roughness length. The latter is retrieved by extending the wind profile with data from the more elevated part of the wind profile that is not significantly affected by the wave field. During the experiments, z 0 estimates varied between 0.2 and 2.5 mm. in the laboratory for reference wind speeds U 10 of 12 m s -1 or more, thereby signifying that the air flow in the boundary layer is in a fully turbulent regime and windsea breaking occurs [START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF].

Sea spray aerosol measurements

The measurement of sea spray in the tunnel was carried out using two CSASP [START_REF] Holmes | Turbulence, Coherent Structures, Dynamical Systems and Symmetry[END_REF][START_REF] Pope | Turbulent Flows[END_REF], with a very weak divergence or convergence zone along the middle of the width of the tunnel. As it is usually done in the IRPHE wind-wave facility, the probes were slightly shifted away from the middle axe line of the facility. For all laboratory configurations, both aerosol probes were temporarily positioned at the tunnel entrance to verify that no background aerosols entered the tunnel, which implies that all particles detected at the 30 m fetch mark are solely produced over the upwind 30 meter fetch length.

After generation at the water surface, the hygroscopic aerosols adjust their size to the ambient humidity and temperature of the air flow. This process is different for salt water than for the fresh water used in the tunnel, as freshwater droplets can evaporate more quickly and completely than saltwater droplets that reach an equilibrium size (e.g. [START_REF] Pruppacher | Microphysics of clouds and precipitation reidel[END_REF]; Andreas (1989); [START_REF] Fairall | Modelling the fate and influence of marine spray. Modelling the Fate and Influence of Marine Spray[END_REF] However, this assuption will fail if the freshwater droplets are relatively small or have long residence times before reaching the aerosol probes, as evaporation can become substantial (Veron, 2015). To avoid such evaporation effects over the length of the wave-wind facility, only radii greater than 7 µm are considered for the source functions proposed in this study (see Sect. 5) in accordance with [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF].

Aerosol concentrations are often expressed as number concentrations dN/dr (cm -3 µm -1 ; the number of particles N of a given radius r measured per unit air) or volume concentrations dV/dr (the volume for a given radius measured per unit air). In this study, we use mostly number concentrations, with a single exception (Sect. 4, Fig. 6). The conversion from number to volume concentrations (cm -3 cm -3 µm -1 ) is made by assuming that the droplets are spherical:

dV dr = dN dr 4 3 πr 3 (2)
As discussed above, we may consider that the freshwater droplet distributions measured in the tunnel are analogous to salt water droplets at RH = 80%.

Since the processes that generate the freshwater droplets in the tunnel are the same as for sea spray in the field, we will denote the droplets in the tunnel as sea spray in the remainder of this paper.

3 Tunnel wave and wind results

Wave measurements

Table 1 characterises all 20 laboratory configurations in terms of the significant wave height H s , the wave slope variance < S 2 >, the friction velocity u * , and the whitecap coverage W(%). The table shows that the wind field forces the wave field, resulting in increased wave height, wave slope variance and breaking, as evidenced by H s , < S 2 > and W(%). In some cases however, significant wave height and wave slope decrease for high wind speeds as wave energy dissipation by wind-induced breaking becomes temporarily greater than the energy input from the wind to the waves. This is especially the case for the intermediate wave forcings for wind speeds increasing from 16 to 18 m s -1

(Table 1) where wave breaking was especially high. Further evidence of the forcing of the wave field by the wind is the decrease in f p for increasing wind speed observed at the 27.2 fetch mark, with the exception of the long wave forcing which conserves the 0.8 Hz frequency prescribed by the wavemaker throughout the experiments. The momentum transfer from the wind to the waves is therefore relatively low for the long wave forcing in comparison to the other wave forcings, resulting in relatively low U(z) gradients (Fig. 2) and whitecap coverages W(%) (Table 1).

Table 1 Wave-wind boundary characteristics for the different laboratory configurations: significant wave height Hs (cm), wave slope variance (< S 2 >), friction velocity u * (m s -1 ), wave phase speed cp (m s -1 ) and whitecap coverage W(%) Wind 3.2 0.026 0.32 0.78 0 This non-linear behaviour of the parameters listed in Table 1 highlights the importance of correctly understanding the boundary processes, such as the state of wind-wave equilibrium. Though not shown here, f -5 and f -4 spectral shapes were identified for the individual wave spectra, but it proved difficult to quantify the wave-wind equilibrium this way. We therefore abide by the heuristic idea that when the phase speed c p is greater than the overlying wind speed (e.g. the friction velocity u * ) then the underlying waves are no longer forced by the wind field. Thus we use the wave age defined as c p /u * to quantify the wind-wave equilibrium.

Forcing U 10 = 8 m s -1 U 10 = 12 m s -1 H s < S 2 > u * c p W(%) H s < S 2 > u * c p W(%)
Our laboratory configurations yield wave age c p /u * values ranging from 1.3 to 9.6 where the higher values correspond to the long wave forcing combined with the lowest wind speed (8 m s -1 ). These values are generally lower than those recorded in the field because of the comparatively much shorter fetch length in the laboratory.

Whitecap measurements

As previously noted, several studies have related whitecapping to the generation of film, jet and spume droplets. For comparison, it is therefore important to ascertain whether the whitecap production in the laboratory differs from the field. To this end, we use data collected during the EMMA campaign which took place in Toulon-Hyeres bay, yielding wave, wind and whitecap coverage data for wind speeds in the 10 -18 m s -1 range and wave ages c p /u * in the 14 -28 range [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF]. We compare our laboratory whitecap coverage to that measured in fetch-limited field conditions during EMMA, using a similar image-processing technique with intensity threshold separation (data available in [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF]). Laboratory data obtained at 8 m s -1 wind speed are not included in this comparison because the relatively small amount of wave breaking may reduce the accuracy of the whitecap coverage estimates.

Multiple independent scaling studies have proven R B to be a successful scaling tool for W(%) (Zhao and Toba, 2001). However, the evaluation of R B requires the wave peak frequency ω p , which differs significantly between the laboratory and the field. The relatively short fetch in the laboratory and the wavemaker settings lead to shorter wavelengths and a relatively greater number of wave crests per unit area [START_REF] Mueller | A sea state-dependent spume generation function[END_REF]. To allow a better comparison between the laboratory and the field, the W(%) value are therefore normalised by the wave peak frequency. Figure 3a shows the relationship between the normalised W(%) and R B . The data from both the laboratory (+) and the field ( ) display a very similar trend yielding nearly identical slopes when fitted by a power law. In absolute magnitude there is a factor 1.5 difference between the laboratory and the field with the lower W(%) values for the laboratory. A possible explanation is the absence of surfactants and salt in the laboratory, which in the field contribute to whitecap formation and increase whitecap lifetime [START_REF] Callaghan | Observed variation in the decay time of oceanic whitecap foam[END_REF]. Consequently, the lower rate of whitecap formation and lifetime in the laboratory may signify that our whitecap coverage is more representative for the process of active wave breaking, which we refer to as the wave breaking coverage. A further comparison between the laboratory and the field is obtained by scaling W(%) to the wave slope variance < S 2 >. In this case, W(%) does not need to be normalised by the peak frequency as the wave slope variance < S 2 > integrates a very large part of the wave frequency spectrum and corresponding wave slopes, unlike the peak wave characteristics required for windsea Reynolds number R B . For the EMMA campaign data [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF], < S 2 > is estimated from the measured wind speed data [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF]) : < S 2 >= 0.003 + 5.12 × 10 -3 U 12.5 ± 0.004

(3)

where the wind speed U 12.5 is calculated from the EMMA campaign U 10 measurements using classical [START_REF] Monin | Basic laws of turbulent mixing in the surface layer of the atmosphere[END_REF] theory. It is worth noting that Eq. 3 [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF] was determined from airborne observations of sun glitter resulting in the contribution of a wide range of wave scales including non-breaking waves, which is to some extent comparable to the wide range of wavelengths included in the laboratory wave slope variance.

