Sensitivity of Sea-Surface Enthalpy and Momentum Fluxes to Sea Spray Microphysics

The air-sea fluxes of enthalpy and momentum are the governing thermal energy source and mechanical energy sink, which control hurricane intensity, but representing these fluxes in simulations is challenging. Many models employ bulk parameterizations of air-sea fluxes that often exhibit a significant sensitivity between the simulated hurricane intensity and the bulk exchange coefficients for enthalpy (CK) and momentum (CD) (Green & Zhang, 2014; Ma et al., 2017; Nystrom et al., 2020; Torn, 2016). The ratio of these coefficients CK/CD is especially important for modeling hurricanes, since it is directly proportional to several key intensity metrics, including the square of the maximum potential intensity (Emanuel, 1986, 1995). While there have been a few studies that used direct measurements from GPS dropsondes, ocean buoys, and/or airborne radar to measure surface fluxes at high wind speeds (Black et al., 2007; Holthuijsen et al., 2012; Powell et al., 2003; Richter & Stern, 2014; Zou et al., 2018), the sparsity of direct observations makes model verification challenging. Additionally, the nature of the near-surface region at high wind speeds presents substantial challenges that inhibit surface flux calculations since the air-sea interface is no longer well-defined due to the presence of sea spray, bubbles, and foam (Emanuel, 2003; Holthuijsen et al., 2012; Sroka & Emanuel, 2021). Theoretical models, laboratory experiments, and numerical simulations have shown that the microphysical processes that govern sea spray generation, evaporation, and acceleration can have a significant effect on the large-scale air-sea exchange of enthalpy and momentum (Andreas & Emanuel, 2001; Jeong et al., 2012; Mueller & Veron, 2014a, 2014b; Peng & Richter, 2017, 2019, 2020; Troitskaya, Druzhinin, et al., 2018; Troitskaya, Kandaurov, et al., 2018).

2 of 14 this model, the sea spray-mediated enthalpy flux is primarily a function of the relative humidity, the air-sea temperature difference, and the sea surface temperature, while the sea spray-mediated momentum flux is primarily a function of the surface wind speed (Andreas, 2004;Andreas & Emanuel, 2001). Since spray drops will undergo more evaporation and accelerate to faster speeds, the longer they remain aloft a residence time formulation is needed. The primary formulation used by this study is from Andreas (1992). Many SSGFs, which describe the rate at which drops of different sizes are ejected, for the open ocean have come from the sea spray aerosol community as reviewed in Lewis et al. (2004), De Leeuw (2007), andDe Leeuw et al. (2011), though these tend to primarily consider small drops with radii less than approximately 10 μm. The present analysis is focused on larger drops with radii ranging from approximately 50-2,000 μm. Sea spray generation functions that primarily consider these larger drop sizes are reviewed in Andreas (2002) and Veron (2015), but relatively few of these were developed from observations in the field or laboratory in the high wind regime. The functions considered in this analysis were all developed using high wind speed observations to reduce the extent to which extrapolation errors affect the estimated sea spray production rate.
The SSGF is likely the largest source of uncertainty in the sea spray-mediated flux calculation. While the total volume flux predicted by the SSGF and the way it changes with wind speed are essential for estimating the sea spray fluxes, the results from this analysis suggest that the drop size distribution may not be as critical. While a drop's mass does affect how much enthalpy and momentum it can mediate, if the majority of the total volume of sea spray undergoes the same temperature and velocity changes, then the spray fluxes can be estimated without the drop size distribution. Emanuel (2003), hereafter E3, presented a mechanistic argument based on an idealized setup and a few simplifying assumptions. Specifically, he assumed that at very high wind speeds, such that all the momentum and heat fluxes are carried by spray, 1. newly ejected, upward traveling drops are at the sea surface temperature T s and have negligible horizontal velocity, while reentrant, downward traveling drops are at the far-field wet-bulb temperature T w and have a mass-weighted average horizontal velocity u sp , 2. the net evaporation is a small fraction of the total lofted mass of sea spray; thus, the net downward spray mass flux is nearly equal to its upward flux.

