1. Introduction
With the Arctic sea ice retreating farther and farther each summer, the Arctic Ocean is beginning to take on characteristics of the ocean at lower latitudes. In particular, heat lost from the now-open ocean can lead to more intense mesoscale storms, and the combination of storm winds and longer open-water fetches will produce higher waves (e.g., Perrie et al. 2012; Asplin et al. 2012). Such evolving conditions will present new hazards for artificial structures like semisubmersible drilling rigs and anthropogenic islands used as oil exploration and production platforms (Jones and Andreas 2009). Although the wind and waves themselves will create hazards for these structures, my interest here is the attendant sea spray that is produced.
Jones and Andreas (2009, 2012) previously considered the spray icing of semisubmersible drilling platforms that had fairly open profiles at the waterline such that most of the spray resulted from breaking waves in open water (also Minsk 1984a; Nauman 1984). Here, I turn to spray effects that small, artificial islands built in the Arctic Ocean can face: spray largely created by waves breaking along their shoreline. At subfreezing temperatures, such spray will accumulate as ice on virtually all surfaces on these small islands (e.g., Minsk 1984b; Itagaki 1984). Even in above-freezing temperatures, the sea salt generated by high wind and waves will collect on raised structures and speed the corrosion of metal surfaces.
To quantify the rate of such shore-induced spray production, I carried out a month-long experiment in January of 2013 on Mount Desert Rock, an unvegetated island with low relief that is located 24 mi (39 km) out to sea from Bar Harbor, Maine. Mount Desert Rock has a size and a topographic profile that are similar to some of the artificial islands now in the Arctic (e.g., Muzik and Kirby 1992; Gerwick 2007, chapter 23). I presume that the spray concentrations and generation rates observed on Mount Desert Rock will be similar to the values near other rocky shorelines and, in particular, will be what artificial islands in the Arctic might experience in the coming decades.
Although the literature contains several papers that report sea spray observations at shorelines, my data are unique in several ways. From a climatological perspective, Mount Desert Rock in January provides a good chance of encountering subfreezing air temperatures and winds high enough to produce copious spray. And, indeed, roughly one-half of my measurements were made at temperatures below freezing. I am unaware of other spray data collected at temperatures below freezing.
Second, most of the previous spray measurements from the coastal zone looked at only relatively small droplets. For example, de Leeuw et al. (2000), Vignati et al. (2001), Clarke et al. (2006), van Eijk et al. (2011), and Piazzola et al. (2015) all reported recent spray observations in coastal regions, and all sampled droplets with radii at formation as small as 0.02–0.1 μm. Only van Eijk et al., however, sampled droplets with radii up to about 30 μm; the other papers reported on droplets with radii up to only 10–20 μm. Although these small droplets are plentiful, they do not carry enough mass to produce the severe icing that larger droplets do (Jones and Andreas 2012).
Therefore, on Mount Desert Rock, I collected spray data with a cloud-imaging probe (CIP) for which the smallest radius bin was centered at 6.25 μm; the instrument was capable of counting droplets with radii up to 775 μm. Although the counting statistics were poor for the largest droplets, I do report here spray-concentration measurements for droplets in a radius bin centered at 143.75 μm—well into what is referred to as the spume regime for open-ocean spray. Thus, I believe that these observations represent the largest spray droplets that have been measured near a shoreline.
In this paper, I report data from the CIP deployed for 27 days near the shoreline on Mount Desert Rock. These data span 12.5-μm-wide radius bins with centers ranging from 6.25 to 143.75 μm and include 10-m winds from 5 to 17 m s−1. A key finding is that the droplet spectra have the same shape at all observed wind speeds. I am thus able to derive an expression for the near-surface droplet concentration as the product of a function of just droplet radius and another function that goes as the cube of the wind speed. This concentration function yields a function for predicting spray generation when ocean waves encroach on a rocky (as opposed to sloping and sandy) shoreline.
2. Measurements on Mount Desert Rock
Mount Desert Rock, which, as mentioned, is located 39 km into the Atlantic Ocean east of Bar Harbor, has a lightkeeper’s house and a stone lighthouse that NOAA has instrumented as a C-MAN station under the National Data Buoy Center (NDBC). The College of the Atlantic in Bar Harbor owns Mount Desert Rock and, as such, facilitates access to the “Rock” and provided us with logistics support.
