Field Observations and Modeling of Surfzone Sensible Heat Flux

Jamie MacMahan Oceanography Department, Naval Postgraduate School, Monterey, California

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Ed Thornton Oceanography Department, Naval Postgraduate School, Monterey, California

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Jessica Koscinski Oceanography Department, Naval Postgraduate School, Monterey, California

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Qing Wang Oceanography Department, Naval Postgraduate School, Monterey, California

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Abstract

Surfzone sensible heat flux (HS,SZ) obtained through direct eddy-covariance estimates was measured at four different sandy beach sites along Monterey Bay, California. The HS,SZ source region is estimated from a footprint probability distribution function (pdf) model and is only considered when at least 70% of the footprint pdf occupies the surfzone. The measured HS,SZ is 2 times the modeled interfacial sensible heat (HS,int) using COARE3.5. A formulation for estimating sensible heat flux from spray droplets (HS,spray) generated during depth-limited wave breaking is developed. The sea-spray generation function for droplet radii ranging over 0.1 < ro < 1000 μm is based on self-similar spectra of spray droplets measured from the surfzone forced by the average depth-limited breaking wave dissipation across the surfzone. However, it is shown that the size of the spume droplets that contribute to HS,spray is limited owing to the relatively short residence time in air as the droplets fall to the sea surface during wave breaking. The addition of the surfzone-modeled HS,spray to the COARE3.5 HS,int gives values similar to the observed surfzone HS,SZ, highlighting the importance of depth-limited wave-breaking processes to sensible heat flux. Measured HS,SZ values are an order of magnitude larger than simultaneous open ocean observations.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jamie MacMahan, jhmacmah@nps.edu

Abstract

Surfzone sensible heat flux (HS,SZ) obtained through direct eddy-covariance estimates was measured at four different sandy beach sites along Monterey Bay, California. The HS,SZ source region is estimated from a footprint probability distribution function (pdf) model and is only considered when at least 70% of the footprint pdf occupies the surfzone. The measured HS,SZ is 2 times the modeled interfacial sensible heat (HS,int) using COARE3.5. A formulation for estimating sensible heat flux from spray droplets (HS,spray) generated during depth-limited wave breaking is developed. The sea-spray generation function for droplet radii ranging over 0.1 < ro < 1000 μm is based on self-similar spectra of spray droplets measured from the surfzone forced by the average depth-limited breaking wave dissipation across the surfzone. However, it is shown that the size of the spume droplets that contribute to HS,spray is limited owing to the relatively short residence time in air as the droplets fall to the sea surface during wave breaking. The addition of the surfzone-modeled HS,spray to the COARE3.5 HS,int gives values similar to the observed surfzone HS,SZ, highlighting the importance of depth-limited wave-breaking processes to sensible heat flux. Measured HS,SZ values are an order of magnitude larger than simultaneous open ocean observations.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jamie MacMahan, jhmacmah@nps.edu

1. Introduction

Sensible heat flux from the surfzone was directly measured for the first time and is the focus of this paper. Simultaneously, the sensible heat flux was measured directly offshore. No models for comparison have been developed specifically for sensible heat flux in the surfzone, although numerous studies have been conducted for the open ocean. In the open ocean, sensible heat flux (HS) and latent heat flux (HL) are described by their components of interfacial and spray contributions:
e1a
e1b
At the sea surface interface, the ocean and atmosphere are always exchanging sensible and latent heat owing to the air–sea temperature and humidity differences. The interfacial transport of sensible heat across the air–sea surface boundary is controlled by wind speed and air–sea temperature differences given by the bulk approximation
e2
where ρa is the density of air, cp is specific heat of air under constant pressure, U10 is the wind speed at 10-m elevation, Tw is sea surface water temperature, and Ta is the air temperature at 10 m. The coefficient CH10 is the bulk transfer coefficient for sensible heat, which is dependent upon wind and thermal stability of the surface layer (Andreas and Murphy 1986):
e3
where CD10 is the drag coefficient, which describes the bulk transfer of momentum, the subscript N10 refers to neutral conditions at 10 m, k is the von Kármán constant, and ψh(10/L) is a stability correction, which is a function of the Monin–Obukhov length L. In the same experiment here, the momentum flux was measured from the surfzone by MacMahan (2017). He found that CD10 in the surfzone was approximately twice that offshore, which he hypothesized to be the result of increased roughness by foam generated by depth-limited breaking waves inside the surfzone. Subsequently, Hansen and MacMahan (2018, manuscript submitted to Bound.-Layer Meteor.) measured the geometric roughness of the surface kj within the surfzone using stereophotogrammetry. They found surfzone kj values were approximately twice suggested open ocean values, confirming the earlier hypothesis. These results suggest, based on Eq. (3), that the bulk transfer coefficient CH10 is increased inside the surfzone relative to that in the open ocean.

There is a paucity of HS,int measurements in the surfzone. The only results available in the literature are by Tuller (1972), who determined HS,int as the residual of the energy budget. Therefore, HS,int described by Eq. (2) will be applied to the surfzone. It is pointed out that the formulations presented herein are approximations, and controversy exists over many issues describing heat fluxes (Veron 2015).

The contribution to sensible and latent heat flux by spray occurs when sea-spray droplets are released into the atmosphere. Veron (2015), in a review of ocean spray generation, identifies two basic mechanisms for spray droplets. The first occurs when bubbles are entrained into the water column during wave breaking and then rise to the surface and burst. The bursting bubbles typically occur on the backside of the breaking wave forming a foamy layer identified as a whitecap. The bursting process creates film and jet droplets. The film droplets occur when the submerged bubble forms a bubble cap protruding from the surface that bursts into a large number of small droplets ejected into air with radii O(0.1–0.5 μm). When the bubble cap has burst, the resulting cavity collapses violently and a vertical jet forms that fragments into several droplets ejected into the air with radii O(1–100 μm).

The second mechanism generates spume droplets. In the open ocean, droplets generated during whitecapping are due to a dynamic instability when vertical accelerations exceed the gravitation restoring force, with droplets flying off the crest vertically owing to steepening of the waves during generation by wind. When the wind speed exceeds approximately 7–11 m s−1, sufficient stress is generated to tear water from the surface of the wave crest in the form of spume with droplet radii O(10–1000 μm or greater).

One of the largest uncertainties in predicting heat fluxes induced by sea-spray droplets in the open ocean is associated with the production function for spray droplets (e.g., Andreas et al. 2015; Veron 2015; Monahan et al. 2017), which is parameterized by wind speed and whitecap coverage. Andreas (1992) suggests that spray-mediated fluxes can be the same order as the interfacial fluxes. The papers by Andreas (1989, 1992, 2005), Fairall et al. (1996), and Andreas DeCosmo (1999), among others, lay the foundation for the modeling of sensible heat flux by sea-spray droplets.

