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  • View in gallery

    (top) A diagram of the ASIST facility. (bottom left) The Dantec ShadowStrobe used equipped with telecentric lens and liquid light guide; this was mounted on a frame opposite (bottom right) the camera used for data collection. The green tinge in the water is from a fluorescent dye used as part of a completely different experiment; the observations presented here were done using nondyed, filtered seawater.

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    Examples of acquired images. The U (L) signifies the upper (lower) acquisition level, and the number refers to 10-m equivalent wind speed. The red boxes and yellow circles represent particles identified and contoured by the automatic processing algorithm. Some identified sprays have been circled (large red circles): clockwise from upper left, these drops have area-equivalent radii of 92.5, 303.5, 181.5, and 396 μm.

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    The sampling strategy used in this study. The far right column, for both levels, provides the total number of image collections, the number of images analyzed per collection, and the visually verified percent success rate of the counting algorithm. The variable total number of images per wind speed regime (middle column) was taken into account when computing the mean particle concentrations. Each set of images for a given wind speed was collected independently, with laboratory conditions reset before starting another trial.

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    Total mass concentration observed for each wind speed (color) and at the upper (circles) and lower (no symbols) collection levels, respectively.

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    The color bar is common across all panels and shows log-scaled (base 10) number concentration (number of particles per unit air volume per radius class). The profiles shown are scaled by the wind regime’s corresponding , and the empty areas signify regions where no particles were counted.

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    Integrated spray volume fraction profiles for all of the wind speed trials using the number concentrations from Fig. 5. These profiles are radius integrated; they have units of volume of spray at a given height per total volume of spray produced for each wind speed (i.e., cm3 cm−3). The profile height is scaled by the appropriate Hs.

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    Volume concentration spectra transformed down to the theoretical source height in volume of water per volume of air per radius increment. A subset of the results from this study (black, ASIST-SIS) is compared to saltwater observations from Fairall et al. (2009) (blue, red, and magenta) and ASIST-CIP (green) data. The curves are referenced to their height above Hs and the corresponding U10. For Fairall et al. (2009), this was estimated from the friction velocity and roughness length reported in Table 1 of that paper using the law of the wall and assuming neutral conditions in the surface layer.

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    A comparison of the spray generation function estimates. The color scaling is common to both panels and represents the 10-m wind speed (m s−1). (a) The blue curves are adapted from Fig. 6 in Veron (2015) and are model functions for U10 = 15 m s−1. The model of Mueller and Veron (2009) at 50 m s−1 and laboratory scale fetch is also shown. The Veron et al. (2012) source function is inferred from particle concentrations observed in a laboratory. (b) The results from this study. Each curve represents a vertically averaged estimate of S0(r), with the shaded region spanning one standard error of the means at each radius class. Slopes with and are provided as a reference.

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    The number concentration spectra for Veron et al. (2012) (ASIST-SIS) at 10-m equivalent wind speeds 41.2 (47.1) m s−1 and 40.5 (49.5) m s−1, respectively, represented by the left axis. The spectra from this study (blue and red) are vertical averages of the lowest six bins of the profile, and the shaded region spans one standard error of the mean. The right axis shows the corresponding S0(r) functions from this study.

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    Results of the multiple linear regression analysis of the estimated source functions from ASIST-SIS. (a) The B parameter shown as a function of wind speed with linear and quadratic fits provided; the dashed lines mark the 5% and 95% confidence intervals. (b) The m parameter shown in a similar manner. The 10-m equivalent wind speed is represented by U.

  • View in gallery

    Results of the nonlinear regression analysis. (a) The S0(r) spectra from Fig. 8b (dots) alongside the corresponding regression curves (lines). Color denotes 10-m wind speed. (b) The corresponding slope functions. The black solid (41.2 m s−1) and dashed (47.1 m s−1) curves are slope functions determined from polynomial fits to the Veron et al. (2012) source functions given in Fig. 8.

  • View in gallery

    Select profiles from Fig. 5. The values at the top of each column mark the particle radius class (μm), while the values on the right side of each row give the wind speed regime (m s−1). Observations from this study (black dots) are given alongside exponential (red), power (blue), and linear (green) regressions to the profile.

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    The S0(r) spectra for wind speed trials (left) 45 and (right) 49.5 m s−1. The source function was calculated using Eq. (12), but the different colored curves represent different slip factor applications; the curves have been normalized to a common intercept. The slip factor was calculated as , where a was the test parameter. The values were set as monotonically decreasing with increasing particle size, but with the smallest radius class always having . The denotes the slip factor for the largest radius class. A line with an slope is provided as reference (note: the purple-cross curve extends much farther but is cut off by the axis limits).

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Sea Spray Generation in Very High Winds

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  • 1 Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida
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Abstract

Quantifying the amount and rate of sea spray production at the ocean surface is critical to understanding the effect spray has on atmospheric boundary layer processes (e.g., tropical cyclones). Currently, only limited observational data exist that can be used to validate available droplet production models. To help fill this gap, a laboratory experiment was conducted that directly observed the vertical distribution of spume droplets above actively breaking waves. The experiments were carried out in hurricane-force conditions (10-m equivalent wind speed of 36–54 m s−1), and the observed particles ranged in radius r from 80 to nearly 1400 μm. High-resolution profiles (3 mm) were reconstructed from optical imagery taken within the boundary layer, ranging from 2 to 6 times the local significant wave height. Number concentrations were observed to have a radius dependence proportional to r−3 leading to spume production estimates that diverge from typical source models, which tend to exhibit a radius falloff closer to r−8. This was particularly significant for droplets with radii circa 1 mm whose modeled production rates were several orders of magnitude less than the rates expected from the observed concentrations. The vertical dependence of the number concentrations was observed to follow a logarithmic profile, which does not confirm the power-law relationship expected by a conventional spume generation parameterization. These observations bear significant implications for efforts to characterize the role these large droplets play in boundary layer processes under high-wind conditions.

Corresponding author address: David G. Ortiz-Suslow, Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098. E-mail: dortiz-suslow@rsmas.miami.edu

Abstract

Quantifying the amount and rate of sea spray production at the ocean surface is critical to understanding the effect spray has on atmospheric boundary layer processes (e.g., tropical cyclones). Currently, only limited observational data exist that can be used to validate available droplet production models. To help fill this gap, a laboratory experiment was conducted that directly observed the vertical distribution of spume droplets above actively breaking waves. The experiments were carried out in hurricane-force conditions (10-m equivalent wind speed of 36–54 m s−1), and the observed particles ranged in radius r from 80 to nearly 1400 μm. High-resolution profiles (3 mm) were reconstructed from optical imagery taken within the boundary layer, ranging from 2 to 6 times the local significant wave height. Number concentrations were observed to have a radius dependence proportional to r−3 leading to spume production estimates that diverge from typical source models, which tend to exhibit a radius falloff closer to r−8. This was particularly significant for droplets with radii circa 1 mm whose modeled production rates were several orders of magnitude less than the rates expected from the observed concentrations. The vertical dependence of the number concentrations was observed to follow a logarithmic profile, which does not confirm the power-law relationship expected by a conventional spume generation parameterization. These observations bear significant implications for efforts to characterize the role these large droplets play in boundary layer processes under high-wind conditions.