Figure 1 shows how small Mount Desert Rock is and identifies the permanent structures there and the 2013 instrument locations. It is truly a desert island: its surface has no vegetation but is simply a rocky outcrop. From our survey (these numbers may differ from the NDBC information), the high point of the island is only 9.2 m above mean sea level; the lighthouse is 18 m tall. Prevailing winds at Mount Desert Rock in January are westerly and northwesterly. All instruments were placed for best exposure to these winds.
A diagram of Mount Desert Rock. The light-gray shading is the island at high tide; the dark-gray shading is the island at low tide. The range between high and low tide is ~3 m. Orange objects are permanent structures: the oval is the lighthouse; the big square is the lightkeeper’s house. The red circle on the small square is the CIP and associated sonic anemometer/thermometer mounted on the foghorn platform. The three-legged symbol denotes the turbulence tripod. The quadrant from 260° to 7° indicates the only wind directions that I retained for my analyses. The arcs at 50 and 75 m show that all samples collected by the CIP were within 75 m of the water; at high tide, most were much closer.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
To provide a rigid base and some security for the expensive Droplet Measurement Technologies, Inc. (DMT), CIP, it was mounted on the foghorn platform (Fig. 1). As such, the probe was 3.24 m above local ground and 8.66 m above mean sea level. Because the wind speed and direction through the probe’s laser array are crucial for computing spray concentration, the CIP was rigidly attached to a Gill Instruments, Ltd., WindMaster sonic anemometer/thermometer (Fig. 2). The sonic anemometer’s sample area was 0.48 m above the CIP’s laser array. This whole system was frequently rotated to orient the CIP into the wind. The appendix summarizes the equations that I used for obtaining spray concentration from the CIP.
The DMT CIP and the Gill sonic anemometer/thermometer mounted on the foghorn platform on Mount Desert Rock.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
To document near-surface meteorological conditions during our measurements, a “turbulence tripod” was deployed near the high-water line (Fig. 1). This tripod held a three-axis sonic anemometer/thermometer from Applied Technologies, Inc. (ATI), 2.35 m above ground, a Li-Cor, Inc., water vapor and carbon dioxide sensor 2.10 m above ground, and an Ophir Corporation hygrometer (which also measured air temperature) 2.23 m above ground. The ground here was 4.4 m above mean sea level. I supplemented our own measurements with the NOAA measurements from the Mount Desert Rock lighthouse, the measurements from another NOAA C-MAN station on nearby Matinicus Rock, and the measurements from two nearby buoys (44034 and 44037) that are owned and maintained by the Northeastern Regional Association of Coastal Ocean Observing Systems.
Figures 3 and 4 show time series of meteorological and oceanographic data for January of 2013 from these various sources. The winds denoted “MDR NOAA” and “Matinicus” were measured by the C-MAN instruments high on the Mount Desert Rock and Matinicus lighthouses, respectively, and thus show higher speeds than the measurements nearer the surface from the two buoys and from the ATI and Gill sonic anemometers. These latter data are more representative of the wave and spray conditions and show that this study sampled in winds up to ~17 m s−1. The temperature panel in Fig. 3 shows that air temperatures were always less than 10°C during the measurements and were frequently below freezing. The stratification was generally unstable (water warmer than air; Figs. 3 and 4).
Wind speed, air temperature, and relative humidity during the experiment on Mount Desert Rock. All legends refer to all panels. “MDR NOAA” identifies the NOAA instruments on the lighthouse; likewise, “Matinicus” denotes the NOAA instruments on Matinicus Rock. “Gill Sonic on MDR” is wind speed from the Gill sonic anemometer associated with the CIP. “Our Data” identifies the wind speed and temperature data from the turbulence tripod.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
Surface water temperature and salinity and significant wave height H1/3 during the experiment on Mount Desert Rock. In the temperature and salinity panels, the data identified as “Ours” are from manual bucket samples. In the wave-height panel, our estimate of H1/3 comes from the Andreas and Wang (2007) algorithm and the wind speed is from the Gill sonic anemometer.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
3. Data analysis
The appendix reviews the equations that I used for processing measurements from the CIP. In brief, I computed spray concentrations in 12 radius bins, each 12.5 μm wide, from 0 to 150 μm. The center radius in each bin locates the bin average in the following plots and calculations.
The CIP ran continuously, except when recording was stopped to allow the CIP to be reoriented into the wind. As such, from its 1-Hz measurements, I computed half-hour averages of spray concentrations for the first 30 min of an hour and for the second 30 min. For instances in which the recording did not start at the top of the hour or end exactly at the top of the hour, I still computed averages from these partial 30-min runs. I did, however, later exclude runs that were shorter than 15 min.