A Mechanistic Argument
The assumption that the sea spray carries all of the momentum and heat fluxes is crucial for this model, but the true distribution between sea spray fluxes and interfacial fluxes in the high wind speed limit is uncertain. While the findings from several studies suggest that sea spray carries at least the majority, if not all, of the air-sea heat flux at extreme wind speeds (Mueller & Veron, 2014a;Richter & Stern, 2014;Troitskaya, Druzhinin, et al., 2018), there is more disagreement surrounding the momentum flux. While the theoretical study of Andreas (2004) suggests that sea spray can support the full air-sea momentum flux at 10-m wind speeds above 60 m/s, albeit with the acknowledgment that this behavior at high wind speeds is "very speculative," other studies attribute most of the momentum flux to the wave form drag. Estimating the wave form drag at extreme wind speeds is very challenging without definitive observations. One technique to do so involves extrapolating results from lower wind speed observations into the high wind speed regime , but this method may overestimate the form drag. At lower wind speeds, there is less spray and the waves likely have steeper slopes than they do at extreme wind speeds where there is some evidence that the wave slopes are suppressed by the copious wave-breaking (Komori et al., 2018). Other estimates that include significant contributions from wave form drag come from Lagrangian particle simulations where the shape of the surface and number of injected particles are prescribed  or from models in which sea spray is assumed to be primarily confined to a very narrow slip layer above the surface (Makin, 2005).
If the aforementioned assumptions are satisfied, then the net surface stress and upward enthalpy flux are given by = (1) and 3 of 14 where M u is the upward flux of spray mass per unit area, c l is the heat capacity of liquid water, T s is the ocean temperature, and T w is the ambient wet-bulb temperature. If we were to represent these fluxes with conventional aerodynamic flux formulae, they would be, respectively, where C Dh is a drag coefficient defined at altitude h, C kh is an enthalpy flux coefficient also defined at altitude h, ρ a is the air density, u h is the wind speed at altitude h, * 0 is the saturation moist enthalpy of the sea surface, and k h is the moist enthalpy at altitude h.
If we now substitute the spray-related stress and enthalpy flux Equations 1 and 2 into Equations 3 and 4, we get E3 chose the height h rather than being a fixed altitude to always be the altitude at which the air velocity equals the spray speed u sp and further assumed that the latter is always some constant fraction of the gradient wind speed u g . If this last assumption is satisfied, then the ratio of exchange coefficients that should be applied to the gradient wind is where C kg and C Dg are, respectively, the exchange coefficients for enthalpy and momentum applicable to the gradient wind. E3 showed that if T s − T w is a small fraction of the absolute temperature, such that the Clausius-Clapeyron equation can be linearized, Equation 6 can be simplified to where c p is the heat capacity at constant pressure for air, L v is the latent heat of vapourization, * is the saturation-specific humidity at the air temperature, R v is the gas constant for water vapor, and T a is the air temperature.
Owing to the strong dependence of * on temperature, the ratio of exchange coefficients given by Equation 7 is a decreasing function of air temperature (as shown in Figure 3 of Emanuel, 2003), but it is not a function of wind speed.
Again, the assumptions from E3 are based on the limiting case in which all of the momentum and heat flux are carried by sea spray. An implication of these assumptions is that the fractions of the thermal and wind speed environmental variables that sea spray drops attain are the same (i.e., T/T w = u/U 10 where T and u are the temperature and speed of the sea spray drops, respectively) and invariant with u * . This implies that the ratio C K /C D also does not vary with u * .
The aim of this study is to use the microphysical model to evaluate if and when the main assumptions of the mechanistic argument are met and to estimate the threshold wind speed beyond which the ratio of the exchange coefficients is expected to become independent of wind speed. The microphysical model and the SSGFs used to calculate the sea spray-mediated enthalpy and momentum fluxes are described in Sections 3 and 4, respectively. Section 5 analyzes an ensemble of drop evaporation time histories to evaluate if and when the assumptions from the mechanistic argument are met. Finally, Section 6 summarizes the results.