Corresponding author address: David G. Ortiz-Suslow, Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-1098. E-mail: dortiz-suslow@rsmas.miami.edu

1. Introduction

a. Motivation

The balance between moist enthalpy input and wind energy dissipation at the air–sea interface is thought to be critical to tropical storm development (Emanuel 1986). Over the last several decades a respectable body of knowledge has been developed on the processes of mass, momentum, and energy fluxes at the ocean surface in light to moderate winds. However, our direct knowledge of these fluxes in high winds remains sparse. At wind speeds (10-m equivalent; U10) above 30 m s−1, there is generally a significant quantity of spray entrained in the atmospheric boundary layer (Fairall et al. 1994). This transition zone from the spray-free to a spray-laden boundary layer seems to correlate with the apparent saturation of the drag coefficient, which occurs in the wind speed range of 30–40 m s−1, as observed in both laboratory (Donelan et al. 2004) and field (e.g., Powell et al. 2003; Potter et al. 2015) studies. One potential explanation for this is that the presence of spray in the boundary layer alters the vertical wind profile (Pielke and Lee 1991; Barenblatt et al. 2005), which can be shown to change the theoretical logarithmic relationships used to derive the aerodynamic roughness (Lykossov 2001). Kepert et al. (1999) demonstrated that including spray effects in a coupled atmosphere–ocean model can have a dramatic effect on the air–sea fluxes during a simulated tropical cyclone. However, direct observations of this remain elusive. The impact that the development of this spray layer has on the exchange of heat and momentum remains relatively unknown (Haus et al. 2010; Jeong et al. 2012). Determining this relationship holds implications for a number of oceanographic and atmospheric processes, including the rate of intensification of tropical cyclones (Soloviev et al. 2014).

The effects of sea spray on the air–sea interface are highly size dependent since particles are generated over a wide distribution of radii (nominally from 1 μm to 1 mm). Droplets with radii less than about 25 μm are likely produced by bubble bursting (e.g., Monahan et al. 1986; Clarke et al. 2006) and have a minimal effect on momentum and heat fluxes. This generation mechanism is likely only a minor source for particles larger than 25 μm (Lewis and Schwartz 2004). These larger particles are referred to as spume and thought to be generated largely by the process of wave breaking. Jones and Andreas (2012) summarized many oceanic spray observations and found that for U10 > 16 m s−1 droplets with radius greater than 50 μm may be generated. In the case of even higher winds, it becomes evident that large spume particles (300–600 μm) can be directly torn from the wave crests (Anguelova et al. 1999) or the destabilized interface (e.g., Marmottant and Villermaux 2004; Soloviev et al. 2014).

b. Spray effects on air–sea momentum exchange

There are a number of alternative explanations for the potential role of spray in altering the air–sea momentum exchange: 1) The return of spray droplets to the water surface suppresses the short waves that carry much of the stress (Andreas 2004). 2) The existence of a turbulence-suppressing, spray-laden layer above the air–sea interface inhibits the direct physical interactions between the sea surface and the atmosphere (Barenblatt et al. 2005; Bye and Jenkins 2006). 3) The onset of Kelvin–Helmholz instabilities leads to the production of spray and spume and the stabilization of the surface roughness as the crests of steep waves are blown off (Soloviev et al. 2014).

Early research suggested that the primary effect of spray would be to enhance air–sea momentum exchange because of the momentum required to accelerate spray droplets to the wind speed, which would then be transferred to the water upon reentry (Munk 1955; Pielke and Lee 1991). Subsequent studies based primarily on the low to moderate wind regime found this effect to be insignificant (Wu 1972). Fairall et al. (1994) calculated that the spray stress (wind to water) would have only a small influence (10% of the total stress) for winds up to = 50 m s−1. However, this result may be primarily relevant to spray, not spume, given assumptions of the initial horizontal velocity of the droplets considered in that work. A confounding factor in these estimates is the difficulty in defining a realistic spray generation function in high winds.

Andreas (2004) suggested that spray’s main role is to redistribute the wind’s momentum in the near-surface layer, with the spray acting to slow the near-surface wind speed by roughly 10% (for winds ~30 m s−1). As a result, although the total surface stress may be the same as in the absence of spray, the spray contribution to that stress increases with wind speed while the interfacial contribution decreases. The author recalculated the spray contribution by separating the stress into an interfacial and a spray contribution and found that spray could have a much stronger role than estimated by the earlier works. Furthermore, he speculates that the spray droplets returning to the sea surface would suppress short waves and thereby lead to a reduction in the surface roughness. The existence of a droplet evaporation layer (Andreas et al. 1995) close to the surface would further suppress turbulence close to the interface (Andreas et al. 2008) and lead to a reduction in interfacial transfers.

Alternatively, a theoretical model developed by Lighthill (1999), and expanded upon by Barenblatt et al. (2005), suggests a mechanism that would produce a sharp reduction in the atmospheric drag coefficient as a result of spray loading. This so-called sandwich model postulates that once the spray droplet size and concentration in the boundary layer reaches a threshold concentration the dynamics will evolve into a stably stratified multiphase flow, where the effective density of each layer is determined by the spray concentration (akin to thermodynamic stratification with spray instead of temperature). This model results in a significant decrease in the stress that is supported across the ocean–atmosphere interface—now the ocean–spray–atmosphere interface. Their spray layer thickness and the boundary layer velocity profile were found to be strongly dependent upon the spray droplet size, with the larger particles being the most significant to the stress reduction.

Bye and Jenkins (2006) and Bye and Wolff (2008) presented a unified boundary layer model that incorporated some of the basic elements of the Lighthill (1999) approach. The model is unified in the sense that it combines a wave model, a spray generation function based on breaking waves, and a boundary layer turbulence model. The unified model predicts a leveling off of because of the suppression of turbulence by spray for winds greater than ~40 m s−1, with a maximum value at 42 m s−1. Their results also show a flattening of the short wave field due to impinging spray, leading to reduced stress and a transfer of wave energy to lower wavenumbers. This sandwich model, along with the alternatives presented, hinges on some knowledge of the vertical distribution of stress-carrying particles in the spray-laden boundary layer. Observations in very high winds where this is expected to be significant are generally lacking, and these theories require further validation.

c. Spray effects on the enthalpy flux

Latent and sensible heat fluxes both contribute to the total moist enthalpy flux. At winds high enough to generate spray, these fluxes are generated through two distinct mechanisms: 1) molecular-scale interfacial fluxes that occur at the air–sea interface and 2) spray fluxes produced by droplets ejected from the water surface into the air (Andreas et al. 2008). Many authors have suggested that the spray contribution becomes important at wind speeds above ~12 m s−1, thereby increasing the overall moist enthalpy exchange coefficient (Wu 1979; Andreas and Decosmo 1999, 2002; Andreas et al. 2008; Emanuel 2003). Models have shown that, for wind speeds greater than approximately 20 m s−1, the spray sensible and latent heat fluxes are as large as the interfacial fluxes (Andreas 1992). Dropsonde data confirm this (Richter and Stern (2014)) for winds up to 70 m s−1. In the laboratory, Jeong et al. (2012) found that the total moist enthalpy transfer was essentially constant with increasing wind speed up to 40 m s−1. However, Andreas and Mahrt (2015) argued that Jeong et al. (2012) only captured the interfacial transfers, pointing to the need for additional spray-mediated enthalpy flux observations.

It has been shown by Andreas and Emanuel (2001) that spray can only cool the water volume by being ejected from the warmer water, cooling in the air, and then returning to the water. To quantify this cooling mechanism, there are three key time constants (following Andreas 1992, 2005, 2010) that must be considered: the duration of suspension of the spray droplet in the airflow , the temperature evolution time or e-folding scale for droplet cooling , and the droplet radius evolution time scale . In the laboratory studies of Haus et al. (2010) and Jeong et al. (2012), the time before a droplet is advected out of the laboratory control volume must also be considered. The scale comes directly from the wind speed in the control volume, the location of spray generation, and the length of the tank.