Although there are numerous studies of open ocean sea-spray production, there are few surfzone measurements. Monahan (1995) speculated that greater sea-spray aerosols would be generated over the surfzone than in the open ocean owing to waves continually breaking across the surfzone. Within the surfzone, spray droplets are generated during depth-limited wave breaking (van Eijk et al. 2011). Depth-limited breaking is due to kinematic instability as the speed of the wave crest exceeds the phase speed of the wave during shoaling. The crest curls forward with droplets ejected horizontally into the air. The strength of wave breaking and the amount of spray droplet generated is dependent on the type of breaking wave. Breaker type is parameterized by the surf similarity parameter ξ = tanβ/(Hsig/Lo)1/2, where tanβ is the beach slope, Hsig is the significant wave height, and Lo is the wavelength calculated for deep water (Battjes 1974). Plunging (waves that curl over) and collapsing (shore break) breaking waves are the most violent, and occur when ξ > 0.4. Spilling breakers occur when ξ < 0.4 and are less violent, similar to whitecapping.

Spume droplets are generated at wave crests and fall down the face of spilling breakers. As the intensity of spilling breakers increases, the crest increasingly curls over, generating greater spume. As opposed to the gentle breaking process of a spilling breaker, a plunging breaker face becomes vertical and then overturns throwing a jet of water forward composed of large spume droplets. No wind is required to generate spume in the surfzone. As the jet crashes into the surface, splashes are sent up forward of the wave as a secondary splash generating more spume droplets Derakhti and Kirby (2014). This process of jet formation and splash down can be repeated several times as the wave moves toward the shore. The waves during the experiment were mostly plunging breakers.

Both mechanisms of generated spray droplets and spume occur within the surfzone. Depth-limited wave breaking produces orders of magnitude more spray droplets than whitecapping in the open ocean. Most measurements in the surfzone have focused on aerosol production of smaller droplet radii (<30 μm) that are transported inland (Neele et al. 1998; de Leeuw et al. 2000; Vignati et al. 2001; Clarke et al. 2006; Piazzola et al. 2015), and the production is parameterized as a function of wind speed.

Owing to depth-limited wave breaking in the surfzone, the correct parameterization should be related to the breaking wave. Chomka and Petelski (1997) relate the total measured droplet sea-salt production, without regard to droplet size, to the average wave dissipation in the surfzone. Van Eijk et al. (2011) relates measured production of spray over the limited range of droplet radii 0.2–10 μm also to the average wave dissipation across the surfzone. Andreas (2016) measured spray production of larger droplets (radii 0–150 μm) from the surfzone along a rocky shoreline applying footprint analysis and found that the spectra of the sea-spray droplet radii had the same shape independent of wind speed. He concluded that the spray concentrations on a rocky shoreline are two to three orders of magnitude greater than open ocean values.

In this paper, sensible heat flux measurements across the surfzone as determined using footprint analysis are presented. The self-similar sea-spray production spectrum by Andreas (2016) is combined with the sea-spray production model by van Eijk et al. (2011) to describe spray-mediated sensible heat flux as a function of the average breaking wave dissipation within the surfzone. The combined estimates of interfacial sensible heat flux [Eq. (2)] and the sensible heat flux spray droplet model developed herein compare reasonably well to surfzone observations of HS. The measured HS values are used to calibrate the developed model.

2. Field experiment

Collocated sonic anemometers, temperature, and relative humidity sensors were mounted on six 6-m-high towers and deployed simultaneously on four different sandy beaches located along 10 km of the Monterey Bay, California, shoreline (Figs. 1a,b). Towers were located on the beach at the high-tide line at each site, with an additional two towers located in the surfzone and inland beach at the southernmost site. The Monterey Bay nearshore bottom profile is composed of a relatively steep (1:7–12) foreshore beach flattening out to a low-tide surfzone terrace (1:100), continuing offshore with a steeper 1:35 offshore slope (MacMahan et al. 2010).

Fig. 1.
Fig. 1.

(a) Topographic and bathymetry map of Monterey Bay. Black dots represent the four beaches on which six towers were deployed. The white triangle represents the NDBC buoy. The dotted white line denotes the outer boundary of Monterey Bay. (b) Sonic anemometers were collocated with temperature–humidity sensors located on top of the tower, solar panels were located in the middle, and the data acquisition system was located in the white box near the bottom. Towers were deployed at the high-tide line, where the tower base was approximately 1.2 m MSL.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The location of the tower measurements is based on measuring turbulence fluxes that originate in the surfzone as determined by its footprint, which is described in detail for this experiment by MacMahan (2017). The footprint represents the source location where the measured turbulence and heat originates. The footprint cross-shore length increases with increasing stability, which determines vertical mixing, and wind speed and measurement elevation, which determine trajectory. The data were filtered based on criteria that the percent contribution of the surfzone source region exceed 70% of the total footprint. Since only times of onshore winds are considered, the footprint of turbulent fluxes originating in the surfzone required the towers be located downwind on the beach.

Observations were obtained continuously for four weeks in May–June 2016 and divided into 15-min blocks for analysis. The analysis for computing momentum fluxes and procedures for quality controlling the data are given in Aubinet et al. (2012). The sensible heat flux was computed from the sonic anemometer measurements by
e4
where w′ is the turbulent vertical velocity, is temperature perturbation, is the average (15 min) air density, and angle brackets denote the 15-min time average. Direct estimates of HL were not obtained.

Waves along with ocean temperatures were measured using a pressure sensor and temperature string deployed in 10-m water seaward of each beach tower. Significant wave height (Hsig), average wave period (Tavg), and wave setup were estimated from the pressure observations (Dean and Dalrymple 1984). The tower position and elevation and beach profile were surveyed with GPS. The distance between the waterline and tower location including wave setup was estimated for each HS measurement. Wave heights Hsig ranged from 0.13 to 1.2 m with a mean of 0.8 m. The quantity Tavg ranged from 6 to 13 s associated with local storm-generated events. The surf similarity parameter ranged from 0.3 to 0.8 with an average of 0.6, indicating mostly plunging breakers, which was verified by observation.

Mean wind speed measured at 6-m elevation U6 ranged from 0 to 11 m s−1, with a mean of 6 m s−1. The maximum winds occurred in the late afternoon and reduced to near zero at night. A diurnal cycle was observed that was occasionally modified by larger mesoscale atmospheric storm events.