Figure 3b presents the W (%) scaling by < S 2 >, demonstrating that laboratory (+) and field ( ) data almost overlap. The laboratory data is well fitted (R 2 = 0.75) by a the power law:

W (%) = 6.02 × 10 3 < S 2 > 3.025 (4)
The good fit of this power law to field data (Fig. 3b) suggests that Eq. 4 may have a validity range extending to both the laboratory and the field. The strong correlation between < S 2 > and W (%) suggests that the wide range of the wave slope spectrum inherent to < S 2 > allows to separate breakers and non breakers. This corroborates conclusions from a north-Pacific field campaign [START_REF] Schwendeman | Observations of whitecap coverage and the relation to wind stress, wave slope, and turbulent dissipation[END_REF], where the wave slope variance amongst the different existing slope parameterizations is found to scale best with W (%) by considering the slopes of the shorter waves, thought to be important for whitecap production. In contrast, the scaling of whitecap coverage with wave steepness (often written as H/(2λ)) has proven difficult [START_REF] Schwendeman | Observations of whitecap coverage and the relation to wind stress, wave slope, and turbulent dissipation[END_REF] or even unsuccessful [START_REF] Holthuijsen | Statistics of breaking waves observed as whitecaps in the open sea[END_REF].

4 Laboratory sea spray results

Sea spray aerosol size distribution spectra

Figure 4 presents two typical size distributions as measured in the laboratory.

The figure shows the sea spray distributions for wind speeds U 10 = 16 m s -1

and U 10 = 20 m s -1 , measured 55 cm above MWL and during the intermediate wave forcing. For convenience, polynomial functions (solid and dashed lines for 16 and 20 m s -1 , respectively) have been fitted to the distributions. The polynomial functions show that the number concentration of all but the smallest particles increases with increasing wind speed. This behaviour is observable at any height above MWL and for all four types of wave forcing. The concentration increase is consistent with the increased W(%) for increasing wind speeds (cf. Table 1) and hence, the enhanced droplet generation. Furthermore, the size distribution shows a relative abundance of particles with sizes around 1 and 10 µm. This corroborates the established size ranges of film and jet droplets, respectively. The droplet spectra for larger radii change markedly at wind speeds lower than 12 m s -1 , where number concentrations for r > 15 µm are negligible. This corroborates the assumption that these larger droplets are predominantly spume droplets, and that their generation mechanism activates at wind speeds around 12 m s -1 . This was confirmed by our high-speed video footage, which revealed surface tearing and bag break-up only for wind speeds higher than 12 m s -1 . In conclusion, the above observations suggest that similar droplet generation mechansisms are active in the laboratory and in the field. forcing, but remains very small with a maximum value approaching 10 -5 cm -3

µm -1 at z = 0.35 m. As the environmental conditions were stationary during the measurements for each individual laboratory configuration, this greater variability (standard deviation) in near-surface concentrations could be associated with wave-induced and phase-locked modulation of the airflow, which can lead to flow separation. These mechanisms have recently been observed in microphysical laboratory experiments [START_REF] Buckley | The turbulent airflow over wind generated surface waves[END_REF][START_REF] Richter | Turbulent transport of spray droplets in the vicinity of moving surface waves[END_REF][START_REF] Husain | Boundary layer turbulence over surface waves in a strongly forced condition: Les and observation[END_REF]. Whether this modulation effect also caused stronger fluctuations in the near-surface sea spray concentrations in the laboratory remains hypothetical as the maximum sample frequency of the particle probes does not allow to resolve these fluctuations assumed to occur at frequencies approaching f p or higher. alone results in the lowest concentrations (dashed curve) and a distribution that strongly decreases for r > 20 µm. The three wavemaker forcings all re-sult in higher volume concentrations than the wind forcing: the order long, short and intermediate for increasing concentration corresponds well with the increase in whitecap W (%) and wave slope variance < S 2 > for these three types of forcing (cf. Table 1), and hence, the production of droplets.

A literature survey for comparison laboratory data identified the SPAN-DEX dataset [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF] as the most suitable. These authors also used a wind-wave interaction tunnel with freshwater and a mechanical wave paddle for the wave forcings. The triangles in Figure 6 (connected by the thin dashed line) represent the volume concentrations reported by [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF], obtained at 31.5 cm height for 16.7 m s -1 wind speed (corresponding to their nominal forcing) measured at 40 cm above MWL (roughly equivalent to 28 m s -1 at U 10 ), 1.36 Hz peak wave frequency (same as our short wave forcing), and friction velocity u * = 1.44 m s -1 . Though the wind speed and friction velocity were 50 % greater than for the present study, the SPANDEX volume concentrations are of the same order of magnitude as our wave-forced data (cf. Fig. 6). This unexpected overlap may be explained by experimental differences such as tunnel dimensions (more than three times the height between the water surface and the tunnel ceiling during MATE2019 compared with SPANDEX) leading to possibly different boundary effects. Another explanation maybe also be related to the different wave amplitudes between both experiments (≈ 5 times greater in the present study) resulting in shorter distances between the probes and the wave crests in the case of MATE2019 despite comparable sample heights in the present comparison.

4.2 Scaling parameters for the sea surface sea spray generation

In the previous section we have demonstrated that the sea spray concentration depends on properties of both the air flow and the sea state. To bridge these two domains, we will scale the sea spray surface generation using nondimensional numbers representing the physical processes on the wind and wave side of the wave-wind boundary. The non-dimensional numbers determined from the set of parameters (u * , ω p , c p , H, λ, X, g, ρ a , ρ w , ν a , ν w , Γ ), where u * is the friction velocity, ω p is the wave peak angular frequency, c p is the wave phase speed, H is the wave height, λ is the wavelength, X is the fetch length, g is gravitational acceleration, ρ a and ρ w are air and water densities respectively. Furthermore, ν a and ν w are air and water kinematic viscosities, respectively, and Γ is the water surface tension.