The and scales have been estimated by Andreas (2005) for a range of salinities; however, the duration of suspension remains uncertain. Andreas et al. (2010) assumed that spray was generated at the elevation of the significant wave height and then would fall back to the mean water surface. Jeong et al. (2012) argued that this conceptual framework does not apply in the case of strongly forced waves. In previous studies, was usually chosen for the suspension height, although considerable lofting above this level clearly can occur because of nonzero vertical droplet velocities at the wave crest (e.g., Fairall et al. 2009). Jeong et al. (2012) showed that the distance over which the droplet must fall before reentering the water depends on the downwind surface elevation in addition to the generation height. Andreas et al. (2010) used (i.e., significant wave amplitude) as the vertical length scale over which the droplet needed to fall, but in strongly forced conditions the droplet will likely impact a downwind wave before reaching this level. It is likely that in wave tank studies this effect is more pronounced than in the open ocean, as the waves grow in height over relatively short downwind length scales. The relevant time scale in this case is then related to the speed of the droplet relative to the wave phase speed and the wavelength. Mueller and Veron (2014) recognized this and developed a stochastic particle model to investigate residence times for a range of particle radii and wind speeds. They found that the droplet residence time is not represented by the simple free-fall concept and that there is a far more complicated relationship between the vertical particle distribution and the near-surface turbulent flow.

d. Spray production

The evolution, development, and ultimate impact of entrained spray and spume in the atmospheric boundary layer all depend on the rate at which spray is produced and the size-dependent vertical distribution of these particles above the ocean surface. This foundational knowledge has yet to be fully described in the literature for the full spectrum of particle sizes, particularly at wind speeds when spray is expected to be most significant for heat and momentum exchange across the air–sea interface. Spray generation source functions derived from limited field observations exhibit a very wide range of values, and none of these studies have achieved reliable measurements in hurricane conditions. The extreme conditions necessary to produce the spray volumes of interest make meaningful field observations an arduous, if not impossible, task (Melville 1996). Although the laboratory is a much simpler environment in which to make spray observations than in the field, it is still a complicated undertaking; consequently, there have been only limited observations of the spray distributions above breaking waves for either fresh or saltwater in the laboratory. Veron et al. (2012) made observations in high wind speeds that show orders of magnitude divergence from the Fairall et al. (2009) production rate (e.g., Fairall et al. 2009). More observational work is necessary to understand these results and to fully characterize the distribution of spume droplets above the wavy surface.

The present study addresses some of the gaps in the literature through laboratory observations in saltwater. Direct measurements of spume concentration profiles were made in hurricane-force winds above actively breaking waves. Experiments were done using filtered seawater and were conducted in 10-m equivalent wind speeds ranging from 36 to 54 m s−1. An unobtrusive optical technique was used that minimized the flow distortion and particle disruption. From these observed profiles, a bulk parameterization was used to estimate the corresponding source functions; these were compared to previous observations and typical source function models. Imaged particles ranged in radius from 80 to just over 1400 μm, which lie in the spume regime of the production spectrum. While laboratory experiments in these conditions are challenging, having controllable, repeatable experimental conditions makes this approach an attractive alternative to similarly aimed field campaigns.

2. Theoretical background: Quantifying spray generation

A comprehensive review of sea spray literature to date can be found in Veron (2015); the reader is directed to this article for further details regarding the theoretical and empirical background for spray generation mechanisms. The following is a condensed treatment of the material relevant to this study.

The cumulative size distribution of spray particles above the air–sea interface is the integrated spray concentration of droplets with radius less than some radius r:
e1
where is the total number concentration of spray drops per unit volume of air per discrete particle radius increment from to (Veron 2015). The quantity is sometimes referred to as the concentration function (Veron et al. 2012). The particle concentration is a function of droplet radius, height above the surface, and time. The temporal evolution of is given as
e2
Here the explicit dependencies of n have been dropped. Equation (2) describes the time dependence of in terms of (from left to right) the three-dimensional particle velocity , the radius-dependent particle diffusivity , the rate of change of the droplet radius, and a source–sink function .
The first step toward a tractable solution to Eq. (2) is applying a standard Reynolds decomposition: that is, , where overbars represent mean quantities and primed values are the fluctuations (i.e., ). This decomposition is also applied to n and r, and Eq. (2) becomes
e3
The last term on the rhs can be considered negligible for the particle sizes considered here [i.e., the relaxation time scale for the droplet radius is sufficiently large (Andreas 1992)]. Also, the source-sink term is brought into the parenthesis on the rhs and becomes the mean, size-dependent flux function, . This term has units of number of particles per unit water surface area per unit time per discrete radius increment . The deposition velocity or settling velocity is defined as the mean particle velocity relative to the mean flow velocity, Substituting this into Eq. (3) and removing the terms yields
e4
Equation (4) can be further simplified by moving the advective term to the lhs and rewriting in terms of the total or material derivative of :
e5
This flux equation can be further reduced if one assumes horizontal homogeneity, steady-state conditions, and that particle diffusion is negligible. Invoking these conditions and rearranging to get an expression for the vertical droplet flux
e6
where the quantity = and w represent the vertical velocity components. This states that the vertical flux of spume droplets can be described as a simple balance between particle deposition and vertical particle transport. Eddy covariance techniques can be used to measure this directly (Norris et al. 2012). However, parameterizing this in terms of an eddy diffusivity model may be a necessary alternative (e.g., Rouault et al. 1991; Fairall et al. 2009). The latter method is used here to infer the source function because the covariance term could not be directly observed during the experiments. Then Eq. (6) becomes
e7
where is a turbulent particle diffusion coefficient,
e8
Here, κ is the von Kármán constant (taken as 0.4), is the wind shear velocity, z is the height above the free surface, is a slip factor, and Sc is the spray droplet turbulent Schmidt number from Rouault et al. (1991). The slip factor attempts to parameterize the inertial diffusion of particles. The functional form of comes from Rouault et al. (1991) and is defined as
e9
where C 2 and is the vertical wind variance. Fairall et al. (2009) assumed that was O(1) for their entire size spectrum (radii from 10 to 600 μm). For the purpose of this study, fs will also be taken as ~1, but sensitivity analysis of this assumption was done and is provided later in this article.
Directly from Eqs. (7) and (8), can be estimated given a measure of the mean vertical droplet concentration . Conceptually, all of the spray observed in the boundary layer is assumed to be generated within some region above the breaking waves. Above this layer no spray is generated and therefore is typically piecewise defined as some delta function (Veron 2015; Fairall et al. 2009). In this conceptual model, h is taken as the height above the surface that defines the generation layer; it is generally referred to as the theoretical source height and is typically referenced to the significant wave height Hs. Following this framework, Eq. (7) then becomes a system of equations:
e10
e11
This is simplified if the concentration gradient within the spray generation layer is negligible (Fairall et al. 2009). These two equations must match at the boundary z = Hs,
e12
and the spray flux can be estimated from a mean size-dependent droplet concentration measured at some height z above the reference level . From Veron (2015), is known as the size-dependent spray generation function.
A critical problem in this formulation is how to represent . Andreas et al. (2010) provides a detailed characterization of the vertical settling velocity for particles ranging from 0.5 to 300 μm. This velocity scale is both a function of height and particle radius:
e13
Here, r0 is the observed particle radius, is the size-dependent gravitational settling velocity, is a molecular sublayer transfer velocity, and , where δ is the sublayer thickness; the reader is directed to Andreas et al. (2010) (and the appendix therein) for details regarding the origin of these parameters. For this study, was calculated following this method and ranged from 0.6 to 10 m s−1 for the smallest to largest drops, respectively. For the size of the particles considered here (radius 801400 μm), the height dependence was found to be negligible. This comes directly from the quantity, which was observed to be >1 for all radii and wind speeds considered here (see Andreas et al. 2010).