The Momentum Flux
The sea spray-mediated momentum flux is computed according to the model presented in Andreas (2004). Drops are assumed to be accelerated from rest by a uniform wind field with a velocity equal to the 10-m wind speed U 10 . The time tendency of the speed of a drop u is given by where ρ l is the density of sea water and r 0 is the initial drop radius. The drag coefficient for a spherical drop C d (Re) is a function of the Reynolds number Re, which is defined as Re = (U 10 − u)(2r 0 )/ν a where ν a is the kinematic viscosity of air. Following Andreas (2004), the drag formulation used here is from Clift et al. (1978). The spray stress from one drop is then m 0 u, where m 0 is the initial mass and u is the horizontal speed the drop attains before returning to the sea. This model technically represents an upper bound on the momentum flux since it neglects evaporation. However, as will be shown in Section 5, the total evaporated mass is expected to be a very small fraction of the total ejected mass.

The Enthalpy Flux
The cloud microphysics evaporation equations from Pruppacher and Klett (1978) formed the basis for the sea spray evaporation model developed throughout Andreas (1989Andreas ( , 1990Andreas ( , 1992Andreas ( , 1995. The coupled system of equations, which describes the evolution of the temperature T and radius r of a saline drop, using the symbolism from Andreas (2005), is where ′ is the thermal conductivity modified for noncontinuum behavior, ′ is the vapor diffusivity modified for noncontinuum behavior, ρ v is the ambient vapor density, ρ v,r is the vapor density at the drop's surface, RH is the percent relative humidity, y is the curvature parameter, R is the universal gas constant, M w is the molar mass of water, and e sat is the saturated partial pressure of water vapor. For this study, the sea water parameters L v , ρ l , and c l are functions of temperature and salinity according to Nayar et al. (2016), the ambient pressure is assumed to be 1,000 mb, and the salinity of sea water is assumed to be 34 ppt. With these assumptions, there are only three external parameters that define the time tendency of evaporation for a drop: the relative humidity RH, the air-sea temperature difference ΔT = T s − T a , and the sea surface temperature T s .
Andreas and Emanuel (2001) described how a drop will quickly cool to T w after ejection, generally losing less than 1% of its mass in the process. The characteristic timescale for this thermal adjustment is τ T , which is the time it takes for a drop's temperature to come within an e-folding fraction of its wet-bulb temperature (Andreas, 1992). After a drop has reached its wet-bulb temperature, it exchanges sensible for latent heat with the atmosphere and loses mass until it has warmed to T a and has evaporated to its equilibrium radius r eq . The mass loss timescale for a drop is τ r , which is the time it takes for a drop's radius to come within an e-folding fraction of its equilibrium radius (Andreas, 1992). Andreas and Emanuel (2001) demonstrated that the two processes of cooling to T w and completely evaporating to a radius of r eq are essentially temporally decoupled; in other words, τ T ≪ τ r .
In this model, drops are assumed to be initially at the sea surface temperature, to experience uniform ambient air conditions until they reenter the sea after a time τ f and to not interact with other drops, which gives an upper bound on the enthalpy flux. Using the symbolism from Troitskaya, Druzhinin, et al. (2018), the enthalpy flux from a drop is calculated as