As a first step, we focus our attention on the air kinematic viscosity. Several studies have indicated that water droplets and water vapor can alter the air viscosity, but the effect on the momentum flux is thought to be small, less than 3% [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF]. We therefore consider the non-dimensional groups ν a /ν w and ρ a /ρ w to be constants. We also expect the surface tension Γ to be constant and remain negligible due to the relatively long wavelengths considered here (strong majority of gravity waves). Then, we can express the sea spray aerosol generation flux as a function of the non-dimensional numbers that are the inverse wave age (= u * /c p ), the windsea Reynolds number R B (= u 2 * /(ν a ω p ), determined from both wind (u * ) and peak wave (ω p ) characteristics), and the wave steepness. In continuity with the previous sections, the wave slope variance < S 2 > is used instead of the wave steepness (H /2λ).

The inverse wave age is preferred to the wave age out of physical coherence, as the former is expected to increase for increasing R B and < S 2 >. We create a fourth scaling parameter by combining the inverse wave age, the windsea Reynolds number and the wave slope variance:

P S = R B < S 2 > cp u * -1
which, considering the deep water dispersion relation c p = g 2π T (T the wave period), reduces to:

P S = u 3 * ν a g < S 2 > ( 5
)
where P S , adding to the P threshold for the activation of droplet and bubble formation at the water surface [START_REF] Newell | Rough sea foam[END_REF][START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF], describes the wave slope variance-modulated wind energy input to the waves. This number combines two experimental quantities, < S 2 > provided by the wave sensor array, and u 3 * provided by the wind speed vertical profiles, providing information on the wind-dependent sea state and wind-induced dissipation, respectively. This allows to study air-sea interaction processes from a multiscale point of view, assuming that the smaller and larger scale wind and wave components significantly contribute to boundary layer mechanisms responsible for sea spray generation.

Scaling of the sea spray generation

This section discusses the scaling of the sea spray by the four scaling parameters introduced above. For this, we use the concentrations measured 35 cm above the MWL, i.e., the lowest height of our aerosol samplers, assumed the most representative of the generation flux and the least affected by sizedependent vertical dispersion effects similar to Wu (1993) and Andreas (1998).

The scaling relationships are presented for droplet radii of 7.5 µm (Fig. 7) and 25 µm (Fig. 8), which are considered representative of the behaviour of the droplets in the 7-20 µm and the 20-35 µm size range, respectively. In this man- [START_REF] Lafon | Whitecap coverage in coastal environment for steady and unsteady wave field conditions[END_REF]. Specifically, for the larger 25 µm particles (cf. Fig. 8a) such a peak can be related to droplet ejection microphysics as younger steeper waves induce airflow separation [START_REF] Reul | Air flow structure over shortgravity breaking water waves[END_REF], thought to play an important role in droplet ejection from the wave crests [START_REF] Mueller | A sea state-dependent spume generation function[END_REF]Veron et al., 2012;[START_REF] Richter | Turbulent transport of spray droplets in the vicinity of moving surface waves[END_REF]. We now turn our attention to Figs. 7b and8b, which present the windsea Reynolds number R B as a scaling parameter for the sea spray concentration.

The Reynolds number has proven to be strongly related to whitecap coverage and wave breaking (cf. Sect. 3.2) as well as sea spray concentrations for wind waves especially [START_REF] Iida | A new expression for the production rate of sea water droplets on the sea surface[END_REF][START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF]Troitskaya et al., 2018). This seems confirmed by the overall (solid black line) trend line in Figures 7b and8b, which is relatively close to the data corresponding to wind waves.

The data show less spread than for scaling with wave age, and most types of forcing follow the overall trend, despite systematic differences in droplet concentrations. The overall fit quality for the 7.5 µm particles amounts to R 2 = 0.49 and similar values were noted for other radii in the 7-20 µm range.

The windsea Reynolds number R B does not perform as well over the 20-35 µm radius range, as demonstrated by R 2 = 0.31 for the 25 µm particles (Fig. 8b). The better performance for smaller radii can find explanation in the information contained in R B about the flow velocity and more specifically the turbulence intensity at the wind-wave boundary layer. We expect this to be key for the smaller droplets that are more subject to turbulent diffusion and less affected by gravitational settling than the larger spume droplets (e.g.

Andreas et al. (2010)).

The scaling of spray concentrations by the wave slope variance < S 2 > is presented in Figs. 7c and8c. The most striking feature of these figures is the bahaviour for the intermediate wave forcing, which yields decreasing aerosol concentrations with < S 2 >, whereas the other types of forcing all yield increasing concentrations. This behaviour can be traced back to the earlier observation (Sect. 3.1) that the intermediate forcing yields a decrease in significant wave height with increasing < S 2 > (and a less clear increase of W (%), which was attributed to (exceptionally) efficient wave energy dissipation that for the other three types of forcing. This contrasting behaviour for the intermediate forcing causes the overall fit quality for smaller particles to be less than when scaling with R B (R 2 of 0.34 versus 0.49). Over the 20-35 µm range however, the wave slope variance offers the best scaling performance for all four scaling parameters (R 2 = 0.55). The wave slope variance thus appears well adapted for the scaling of near-surface spume droplet concentrations (Fig. 8c). Finally, we scale near-surface concentrations as a function of the combination of non-dimensional numbers u 3 * νag .< S 2 >. Results show that the combined number P S scales the particle concentrations better than either the wave age or the windsea Reynolds number. In comparison with the wave slope variance the combined number performance is better over the 7-20 µm range (R 2 = 0.60 versus R 2 = 0.34 for r = 7.5 µm), but about equal for particles greater than 20 µm (R 2 = 0.5 versus R 2 = 0.55 for r = 25 µm). However, the combined number results in similar trends for all four types of wave forcing, including the intermediate forcing (compare panels c and d). This suggests that the combined number is capable of scaling sea spray generation for a wider range of environmental conditions than < S 2 > alone. We therefore conclude that the combined number is well suited for the simultaneous scaling of breaking wave (bubble bursting) and surface tearing mechanisms.

Combined scaling parameters

Our fourth scaling parameter is similar to the non-dimensional numbers suggested by [START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF] and [START_REF] Lenain | Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer[END_REF]. The latter authors combine the wave steepness, the wave age and a Reynolds number depending on the significant wave height H s (R H = Hsu * ν ). A similar number was also used by [START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF] for the scaling of whitecap coverage.

Preliminary laboratory studies on the scaling of sea spray concentrations in the 7-35 µm radius range by the number proposed by [START_REF] Lenain | Evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer[END_REF] suggest that the scaling does not significantly change when substituting R H with R B . However, significantly better scaling is achieved when the wave steepness (H /2λ) is replaced with < S 2 >.