Beach air temperature Ta ranged from 12° to 17°C with a mean of 14°C. Near-surface (<1 m below the surface) water temperatures also ranged from 12° to 17°C with a mean of 16°C. The difference of air and water temperatures ΔT ranged from −3° to 1.3°C and was predominantly negative, implying the atmosphere behaved as an unstable system with transfer of heat to the atmosphere. The relative humidity averaged 85%. Owing to the limitations of available empirical formulations to raise U6 measured winds to UN10 neutral stability winds used in comparing results, momentum flux data are limited to atmospheric stabilities (ψ) in the range −2 < ψ < 0.5, U6 > 3 m s−1, and to onshore wind directions that are ±40° relative to shore normal. These limitations reduced the analyzed data to 3031 onshore records, of which 630 records are represented by the surfzone.

In addition to the beach tower measurements, open ocean HS was measured from a moving vessel using similar instrumentation. The vessel moved throughout Monterey Bay for most of the tower operation. The heat flux observations are taken as representing the open ocean, and hence are referred to as HS,O. The vessel operation was limited to daytime hours and to lower wind conditions for safety concerns, resulting in 457 overlapping vessel and surfzone observations that are the basis of the analysis.

3. Surfzone sensible heat flux spray model

Winds during the experiment were generally mild and less than 11 m s−1 such that they generated minimal spume. Hence, it is assumed that the spray droplets are all generated by the breaking waves and that the air turbulence was insufficient to elevate the droplets. Therefore, spume droplets generated at the crest of a breaking wave are assumed to fall to the water surface as in quiescent air turbulence. A droplet with initial radius ro generated at the crest of a breaking wave has a flight time
e5
where uf is the Stokes fall velocity modified to account for larger Reynolds numbers owing to turbulence that characterize the fall of the larger spray droplets, and h is the flight distance of the droplets with mean radius ro (Andreas1990; Veron 2015). For plunging breakers, the flight distance h = KHsig, where Hsig is the significant wave height of the depth-limited breaking waves and K ranges from 0.5 for the initial fall from the crest to the wave face where the droplets enter the water at the approximate mean water level to a value of 1 or more to account for splash up of the plunging breaker.
A spray droplet rapidly exchanges sensible heat with the atmosphere as it falls, and cools to a constant evaporation temperature Tev below the air temperature to warm the atmosphere, which differs slightly form the wet bulb temperature (Andreas 1995). The quantity Tev is a function of the salinity of the water droplet and relative humidity of the air. This exchange of sensible heat occurs in time τT and is modeled based on microphysical equations of sea-spray evolution by Andreas (1989, 1992, 1995)
e6
where is defined as the time when the right-hand side of Eq. (6) reaches 1/e, the e-folding scale. The value of is a function of droplet radius where small droplets transfer their sensible and latent faster than larger droplets. At this point, the droplet has reached thermal equilibrium with the atmosphere and has exchanged its sensible heat with the atmosphere HS,spray. Up to this point, the droplet has retained most of its water mass.
Subsequently, the droplet will start to evaporate giving off water vapor in the process of extracting latent heat from the atmosphere HS,spray. However, the evaporation process is much slower, occurring in characteristic time τr, which is the time scale required for an initial droplet of radius ro to reach moisture equilibrium with its environment while losing a significant amount of its water mass via evaporation, given by
e7
where the droplet temperature stabilizes at an equilibrium temperature Teq when the equilibrium radius req is reached after evaporation. Again, τr is the e-folding time when the droplet has experienced 1/e of its radius change and has only the time to act during the fall of the droplet from the crest to when it enters the water surface. For example, Andreas (1995) shows that a 100-μm droplet reaches its evaporation temperature Tev in less than 1 s, but the droplet does not show significant reduction in size caused by evaporation until after about 30 s and would not lose all its water at equilibrium temperature Teq until more than 500 s, well after it had fallen into the water.

The quantity HS,spray is dependent on relative humidity and radius of the droplet. The evaporation of the droplet cools the atmosphere by HL,spray such that the net spray-mediated sensible heat flux is HS,sprayHL,spray. However, the time scales for these processes are very different, resulting in the processes being essentially independent (Veron 2015). The HL,spray may be ignored for τf < τr since there is not time to exchange a significant amount of latent heat before the droplet falls back into the sea. For the average wave height during the experiment, Hsig = 0.8 m, τf < τr for ro ≥ 20 μm.

For the nominal environmental conditions during the experiment, the characteristic time scales τf for the range of wave heights (0.13–1.2 m) and τr for sea temperatures (12°–20°C) with a constant temperature difference between air and water ΔT = −2°C, salinity of 34 psu, and relative humidity range of 75%–95% are plotted as a function of ro in Fig. 2. Veron (2015) points out that for larger spume droplet when τf < τr the droplets will not reach thermal equilibrium before they fall back into the water. The spume droplets then will not reach Teq, and Tev is the temperature scale that measures the amount of sensible heat exchanged. The criteria τf < τr when there is not time to exchange latent heat before falling back into the ocean occurs at approximately ro ≥ 20 μm for these experiments (left vertical dashed line in Fig. 2). At the other end of the spectrum for the largest spume droplets, when τf < the droplets fall back into the ocean before having time to exchange all their sensible heat, which occurs at approximately ro ≥ 200–400 μm (right vertical dashed line in Fig. 2). For higher waves, the flight times τf are greater and the ro criteria are greater (see discussion section).

Fig. 2.
Fig. 2.

Characteristic droplet e-folding times to reach evaporation temperature τTev (black line) equilibrium temperature τr (light gray band), and droplet fall time τf (darker gray band) as a function of spray radii ro. The τTev is for a range of seawater temperatures Tw = 12°–20°C with a constant temperature difference between water and air ΔT = 2°C, salinity of 34 psu, and relative humidity range of 75%–95%; τf values are for range of wave heights 0.13–1.2 m (adapted after Veron 2015). Left vertical dashed line: τfτr. Right vertical dashed line: τfτTev.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