3. Laboratory observations

a. The facility

The experiments were carried out in the University of Miami Air–Sea Interaction Saltwater Tank (ASIST), which has a 15 m × 1 m × 1 m acrylic test section (Fig. 1). This facility is capable of generating both wind waves with a single turbine fan and one-dimensional mechanical waves. Spray images were collected 11.05 m downwind from the wind inlet, and the maximum sustained winds in the tank reached 54 m s−1 U10. This was observed via sonic anemometer 2.35 m upwind of the imaged volume, and the sampling volume of the anemometer was 20 cm above the still water line. The winds were referenced to 10 m following previous work done in ASIST (Donelan et al. 2004; Haus et al. 2010). All of the experiments presented here were done with an initial water depth of 0.42 m and using 10-μm filtered seawater pumped in from a local tidal inlet (Bear Cut). There are no nearby freshwater sources, and before being filtered the seawater was settled in a large basin to remove large suspended particulates. For all of the experiments, the salinity of the seawater was ~33 psu.

Fig. 1.
Fig. 1.

(top) A diagram of the ASIST facility. (bottom left) The Dantec ShadowStrobe used equipped with telecentric lens and liquid light guide; this was mounted on a frame opposite (bottom right) the camera used for data collection. The green tinge in the water is from a fluorescent dye used as part of a completely different experiment; the observations presented here were done using nondyed, filtered seawater.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

An important physical reference in spray observations is the wave height, typically generalized via the significant wave height . The wave heights in ASIST were sampled at 10 Hz using a downward-looking ultrasonic distance meter (UDM) mounted 5.7 m downwind of the inlet on the roof of the tank. The wave sampling was done in discrete 300-s blocks for separate wind speed regimes inside the tank. The conditions in the tank were allowed 120 s to become stationary prior to sampling. The used in this study was calculated spectrally:
e14
where is the 0th moment of the elevation variance spectrum. The particle concentration profiles were adjusted to account for the change in mean water level (MWL) as a result of spray exiting the test section; this was done using the low-frequency trend in the UDM time series. This trend in the water surface elevations was removed prior to the spectral analysis. This can be considered a conservative correction to the profile height because all of the spray imaging was done in less than 200 s of stationary wind forcing.
Equation (8) requires some knowledge of the wind forcing on the water surface in order to determine the . For a given , the can be calculated following
e15

The drag parameter used in the present study comes from work done in ASIST by Donelan et al. (2004), where three independent methods were used to estimate this parameter as a function of wind speed. This laboratory study compared the results of the eddy correlation technique (e.g., Edson et al. 2013) with those from a profiling and momentum budget method, the latter being a technique that uses mass conservation in the flume and the pressure–slope relation. This provides a robust estimation of the aerodynamic drag as a function of wind speed for this facility. The observed and in ASIST for a given wind speed are provided in Table 1.

Table 1.

Multiple regression results for the generation function S0(r). The estimated mean, integrated spray flux in thousands of particles per unit water surface area per second (m−2 s−1) is given by . The coefficients from Eq. (22) are also given. The uncertainty for B and m gives the 95% confidence interval.

Table 1.

b. Data collection and processing

A Dantec Dynamics particle image velocimetry (PIV) data acquisition system was used to collect the spray imagery used in the analysis of the concentration function. The PIV system was modified for spray observations by rerouting the laser sheet through a liquid light guide to a strobe (Dantec ShadowStrobe). The strobe produced a collimated beam that helped minimize size distortion based on the distance from the light source. The beam illuminated a small section of a diffuser screen mounted on the outside of the ASIST wall and a camera (JAI CV-MSCL, 1.9 MP, 30 fps) was oriented directly opposite in order to capture images of this region. Spray droplets being advected through the volume between the camera and screen were imaged as a shadow projection (see Fig. 2). The camera–strobe system was mounted outside the acrylic tank and enabled undisturbed observations of vertical spray concentration profiles.

Fig. 2.
Fig. 2.

Examples of acquired images. The U (L) signifies the upper (lower) acquisition level, and the number refers to 10-m equivalent wind speed. The red boxes and yellow circles represent particles identified and contoured by the automatic processing algorithm. Some identified sprays have been circled (large red circles): clockwise from upper left, these drops have area-equivalent radii of 92.5, 303.5, 181.5, and 396 μm.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

Sampling was done at two reference levels centered at 95 mm (lower) and 145 mm (upper) above the MWL in order to reconstruct profiles of sufficient length to capture the vertical variability in the droplet distribution. The acquisition was done in a “double-frame mode,” where images were collected in pairs separated by 500 . A total of 250 such pairs per collection were acquired at 15 Hz for five different wind speed regimes and for both the lower and upper reference levels. The pair sampling was limited by the laser flash rate, not the camera acquisition rate (30 Hz). The timing of the PIV system is precisely controlled, and a collection of 250 paired images took 16.667 s to complete. Multiple collections of these sets of 250 double-frame images were carried out continuously under stationary wind forcing conditions, with maximum acquisition time not exceeding 175 s. For each wind speed regime, it is possible that a variable number of collections of 250 images were acquired during the sampling (details in Fig. 3). Though image pairs were acquired, only one frame from each pair was used for determining the size-dependent droplet number concentrations. Unfortunately, it was determined during the image analysis that the experimental conditions were not optimal for using these double frames to extract the particle trajectories; however, single images are sufficient for quantifying the height- and size-dependent spray concentrations.

Fig. 3.
Fig. 3.

The sampling strategy used in this study. The far right column, for both levels, provides the total number of image collections, the number of images analyzed per collection, and the visually verified percent success rate of the counting algorithm. The variable total number of images per wind speed regime (middle column) was taken into account when computing the mean particle concentrations. Each set of images for a given wind speed was collected independently, with laboratory conditions reset before starting another trial.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

Image processing was done in two steps using the Dantec Dynamics shadow imaging software package. Each raw image was balanced initially to correct for irregularities in the image light sheet by taking the mean intensity of the set of 250 images. The raw frames were then normalized by this mean image, which resulted in higher contrast and easier particle detection. Droplet characterization was then carried out using an automatic shadow sizing routine. The detection algorithm was trained first by selecting a particle in one image in order to get a baseline for gray-level contrast and edge gradients. The steepness of the edge gradient determines how in and out of focus detected particles are: only gradients above a threshold steepness are considered in the plane of focus and counted. After the detection parameters were determined based on this “training,” the detection algorithm was automatically applied to every set of shadow images (>17 500 individual frames). The end result provided droplet centroid location and surface area, and the radius reported in this study was calculated assuming circular droplet projections.

This clearly begins to stop being valid for particles with radii exceeding 500 μm (see Fig. 3). This is an issue for the radius-dependent spray generation function, which relies on direct measurement of the particle radius at formation . For the observations in ASIST, some large particles are ellipsoids, and may in fact be unstable or at least ill-defined; however, few observational data exist that can quantify the significance of this distinction with regards to sea spray research. Mueller and Veron (2009) present a numerical model that does take into account these effects (as well as other processes related to particle deformation), which is partially based on previous laboratory experiments that investigated solid particle dynamics in turbulent flows (e.g., Clift and Gauvin 1971). For the purposes of this work, a simplified approach was used, and the particle radius in question represents an area-equivalent estimate.