As mentioned in the introduction, u 3 * has proven to be a worthy candidate to scale wave energy dissipation and input from the wind field necessary for bubble and droplet production [START_REF] Newell | Rough sea foam[END_REF]Zhao and Toba, 2001;[START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF][START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF][START_REF]A review of the sea spray generation function for the open ocean[END_REF][START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF]. Though not detailed in the present scaling analysis, a preliminary study allowed to evaluate the scaling performance of u 3 * for near-surface concentrations. Results reveal similar performance to the combined number with good scaling results over the 7-20 µm range (R 2 = 0.56 for r = 7.5 µm) with less satisfactory performance for larger droplets (R 2 = 0.23 for r = 25 µm). Associating scaling performances of u 3 * (best for r < 20 µm) with < S 2 > (best for r > 20 µm) in the combined number (Eq. 5) allows good scaling of sea spray aerosol generation over the 7-35 µm range, suggesting that the combination of both allows to scale production in a wider range of conditions than < S 2 > alone.

The laboratory generation flux

In this section, we will consider a suitable scaling parameter for the spray generation flux (dF/dr ). We will derive this flux from the sea spray concentration profiles measured in the laboratory (cf. Fig. 5), at each resolved particle size.

We only use the data obtained for the higher wind speeds (16, 18 and 20 m s -1 ), but we include all four types of wave forcing. As a first step we approach the vertical concentration profiles with a function depending on the natural logarithm of measurement height (cf. Sect. 4.1 and Fig. 5):

N r (z) = N r * ln(z) + C r (6)
where radius-dependent the aerosol concentration at the surface N r * (m -3 ) is determined by extending the measured aerosol concentration profiles to MWL.

r denotes the dependence on the droplet radius. The sea spray flux dF/dr (m -2

s -1 ) is subsequently obtained by multiplication with the friction velocity u * :

dF dr = N r * u * (7)
We evaluate N r * for each radius (bin) greater than 7 µm measured by our aerosol probes. This method is commonly used for the estimation of the sea spray flux in the field [START_REF] Petelski | Studies of vertical coarse aerosol fluxes in the boundary layer over the baltic sea[END_REF], as well as for numerical LES (Large Eddy Simulation) data [START_REF] Richter | Turbulent transport of spray droplets in the vicinity of moving surface waves[END_REF]. However, the use of a logarithmic function to describe the concentration gradient is debated, and other authors have prefered a power law (e.g., [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF][START_REF] Ortiz-Suslow | A laboratory study of spray generation in high winds[END_REF]).

Rather than entering this debate, we abide by the adequate fit of logarithmic functions to our data (cf. Fig. 5).

As discussed in the previous section, both the wave slope variance and the combined number are good candidates to scale droplet generation. The combined number is found suitable over the entire study radius range, and the wave slope variance for spume droplets. Thus, Figure 9 shows the sizedependent sea spray generation flux dF/dr (evaluated using Eq. 7) as function of both the combined number (panel (a)) and the wave slope variance (panel (b), for various representative droplet radii between 8.5 and 30 µm. Individual data for a specific radius was fitted to a power law presented as lines in Fig. 9. As expected, the figure demonstrates that the combined number and the wave slope variance are also good scaling parameters for the generation flux.

In accordance with the positive slopes in Figs. Finally, and interesting feature in both Figs. 9a and 9b is the increase in the curve slopes for increasing radius as function of the scaling parameters. The lower slopes are found for the larger droplets. These slopes, seem to converge towards a maximum slope in the jet droplet range as the curves become almost parallel for r < 15 µm. This suggests uneven radius-dependent flux strength variations over the sea spray spectrum according to the forcing.

Comparison with other studies

This section presents a comparison of our generation flux to others reported in the literature. Since most existing fluxes rely on data acquired in the field, we must ascertain that our laboratory data can be compared to the field.

Comparing air-sea interaction processes and resulting sea spray generation in laboratory conditions to the field is not a straightforward task, due to the greater complexity of the natural environment. It is important that physical mechanisms at play in the laboratory, as well as the resulting sea spray generation fluxes, be similar to those observed in the field. The former question has already been discussed in this paper; the wind flow (Sect. 2.4), the wave field (Sect. 3.1), and the whitecap coverage (Sect. 3.2) were all found to follow the same physics as in the field. As for the sea spray concentrations, Sect.

4.1 demonstrated the expected behaviour with increasing concentrations for increasing wind speed, a dependence on wave state, as well as a near-logarithmic concentration profile later used to calculate the laboratory generation fluxes (Eqs. 6 and 7).

The above reasoning leads us to compare our laboratory sea spray generation flux to four (field and laboratory) flux formulations published in the literature. For this comparison we have evaluated our generation flux for the laboratory pure wind forcing for 18 probe size bins over the 5-30 µm radius range, with friction velocity u * = 1.05 m s -1 and wind speed U 10 = 20 m s -1 (cf.

Table 1). The flux is depicted in Fig. 10 as the black solid line. The triangles denote the radii for which the dF/dr was evaluated, to which a polynomial function is fitted to facilitate comparison with the other generation spectra. (wave age equal to 1.25) was obtained by estimating the L18 flux for a wave age value of 3.9 using a fetch model adapted to the north-west Mediterranean [START_REF] Lafon | Analysis of the variations of the whitecap fraction as measured in a coastal zone[END_REF], corresponding with a MIRAMER campaign sample point located at 12 km fetch [START_REF] Demoisson | A model for the atmospheric transport of sea-salt particles in coastal areas[END_REF][START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF] used to parameterise the L18 SSGF. Figure 10 shows that the various flux estimates have a spread of an order of magnitude. While this may seem significant, the spread is quite typical as evidenced by reviews of the various source functions reported over the years [START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF][START_REF] Lewis | Sea salt aerosol production: mechanisms, methods, measurements, and models[END_REF]Veron, 2015). Our flux function has the same strength as S93, A98 and L18 for particles of 5 µm, but suggests a stronger flux than these other functions as radius increases. Specifically, our flux curve includes a shoulder (or peak) around 10-15 µm, also seen in S93, which we attribute to a peak in jet droplet production. A similar shoulder is observed in the aerosol size distributions measured at 55 cm height above the surface (cf. Fig. 4). Moving forward to radii in excess of 15 µm, the typical domain of spume droplets, the strength of L18 and S93 generation functions decrease rapidly. In both cases, this decrease was attributed to an underestimation of spume droplet production, for L18 because the experiment was hampered by the near-absence of high wind speed events, and because for L18 and S93 the height of the measurement towers prevented efficient dispersion of the spume droplet location. In each case this can result in poor count statistics, and the larger droplet concentrations are often discarded as done for r > 35 µm in the present study. Examples of efforts to compensate such effects include the reformulation of S93 in A98, where the generation flux was corrected over the spume droplet range [START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF]. For the larger radii (r > 25 µm), our flux function yields equal strength as F09. Because these largest particles reflect the limits of our PMS probes it is difficult to conclude, but both our flux curve and F09 seem to indicate that the decrease in strength becomes less strong with radius. This may point to the presence of another shoulder around 30 µm, reflecting a peak in spume droplet generation.