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where m f is the drop's mass at reentrance. Several studies including Mueller and Veron (2014b) and Peng and Richter (2019) suggested that these assumptions overestimate the total sea spray-mediated flux due to smaller drops rapidly condensing and warming right before reentrance as they approach the sea even if they were able to thermally adjust to nearly their wet-bulb temperature at some point during their flight. Peng and Richter (2020) used Lagrangian particle simulations to look for interactions between drops of different sizes and found that large drops are more heavily concentrated near the bottom of the spray layer and can increase the moist enthalpy of the lower region to further reduce the net enthalpy contribution of small drops. Fairall et al. (2009) found that the slope of the waves played an important role in determining whether large drops would spend a significant time aloft. Mueller and Veron (2014b), Richter et al. (2019), and Peng and Richter (2020) all raised the concern that large drops may not be transported high enough to experience ambient conditions of T a , RH, or U 10 during their flight. One consideration is that most of these studies, with the exception of Mueller and Veron (2014b) who simulated 10-m wind speeds as high as 50 m/s, generally reported results for 10-m wind speeds below the high wind speeds that are primarily of interest in this study; at lower wind speeds, less sea spray is expected to be produced and the ejected spray is not expected to be lofted as high or remain aloft for as long. However, incorporating these interactions could change the threshold wind speed at which the mechanistic argument assumptions are satisfied but would not change the conclusions about the high wind speed limit.
This analysis also assumes that there are no spray-feedback effects on the external environmental parameters. The feedback model from Andreas et al. (2015) considered the sea spray-mediated enthalpy flux as part of a positive feedback loop that helped extract more enthalpy from the sea surface, while the results from the Lagrangian simulation from Peng and Richter (2019) found that sea spray-mediated enthalpy flux modulated the near-surface region as part of a negative feedback loop, which suppressed the enthalpy flux from the sea surface. While feedback effects are likely to change the amount of sea spray-mediated flux, they are less likely to affect the fundamental dependencies between T s , T w , and U 10 . Moreover, if the vertical profiles of enthalpy and momentum in the spray layer obey the same law (e.g., a logarithmic dependence on z), then spray feedbacks should not affect the ratio of the exchange coefficients.
Following the format of the figures from Andreas (1995) and Andreas and Emanuel (2001), Figure 1 illustrates how the three external parameters (RH, ΔT, and T s ) and the initial radius r 0 affect the temperature and radius evolution of an evaporating drop. As shown in Figure 1a, increasing the relative humidity has two opposing effects. The first is that a higher RH leads to a higher T w , which decreases the enthalpy flux potential. The second effect is that a higher RH suppresses evaporative mass loss, which increases the enthalpy flux potential primarily for drops that remain aloft longer than τ r . Figures 1b and 1c show that changing ΔT or T s has a negligible effect on the drop's mass loss rate, but does affect the enthalpy flux potential. A larger ΔT at the same T s lowers the wetbulb temperature, increasing the enthalpy flux potential. Increasing T s for the same ΔT does slightly increase the enthalpy flux potential (see Figure 1c annotations) through the temperature dependence of the saturation-specific humidity. Finally, Figure 1d shows that drops of different sizes will evaporate at different rates; larger drops take longer to reach both T w and r eq , but transfer more enthalpy in the process. Andreas and Emanuel (2001) demonstrated that a significant enhancement to the air-sea enthalpy flux in hurricanes could come from reentrant spray, which are spray drops that reenter the sea after partially evaporating. The residence time proposed by Andreas (1992

The Residence Time
where A s is the significant wave amplitude and u f is the Stokes fall speed modified for large Reynolds numbers and large drops as defined in Andreas (1989Andreas ( , 1990) and based on Batchelor (1970) and Friedlander (1977). This parameterization considers drops to remain aloft for as long as it takes them to fall a distance A s through still air. The findings from several numerical simulation studies of the drop spray layer, including Andreas et al. (1995), Edson et al. (1996), and Van Eijk et al. (2001), support the use of A s as characteristic length scale for the residence time. Turbulence-enhanced residence times are indirectly parameterized through the significant wave amplitude A s . Andreas (1992) uses the parameterization = 0.015 2 10 following the results from Kinsman (1965); Wilson (1965) and Earle (1979); note that the coefficient 0.015 effectively has the units of s 2 /m for U 10 with units of 6 of 14 m/s. Figure 1d shows how the τ f decreases as the initial radius of the drop and therefore, the modified Stokes fall speed increases. Some Lagrangian particle simulations found a much weaker dependence of τ f on U 10 or did not find a clear relationship between τ f and A s Mueller & Veron, 2014b). However, as discussed in Troitskaya, Druzhinin, et al. (2018), one of the problematic aspects of Lagrangian particle simulations is their choice of initial velocities for the spray particles to which the residence time is very sensitive. While imperfect, τ f from Andreas (1992) is a good heuristic for the goals of this analysis. Additionally, as will be discussed later, the results of this analysis are robust to a few variations of the residence time formulation. Figure 2 compares the four characteristic timescales τ r , τ T , τ f , and τ ac for a sample of drops; these plots are similar to the curves shown in Figure 1 of Andreas (1992) and Figure 1 of Andreas (2004), except here the 10-m wind speed is the independent variable to emphasize the wind speed dependence of τ f and τ ac . For comparison, the contours of τ f and τ ac for the other drop sizes are plotted in gray.
By examining the curves in Figure 2, it is possible to approximately bound the drop sizes, which are expected to mediate the maximum amount of enthalpy and momentum for their size. Drops with initial radii less than approximately r 0 = 500 μm have a residence time τ f that is greater than τ T for U 10 above 30 m/s. Therefore, drops in this range can be expected to reach their wet-bulb temperature. However, drops smaller than approximately r 0 = 100 μm are expected to lose a substantial amount of their mass and warm to nearly T a since at high wind speeds, their residence time is expected to exceed τ r . Drops much larger than r 0 = 500 μm may not have sufficient time aloft to cool to T w before reentering since for very large drops, τ f is much less than τ T . Since the amount of enthalpy a drop can mediate scales with 3 0 , larger drops can mediate much more enthalpy than smaller drops. Therefore, even if larger drops do not transfer the maximum amount of enthalpy by reentering at T w , they can still account for a substantial contribution to the net enthalpy flux. Since a drop extracts more momentum as it accelerates to higher speeds, it is important to compare a drop's residence time to its acceleration timescale τ ac , which is when the drop's velocity is within an e-folding fraction of U 10 (Andreas, 2004). Figure 2, like figure 1 of Andreas (2004), shows how τ ac compares to τ f for different drop sizes. For U 10 > 30 m/s, even the largest drops will have accelerated to nearly U 10 . The Weber number, defined as 2 10 0∕ , where σ is the surface tension, compares inertial forces to surface tension forces. The Weber number far exceeds the critical value of 6 (Villermaux & Bossa, 2009) for the case of a 2,000 μm drop moving at 30 m/s. This suggests that the drop would breakup if it did not reenter the sea first. However, drop breakup would only produce smaller drops that would be accelerated more quickly. Since each figure shows τ f > τ ac for U 10 > 30 m/s, all drops in the range considered here are expected to mediate the maximum amount of momentum.