Applying the identification criteria universally does not maximize detections for a particular set of 250 images, but it is a standardized means of spray detection and sizing, enabling direct comparison between respective data collections. This method is not only more expeditious than employing visual identification criteria, but it also minimizes the experimenter biases. It is expected that these biases would have been significant given the difficulty of consistently analyzing thousands of images. The success rate of the automatic processing algorithm was tested against visual inspections of a portion of the image sets. The results of the user-observed particle detection and the automatic processor were compared for every twenty-fifth frame of the 250 image sets. In general, the algorithm successfully detected 75%–90% of the droplets. The lowest-wind-speed trial tended to be underdetected by the algorithm, with a success rate just above 60%. Each set of 250 images was collected independently, and it is possible that this may be a result of low image contrast in this particular trial, which was observed when the images were inspected and compared to other trials. For all of the experiments, a radius dependence was observed in the algorithm’s success rate, in that smaller particles (10 pixels or less in diameter) were more likely to be missed than larger particles.

The camera used to acquire the droplet images was a medium telephoto lens with a 23.3° field of view. This is a nontelecentric lens, and thus the image magnification exhibits a dependence on an object’s location within the depth of field; however, experimentally this source of error in the reported particle sizes is small. The focal plane of the camera was calibrated 0.59 m away from the lens (center of the air space in ASIST). This yields a depth of field of order 3 mm and results in a magnification error in the particle sizing around 1%. This is much less than the uncertainty associated with the automatic detection and sizing algorithm used to process the imagery. In the plane of the ASIST center line, the sampling volume represented by the camera frame was 55 mm × 75 mm (Fig. 2). The across-tank dimension was determined in postcalibration to be 70 mm. This was found to be the operational depth of field and was quantified using a target with standardized circles of known diameters (and separation) between 1 and 2.5 mm. The edge-detection algorithm was unable to discriminate between in- and out-of-focus droplets to the precision of the camera lens’ depth of field (i.e., ±1.5 mm). The pixel resolution of each frame was 42 μm, which was determined using the standardized calibration target.

4. Results

Spray concentrations were measured in ASIST for five wind conditions with 10-m equivalent wind speeds ranging from 36 to 54 m s−1 and at two vertical reference levels (upper and lower) above the MWL in the tank; all of the experiments were done using filtered seawater (Fig. 3). Tests were carried out independently for a given wind speed and reference height with several collections of 250-image sets acquired per test. From these images, spray droplets were identified, sized, and then segregated into 50-μm-radius classes.

a. Observed number concentrations

The mass concentration for each discrete radius class was observed to decrease with height above the MWL and increase with wind forcing (Fig. 4). The total mass concentration was calculated from the raw spray counts at each acquisition level and normalized over the entire imaged volume. For both acquisition levels, a discernible peak in the mass concentration spectra observed between 500 and 800 μm. The postpeak slope tends to be steeper than the prepeak slope, and this is most pronounced at the higher wind speeds. When integrated across all radii, about 150% more water mass per unit air volume is observed in the lower level versus the upper level, with this difference increasing slightly with increasing wind speed. The vertical difference was most pronounced for the larger particles. The mass concentration observed in the upper frame saturates between 49.5 and 54 m s−1 , and except at the largest droplet sizes this does not occur in the lower acquisition level.

Fig. 4.
Fig. 4.

Total mass concentration observed for each wind speed (color) and at the upper (circles) and lower (no symbols) collection levels, respectively.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

The raw image sets taken at the lower and upper levels were stitched together into continuous profiles with 3-mm vertical resolution (i.e., horizontal slices through the entire imaged air volume that are 3 mm thick). The droplet concentration observed across each vertical slice and for each radius class (50 μm wide) was calculated using
e16
where is the total number of observed particles in the ith radius class and jth profile bin, is the air volume of each vertical bin, is the total number of images in an observation period (e.g., Fig. 3 would give 7 × 250 = 1750), and is the width of each radius class. Equation (16) gives the number of particles per unit volume of air per radius increment for each vertical bin along the reconstructed profile. These concentrations are given in Fig. 5 in two-dimensional grids. The vertical profiles were all scaled by their respective for the given wind speed (see Table 1). As opposed to the mass concentration, the number concentrations clearly show that the largest numbers of particles were observed in radius classes <500 μm. The two-dimensional distributions may have gaps where, for a given wind speed, vertical location, and radius increment, no particles were observed (see Fig. 5). However, with increased forcing, these gaps tend to be filled as the imaged portion of the boundary layer becomes laden with spray across the entire size spectrum. In fact, from 36 to 54 m s−1 the amount of “empty” space in the distribution decreases from nearly 85% to 32%. Physically, this signifies the filling of the boundary layer with spume drops. At the strongest wind forcing, particles >500 μm are consistently observed at more than 4 times the local significant wave height, and particles around 1 mm become frequently observed at nearly 3 times .
Fig. 5.
Fig. 5.

The color bar is common across all panels and shows log-scaled (base 10) number concentration (number of particles per unit air volume per radius class). The profiles shown are scaled by the wind regime’s corresponding , and the empty areas signify regions where no particles were counted.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

To isolate the effect increased wind forcing has on the vertical distribution of spray, it is useful to look at radius-integrated profiles. This is done by transforming the grids given in Fig. 5 into fractional spray volume profiles or, in other words, the volume concentration at each profile bin normalized by the total spray volume across the entire profile (see Fig. 6). The radius-integrated volume concentration at each vertical bin is calculated using
e17
which is then normalized by the total water volume observed for all . In removing the concentration information, these profiles isolate the vertical dependence of the droplet distributions and highlight its dependence on wind forcing. The normalized profile at 36 m s−1 held more of the total observed spray volume lower in the profile when compared to the 54 m s−1 profile where a downshift was observed, signifying movement toward a more uniform vertical distribution. This transition is evident in the intermediate wind speeds between the 36 and 54 m s−1 experiments; however, the absolute differences observed across the five trials are relatively small. The overall profile shape was observed to be fairly consistent for all the test conditions. The apparent compression of the profile at higher wind speeds (Fig. 6a) is primarily due to the relative distance between the profile bins (which are fixed in the laboratory frame of reference) and significant wave height, which is increasing with the wind speed. This also explains the vertical offsets between the cumulative distributions in Fig. 6b.
Fig. 6.
Fig. 6.

Integrated spray volume fraction profiles for all of the wind speed trials using the number concentrations from Fig. 5. These profiles are radius integrated; they have units of volume of spray at a given height per total volume of spray produced for each wind speed (i.e., cm3 cm−3). The profile height is scaled by the appropriate Hs.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

The validity of the assumptions used to build the spray generation parameterization presented in section 2 can be tested by transforming the profiles down to the source height using Eq. (12). Theoretically, for a given wind speed and radius class, this transformation should capture all of the vertical variability in the profile, and measurements made at discrete heights above Hs should collapse onto a single effective source value.

A subset of the results is given in Fig. 7 alongside similar results from the Fairall et al. (2009) study and unpublished saltwater observations made in ASIST during the Jeong et al. (2012) study. The Fairall et al. (2009) study made observations in both fresh and saltwater (only the latter is used for comparison here), and both wind and mechanical waves were used to generate spray droplets. The work reported from ASIST was conducted using saltwater and only tested wind-generated waves. For a comparison of fresh and saltwater droplet production, see Ortiz-Suslow et al. (2016).