Formulation of the new sea spray generation function

The previous sections demonstrated that the laboratory generation flux depends on both wind and wave characteristics, with different responses for individual radii. The dependence on radius is traditionally accounted for by parameterising the SSGF with one or more modes centered around modal radii [START_REF] Monahan | A model of marine aerosol generation via whitecaps and wave disruption[END_REF][START_REF] Demoisson | A model for the atmospheric transport of sea-salt particles in coastal areas[END_REF][START_REF] Ovadnevaite | A sea spray aerosol flux parameterization encapsulating wave state[END_REF][START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF]. These modes can be represented with normal, log-normal, or other distributions that are commonly used to reproduce measured aerosol distribution characteristics. Modes are often associated with specific aerosol processes, such as the generation of jet or spume droplets. We adopt this methodology by introducing two modes at 7 and 25 µm radius, which we consider representative for jet and spume droplets, respectively. The choice of these centre radii was inspired by the shapes of the flux and concentration curves shown in Figs. 4 and 10, respectively. As mentioned in Sect. 2.5, we have excluded droplets with radii less than 7 µm radius for our analysis, but these droplets are evidently present in the tunnel (Fig. 4). On the basis of the shape of the aerosol size distribution shown in Fig. 4, we add a third mode centered around 2.5 µm. Taking 3 µm as the lower limit, the flux strength of the L18 SSGF is used over 3-7 µm. A smooth transition between the field-determined L18 and the laboratory data is attained by seeking a best fit between L18 flux distributions over the 3-7 µm range, and the laboratory flux distributions. The 7 µm radius marks the transition between both fluxes (cf. Fig. 11). To achieve this combination of flux functions, the whitecap coverage used in L18 (originally calculated from the wave age) [START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF] is recalculated here as a function of present study scaling parameters (cf. Sect. 4.2). In the following, the L18 W (%) is estimated from < S 2 > using Eq. 4. Section 4.3 revealed that the flux can be successfully scaled by a combined number P S , but that the < S 2 > also yields acceptable results, especially for larger particles. Therefore, we formulate two SSGFs in terms of three normally distributed modes, valid for droplets between 3-35 µm radius and wind speeds U 10 ranging from 12-20 m s -1 :

dF X dr 80 = n i=1 F i (X)τ -1 σ i √ 2π exp(- 1 2 ( r 80 -µ i σ i ) 2 ) ( 8
)
where X is the scaling parameter (P S or < S 2 >), r 80 is the particle radius at RH = 80%, dF X dr80 is the size dependent SSGF determined from environmental parameters contained in F i (X), and τ is the whitecap decay rate. µ i and σ i are the mean radius and standard deviation of each of the three modes. The SS-GFs can be given in terms of r 80 , because the underlying laboratory data was obtained for 80% humidity (cf. the discussion in Sect. 2.5). In formulating the SSGFs, we found best results were obtained using normal modes, whereas other authors have preferred lognormal modes (e.g. [START_REF] Ovadnevaite | A sea spray aerosol flux parameterization encapsulating wave state[END_REF]). Possibly, this signals that normal modes are more suitable for the larger droplets studied here. Numerical values for Eq. 8 are specified in Table 2. In addition, the whitecap decay rate was given a value of 3.53 [START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF]. Despite a focus on the 16-20 m s -1 range in Sect. 4, we are confident that the SSGFs are valid over the 12-20 m s -1 range as a result of the strong relationship between numbers < S 2 > and P S and the physical mechanisms known to drive production (cf. sects. 2.4 and 3.2) for these wind speeds.

Table 2 shows that flux amplitudes are expressed as power laws of < S 2 > and P S , as suggested with the apparent power law behaviour between scaling parameters and fluxes presented in Fig. 9.

i σ i µ i F i ( u * 3 νag < S 2 >) F i (< S 2 >)
1 2.1 2.5 4.37 × 10 2 ( u * 3 νag < S 2 >) 0.92 4.94 × 10 7 (< S 2 >) 2.45 2 7 7 6.84 × 10 1 ( u * 3 νag < S 2 >) 1.41 7.88 × 10 7 (< S 2 >) 2.3 3 12 25 4.75 × 10 1 ( u * 3 νag < S 2 >) 1.11 1.3 × 10 7 (< S 2 >) 2.39 The two new SSGFs are presented in Figure 11 (Tsyro et al., 2011;[START_REF] Chen | Sea salt emission, transport and influence on size-segregated nitrate simulation: a case study in northwestern europe by wrf-chem[END_REF][START_REF] Neumann | A comparison of sea salt emission parameterizations in northwestern europe using a chemistry transport model setup[END_REF], we consider this performance adequate. The figure also demonstrates that the two modes at 7 and 25 µm adequately reproduce the shape of the tunnel spectra, and this better than flux functions with less modes in the large particle size domain (e.g., S93 and L18). Finally, Fig. 11 also shows that both SSGFs connect reasonably well to L18. While this was expected with a 2.5 µm mode inspired by L18 flux strengths, this result offers a perpective for a future coupling between the new SSGFs and L18, thereby extending a universal function to the 0.1-35 µm range. These results also offer a perspective for future improvements on the combination of laboratory and field sea spray measurements.

6 Discussion and conclusion

Generation mechanisms

The aim of this study is to investigate the sea spray generation processes for different wind and wave combinations. We performed our studies in a wavewind interaction laboratory and thus, our first task was to demonstrate that important generation mechanisms such as wave breaking (cf. Sect. 3.2) and airflow characteristics (cf. Sect. 2.4) are similar in the laboratory and in the field. Sea spray concentrations over the 7-35 µm radius range are found to depend on both wind speed and the sea state, and are found to decrease nearlogarithmically for increasing distance from the water surface. The concentration spectra (Fig. 4) exhibit peaks at approximately 2.5 and 7 µm similar to observations in the field [START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF], attributed to regimes of film and and jet droplet generation predominance, respectively. A third peak was identified from the volume concentration spectra (Fig. 6) and corresponds to the spume droplet size range. This peak was absent for wind speeds under 12 m s -1 (Sect. 4.1), in accordance with the threshold for spume droplet production [START_REF] Monahan | A model of marine aerosol generation via whitecaps and wave disruption[END_REF][START_REF] Jones | Production velocity of sea spray droplets[END_REF]. The larger droplet concentrations are found in conditions with high values for whitecap coverage and wave slope variance. These conditions correspond to intermediate and short wave forcing in the laboratory (cf. Table 1). In contrast, long wave forcing or forcing by wind alone result in lower concentrations.

6.2 Scaling sea spray generation with < S 2 >

The sea spray generation flux is calculated assuming logarithmic concentration profiles (Sect. 4.5), motivated by the near-logarithmic profiles obtained in the laboratory (Fig. 5). The sea spray generation is scaled against four parameters that reflect the wind-wave conditions: wave age, windsea Reynolds number R B , wave slope variance < S 2 >, and a combined number u * 3 νag < S 2 >, denoted P S , describing the wave slope variance-modulated wind energy input to the waves. Whilst the wave age is a useful heuristic tool to estimate wave-wind equilibria, our results indicate that it does not allow satisfactory scaling of sea spray generation for different wind and wave combinations (cf. Figs. 7 and8). The windsea Reynolds number R B , also combining wind and peak wave characteristics, provides good results for smaller droplets (7-20 µm range), comparable to the performance for < S 2 >. However, < S 2 > significantly outperforms R B for spume droplets with radii greater than 20 µm (cf. Fig. 8).