Sea Spray Generation Functions
The three SSGFs considered in this study are shown in Figure 3 and were developed using observations from high wind speed conditions. A SSGF, denoted 0 , defines the number of drops produced per square meter, per second, per increment drop radius. Zhao et al. (2006) developed a SSGF by curve fitting observations of sea spray volume flux from field and laboratory experiments. The authors considered the volume flux to be a function of the dimensionless windsea Reynolds number, which depends on both the wind speed and the development of the sea surface . The windsea Reynolds number is defined as = 2 10 ∕( ) , where C D is the sea surface drag and ω p is the peak spectral frequency of the surface wave field. Using Re B rather than a wind speed variable was advantageous in other air-sea exchange studies (Iida et al., 1992;Toba & Koga, 1986;Toba et al., 2006;Zhao & Toba, 2001;Zhao et al., 2003) and is especially helpful when analyzing data from both laboratory and field experiments since the differences in fetch are accounted for through ω p , although ω p is not truly an external parameter. The data spanned 10-m wind speeds from 8 m/s to 41 m/s and Re B from 2,000 to 30,000. Since the observations were collected at different sea surface-relative heights, the authors used the methodology from Slinn and Slinn (1980) and Fairall and Larsen (1984) to estimate the flux at the sea surface. The curve fit of the volume flux was combined with the drop size distribution from Monahan (1968) to arrive at their final SSGF. As shown in Figure 3b, their SSGF (Equation 17 in their paper) predicts that drops with r 0 between 75 and 200 μm make up the largest share of the total spray volume flux.  Zhao et al. (2006), also used curve fitting to create an SSGF (here, we use the fitted relation in Equation 22 in their paper rather than their empirical formulation). There are a couple of possible reasons this function exhibits a much lower flux than the other wave tank experiment considered in this study by Troitskaya, Kandaurov, et al. (2018). The first simply has to do with differences in the experimental setups, including the tank dimensions, the salinity of the water, and the height at which drops were observed. Ortiz-Suslow et al. (2016) observed drops at 2.5H s , where H s is the significant wave height, and then calculated the equivalent spray generation at H s compared to Troitskaya, Kandaurov, et al. (2018) who observed drop production at the surface. A second possible explanation has to do with how the equivalent profile at H s was calculated. As explained in both Ortiz-Suslow et al. (2016) and Mehta et al. (2019), the profile transformation relies on a standard, albeit imperfect, parameterization of the drop deposition velocity. This experiment still observed many more large drops than previous, lower wind speed experiments and helps this analysis consider the possibility that drops need to rise above H s to begin evaporating. Their SSGF predicts that drops with r 0 between approximately 200 and 400 μm make up the largest share of the total spray volume flux.
The results from the wave tank experiments conducted by Troitskaya, Kandaurov, et al. (2018) demonstrated why it is critical to consider SSGFs created from high wind speed observations rather than functions that were extrapolated from low wind speed observations into the high wind speed regime. The authors tested a range of equivalent 10-m wind speeds from 18 m/s to 33 m/s and found that the dominant the sea spray creation mechanism at high wind speeds, known as bag-breakup (Veron et al., 2012), both significantly changed the sea spray drop size distribution and was only activated beyond a certain threshold wind speed. In their setup, this generation mechanism, which leads to the production of many more large drops, became the dominant mechanism of sea spray production above an equivalent U 10 of about 24 m/s and a windsea Reynolds number of 8,000. The authors note that in open ocean conditions where the fetch is not limited, this threshold wind speed would likely be lower. As previously noted, unlike Ortiz-Suslow et al. (2016), spray production in these experiments was observed at the water surface. Their SSGF (Equation 24 in their paper) predicts that drops with r 0 between approximately 400 and 500 μm make up the largest share of the total spray volume flux.
Many studies write the windsea Reynolds number in terms of the wave age parameter β = g/(ω p U 10 ) such that = 3 10 ∕( ) , where g is gravity. The SSGFs from Zhao et al. (2006) and Troitskaya, Kandaurov, et al. (2018) are both proportional to β 1.5 since Troitskaya, Kandaurov, et al. (2018) followed Zhao et al. (2006) during the part of their derivation. The SSGF from Ortiz-Suslow et al. (2016) does not extrapolate the sea spray flux based on a wave state parameter like the wave age or the windsea Reynolds number since it was developed from direct observations of sea spray at a fixed height. Typical field conditions have a wave age of β = 0.4, so this  Zhao et al. (2006) and Troitskaya, Kandaurov, et al. (2018) are evaluated at a wave age of β = 0.4. 9 of 14 value is used in both SSGFs from Zhao et al. (2006) and Troitskaya, Kandaurov, et al. (2018), but the proportionality of the spray volume flux to β is such that the three normalized ratios in Section 5 are insensitive to the choice of β.