Andreas (1992, 2005) developed spray-mediated sensible and latent heat flux as a function of initial droplet radius ro:
e8a
e8b
where ρw is density of seawater, cw is specific heat of seawater, Tw is initial seawater temperature, and Ta is air temperature. The minus sign in Eq. (8b) means that the spray droplets are extracting heat from the air if they are evaporating. The term dF/dro is the sea-spray generation function (SSGF), where is the rate at which the volume of droplets is produced. Equation (8b), divided by the latent heat of evaporation of water Lυ, is the mass of water droplets in the air during their flights. The term in the square brackets in Eq. (8a) is a magnitude function that limits sea-spray droplet contributions to the sensible heat flux.
Van Eijk et al. (2011) evaluated the depth-limited wave-breaking SSGF that originates within the surfzone. They measured the difference in aerosol spray concentrations upwind and downwind of the surfzone for the range of ro from 0.1 to 10 μm. Their SSGF is dependent on average breaking wave dissipation D, parameterized on wave height (Thornton and Guza 1983):
e9
where a = 10, b = −0.35, and c = −1.5 are coefficients that possess units. Units of dF/dro are μm−1 m−2 s−1.
Andreas (2016) measured spray concentration and the rate of spray production using a cloud-imaging probe (CIP) mounted on a tower at an elevation of 8.7 m above mean sea level located 50–75 m shoreward of the surfzone on a rocky shoreline. The CIP continuously measured spray concentrations in 12 radius bins, each 12.5 μm wide, from 0 to 150 μm. The measurements include spume generation. Footprint analysis suggested that all measured droplets came from the surfzone. It was found that the shape of the concentration spectra as a function of spray radii ro did not change with respect to wind speed, that is, the spectra are self-similar for different forcing. A common assumption is that the shape of the SSGF is universal, whereas the magnitude depends only on forcing parameters (e.g., Monahan et al. 1986; Andreas 1992, 2016; Wan et al. 2017),
e10
where g(D) is the magnitude of the forcing function and f(ro) is a shape function describing the self-similar droplet size spectrum (Andreas 2016):
e11
where f(ro) is normalized for the value ro = 6.25 μm; that is, f(ro = 6.25 μm) = 1. The shape function is composed of two power-law slopes (Fig. 3) that have been combined as a hyperbola in Eq. (11).
Fig. 3.
Fig. 3.

Self-similar spectrum of sea-spray droplets f(ro) (after Andreas 2016; solid line) and Andreas (2016) modified to fit data (dashed line).

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The volume spray production spectrum represents the volume of droplets generated as a function of droplet size and is obtained by multiplying the shape function by the volume of the droplets:
e12
The quantity fV is plotted (Fig. 4a) in linear dimensions to emphasize the sharp increase and then rapid decrease that limits the contribution by larger spume droplets. A maximum value occurs at ro = 60 μm. In multiplying by in Eq. (12), the slopes of the shape function spectrum are increased by a factor of 3.
Fig. 4.
Fig. 4.

(a) Volume f(ro) multiplied by the magnitude function of Andreas (2016; solid line) and modified version to fit data (dashed line). The fV(ro) maximum occurs at ro = 60 μm. (b) Magnitude function in the sensible heat flux Eq. (15) for Hsig = 0.13 (broken line), 0.8 (dashed line), and 1.2 (solid line) m and Ta = 14°C. (c) Cumulative distributions for spectra (solid black) in (a) and also multiplied by magnitude function (dashed black) in (b) for H = 0.8 m. Calculations are for ro = 0–1000 μm.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

Total spray-mediated heat fluxes are obtained by integrating over the range of droplet sizes,
e13a
e13b
where r1 and r2 represent the lower and upper limit of the droplet radii (Andreas 1992). The net spray-mediated sensible heat flux is HS,sprayHL,spray. However, the HL,spray was found to only contribute for ro < 20 μm, which represents less than 5% of fV (Fig. 4c). Therefore, for simplicity HL,spray is neglected in calculating total sensible heat flux.
Andreas (2016) assumed that the magnitude function g was dependent on wind speed. Here, it is assumed that g(D) is a function of the average breaking wave dissipation across the surfzone D. The surfzone observations by van Eijk et al. (2011) that the SSGF as a function of breaking wave dissipation over the limited range 0.2–10 μm fortuitously included ro = 6.25 μm that is used to normalize the Andreas (2016) shape function, which is used to define the magnitude function
e14
with units μm−1 m−2 s−1. Substituting Eqs. (12) and (14) into Eq. (10) and then into Eq. (13a) and integrating across the range of radii,
e15
where the limits of integration extend the range of spray droplets radii from 0.1 to 1000 μm. The units for HS,spray are watts per meter squared.
The average breaking wave dissipation D is calculated using the wave energy flux transformation model by Thornton and Guza (1983),
e16
where individual waves are described by a Rayleigh wave height distribution parameterized by the significant wave height , with the mean incident wave energy E = 1/16ρg; is the group velocity, and is the averaged local breaking wave dissipation. Assuming normally incident waves (good assumption for experiment locations) and negligible wave reflection, the energy flux is conserved up to breaking outside the surfzone. Therefore, the measured waves in 10-m water depth are well before breaking and are used to specify the energy flux. Only the depth-limited breaking waves contribute to dissipation with larger waves breaking further offshore. An empirical dissipation function is used to describe the breaking wave height distribution as a function of depth [see Thornton and Guza (1983) for details]. As the waves shoal and break, the mean wave energy first decreases slightly and then increases to a maximum before significant wave breaking, and then decreases shoreward as the waves break and dissipate across the surfzone. The total breaking wave dissipation is calculated by integrating across the surfzone:
e17
where the outer edge of the surfzone xb is defined at the location where the averaged shoaling/breaking waves are maximum, and the inner limit zero is the shoreline. Hence, xb is equal to the average width of the surfzone. The average dissipation is given by
e18

4. Results and discussion

The average breaking wave dissipation D for the range of Hsig from 0.13 to 1.3 m during the experiment ranged from 4 to 113 W m−2 with a mean of 60 W m−2. Values of HS,spray as a function of D values during the experiment are shown in Fig. 5. A sensitivity analysis finds that a ±20% error in average dissipation D results in an approximate error from +70% to −40% in HS,spray. This suggests HS,spray is sensitive to D for this model.

Fig. 5.
Fig. 5.

Calculated sensible heat flux for sea-spray droplets HS,spray as a function of average breaking wave dissipation for the wave heights during the experiment (Hsig ≤ 1.3 m) for Tw = 16°C and Ta = 14°C. The ±20% error for D is shown by the dashed lines.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The observations of HS,SZ are larger than HS,O, implying that the surfzone produces greater sensible heat flux, which is hypothesized to be related to the increased spray contribution by breaking waves as well as generally warmer nearshore waters for this site (Fig. 6). A significant number of HS,SZ values occur for near-zero values of HS,O, which demonstrates that even in low winds over the ocean there is significant HS,SZ owing to depth-limited breaking waves in the surfzone.

Fig. 6.
Fig. 6.

Observations of surfzone sensible heat flux (HS,SZ) compared with open ocean sensible heat flux (HS,O) observed at the same time.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

Surfzone HS,SZ observations are compared with the COARE3.5 HS,int estimates (Fig. 7a). The HS,SZ and HS,int are linearly correlated at the 95% significance level (r2 = 0.63) with a linear regression slope of 0.46. This suggests that about 50% of the surfzone contribution to HS,SZ was owing to HS,int. Modeled HS,spray [Eq. (15)] added to modeled HS,int [Eq. (2)] is referred to as HS,int+spray. The modeled HS,int+spray is linearly correlated with HS,SZ at the 95% significance level (r2 = 0.7) with a linear regression slope of 0.79 (Fig. 7b). The total sensible heat flux in the surfzone was composed of near-equal contributions by interfacial and spray-mediated fluxes.