This difference may be expected because R B only includes information about peak wave statistics, whereas < S 2 > is related to turbulence strength at the air-sea interface and wave breaking phenomena on a range of spatial scales. This is in agreement with an increasing number of microphysical studies that relate wave slope to turbulent events such as airflow separation and wind shear, which are thought to drive the surface tearing of spume droplets at the wave crests [START_REF] Banner | On the separation of air flow over water waves[END_REF][START_REF] Kawai | Visualization of airflow separation over wind-wave crests under moderate wind[END_REF][START_REF] Reul | Air flow structure over shortgravity breaking water waves[END_REF][START_REF] Mueller | Impact of sea spray on air-sea fluxes. part i: Results from stochastic simulations of sea spray drops over the ocean[END_REF][START_REF] Buckley | The turbulent airflow over wind generated surface waves[END_REF].

Of the four tested scaling parametersn the combined number P S gives the best overall performance: it is particularly well suited for the scaling of sea spray generation for radii in the 7-20 µm range, where bubble bursting generation dominates, but the larger spume droplets are also well scaled. The spume droplet scaling performance reflects the presence of < S 2 >, and the scaling performance for smaller droplets may be attributed to u 3 * as a result of its well documented relationship with wave energy dissipation. The concept of combined scaling parameters has also been explored by other authors [START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF]Lenain and Melville, 2017) (cf. Sect. 4.4). A comparative study (Sect. 4.3) shows that minor differences in the definition of the combined number (e.g. by using a Reynolds number defined in terms of significant wave height) do not impact on the performance, in contrast to the significant difference obtained when replacing wave steepness with the multiscale wave slope variance.

From a practical point of view, it is interesting to compare scaling performance to the difficulty to measure the scaling parameters. As mentioned in the previous section, it may be difficult to measure < S 2 > in the field. The use of the approximate equations to infer < S 2 > from more accessible parameters such as wind speed U 10 (Eq. 3), or whitecap coverage W (%) (Eq. 4) may then be considered, as the wave slope variance < S 2 > has often been considered proportional to both the wind speed at U 10 and the friction velocity u * [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF][START_REF] Lenain | Airborne measurements of surface wind and slope statistics over the ocean[END_REF]. In a similar fashion, tt is important to note that many authors obtain W (%) from wind speed [START_REF] Monahan | Optimal power-law description of oceanic whitecap coverage dependence on wind speed[END_REF]. Though not explicitly presented here, u * 3 νag < S 2 > and < S values reaching maxima of 0.49 and 0.54 (for r = 7 µm), respectively. These better results over the jet droplet range are coherent with the performances of the combined number P S with the u 3 * term. Furthermore, this shows that < S 2 > carries additional information (despite the good correlation between < S 2 > and W (%) -cf. Eq. 4) about the wave field relative to these three parameters, such as the presumed role of the wave slope in the modulation of the air flow and surface tearing mechanisms, as discussed in Sect 4.1.

Unlike < S 2 >, U 10 and u * are not found to be appropriate tools for the upscaling and extrapolation of sea spray generation and whitecap coverage from the laboratory to the field, similar to observations made by [START_REF] Toba | Similarity and dissimilarity in airsea momentum and co2 transfers: the nondimensional transfer coefficients in light of windsea reynolds number[END_REF] when comparing tunnel and field data. Altough < S 2 > outperforms U 10 and u * , there are conditions in which the wind parameters scale the aerosol concentrations as successfully. This pertains to smaller droplets (r < 12.5 µm)

and relatively low wind speeds of 8 and 12 m s -1 , and a wave field that is forced by the wind. In these circumstances, sea spray consists almost exclusively of the bubble-mediated jet droplets produced from breaking waves under conditions of strong wave-wind equilibrium. Further analysis of our laboratory data reveals that the linear relation between U 10 and < S 2 > presented by [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF] (Eq. 3) is best observed for the conditions corresponding to pure wind forcing. This is coherent with the good scaling performance of U 10 and u * under these conditions, as mentioned above. However, notable deviations from this linear relationship are observed with other types of wave forcing, which we attribute to the sensitivity of < S 2 > to wave-wind equilibria (quantified here with wave age). The monochromatic properties of the longer wave conditions that experience less wind forcing, resulting in low wave energy at the higher frequencies of the wave spectrum, thereby affecting the value of < S 2 >. In this respect, a future laboratory study with more realistic wave fields such as the JONSWAP spectra [START_REF] Hasselmann | Measurements of wind-wave growth and swell decay during the joint north sea wave project (jonswap)[END_REF] would be worthwhile.

Validation against field data

The sea spray generation fluxes measured in the laboratory are compared to other existing source functions obtained in the field and in laboratory conditions. Our data compare favourably with the SPANDEX laboratory data reported by [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF]. Flux estimates differ typically by less than an order of magnitude when compared to flux functions obtained in the field [START_REF] Smith | Marine aerosol concentrations and estimated fluxes over the sea[END_REF][START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF], which is in accordance with the typical spread in the literature [START_REF]A new sea spray generation function for wind speeds up to 32 m s1[END_REF]Veron, 2015). More substantial differences are noted from the spume droplet domain, when we compare our flux estimates to a function that does not accommodate these large particles explicitly [START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF]. These results prove that the laboratory is a good instrument for determining generation fluxes. This inspires us to continue the tunnel experiments, since the tunnel is better suited for the study of sea spray production for a wide range of wave fields and in high winds representative of extreme events. Also, the tunnel facilitates the complex experiments required to understand the generation processes at the microphysical scale, such as airflow separation, and the effects of sea spray on heat, moisture and momentum fluxes at the air-sea interface. Ideally, such experiments should be performed with salt water, for easier comparison with field experiments, because saltwater and freshwater lead to differences in the aerosol concentrations and distributions [START_REF] Fairall | Investigation of the physical scaling of sea spray spume droplet production[END_REF][START_REF] Mehta | A laboratory investigation of spume generation in high winds for fresh and seawater[END_REF].

Sea spray generation functions (SSGFs) derived from laboratory experiments

The laboratory experiments culminated in two sea spray generation functions (SSGFs) (cf. Fig. 11 and Table 2). These SSGFs describe the droplet generation spectrum as a sum of three normally distributed modes, and are validated for wind speeds ranging from 12-20 m s -1 and droplet radii 3-35 µm. The radius range spans the major part of the film and jet ranges, as well as an appreciable start of the spume droplet range. One SSGF solely dependent on the wave slope variance, and to our knowledge is the first of its kind. Wave slope variance measurements in the field are scarce, and for practical purposes it may be necessary to estimate the wave slope variance from more readily available variables such as wind speed (Eq. 3, [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF]), or from measured or modelled wave spectra [START_REF] Elfouhaily | A unified directional spectrum for long and short wind-driven waves[END_REF]. As shown in Section 6.3, such approximations may reduce the accuracy of the SSGF. The second SSGF depends on a combined scaling parameter in terms of both < S 2 > and u 3 * . Though obtaining accurate measurements or predictions of u 3 * may be challenging in the field (and thus renders the use of the second SSGF even more difficult than the one depending solely on < S 2 >), this non-dimensional number is undeniably the best scaling tool for the generation of film and jet droplets, and also scales the larger spume droplets satisfactorily. In extrapolating the P S -dependent SSGF down to 12 m s -1 the flux may be underestimated at these lower wind speeds, following the suggestion by Andreas (1998) that the rate of spume droplet generation increases with u 2 * and not u 3 * for winds below 15 m s -1 .