Results
The assumptions evaluated in this section, whether the majority of the sea spray volume reenters the sea at nearly T w , whether the evaporated volume of sea spray is a small fraction of the total lofted volume, and whether the majority of the sea spray volume is moving at nearly the free stream wind speed before reentrance, were found to be true for a drop with r 0 = 100 μm under typical hurricane spray layer conditions (T s = 28°C, ΔT = 1°C, and RH = 80%) in Andreas and Emanuel (2001). The present analysis evaluates a wider range of conditions and drop sizes to explore the sensitivity of the sea spray-mediated fluxes to the size distributions of the three aforementioned SSGFs.
In the following three sections, we evaluate the three main assumptions in the mechanistic argument using an ensemble of 8,400 integrations of Equations 9 and 10 corresponding to each permutation of the set of RH, ΔT, T s , and r 0 listed in Table 1. This range of r 0 was chosen because drops smaller than 50 μm are not expected to contribute much to the net spray fluxes under high wind speeds, and none of the SSGFs are valid for drop sizes larger than 2,000 μm. Each SSGF is only evaluated for the range of drop sizes within this set for which the SSGF is valid; the Zhao et al. (2006) SSGF is evaluated for initial radii r 0 ∈ [50−500] μm, the Ortiz-Suslow et al. (2016) SSGF is evaluated for initial radii r 0 ∈ [100−1,000] μm, and the Troitskaya, Kandaurov, et al. (2018) SSGF is evaluated for initial radii r 0 ∈ [50−2,000] μm. The circles in Figure 4 indicate the mean value of the ensemble at the corresponding wind speed and the whiskers represent one standard deviation from the mean.