For the CIP site on Mount Desert Rock, the counting statistics for the largest bins that the CIP could sample were poor. Hence, the bin centered at a radius of 143.75 μm was the largest one that I retained for analysis. Moreover, for any bin, I retained its average only if it had counted at least 10 droplets during the averaging period.
The Gill sonic anemometer attached to the CIP sampled the three wind components and the sonic temperature roughly 6 times per second. I averaged these data over the same averaging periods as for the CIP. From the average along-wind 
From 
I also sequenced the analysis with the nearest tidal record, from Bar Harbor (NDBC station 8413220), and thereby assigned to each half-hour run a tidal height. The arcs at 50 and 75 m in Fig. 1 show that, at high tide, the CIP was well within 50 m of open water. Even at low tide, it was no more than ~75 m from open water and was often much closer.
Nevertheless, to judge whether distance from the water affected the spray counts, subsequent plots distinguish between the data collected during high water and low water. The tidal range during our observations was from −0.43 to 3.93 m. Therefore, I designate as low-water runs those collected when the tide was between −0.43 and 1.75 m; high-water runs were collected when the tide was between 1.75 m and 3.93 m.
Last, A1/3 in Eq. (3.5) comes from the algorithm that Andreas and Wang (2007) derived from data collected by NDBC buoys off the northeastern coast of the United States, including several in the vicinity of Mount Desert Rock. Figure 4 compares the estimates of H1/3 from this algorithm with the data from buoys 44034 and 44037. Agreement between the Andreas and Wang algorithm and the buoy data is generally good, but the Andreas and Wang algorithm does predict a nonzero lower limit for H1/3 in light winds. This lower limit is obvious in Fig. 4 but is not an issue for this analysis because it occurs when the wind speed was less than 5 m s−1, and I ignore these wind speeds in the following results.
4. Sea spray concentration
Figures 5 and 6 show the near-surface spray-droplet concentration spectra (i.e., C0) as measured by the CIP. Each panel breaks out measurements for wind speeds (UN10 in this case) in ranges between 6 and 17 m s−1. Each panel also identifies measurements made during high water and low water.
Near-surface spray-droplet concentration spectra [i.e., C0 from Eq. (3.5)] for wind speeds UN10 between 6 and 10 m s−1. The black and red curves distinguish between measurements made during high water and low water, respectively. The green curve is the fit to these concentration spectra [i.e., Eq. (4.5)], where the UN10 used to calculate each green curve is the middle value of the indicated wind speed range.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
As in Fig. 5, but for wind speeds between 10 and 17 m s−1.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
Figures 5 and 6 do not reveal any obvious differences between the measurements made during high water and low water. Both the magnitude of the concentrations and the shape of the spectra as a function of radius are similar for the two types of observations.
In fact, in Figs. 5 and 6, the spectral shape seems to be the same for all wind speeds. I therefore nondimensionalized all of the spectra in Figs. 5 and 6 with the concentration measured at r0 = 6.25 μm for each spectrum. Figure 7 plots nondimensional versions of all 363 spectra collected in wind speeds of 5 m s−1 and higher. Nonetheless, the figure distinguishes the 170 spectra collected during high water from the 163 spectra collected during low water to reiterate that the distance to open water does not seem to have influenced the results. That is, the medians for all of the data in a radius bin and the medians for just the high-water and low-water observations in a bin are all largely indistinguishable.
All of the concentration spectra (e.g., Figs. 5 and 6) measured in wind speeds UN10 of 5 m s−1 and higher are nondimensionalized with the respective concentration measured in the radius bin centered at 6.25 μm. Hence, all spectra are identically 1 for r0 = 6.25 μm. The plot still distinguishes measurements made during high water from those made during low water. The plot also shows the bin medians for all of the data and individually for the high-water and low-water data. The small radius bins and the large radius bins fall along straight lines in this log-log plot (the two black lines). I thus represent the median nondimensional spectrum with a hyperbola: Eq. (4.3) with a = 0.10.
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
In concept, one can use Eq. (4.3) to predict spray concentration if one can associate a wind speed dependence for the spectra plotted in Figs. 5 and 6. All one needs to know is how C0(r0 = 6.25 μm), the concentration for droplets in the bin centered at 6.25 μm used to nondimensionalize the spectra in Fig. 7, depends on wind speed.
To evaluate this wind speed dependence, I first looked at the wind speed dependence of all of the concentration data because any wind speed dependence that I assign to the 6.25-μm radius bin must be appropriate for all radius bins up to 143.75 μm. Figure 8 therefore plots normalized droplet concentrations from all 333 droplet spectra. I calculated these normalized concentrations by dividing all concentrations in a specific radius bin by the average concentration for that bin. Consequently, the normalized concentrations in Fig. 8 tend to distribute equally below and above 1.