Outlook

Recent improvements in the integration of higher order wave field properties in numerical wave models [START_REF] Cathelain | Development of a deterministic numerical model for the study of the coupling between an atmospheric flow and a sea state[END_REF] and the coupling of wave, atmospheric and circulation models [START_REF] Pianezze | A new coupled ocean-waves-atmosphere model designed for tropical storm studies: example of tropical cyclone bejisa (2013-2014) in the south-west indian ocean[END_REF] provide an impetus for the study of sea spray generation processes. Present study results have shown that the integration of the wave field is essential for the better scaling of the sea spray generation. As we work towards universal SSGFs valid for a wide range of (complex) environmental conditions, a further understanding is required of the effect of multiscale (i.e. millimeter to meter scale) boundary processes sea spray fluxes. This may include first and higher order statistics, such as for the consideration of overlapping wave fields, the directional spreading of wave spectra [START_REF] Peureux | Note on the directional properties of meter-scale gravity waves[END_REF] and wave-current interactions affecting surface wave properties [START_REF] Ardhuin | Small-scale open ocean currents have large effects on wind wave heights[END_REF]. As the present study has highlighted the importance of the wave slope variance in modelling droplet fluxes, we signal an urgent need for a better understanding of small-scale sea surface characteristics (Jähne and Riemer, 1990). Unfortunately, field measurements of these characteristics have been relatively sparse [START_REF] Munk | An inconvenient sea truth: Spread, steepness, and skewness of surface slopes[END_REF], not in the least because the spatial resolution of airborne and satellite-based sensors is limited and the presence of whitecaps complicates the retrieval of slope variance estimates [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter De Leeuw G (1986) Vertical profiles of giant particles close above the sea surface[END_REF][START_REF] Lenain | Airborne measurements of surface wind and slope statistics over the ocean[END_REF].

Finally, having demonstrated that the tunnel is a good proxy to the field in determining sea spray fluxes, we would now like to extend the comparison to the aerosol concentrations at some height above the water surface. However, this is not a simple task since the differences in dispersion characteristics, background concentrations and production footprints between the tunnel and the field need to be elucidated. Efforts to do so are underway, and will be reported elsewhere.

  2, wind and wave results are discussed in Sect. 3, and sea spray results in Sect. 4. Study results include a comparison between the laboratory data and other laboratory and field SSGFs presented in the literature. Finally, two new SSGFs are introduced in Sect. 5, one depending on the wave slope variance alone, and a second on both the wave slope variance and u 3 * . Both SSGFs combine laboratory and field data, and are valid for wind speeds 12-20 m s -1 and radii 3-35 µm.

Fig. 1

 1 Fig. 1 Side view of the experimental configuration in the laboratory

Figure 2

 2 Figure 2 presents the experimental wind profiles for all 20 laboratory configurations (data points with horizontal error bars) as well as the corresponding theoretical profiles obtained with Eq. 1. For clarity and indicative purposes only, are also presented the average friction velocities < u * > calculated over the 4 different wave types for each individual tested wind speed. The experimental profiles exhibit near-logarithmic behaviour, and the gradient increases for increasing reference wind speed U 10 , in accordance with a fully developed turbulent layer near the water surface as encountered in the field. This is further evidenced by the windsea Reynolds number (R B ) found greater than 10 3

Fig. 2

 2 Fig. 2 Measured U(z) profiles for all twenty laboratory configurations (horizontal bars) with associated theoretical profiles (lines) calculated with Eq. 1. Average friction velocities values < u * > pertain to the five wind speeds set in the laboratory.

  ;[START_REF] Van Eijk | Seacluse: Numerical simulation of evaporating sea spray droplets[END_REF];[START_REF] Mueller | Impact of sea spray on air-sea fluxes. part i: Results from stochastic simulations of sea spray drops over the ocean[END_REF];[START_REF] Mehta | A laboratory investigation of spume generation in high winds for fresh and seawater[END_REF]). During the experiments, the relative humidity (RH) in the laboratory varied between 79 and 82%, with an average water temperature at 0.2 m depth of 18 • C, and an average air temperature T a at 85 cm height of 25 • C. We therefore assume that sea spray number concentrations correspond (roughly) to RH = 80%. Since the rate of freshwater droplet evaporation at RH = 80% is relatively small, we assume that out measured droplets are representative for saltwater droplets at their RH = 80% equilibrium radii.

Fig. 3

 3 Fig. 3 Comparison between laboratory and field (Lafon et al., 2007) (a) fp-normalised whitecap coverage W(%) estimates as function of the windsea Reynolds number R B , and (b) W(%) as function of the wave slope variance < S 2 >. Lines and corresponding R 2 statistics represent power laws fitted to the data.

Fig. 4

 4 Fig. 4 Sea spray number concentration size distribution at 55 cm above the MWL for the intermediate wave forcing.

Fig. 5

 5 Fig. 5 Sea spray number concentration profiles at 20 m s -1 winds as function of height, represented as ln(z). Symbols denote experimental data, lines linear fits to the data.

Figure 5

 5 Figure 5 also demonstrates that the type of forcing affects the vertical concentration gradients. The stronger gradients are observed for intermediate and short wave forcings, whereas the forcing by wind alone results in a less pronounced concentration decrease with height. To further investigate the effect of sea state, Fig. 6 focuses on the aerosol size distributions over the 6 -47.5 µm radius range obtained at z = 35 cm, and for wind speed U 10 = 20 m s -1 . Individual datapoints represent an average over several particle bin sizes (spanning ± 4 µm) for clarity, and horizontal and vertical error bars illustrate the standard deviations in average size and concentration, respectively. The data is presented on a log-log scale, and individual datapoints are connected

Fig. 6

 6 Fig. 6 Sea spray volume concentrations for U 10 = 20 m s -1 at 35 cm above the mean water level, for the four forcings used in the laboratory. SPANDEX data measured at 31.5 cm above MWL corresponding to their nominal condition is presented for comparison.

Figure 6

 6 Figure 6 depicts volume rather than number concentrations. Comparing with Fig. 4 reveals that while large droplets are less numerous, they represent the larger part of the volume (or mass). Presenting the data as volume concentrations allows us to better detail the differences between the four types of wave forcing. Visual comparison of the four curves reveals that wind forcing

Fig. 7

 7 Fig. 7 Scaling of dN/dr with (a) wave age, (b) R B , (c) < S 2 > and (d) P S = u 3 * νag .< S 2 > for particles of radius 7.5 µm, 35 cm above MWL. Individual types of wave forcing are represented in color, with U 10 wind speeds ranging from 16 to 20 m s -1 . Solid black lines in all panels represent linear fits to all 12 datapoints.