Fig. 7.
Fig. 7.

(a) The HS,SZ observations compared with COARE3.5 HS,int [Eq. (2)]. (b) The HS,SZ observations compared with COARE3.5 HS,int added to modeled HS,spray. Black lines represents the 1:1 lines. Dashed lines are the linear regression lines, where m = 0.46 and r2 = 0.63 in (a) and m = 0.84 and r2 = 0.7 in (b). The white circles represent the average of 10 W m−2–wide bins. The dot color represents the difference in Tair relative to Twater with the color scale on the right.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

Andreas (1992) and Andreas and DeCosmo (1999) suggest that spray droplet contributions to the sensible heat flux in the open ocean start to become important when U10 > 12 m s−1, and at 20 m s−1 are as important as interfacial heat flux contributions. Here, spray droplet contribution to heat flux is important starting at the lowest wind speeds considered (U6 > 3 m s−1) because the generation of spray droplets by depth-limited breaking in the surfzone is not directly dependent on wind speed. However, it is noted that some wind is necessary for the sensible heat released by the droplets within the surfzone to reach the measurement location on the beach.

When depth-limited breaking occurs, a large range of spume droplet sizes can be generated up to 10 mm and greater. However, the size of spume droplet radii generated by depth-dependent breaking waves that contributes to the sensible and latent heat flux is dependent on the wave height. As the droplet generated at the wave crest falls, it has a limited amount of time to give off sensible and latent before reaching the water surface. For the smaller size spray droplets, the latent heat contribution is limited by evaporation time before falling back into the sea. For conditions during the experiment, τr < τf for only ro < 20 μm, and the latent heat by spray droplets could be neglected. For larger spume spray droplets, the time to give off sensible heat is limited by the fall time, which is described by the magnitude function [term in square brackets in Eqs. (8a) and (15)]. The magnitude function is dependent on fall time, which in turn is a function of the wave height (Fig. 4b). Applying the criterion that the spume radii that contribute to the sensible heat are limited to ro values at which the cumulative distribution of the total sensible heat flux reaches 99% [ro(0.99)], we find that HS,spray for the experiment was limited approximately to ro < 400 μm (Fig. 4c). For larger waves, the fall distance and time increases. Allowing a range of fall distances, 0.5HsighHsig for Hsig up to 10 m, the calculated ro(0.99)range to over 700 μm (Fig. 8).

Fig. 8.
Fig. 8.

The ro value at which the cumulative distribution of [1 − exp(τf T)]fV(ro) is greater than or equal to 0.99 for the Andreas (2016) modification as a function of 0.5Hsigh ≤ 2Hsig (gray band), with Ta = 14°C.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The modeled total HS,SZ values give an O(1) estimate of the measured values with a 21% underestimate. Reasons for the underestimation include errors in the SSGF composed of the spectral shape for ro by Andreas (2016) and the magnitude function dependent on the average breaking wave dissipation by van Eijk et al. (2011). Andreas (2016) points out that his SSGF spectrum for large spray radii ro > 100 μm converge to open ocean values described by a joint Monahan et al. (1986) and Fairall et al. (1994) function given in Andreas (2010). He suggested this convergence could be that the larger droplets settled out before they reached the CIP. He suggests that the spray generation function is robust for spray droplets less than 50–100 μm, but less certain for larger droplets. In the application to sensible heat flux by spray, all spume droplets generated by the breaking waves can contribute. However, most of the spume droplets fall back into the water almost immediately in front of the wave; many of these larger droplets would not be measured 75 m shoreward at an elevation of 8.7 m above mean sea level, and are not expected to be included in the Andreas (2016) spectral values. Therefore, it is expected that the Andreas (2016) slope of the SSGF tail for the spume droplet spectrum ro > 100 μm is too steep at .

The spectral shape for the spume region ro > 100 μm varies between SSGF models proportional to from to . Ortiz-Suslow et al. (2016) optically measured the vertical distribution of spume droplets just above the breaking waves under hurricane-force winds in a wave tank. Their observed droplet radii ranged from 80 to 1400 μm. Veron et al. (2012) obtained similar results in a wave tank at high wind speeds. Both experiments observed SSGF radius dependence ranging from to for the larger spume droplets. Interestingly, the observed Ortiz-Suslow et al. (2016) spectra are at least qualitatively self-similar in shape at all wind speeds.

The HS,spray model is calibrated with measurements by increasing the tail slope of the SSGF to (Fig. 3), which increases the amount of spume droplets. The combined calibrated HS,spray with the modeled COARE3.5 HS,int then match the measured values of HS. The revised slope in the spume region of the revised SSGF is similar to the slopes measured just above the waves under simulated hurricane winds by Veron et al. (2012) and Ortiz-Suslow et al. (2016). Therefore, the amount of spume generated even under small to moderate depth-limited wave breaking in the surfzone is comparable to the spume generated by high winds over the ocean.

Another source of uncertainty is the driving mechanism expressed as a function of the average breaking wave dissipation D given by the van Eijk et al. (2011) formulation, which is based on field measurements over the limited range of ro = 0.2–10 μm. The curved shape of the van Eijk et al. (2011) g(D) ranges in slope between D1 and D3 as compared with the D3/4 dependence in the Chomka and Petelski (1997) formulation.

A third source of possible error is in calculating the average breaking wave dissipation. Neele et al. (1998) applied the model by Chomka and Petelski (1997) that parameterizes the SSGF on average breaking wave dissipation. The total wave dissipation is reasonably well described. However, they note that the average is dependent on how the width of the surfzone is calculated. They used a formulation for D similar to the application here, which defines the surfzone width as the distance between where the maximum modeled breaking wave height occurs to the shoreline. Chomka and Petelski (1997) defined the outer limit as where dissipation is equal 0.003 W m−2 that results in a much wider surfzone and concomitant decrease in the average dissipation.

Observations of spray droplets generated in the surfzone at levels below the peak of the breaking wave are required to better estimate HS. The impact of the surfzone as a conduit for releasing heat into the atmosphere is currently underestimated. The ratio of measured surfzone HS,SZ to measured open ocean HS,O as a function of wind speed is shown in Fig. 9. Whereas the interfacial heat flux contribution is dependent on the air–seawater surface temperature difference that varies by location and was either positive or negative, the spray-mediated surfzone heat flux was always positive and dependent on breaking wave height. The spray-only-mediated HS,SZ-spray is estimated by subtracting HS,int (COARE3.5) from HS,SZ measured and is compared with HS,O in Fig. 9. The ratios are similar for low wind speeds but increase by an order of magnitude by wind speed 8 m s−1.

Fig. 9.
Fig. 9.