Fig. 7.
Fig. 7.

Volume concentration spectra transformed down to the theoretical source height in volume of water per volume of air per radius increment. A subset of the results from this study (black, ASIST-SIS) is compared to saltwater observations from Fairall et al. (2009) (blue, red, and magenta) and ASIST-CIP (green) data. The curves are referenced to their height above Hs and the corresponding U10. For Fairall et al. (2009), this was estimated from the friction velocity and roughness length reported in Table 1 of that paper using the law of the wall and assuming neutral conditions in the surface layer.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

All of the concentration spectra given in Fig. 7 have been transformed down to the source level using Eq. (12). Like these previous studies, the presented here have been converted to volume concentration [the nonintegral form of Eq. (17)] and are denoted as dvdr. Both Fairall et al. (2009) and Jeong et al. (2012) used the cloud imaging probe [CIP; see Baumgardner et al. (2001)] to observe droplet concentrations. The data collected in ASIST using the CIP will be referred to as ASIST-CIP in order to differentiate it from the shadow images observed in ASIST as part of this work (denoted ASIST-SIS). The ASIST-CIP data were collected under comparable salinity conditions (filtered seawater) and approximately 2.5 m upwind of the ASIST-SIS observations. Both ASIST datasets show a size-dependent falloff in the normalized volume spectra, unlike the Fairall et al. (2009) observations, which level off for radii greater than 100 μm. In that study, the authors partially attributed this phenomenon to a sampling bias in the functionality of the CIP. The investigators believed that this instrument was erroneously counting two medium-sized particles as one large particle if the individual cross-sections overlapped within the measurement volume. However, the ASIST-CIP observations do not appear to confirm this behavior. It should be noted that the Fairall et al. (2009) and ASIST-CIP spectra have been smoothed to fill gaps in the curves; this was not done for the ASIST-SIS spectra.

The Fairall et al. (2009) observations in Fig. 7 come from the same wind forcing but different measurement heights and show within one order of magnitude collapse onto an effective dvdr value at the source level. The convergence tends to get better with increasing particle radius; however, it is unclear if this is a physical phenomenon or a result of the instrument bias noted in that previous study. In comparison, the ASIST-SIS data exhibit between half and one order of magnitude convergence, which remains fairly consistent across the entire size spectrum. In their analysis, Fairall et al. (2009) considered this level of collapse as satisfactory, but this conclusion may be questionable in the present study, given the ASIST-SIS spectra.

The differences in dvdr within the Fairall et al. (2009) and ASIST-SIS datasets seems to be most sensitive to the position of the original measurement relative to the source height. This may also explain the relative differences between all of the volume concentration spectra for the three datasets from Fairall et al. (2009), ASIST-SIS, and the ASIST-CIP. This is somewhat counterintuitive, since wind forcing (or some other physical variable) would be expected to be a stronger predictor of the volume concentration at the source height. This suggests that there is vertical variability in the profiles that cannot be removed by this transformation. This may explain why the collapse of dvdr onto a single value was limited for the ASIST-SIS observations.

b. Estimates of the generation function

The following analysis is done with regard to the ASIST-SIS dataset and reflects the observations of the present study. The observed are useful for characterizing the vertical distribution of spume above the actively breaking water surface, but the ultimate goal of these types of observations is to quantify the vertical flux of droplets across a spectrum of particle sizes.

The was inferred by scaling the measured number concentration at some radius class and profile bin by the appropriate deposition velocity and transforming down to the theoretical source level of 1 = [Eq. (12)]. Given the limiting success of this transformation (Fig. 7), this was considered a first-order estimate to the spume flux and was done in order to compare these observations to previously modeled generation functions. That the transformation used to infer does not account for all of the observed vertical variability is expected to add some uncertainty to the estimate of the amount of spray generated rather than affecting the size dependence, which is more indicative of the observed dynamics.

The ASIST-SIS estimates are provided alongside estimates from various other works (Fig. 8). A compilation of curves from Veron (2015) is provided as a relatively low wind reference (15 m s−1 ) and comes from several model functions available in the literature. It should be noted that the Fairall et al. (2009) curve referenced in Fig. 8a comes from an unpublished physically based model developed during the original study (see the appendix of that article). The generation function from Mueller and Veron (2009) is also given for a high-wind (50 m s−1 U10) model comparison. Two source functions from the observational work of Veron et al. (2012) are also provided in Fig. 8a and are inferred from the number concentrations presented in Fig. 4 of that paper. This was done using Eq. (12), and since wave information was not explicitly provided in that study, the appropriate Hs was estimated using fetch-limited wave growth (Stiassnie 2012). This leads to an effective of 1.396 and 1.186 for the 41.2 and 47.1 m s−1 spectra, respectively. Following the authors’ suggestion in that article, the deposition velocity was estimated using Fairall et al. (1994).

Fig. 8.
Fig. 8.

A comparison of the spray generation function estimates. The color scaling is common to both panels and represents the 10-m wind speed (m s−1). (a) The blue curves are adapted from Fig. 6 in Veron (2015) and are model functions for U10 = 15 m s−1. The model of Mueller and Veron (2009) at 50 m s−1 and laboratory scale fetch is also shown. The Veron et al. (2012) source function is inferred from particle concentrations observed in a laboratory. (b) The results from this study. Each curve represents a vertically averaged estimate of S0(r), with the shaded region spanning one standard error of the means at each radius class. Slopes with and are provided as a reference.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

For the ASIST-SIS curves in Fig. 8b, was estimated at each profile level and for each radius class and then vertically averaged to get a mean size-dependent estimate of the production:
e18
where Nj is the total number of estimates along a profile for that particular radius class ri. From 36 to 54 m s−1 the effective of these mean spectra range from 4.25 to 3.38, respectively; the decrease in effective height is due to increasing Hs with increasing wind speed. More than an order of magnitude increase in the mean bulk production was observed from 36 to 54 m s−1 U10. The uncertainty of this estimate was quantified as the standard error of the mean (SEM) at each radius class (the shaded region in Fig. 8b). This was done so that deviations from the mean were directly comparable across radius classes and wind speeds, regardless of the number of samples used to generate the vertical average. The relatively small uncertainty demonstrates that across the five different wind trials these mean spectra are fairly robust and the size and wind speed dependence of the spume droplet flux is well represented. In general, the uncertainty tended to decrease with increased wind forcing because the statistics better converge as the boundary layer becomes filled with spume droplets. The largest uncertainties were observed for particles with radii exceeding 500 μm (especially at the low winds), which is most likely because of gaps in the profiles increasing the sample variability (see Figs. 5 and 7).

For comparable wind speeds, the estimates of S0(r) are about one-half order of magnitude less than the estimates of Veron et al. (2012). However, for both of these studies the radius dependences of the S0(r) spectra are remarkably similar (R2 > 0.98 for all wind speeds) and exhibit radius dependences between r−3 and r−5. Some of this similarity stems from these spectra being converted from concentration to source functions using the same parameterization. Even with less overall production observed, the ASIST-SIS results show several orders of magnitude more large particles (radii approaching 1 mm) than a production model with a size falloff closer to r−8 (Mueller and Veron 2009).

The directly observed concentration spectra from both Veron et al. (2012) and ASIST provides a more explicit comparison between these two observational studies (Fig. 9). The spectra from ASIST given in Fig. 9 are vertically averaged over the lowest six bins of the profile and are effectively from a of ~2.5, while the Veron et al. (2012) data come from imagery taken very close to the spray generation layer (i.e., close to 1). In general, the ASIST-SIS measurements show fairly good agreement with Veron et al. (2012), and this demonstrates that the differences in the estimated spray flux (Fig. 8b) may be largely attributed to the transformation used to infer S0(r). This may further exemplify the bias observed when comparing the ASIST-SIS dataset to the Fairall et al. (2009) observations of dvdr at the source height.