Fig. 8

 8 Fig. 8 Scaling of dN/dr with (a) wave age, (b) R B , (c) < S 2 > and (d) P S = u 3 * νag .< S 2 > for particles of radius 25 µm, 35 cm above MWL. Individual wave forcings are denoted by colours, for U 10 wind speeds ranging from 16 to 20 m s -1 . Solid black lines in all panels represent linear fits to all 12 datapoints.

  7 and 8 (panels c and d), increasing values of combined number or wave slope variance lead to a stronger flux. Although it is difficult to conclude visually from Fig. 9, a comparison of panels a and b reveals the better scaling performance of the combined number for smaller radii, as reflected in the quality of the fit for 8.5 particles µm.

Fig. 9

 9 Fig. 9 The laboratory dF/dr sea spray flux as a function of (a) the combined number u * 3 νag < S 2 > and (b) the wave slope variance < S 2 >. Lines denote power law fits to data for individual radii.

Figure 10

 10 Figure 10 also represents fluxes from the literature; Smith et al. (1993) denoted by S93 and the grey solid line, Andreas (1998) denoted by A98 and the dotted line, Laussac et al. (2018) denoted by L18 and the dashed line, and Fairall et al. (2009) denoted by F09 and the grey dashed line. The latter flux was obtained from laboratory data, the other three from field data. The Andreas (1998) and Smith et al. (1993) flux models solely depend on wind speed U 10 and are evaluated here for U 10 = 20 m s -1 . The F09 flux is estimated for u * = 1.35 m s -1 , and is only valid for r ≥ 24 µm. Finally, L18 flux strength depends on the whitecap coverage, in turn defined in terms of the wave age, and has a 0.5-20 µm radius validity range. The closest match with laboratory conditions

Fig. 10

 10 Fig. 10 Vertical sea spray concentration fluxes at U 10 = 20 m s -1 .

  as two series of solid lines, where panels a and b denote results for the SSGF in terms of the combined number P S and < S > respectively. These lines are colour-coded according to the values of the scaling parameters; the colour scale is indicated on the right of the individual panels. The range of values was chosen to correspond with the laboratory configurations for all types of wind speeds between 16 and 20 m s -1 . The experimental flux data obtained in these configurations is visualised by the color-coded plus signs in Fig.11. Finally, Figure11also presents the flux spectra prescribed by the L18 SSGF[START_REF] Laussac | Development of a fetch dependent sea-spray source function using aerosol concentration measurements in the north-western mediterranean[END_REF] over the 3-7 µm range, which, as mentioned above, was modified so that the whitecap coverage W (%) scaling parameter (originally calculated from the wave age), was recalculated to depend on either P S or < S 2 >. The recalculated L18 flux spectra are represented by the color-coded dashed lines.

Fig. 11

 11 Fig. 11 The altered L18 SSGF (dashed lines) and the (a) combined number P S and (b) wave slope variance < S 2 > SSGFs. Line colors depend on respective non-dimensional (a) P S and (b) < S 2 > values.

Figure 11

 11 Figure 11 demonstrates that the two SSGFs reproduce the experimental flux data obtained in the tunnel quite well, although differences of up to a factor 2 remain. In view of the already noted significant spread in individual flux functions reported in the literature(Tsyro et al., 2011;[START_REF] Chen | Sea salt emission, transport and influence on size-segregated nitrate simulation: a case study in northwestern europe by wrf-chem[END_REF]

2 >

 2 (and to a lesser extent R B ) outperform the measured U 10 , u * and W (%) for the scaling of sea spray generation in the tested laboratory configurations, especially for larger droplets. W (%) presents R 2 values ranging between 0.2 and 0.45 over the 7-35 µm range, with best results over the jet droplet range. U 10 and u * scaling performances are lower than for W (%) overall, except for the smaller radii of the jet droplet range where U 10 and u * show good correlation with spea spray generation, with R 2

  Data of the same type of forcing are fitted to a linear function, denoted by a dashed line of the same colour. The black solid line represents a linear fit to all 12 datapoints, and the R 2 value of the fit is given in the graphs

	ner, we provide separate scaling for the sea spray predominantly produced by
	bubble bursting (7-20 µm) and surface-tearing (20-35 µm) mechanisms.
	Figures 7a and 8a report the scaling with wave age. The presented data
	correspond to the wind-wave (blue dots), long wave (pink dots), intermediate
	wave (red dots) and short wave (green dots) forcing at 16, 18 and 20 m s -1 U 10
	wind speeds.

(R 2 = 0.13 for scaling with wave age for particles of 7.5 µm). Although the wave age seems to correctly scale concentrations for individual wave forcings, no clear relationship is found between the measured concentrations and wave age when all data is included. Therefore, we conclude that wave age is not well suited for the scaling of sea spray generation for both young wind-forced waves, and older swell-type waves.

Nevertheless, it is interesting to further discuss Figs.

7a and 8a

. The overall decrease in near-surface concentrations for increasing wave age (Figs.

7a and 8a

) corroborates observations made in the field, as less whitecap is produced by older swell-type waves or wind waves modulated by older waves in contrast with wind waves alone

[START_REF] Schwendeman | Observations of whitecap coverage and the relation to wind stress, wave slope, and turbulent dissipation[END_REF][START_REF] Brumer | Whitecap coverage dependence on wind and wave statistics as observed during so gasex and hiwings[END_REF]

. Both figures show that relatively high sea spray concentrations are found for the intermediate and short forcings, with corresponding wave age values of approximately 1.7. This can be expected considering the high values of W(%) and < S 2 > for these types of forcing (cf. Table

1

). High droplet concentrations associated with young, steep and strongly breaking waves is typical of fetch-limited wave fields

Table 2

 2 Parameters for the two SSGFs.

  Both wave age and the windsea Reynolds number R B require a wind parameter and relatively common wave parameters. The wave age does not scale the flux properly for the range of tested forcings, and R B scaling performances are mainly limited to the smaller jet droplet particles. The measurement difficulty increases when considering the multiscale information (wave spectrum) required for < S 2 >, and the combined number P S adds further complexity by requiring the wind friction velocity u * . The use of approximate equations to estimate < S 2 > from more readily-accessible parameters (e.g. Eqs. 3 and 4) may thus be considered,

	albeit with loss of scaling performance.
	6.3 < S 2 > and traditional scaling parameters

Acknowledgements

A special thanks to engineer Rémi Chemin (University of Toulon) for his thoughts and contribution during the laboratory experiment. We are grateful for the sponsorship by the Agence Innovation Défense (AID-DGA) under contract 2018-60-0038 and the Region SUD contract 2018-06085. This work also benefitted from the MATRAC research effort sponsored by ANR-ASTRID under contract ANR-18-ASTR-0002.