Measured surfzone sensible heat flux divided by measured open ocean HS,O (gray line) and surfzone spray-mediated sensible heat flux (black line) computed by subtracting the COARE3.5-modeled HS,int [Eq. (2)] from the measured HS,SZ divided by HS,O. The ratio is binned in 1 m s−1 intervals. Confidence intervals are provided for 95% significance.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The increasing large ratio of the surfzone interfacial heat flux to open ocean sensible heat flux is primarily owing to an average 3°C warmer seawater surface temperature in the nearshore (10-m depth) when compared with offshore temperature measured at the National Data Buoy Center (NDBC) buoy (Fig. 10). The average difference in the tower air temperature with the nearshore surface water temperature is −2°C resulting in mostly unstable conditions. However, at the NDBC buoy offshore, the air–surface water temperature differences are mostly positive resulting in stable conditions on average. The differences in the open ocean and nearshore temperature differences are due to oceanographic surface conditions forced by the wind and alongshore currents, and is the topic of ongoing research.

Fig. 10.
Fig. 10.

Histograms of surface temperature differences (°C): (a) nearshore (10-m depth) water minus NDBC water; (b) air at tower minus nearshore water; (c) air NDBC minus water NDBC. The location of the NDBC buoy is shown in Fig. 1.

Citation: Journal of Applied Meteorology and Climatology 57, 6; 10.1175/JAMC-D-17-0228.1

The surface area of Monterey Bay is O(600 km2) (Fig. 1, inside dashed white line). The surfzone surface area assuming a 50-m width for Monterey Bay is O(7 km2) giving a ratio of Monterey Bay surfzone–ocean areas of 1:90. Applying the 20:1 ratio (Fig. 9) to the area ratio suggests that HS,SZ represents O(20%) of the Monterey Bay sensible heat flux estimate. This suggests that the surfzone has a potential contribution to the sensible heat flux that has not been previously considered. This will differ for different regions based on air and water temperature differences and waves.

5. Summary and conclusions

Surfzone sensible heat flux (HS,SZ) obtained through direct eddy-covariance estimates was measured at four different sandy beach sites along Monterey Bay. The HS,SZ source region is estimated from a footprint probability distribution function (pdf) model and is only considered when at least 70% of the footprint pdf occupies the surfzone. The HS,SZ measured are 2 times the modeled interfacial sensible heat (HS,int) using COARE3.5. The HS,SZ is associated with larger sea-spray droplet production owing to depth-limited wave breaking. A formulation for estimating sensible heat flux from spray droplets (HS,spray) is developed based on self-similar spectra of spray droplet radii measured from the surfzone (Andreas 2016) forced by the average depth-limited breaking wave dissipation across the surfzone (van Eijk et al. 2011) to describe the generation of sea-spray droplet radii ranging 0.1 < ro < 1000 μm. However, it is shown that the size of the spume droplets that contribute to HS,spray is limited to approximately 700 μm even for the largest waves owing to the relatively short residence time in air as the droplets fall to the sea surface. Combining surfzone-modeled HS,spray with the COARE3.5 HS,int underestimates the measured surfzone HS,SZ by 21%, highlighting the importance of depth-limited wave-breaking processes to sensible heat flux. By increasing the slope of the tail of the SSGF, the modeled HS,spray values are increased to match the measured HS,SZ. Measured HS,SZ values are an order of magnitude larger than simultaneous open ocean observations. Although more work is required to improve the model, the measurements highlight the importance of the surfzone spray-mediated HS,SZ contribution.

Acknowledgments

This work is dedicated to the memory of Edward L Andreas who indirectly inspired this manuscript from his many publications on spray. This work was supported as part of the Office of Naval Research Coastal Land Air Sea Interaction (CLASI) pilot experiment (N0001417WX00612; N0001417WX01138). Appreciation is extended to the NPS CLASI field team (Darin Keeter, Paul Jessen, Keith Wyckoff, Mathias Roth, and Tucker Freismuth) and CLASI collaborators (University of Miami: Brian Haus, Hans Graber, Dave Ortiz-Suslow, and Neil Williams; Naval Postgraduate School: Dick Lind and Ryan Yamaguchi; and Naval Research Laboratory: Jim Doyle and David Flagg). The authors thank reviewer Elisa Canepa and the anonymous reviewer whose constructive critical comments resulted in an improved manuscript.

REFERENCES

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    • Crossref
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    • Crossref
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    • Crossref
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  • Andreas, E. L, and J. DeCosmo, 1999: Sea spray production and influence on air-sea heat and moisture fluxes over the open ocean. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Atmospheric and Oceanographic Sciences Library, Vol. 20, Springer, 327–362.

    • Crossref
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  • Andreas, E. L, L. Mahrt, and D. Vickers, 2015: An improved bulk air-sea surface flux algorithm, including spray-mediated transfer. Quart. J. Roy. Meteor. Soc., 141, 642654, https://doi.org/10.1002/qj.2424.

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  • Battjes, J. A., 1974: Surf similarity. Proc. 14th Conf. on Coastal Engineering, Copenhagen, Denmark, ASCE, 466–480.

    • Crossref
    • Export Citation
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    • Export Citation
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    • Crossref
    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
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  • MacMahan, J., 2017: Increased aerodynamic roughness owing to surfzone foam. J. Phys. Oceanogr., 47, 21152122, https://doi.org/10.1175/JPO-D-17-0054.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacMahan, J., and Coauthors, 2010: Mean Lagrangian flow behavior on an open coast rip channeled beach: A new perspective. Mar. Geol., 268, 115, https://doi.org/10.1016/j.margeo.2009.09.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., 1995: Coastal Aerosol Workshop Proceedings. Naval Research Laboratory Rep. NRL/MR/7542-95-7219, 138 pp.

  • Monahan, E. C., D. E. Spiel, and K. L. Davidson, 1986: A model of marine aerosol generation vie whitecaps and wave disruption. Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E.C. Monahan and G. Mac Miocaill, Eds., D. Reidel, 167–174.

    • Crossref
    • Export Citation
  • Monahan, E. C., A. Staniec, and P. Vlahos, 2017: Spume drops: Their potential role in air-sea gas exchange. J. Geophys. Res. Oceans, 122, 95009517, https://doi.org/10.1002/2017JC013293.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neele, F. P., G. de Leeuw, J. Martijn, and M. Stive, 1998: Quantitative assessment of surf-produced sea spray aerosol. Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, Ed., International Society for Optical Engineering (SPIE Proceedings, Vol. 3433), https://doi.org/10.1117/12.330242.