All concentration data in the 333 runs are normalized and plotted against UN10. The normalization is for each radius bin such that all concentrations measured in that bin are divided by the bin average. The data are identified as to whether they were collected during high water or low water. Three fitting lines are shown: one calculated using least squares linear regression as y vs x, one taken as the bisector of y-vs-x and x-vs-y fits, and one for which a 
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
I fitted straight lines through the log-log data in Fig. 8. The standard approach is to do least squares linear regression with y as the dependent variable and x as the independent variable. When both x and y have comparable uncertainties, however, such a fitting can be biased because least squares algorithms presume that the x values are perfectly known. Consequently, I also like to derive a fitting relation from the bisector of y-versus-x and x-versus-y least squares fits (e.g., Andreas 2002a). Figure 8 also shows this bisector fit. Last, since both fitting lines are close to cubic in wind speed, Fig. 8 shows the cubic relation for which the normalized concentration goes as 
The near-surface spray-concentration data (i.e., C0) for the bin centered at r0 = 6.25 μm are plotted vs the neutral-stability wind speed at 10 m UN10. The blue line is the best-fitting cubic relation through these data: Eq. (4.4).
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
With the green curves, each panel in Figs. 5 and 6 displays Eq. (4.5), where UN10 for each green curve is taken as the midrange wind speed for the wind speed range indicated in the panel. I draw two conclusions from these green curves. First, the shape of the droplet spectra is consistent for all of the wind speeds depicted. Second, the cubic dependence on UN10 does well in representing the spectral levels at all wind speeds in the dataset.
5. Spray-generation function
The Mount Desert Rock (labeled MDR) spray-generation function [i.e, Eq. (5.1)] as a number flux for various values of the wind speed at a reference height of 10 m U10. For these calculations, the surface temperature Ts was 1°C, the air temperature Tr was 0°C, the relative humidity RHr was 80%, the surface salinity was 34 psu, and the barometric pressure was 1000 hPa. For comparison, the plot also shows the joint Monahan et al. (1986) and Fairall et al. (1994) function (labeled Joint M & F) [from Andreas et al. (2010)].
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
For comparison with an open-ocean spray-generation function, I also plot in Fig. 10 the function that Andreas et al. (2010) created by smoothly joining the bubbles-only function from Monahan et al. (1986) with the large-radius function that Fairall et al. (1994) formulated from an earlier function from Andreas (1992). After reviewing the field, Andreas (2002b) had concluded that the Monahan et al. function provides an “anchor” for predicting the generation of small droplets over the open ocean while the Fairall et al. function has the best overall properties for high winds and larger droplets.
In Fig. 10, Eq. (5.1) is roughly three orders of magnitude as large as the joint Monahan and Fairall function for droplets smaller than ~30 μm in radius. As the radius increases, this difference decreases until the level of Eq. (5.1) extrapolated to r0 = 200 μm is very close to the level of the joint Monahan and Fairall function. The large-radius slope of my new function is also very close to the large-radius slope of the Monahan and Fairall function.
De Leeuw et al. (2000) previously measured surf-zone production at the Scripps pier in La Jolla, California. Likewise, van Eijk et al. (2011) measured surf-zone production at La Jolla and also at the Field Research Facility in Duck, North Carolina. Both of these surf zones are characterized by gently sloping beaches, in contrast to the abrupt, rocky shoreline and the absence of a beach at Mount Desert Rock. De Leeuw et al. (2000) concluded that the breaking waves at the La Jolla site enhanced spray production by up to two orders of magnitude. For their two sites, van Eijk et al. (2011) concluded that the surface zone added from 0.7 to one order of magnitude to the spray concentration. Remember, though, that both groups observed spray droplets with radii that were no bigger than 30 μm. The next section continues this discussion of the enhanced spray production that I observed.
6. Discussion
a. Footprint analysis
The explanation for the magnitude of the spray flux observed at Mount Desert Rock is intimately tied to the upwind footprint that influenced measurements at the CIP. In classic terms, the flux footprint is a function of distance x upwind from an instrument that is at height zm; the origin of this distance is at the instrument. By integrating over all x the surface flux at location x multiplied by the footprint function at x, the flux is derived at the origin and at the height zm that the instrument sees (e.g., Horst and Weil 1992, 1994; Wilson 2015).