Fig. 9.
Fig. 9.

The number concentration spectra for Veron et al. (2012) (ASIST-SIS) at 10-m equivalent wind speeds 41.2 (47.1) m s−1 and 40.5 (49.5) m s−1, respectively, represented by the left axis. The spectra from this study (blue and red) are vertical averages of the lowest six bins of the profile, and the shaded region spans one standard error of the mean. The right axis shows the corresponding S0(r) functions from this study.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

The ASIST observations show a slightly shallower radius falloff and thus significantly more circa 1-mm-radius particles, which is somewhat unexpected given the relative heights of the observations. The ASIST measurements were made at more than twice the fetch of those from Veron et al. (2012), so differences in the local wave development may be a reasonable explanation for this discrepancy. Regardless of these differences, in the context of the various model spectra given in Fig. 8a, there is relatively strong agreement across these two studies that the large particle production is significantly underpredicted by existing model functions (e.g., Mueller and Veron 2009).

c. Regression analysis

Statistical methods can be used to quantify the wind speed and radius dependence of the source functions given in Fig. 8b. This is primarily done here as an empirical exercise to quantify the variability within the ASIST dataset, and the physical implications of this analysis are largely secondary. Following Fairall et al. (1994), the spectra given in Fig. 8 can be represented as the interaction of two independent functions of wind speed and particle radius:
e19
where U is typically taken as a 10-m referenced wind speed and is the source function; W is a function of the surface fraction covered by whitecaps; and is some mean size-dependent distribution (Fairall et al. 1994). Equation (19) suggests that the shape of the spectrum is determined by , while the amount of spray generated is determined by W.
To validate this assumption, the S0(r) spectra from ASIST were tested using a least-squares multiple regression. As a first estimate, the spectra given in Fig. 8 can be described using a power-law relationship, and Eq. (19) takes the form
e20
where (r) is the source function observed in this laboratory study. For a given wind speed and radius class, this model suggests that m is a constant. When transformed into log space, this provides a linear model,
e21
where S is the log base-10 scaled source function [the lhs of Eq. (20)], R is the log-scaled particle radius, m is the power from Eq. (25), and B is the log-scaled W term. In this form, B and m are the linear coefficients and were determined statistically (Table 1). The B parameter is well described as a second-order function of wind speed (R2 > 0.98) and was observed to decrease with increasing wind speed (Fig. 10a). The parameter B exists over a relatively limited parameter space and tends toward a minima as the wind speed increases from 36 to 54 m s−1 U10. This suggests that less additional spume production is observed for each incremental increase in wind forcing. The power m was observed to vary slightly with wind speed and increased from −4.4 to nearly −3.5 (Fig. 10b). The power m was found to increase nonlinearly with wind speed and could be well described with a second-order polynomial (R2 > 0.98). These findings demonstrate that the size-dependent distribution of particles observed in ASIST is a function of wind forcing, which does not confirm the assumed separation of variables presented in Eqs. (19) and (20).
Fig. 10.
Fig. 10.

Results of the multiple linear regression analysis of the estimated source functions from ASIST-SIS. (a) The B parameter shown as a function of wind speed with linear and quadratic fits provided; the dashed lines mark the 5% and 95% confidence intervals. (b) The m parameter shown in a similar manner. The 10-m equivalent wind speed is represented by U.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

Equation (21) is a first-order approximation to the ASIST spectra from Fig. 8b, which is a convenient simplification to make for testing the assumption built into Eq. (19). However, S(R) may be a nonlinear function of R and in order to test this Eq. (21) can be rewritten as a second-order function:
e22
Each wind condition was tested independently to determine the pn regression coefficients (Table 1), and this quadratic relation was observed to capture most of the variability in the mean S0(r) spectra (see Fig. 11a). Higher-order polynomials (up to order 6) were also tested, but no statistical advantage was observed with using a polynomial above order 2.
Fig. 11.
Fig. 11.

Results of the nonlinear regression analysis. (a) The S0(r) spectra from Fig. 8b (dots) alongside the corresponding regression curves (lines). Color denotes 10-m wind speed. (b) The corresponding slope functions. The black solid (41.2 m s−1) and dashed (47.1 m s−1) curves are slope functions determined from polynomial fits to the Veron et al. (2012) source functions given in Fig. 8.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

The change in the size dependence of the inferred source function with increased wind forcing was quantified directly as the slope of this new S(R) [i.e., the first derivative (Fig. 11b)]. A clear positive wind speed dependence was observed, and slopes ranged from −1 to −6. This analysis was applied to the Veron et al. (2012) spectra and revealed a similar trend. This empirical relationship suggests an altered version of Eq. (20), which can be found by transforming Eq. (22):
e23
where P3 is 10p3. This is a highly nonlinear relationship, largely because of the leading term on the rhs. The terms in parentheses are similar to the Fairall et al. (1994) relationship, but as a whole this empirically derived form of S0(r) highlights that the ASIST observations diverge significantly from conventional parameterizations.

Up to this point, wave-state-dependent parameters have not been explicitly considered. However, the observed or other similar wave-phase-averaged quantity would not be a meaningful addition to the multiple regression model. This is because the wind speed is assumed steady for each experimental condition, and the waves in ASIST are solely forced by the wind. In the laboratory, Fairall et al. (2009) show some relationship between the spray mass flux and the surface wave energy flux, but these experiments were conducted in the presence of both wind-forced and simulated swell waves, creating a surface condition not solely dependent on the wind speed in the tank. Wave-related processes may play a role in isolating some of the observed variability, but this cannot be determined from the experimental data.

5. Discussion

The results of this study demonstrate the breakdown of Eq. (12) and the theoretical framework used to develop this parameterization (section 2). This is clearly evident in Fig. 7, where larger values of dvdr at the theoretical source height came from observations made closer to Hs, and the wind forcing on the system was of secondary importance. This suggests a vertical dependence that is not removed by the transformation. This was also evident when comparing the estimated source functions of Veron et al. (2012) and ASIST-SIS. While both studies observe comparable number concentrations (Fig. 9), it is clear that the estimates of S0(r) inferred from Veron et al. (2012) concentrations were high relative to ASIST-SIS, because these measurements come from much closer to the generation level (Fig. 8b). The spume generation model used to estimate S0(r) relies on an eddy viscosity [Eq. (8)] as well as a conceptual model describing the vertical distribution of droplets about the theoretical source height (Veron 2015). Invoking these conditions effectively prescribes a number concentration profile that can be seen by rearranging Eq. (12):
e24
where the first parameter on the right-hand side is the number concentration at the source height. For a particular radius class and wind speed, the power term is theoretically constant and , which describes a profile shape that follows a power-law relationship. This profile is used to transform measurements made at some height z above HS, effectively assuming some knowledge about the variability in the vertical distribution. This theoretical profile can be explicitly tested against the directly observed profiles reconstructed from the raw imagery acquired as part of this study.
Select number concentration profiles are given in Fig. 12 and have been taken directly from the two-dimensional arrays in Fig. 5. These profiles represent a range of wind speeds and particle sizes, and each profile was independently tested against a power, exponential, and linear relation. The regression model that performed best was determined by which minimized the mean residual between observed and predicted values. This analysis was performed in profile space:
e25
e26
e27
Fig. 12.
Fig. 12.