    • Crossref
    • Export Citation
  • Ortiz-Suslow, D. G., B. K. Haus, S. Mehta, and N. J. M. Laxgue, 2016: Sea spray generation in very high winds. J. Atmos. Sci., 73, 39753995, https://doi.org/10.1175/JAS-D-15-0249.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Piazzola, J., G. Tedeschi, and A. Demoisson, 2015: A model for the transport of sea-spray aerosols in the coastal zone. Bound.-Layer Meteor., 155, 329350, https://doi.org/10.1007/s10546-014-9994-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thornton, E. B., and R. T. Guza, 1983: Transformation of wave height distribution. J. Geophys. Res., 88, 59255938, https://doi.org/10.1029/JC088iC10p05925.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tuller, S. E., 1972: Energy balance microclimatic variations on a coastal beach. Tellus, 24, 260270, https://doi.org/10.1111/j.2153-3490.1972.tb01552.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • van Eijk, A. M. J., J. T. Kusmierczyk-Michulec, M. J. Francius, G. Tedeschi, J. Piazolla, D. L. Merritt, and J. D. Fontana, 2011: Sea-spray aerosol particles generated in the surf zone. J. Geophys. Res., 116, D19210, https://doi.org/10.1029/2011JD015602.

    • Search Google Scholar
    • Export Citation
  • Veron, F., 2015: Ocean spray. Annu. Rev. Fluid Mech., 47, 507538, https://doi.org/10.1146/annurev-fluid-010814-014651.

  • Veron, F., C. Hopkins, E. L. Harrison, and J. A. Mueller, 2012: Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett., 39, L16602, https://doi.org/10.1029/2012GL052603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vignati, E., G. deLeeuw, and R. Berkowicz, 2001: Modeling coastal aerosol transport and effects of surf-produced aerosols on processes in the marine atmospheric boundary layer. J. Geophys. Res., 106, 20 22520 238, https://doi.org/10.1029/2000JD000025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wan, Z.-H., J.-B. Zhu, K. Sun, and K. Zhou, 2017: An integrated turbulent simulation and parameter modeling study on sea-spray dynamics and fluxes. Ocean Eng., 130, 6471, https://doi.org/10.1016/j.oceaneng.2016.11.041.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save
  • Andreas, E. L, 1989: Thermal and size evolution of sea spray droplets. CRREL Rep. 89-11, 47 pp., http://www.dtic.mil/dtic/tr/fulltext/u2/a210484.pdf.

  • Andreas, E. L, 1990: Time constants for the evolution of sea spray droplets. Tellus, 42B, 481497, https://doi.org/10.3402/tellusb.v42i5.15241.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 1992: Sea spray and the turbulent air–sea heat fluxes. J. Geophys. Res., 97, 11 42911 441, https://doi.org/10.1029/92JC00876.

  • Andreas, E. L, 1995: The temperature of evaporating sea spray droplets. J. Atmos. Sci., 52, 852862, https://doi.org/10.1175/1520-0469(1995)052<0852:TTOESS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 2005: Approximation formulas for the microphysical properties of saline droplets. Atmos. Res., 75, 323345, https://doi.org/10.1016/j.atmosres.2005.02.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 2010: Spray-mediated enthalpy flux to the atmosphere and salt flux to the ocean at high winds. J. Phys. Oceanogr., 40, 608619, https://doi.org/10.1175/2009JPO4232.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, 2016: Sea spray generation at a rocky shoreline. J. Appl. Meteor. Climatol., 55, 20372052, https://doi.org/10.1175/JAMC-D-15-0211.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, and B. Murphy, 1986: Bulk transfer coefficients for heat and momentum over leads and polynyas. J. Phys. Oceanogr., 16, 18751883, https://doi.org/10.1175/1520-0485(1986)016<1875:BTCFHA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Andreas, E. L, and J. DeCosmo, 1999: Sea spray production and influence on air-sea heat and moisture fluxes over the open ocean. Air-Sea Exchange: Physics, Chemistry and Dynamics, G. L. Geernaert, Ed., Atmospheric and Oceanographic Sciences Library, Vol. 20, Springer, 327–362.

    • Crossref
    • Export Citation
  • Andreas, E. L, L. Mahrt, and D. Vickers, 2015: An improved bulk air-sea surface flux algorithm, including spray-mediated transfer. Quart. J. Roy. Meteor. Soc., 141, 642654, https://doi.org/10.1002/qj.2424.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Aubinet, M., T. Vesala, and D. Papale, 2012: Eddy Covariance: A Practical Guide to Measurement and Data Analysis. Springer Science and Business Media, 451 pp.

    • Crossref
    • Export Citation
  • Battjes, J. A., 1974: Surf similarity. Proc. 14th Conf. on Coastal Engineering, Copenhagen, Denmark, ASCE, 466–480.

    • Crossref
    • Export Citation
  • Chomka, M., and T. Petelski, 1997: Modeling the sea aerosol emission in the coastal zone. Oceanologia, 39, 211225.

  • Clarke, A. D., S. R. Owens, and J. Zhou, 2006: An ultrafine sea-salt flux from breaking waves: Implications for cloud condensation nuclei in the remote marine atmosphere. J. Geophys. Res., 111, D06202, https://doi.org/10.1029/2005JD006565.

    • Search Google Scholar
    • Export Citation
  • Dean, R. G., and R. A. Dalrymple, 1984: Water Wave Mechanics for Engineers and Scientists. Prentice-Hall, 353 pp.

  • de Leeuw, G., F. P. Neele, M. Hill, M. H. Smith, and E. Vignati, 2000: Production of sea spray aerosol in the surf zone. J. Geophys. Res., 105, 29 39729 409, https://doi.org/10.1029/2000JD900549.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Derakhti, M., and J. T. Kirby, 2014: Bubble entrainment and liquid–bubble interaction under unsteady breaking waves. J. Fluid Mech., 761, 464506, https://doi.org/10.1017/jfm.2014.637.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., J. D. Kepert, and G. J. Holland, 1994: The effect of sea spray on surface energy transports over the ocean. Global Atmos. Ocean Syst., 2, 121142.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., E. F. Bradley, D. P. Rodgers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmospheric Coupled-Ocean Response Experiment. J. Geophys. Res., 101, 37473764, https://doi.org/10.1029/95JC03205.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacMahan, J., 2017: Increased aerodynamic roughness owing to surfzone foam. J. Phys. Oceanogr., 47, 21152122, https://doi.org/10.1175/JPO-D-17-0054.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacMahan, J., and Coauthors, 2010: Mean Lagrangian flow behavior on an open coast rip channeled beach: A new perspective. Mar. Geol., 268, 115, https://doi.org/10.1016/j.margeo.2009.09.011.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monahan, E. C., 1995: Coastal Aerosol Workshop Proceedings. Naval Research Laboratory Rep. NRL/MR/7542-95-7219, 138 pp.