Spray Drops Reenter at a Temperature of Nearly T w
The temperature time histories from the ensemble showed that most of the sea spray mass is expected to reenter the sea very close to the wet-bulb temperature. Figure 4a shows γ 1 , which compares the amount a drop cools between ejection and reentrance (T s − T(τ f )) to the maximum potential cooling (T s − T w ) weighted by the total sea spray volume flux For the SSGF from Zhao et al. (2006), which covers the lower range of drop sizes, γ 1 is generally above 90%, owing to most of the mass being concentrated in the r 0 = 75-200 μm range. The SSGF from Ortiz-Suslow et al. (2016) provides an γ 1 that is consistently above 80%, and the SSGF from Troitskaya, Kandaurov, et al. (2018), which covers the widest range of drop sizes, provides an γ 1 that is above 50% at U 10 = 40 m/s and above 80% by U 10 = 55 m/s. Recall only the very smallest drops with radii less than about 100 μm are predicted to evaporate completely at high wind speeds and reenter the sea at nearly the air temperature in this model. Small drops have less enthalpy flux potential than large drops, and their long residence times further limit their contribution to the enthalpy flux. If the volume of the smaller drops (r 0 < 100 μm) was predicted by the SSGFs to exceed that of the larger drops, the majority of the ejected sea spray volume would not be expected to reenter near the wet-bulb temperature. However, the SSGFs examined here all reinforce the conclusion that the majority of the sea spray reenters very close to the wet-bulb temperature such that a large fraction of the total possible enthalpy flux potential from sea spray is realized. This first assumption is well-satisfied for U 10 ≥ 55 m/s across all SSGFs.

The Evaporated Mass Is Small
The results from the ensemble also show that the net evaporation is a small fraction of the total ejected mass of sea spray. Figure 4b shows γ 2 , which is the fraction of a drop's mass that it is expected to retain upon reentrance, weighted by the total sea spray volume flux from the SSGF As expected, more mass evaporates at higher wind speeds as drops remain aloft longer and progress further toward their equilibrium radius r eq . However, the total fraction of reentrant mass is still very large at all wind speeds for all SSGFs. Since small drops will evaporate to their equilibrium radius more quickly than larger drops, the SSGF from Zhao et al. (2006), evaluated for only the smaller drop sizes, exhibits the smallest γ 2 at all wind speeds. The results generally support this second assumption that a very small fraction of the total of ejected mass will evaporate before the drops reenter the sea at all wind speeds.

Spray Drops Are Accelerated to U 10
The velocity time histories, calculated by integrating Equation 8 for all drop sizes, showed that virtually all of the sea spray mass is expected to reenter after having been accelerated to nearly the free stream wind speed U 10 . Figure 4c shows the sea spray volume flux-weighted fraction γ 3 , which compares the speed of the drop at τ f to U 10 Figure 4. Each filled circle represents the mean of the ensemble, and the whiskers indicate one standard deviation. The top plot shows the fraction of the total spray volume, which reenters at a temperature close to T w ; the average whisker lengths for the black, green, and red curves in this plot are 1.7(10 −2 ), 6.4(10 −3 ), and 5.5(10 −3 ), respectively. The middle plot shows the fraction of the total ejected spray volume that reenters the sea without evaporating; the average whisker lengths for the black, green, and red curves in this plot are 5.5(10 −2 ), 6.7(10 −3 ), and 5.3(10 −3 ), respectively. The bottom plot shows the fraction of the total spray volume, which is accelerated to a velocity U 10 before reentrance; the average whisker lengths for all three curves in this plot are machine zero. The 50% and 80% levels are indicated with dashed and dotted gray lines, respectively.

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Recall that the drops are assumed to initially have a negligible horizontal velocity. The results show that this third assumption is well-satisfied for U 10 ≥ 30 m/s. As previously mentioned, this calculation technically represents a lower bound on the momentum flux, since the initial radius of the liquid drop is used for the whole integration. Accounting for the fact that the evaporated vapor would readily adjust to the free stream wind speed would slightly enhance γ 3 , but would not substantially affect these results since the net evaporated mass is a very small fraction of the total mass of sea spray above U 10 = 30 m/s across all SSGFs considered here.