Select profiles from Fig. 5. The values at the top of each column mark the particle radius class (μm), while the values on the right side of each row give the wind speed regime (m s−1). Observations from this study (black dots) are given alongside exponential (red), power (blue), and linear (green) regressions to the profile.

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

where and a and b are the regression coefficients. Note that the power-law relationship [Eq. (25)] is the expected profile shape based on Eq. (24). The exponential model generally performed the best in explaining the observed profile variability (R2 values between 0.7 and 0.96). The linear model sometimes outperformed the exponential, but this may be a result of the profile length, and it is unclear if this result would change for a longer profile. It is important to note that the power-law relationship never performed better than either the exponential or linear models.
The exponential relationship in Eq. (26) can be inverted to give as a function of ζ,
e28
this describes a logarithmic number concentration profile that is at odds with the expected power-law relationship. The regression coefficients, a and b, are provided in Table 2. Equation (28) cannot be analytically derived from the system of equations posed by Eqs. (10) and (11). This suggests that, for the ASIST observations, this system is ill-defined and Eq. (12) is limited in providing an estimate of the spume generation. As a result, the prescribed profile shape does not best describe the vertical variability in the observed profile data, which may explain the spectral behavior noted in both Figs. 7 and 8. The strong similarity between the observations presented here and those from Veron et al. (2012) suggests that both laboratory studies measured similar dynamics, and thus Eq. (28) may be applicable in some form across these independently conducted experiments. Unfortunately, there are no profile data available from Veron et al. (2012), so a direct comparison cannot be made to confirm this hypothesis.
Table 2.

Regression coefficients to the empirical number concentration profile given in Eq. (28). MSE is the mean square error.

Table 2.

As an empirical solution to the number concentration profile, Eq. (28) could suggest that the term in the spray balance equation is negligible. Removing this term from Eq. (7) and solving for yields a logarithmic solution. From a physical perspective, it does not seem reasonable that the vertical deposition of particles is negligible for spume, even though this would be an empirically justified conclusion given the statistical analysis. It is more likely that the term has some vertical dependence that is being neglected. This phenomenon may be partially a result of using a solely size-dependent , which may not be appropriate for spume (E. Lewis 2015, personal communication). Recent modeling work by Mueller and Veron (2014) supports this claim, as they examined the size and height dependence of the spume transport and also found significant vertical dependence. Theoretically, the deposition velocity used for this study is height dependent [Eq. (13)], but the dependence was found to be negligible across our size regime. The significance of Eq. (28) is that it suggests some gaps in the theoretical framework used to model spume generation. However, as a purely empirical finding, generalizing this result may be challenging and drawing direct conclusions about what this implies for spume transport equations goes beyond the scope of this work.

As an additional note, the recent review by Veron (2015) includes a slip factor parameterization in the calculation of the generation function [Eq. (9) of this paper]. This coefficient is more of a counterdiffusion parameter, since it characterizes how the inertia of the large particles reduces their diffusion because of turbulence (Rouault et al. 1991). Fairall et al. (2009) approximates this term as of O(1) for spume droplets; for lack of a better scheme, this was also used for this study. By inserting realistic values from the ASIST-SIS dataset into Eq. (9), fs may actually range from near 0 to roughly 1, depending on the particle size considered. A simple test is devised to analyze the sensitivity of estimates of S0(r) to changing values of fs (Fig. 13). The effective droplet flux for the largest particles becomes negligible as fs approaches 0 (i.e., these particles do not diffuse and thus are not transported beyond the theoretical source height). This illustrates that there is significant outcome sensitivity embedded in this model, which may be overlooked simply by assuming fs O(1). However, the observations presented in this study contradict the physical implications of this test because very large particles are readily observed well above Hs and in significant concentrations (Fig. 5). This suggests that the basis from which this parameter is defined does not realistically capture the dynamics of these large spume droplets in these very strongly forced conditions.

Fig. 13.
Fig. 13.

The S0(r) spectra for wind speed trials (left) 45 and (right) 49.5 m s−1. The source function was calculated using Eq. (12), but the different colored curves represent different slip factor applications; the curves have been normalized to a common intercept. The slip factor was calculated as , where a was the test parameter. The values were set as monotonically decreasing with increasing particle size, but with the smallest radius class always having . The denotes the slip factor for the largest radius class. A line with an slope is provided as reference (note: the purple-cross curve extends much farther but is cut off by the axis limits).

Citation: Journal of the Atmospheric Sciences 73, 10; 10.1175/JAS-D-15-0249.1

6. Conclusions

A laboratory investigation into sea spray generation in wind speeds ranging from 36 to 54 m s−1 U10 was conducted to fill gaps in the literature regarding the spume production rate. An extensive set of spume droplet shadow images has been collected showing the vertical distribution of particles above actively breaking waves. The range of observed particle radii was roughly 801400 μm, and the methods used enabled direct quantification of the mean size-dependent number concentration profiles necessary to estimate the vertical flux of sea spray at the water surface. Spume drops were imaged between 2 and 6 times the local Hs, and for the highest wind speeds droplets circa 1 mm in radius were observed in relatively high quantities at 3–4 times Hs. This may suggest that these large droplets have a longer-than-expected lifetime in the atmospheric boundary layer, which could affect the role these particles play in the fluxes across the air–sea interface. However, the particle transport information necessary to confirm this was not measured as part of the present study. This observation is limited to pure wind waves, and making similar observations, including droplet transport, with both wind and swell waves will be the focus of future efforts.

A bulk spume generation model (Fairall et al. 2009; Veron 2015) was used to infer the size-dependent generation function from the droplet concentration measurements. These estimated source functions affirm previous laboratory work in similarly high winds (Veron et al. 2012) that demonstrated that large spume droplets (in the vicinity of 1 mm) are produced at rates several orders of magnitude higher than would be predicted by a typical source model (Mueller and Veron 2009). Further statistical analysis showed that less additional spray flux was observed for each incremental increase in wind forcing. Also, the size dependence of the source function was found to exhibit a clear wind speed dependence, which does not agree with spume production theory (Fairall et al. 1994). A similar relationship was found in a recently published study (Veron et al. 2012), which had not been previously described. The results of converting the observed concentrations to size-dependent source functions, using the spume generation model, demonstrated that there was variance in the observational data that was not fully captured by the parameterization. To investigate this further, least-squares regression analysis was used to test the concentration profile implied by the model against the directly measured profile acquired from the shadow images. These tests demonstrate that the measured concentrations follow a logarithmic profile rather than the power-law profile prescribed by the model. This finding has significant implications for estimating the vertical flux of spume droplets, which is critical to understanding the role sea spray plays in the lower portion of the atmospheric boundary layer, particularly in tropical cyclones. It must be emphasized that these findings are purely empirical, but they do suggest that it is necessary to reevaluate the governing transport equations in order to better capture spume dynamics in these strongly forced conditions.

Acknowledgments

The laboratory experiments were supported by the NSF through Grant 0933943. Additional support was provided through ONR Grants N000141410643, N000141310144, and N000141210448. The authors appreciate the efforts of Mike Rebozo and Dr. Neil Williams for their help with the data collection. The constructive criticisms of three anonymous reviewers are greatly appreciated, as their careful efforts greatly improved this study. E. Lewis is thanked for his thoughtful comments that helped to strengthen this work, as is C. Fairall for the use of the CIP in ASIST. Also, M. Donelan is thanked for help acquiring and analyzing previously collected data in ASIST.

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