  • Monahan, E. C., D. E. Spiel, and K. L. Davidson, 1986: A model of marine aerosol generation vie whitecaps and wave disruption. Oceanic Whitecaps and Their Role in Air-Sea Exchange Processes, E.C. Monahan and G. Mac Miocaill, Eds., D. Reidel, 167–174.

    • Crossref
    • Export Citation
  • Monahan, E. C., A. Staniec, and P. Vlahos, 2017: Spume drops: Their potential role in air-sea gas exchange. J. Geophys. Res. Oceans, 122, 95009517, https://doi.org/10.1002/2017JC013293.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neele, F. P., G. de Leeuw, J. Martijn, and M. Stive, 1998: Quantitative assessment of surf-produced sea spray aerosol. Propagation and Imaging through the Atmosphere II, L. R. Bissonnette, Ed., International Society for Optical Engineering (SPIE Proceedings, Vol. 3433), https://doi.org/10.1117/12.330242.

    • Crossref
    • Export Citation
  • Ortiz-Suslow, D. G., B. K. Haus, S. Mehta, and N. J. M. Laxgue, 2016: Sea spray generation in very high winds. J. Atmos. Sci., 73, 39753995, https://doi.org/10.1175/JAS-D-15-0249.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Piazzola, J., G. Tedeschi, and A. Demoisson, 2015: A model for the transport of sea-spray aerosols in the coastal zone. Bound.-Layer Meteor., 155, 329350, https://doi.org/10.1007/s10546-014-9994-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thornton, E. B., and R. T. Guza, 1983: Transformation of wave height distribution. J. Geophys. Res., 88, 59255938, https://doi.org/10.1029/JC088iC10p05925.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tuller, S. E., 1972: Energy balance microclimatic variations on a coastal beach. Tellus, 24, 260270, https://doi.org/10.1111/j.2153-3490.1972.tb01552.x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • van Eijk, A. M. J., J. T. Kusmierczyk-Michulec, M. J. Francius, G. Tedeschi, J. Piazolla, D. L. Merritt, and J. D. Fontana, 2011: Sea-spray aerosol particles generated in the surf zone. J. Geophys. Res., 116, D19210, https://doi.org/10.1029/2011JD015602.

    • Search Google Scholar
    • Export Citation
  • Veron, F., 2015: Ocean spray. Annu. Rev. Fluid Mech., 47, 507538, https://doi.org/10.1146/annurev-fluid-010814-014651.

  • Veron, F., C. Hopkins, E. L. Harrison, and J. A. Mueller, 2012: Sea spray spume droplet production in high wind speeds. Geophys. Res. Lett., 39, L16602, https://doi.org/10.1029/2012GL052603.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vignati, E., G. deLeeuw, and R. Berkowicz, 2001: Modeling coastal aerosol transport and effects of surf-produced aerosols on processes in the marine atmospheric boundary layer. J. Geophys. Res., 106, 20 22520 238, https://doi.org/10.1029/2000JD000025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wan, Z.-H., J.-B. Zhu, K. Sun, and K. Zhou, 2017: An integrated turbulent simulation and parameter modeling study on sea-spray dynamics and fluxes. Ocean Eng., 130, 6471, https://doi.org/10.1016/j.oceaneng.2016.11.041.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    (a) Topographic and bathymetry map of Monterey Bay. Black dots represent the four beaches on which six towers were deployed. The white triangle represents the NDBC buoy. The dotted white line denotes the outer boundary of Monterey Bay. (b) Sonic anemometers were collocated with temperature–humidity sensors located on top of the tower, solar panels were located in the middle, and the data acquisition system was located in the white box near the bottom. Towers were deployed at the high-tide line, where the tower base was approximately 1.2 m MSL.

  • Fig. 2.

    Characteristic droplet e-folding times to reach evaporation temperature τTev (black line) equilibrium temperature τr (light gray band), and droplet fall time τf (darker gray band) as a function of spray radii ro. The τTev is for a range of seawater temperatures Tw = 12°–20°C with a constant temperature difference between water and air ΔT = 2°C, salinity of 34 psu, and relative humidity range of 75%–95%; τf values are for range of wave heights 0.13–1.2 m (adapted after Veron 2015). Left vertical dashed line: τfτr. Right vertical dashed line: τfτTev.

  • Fig. 3.

    Self-similar spectrum of sea-spray droplets f(ro) (after Andreas 2016; solid line) and Andreas (2016) modified to fit data (dashed line).

  • Fig. 4.

    (a) Volume f(ro) multiplied by the magnitude function of Andreas (2016; solid line) and modified version to fit data (dashed line). The fV(ro) maximum occurs at ro = 60 μm. (b) Magnitude function in the sensible heat flux Eq. (15) for Hsig = 0.13 (broken line), 0.8 (dashed line), and 1.2 (solid line) m and Ta = 14°C. (c) Cumulative distributions for spectra (solid black) in (a) and also multiplied by magnitude function (dashed black) in (b) for H = 0.8 m. Calculations are for ro = 0–1000 μm.

  • Fig. 5.

    Calculated sensible heat flux for sea-spray droplets HS,spray as a function of average breaking wave dissipation for the wave heights during the experiment (Hsig ≤ 1.3 m) for Tw = 16°C and Ta = 14°C. The ±20% error for D is shown by the dashed lines.

  • Fig. 6.

    Observations of surfzone sensible heat flux (HS,SZ) compared with open ocean sensible heat flux (HS,O) observed at the same time.

  • Fig. 7.

    (a) The HS,SZ observations compared with COARE3.5 HS,int [Eq. (2)]. (b) The HS,SZ observations compared with COARE3.5 HS,int added to modeled HS,spray. Black lines represents the 1:1 lines. Dashed lines are the linear regression lines, where m = 0.46 and r2 = 0.63 in (a) and m = 0.84 and r2 = 0.7 in (b). The white circles represent the average of 10 W m−2–wide bins. The dot color represents the difference in Tair relative to Twater with the color scale on the right.

  • Fig. 8.

    The ro value at which the cumulative distribution of [1 − exp(τf T)]fV(ro) is greater than or equal to 0.99 for the Andreas (2016) modification as a function of 0.5Hsigh ≤ 2Hsig (gray band), with Ta = 14°C.

  • Fig. 9.

    Measured surfzone sensible heat flux divided by measured open ocean HS,O (gray line) and surfzone spray-mediated sensible heat flux (black line) computed by subtracting the COARE3.5-modeled HS,int [Eq. (2)] from the measured HS,SZ divided by HS,O. The ratio is binned in 1 m s−1 intervals. Confidence intervals are provided for 95% significance.

  • Fig. 10.

    Histograms of surface temperature differences (°C): (a) nearshore (10-m depth) water minus NDBC water; (b) air at tower minus nearshore water; (c) air NDBC minus water NDBC. The location of the NDBC buoy is shown in Fig. 1.

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