Alternate Residence Time Formulations
To help confirm that these results are not overly sensitive to the particular choice of τ f , the analysis was repeated using two other residence time formulations. The first was a ballistic timescale τ b where all drops had an initial upward velocity of U 10 such that τ b = 2U 10 /g. This formulation does not change with the size of the drops, and for the range of 10-m wind speeds considered here, τ b is generally on the order of 10 s. The second residence time formulation keeps the structure of the Andreas (1992) formulation, but the parameterization of the significant wave height H s from Hsu et al. (2017) is used such that τ Hsu = 2H s /u f . This residence time is approximately 66% of the corresponding τ f for all drop sizes and 10-m wind speeds. The results using these two other residence times (not shown) are very similar to those in Figure 4 with the same threshold at approximately U 10 = 55 m/s and the same behavior in the high wind speed limit, owing largely to the very long time that the drops remain at T w as shown in Figure 1.

Summary
Our results suggest that at extreme wind speeds, the sea spray fluxes are determined by environmental wind and thermodynamic conditions and by the total spray mass flux, but are not sensitive to the shape of the SSGF. The air-sea enthalpy and momentum fluxes are largely determined by U 10 and the upward spray mass flux. The parameters T s and T w will modify the enthalpy flux from sea spray in the hurricane boundary layer. However, if we can consider τ f from Andreas (1992) to be a good measure of the residence time and the parameter ranges in Table 1 to be representative of typical conditions in the hurricane boundary layer, the variation in T s and T w is insufficient in the high wind speed regime to effect a significant change in the air-sea enthalpy flux. The free stream wind speed, U 10 , is directly proportional to the momentum flux since this wind speed accelerates the lofted spray drops. However, in the high wind speed regime, nearly all of the spray is expected to be accelerated to U 10 before reentrance. Therefore, the amount of spray produced by the sea surface predominately governs the air-sea enthalpy and momentum fluxes, and the upward sea spray mass flux primarily depends on the wind speed.
All three assumptions used in the mechanistic model are well-satisfied at a 10-m wind speed of around 55 m/s or above for the SSGFs considered here. For typical hurricane spray layer conditions, the microphysical model suggests that above U 10 = 55 m/s, the ratio C K /C D becomes independent of wind speed. This agrees well with the results from recent wave tank experiments conducted by Golbraikh and Shtemler (2020) who studied the impact of foam on the surface fluxes. The dependence of the ratio of the exchange coefficients on U 10 weakens significantly for wind speeds above 50 m/s according to their results.
For a self-similar air-sea transition layer where the ratio of the exchange coefficients no longer depends on the wind speed, the air-sea fluxes could be modeled as functions of the ejected spray volume specified by the SSGF. This means that the relationship between the volume flux of sea spray and U 10 could be used to simplify the parameterization of sea spray-mediated fluxes in the high wind speed regime. The sea spray volume flux predicted by different SSGFs varies wildly-by many orders of magnitude-among the various SSGFs as shown in Figure 5.

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To estimate the sensitivity of the volume fluxes from each SSGF to the 10-m wind speed, each volume flux formulation is written in terms of, or fitted to, a power law function of U 10 . The SSGF from Zhao et al. (2006) is proportional to 1.5 and in their formulation ∝ 0.5 10 . Recall that = 3 10 ∕( ) , so the volume flux is proportional to ( 3.5 10 ) 1.5 = 5.25 10 . For the next two SSGFs, a least squares regression of the volume flux is used to calculate the coefficients of the power law. The power of U 10 that results from fitting the volume flux of the SSGF from Ortiz-Suslow et al. (2016) is approximately 9.1 with an R-squared statistic of >0.99 . Since the volume flux calculated using the SSGF from Troitskaya, Kandaurov, et al. (2018) is not globally very amenable to this type of fitting, and because this analysis is primarily interested in the high wind speed regime, the least squares fit for this function only considers volume fluxes corresponding to wind speeds above U 10 = 30 m/s. The fitted power of U 10 for this high wind speed portion of the volume flux is approximately 0.89 with an R-squared statistic of >0.91 . These three scalings, shown in Figure 5, underscore that the volume flux could be quite sensitive to changes in the wind speed. Since the SSGF is the element of sea spray-mediated fluxes that, especially in the high wind regime, appears to account for the greatest uncertainty more simulations and experiments of spray generation are needed. Additionally, these should focus on the net spray mass flux rather than on the dependence on drop radii.

Data Availability Statement
The code for the microphysical model used in this study is available at https://doi.org/10.5281/zenodo.5089527.