Besides zm, which is 3.24 m for the CIP, another parameter that is important in most footprint analyses is the aerodynamic roughness length z0. For a typical wind speed in my dataset, 12 m s−1, I estimate z0 = 3.4 × 10−4 m. Hence, zm/z0, another important quantity, is approximately 9500. The height of the atmospheric boundary layer h and the ratio zm/h are also required in some footprint analyses. Without measurements of h, I surmise that it was rarely less than 400 m; therefore, zm/h ≤ 0.008.
The footprint function is zero for some distance immediately upwind of the instrument (Horst and Weil 1994; Hsieh et al. 2000; Wilson 2015). In essence, material escaping the surface too close to the instrument does not have time to reach height zm and be observed before it is blown beyond the instrument. I denote this distance X for “excluded.”
The total upwind extent of the flux footprint itself I denote as F (in meters). From figures in Kljun et al. (2004; e.g., their Fig. 1), I estimate that, for the given values of zm, z0, h, and stratification, the footprint is approximately zero for F larger than ~200 m. In other words, the CIP is most sensitive to the surface within 200 m upwind from it. Meanwhile, the peak of the footprint function—the region of upwind fetch that contributes the most to observations at height zm—is roughly 50–70 m upwind of the instrument (Horst and Weil 1994, their Fig. 3; Kljun et al. 2004, their Fig. 1). From our Fig. 1, it can therefore be concluded that most of the spray reaching the CIP originated in or near the surf zone.
In Eqs. (6.2) and (6.3), W(U10) is the fractional whitecap coverage for the open ocean as estimated from Eq. (5.4). In Eq. (6.3), R is the distance over rock from the CIP to the shoreline on Mount Desert Rock; I estimate it as, typically, 30 m (see Fig. 1). This portion of the footprint obviously produces no spray; the footprint function is thus zero here. In contrast, the surface zone is one continuously renewed whitecap; the fractional whitecap coverage is 1 here [de Leeuw et al. 2000; i.e., the 1 multiplying the S term in Eq. (6.3)]. Moreover, as I will discuss shortly, the surf zone is more productive white water than would be characterized by just whitecap coverage [Eq. (5.4)]. Therefore, I include the γ coefficient in the S term and expect γ to be 1 or greater.
The white water in the surf zone more closely resembles a stage-A whitecap than a stage-B whitecap. Stage-A whitecaps are associated with actively breaking waves, whereas stage-B whitecaps result from the rising, decaying bubble plumes left after a wave breaks (Monahan and Lu 1990). The surf zone at Mount Desert Rock during winds of 10 m s−1 and higher was a very energetic and turbulent region of total white water and continually breaking waves (cf. Brocchini and Peregrine 2002).
Woolf et al. (1987) and Cipriano et al. (1987) studied spray formation in a laboratory whitecap-simulation tank. Although they could measure only spray droplets with radii of about 10 μm or less, their results are, nevertheless, suggestive of what one might see on Mount Desert Rock. Figures 4 and 5 in Woolf et al. (1987) and Fig. 2 in Cipriano et al. (1987) suggest that a newly formed whitecap (the stage-A whitecap) produces about an order-of-magnitude more spray droplets per unit time than does the later decaying phase (stage B) of the whitecap. On reevaluating these papers, E. Monahan (2015, personal communication) estimated that the production of these droplets, which have radii at the small end of my spectrum, may even be up to two orders of magnitude higher in stage-A whitecaps than in stage-B whitecaps.
These studies by Woolf et al. (1987) and Cipriano et al. (1987) generally quantified only the spray production by bursting bubbles—that is, film and jet droplets. In the surf zone, with an onshore wind, other mechanisms can also create spray droplets (e.g., Peregrine 1983; Monahan et al. 1986; Andreas et al. 1995, their Fig. 1; Brocchini and Peregrine 2002). Spume droplets, which the wind tears right off the wave crests (e.g., Soloviev et al. 2012), are generally larger than film and jet droplets. In the very turbulent surf zone, where waves reflected from the steep shore collide with incoming waves from the ocean, so-called splash and chop droplets also occur. It is therefore not implausible to speculate that these latter processes, especially, can enhance the spray production by another order of magnitude.
In summary, spray production in a surf zone at a rocky shoreline, where white water is ubiquitous and continually renewed, could be from 10 to 1000 times as high at comparable winds speeds as over the open ocean, where spray production predominantly comes from stage-A and stage-B whitecaps. Therefore, Fig. 11 displays the ratio in Eq. (6.5) for γ ranging from 1 to 1000.
The ratio of surf-zone production to open-ocean production of spray, as predicted by Eq. (6.5), is plotted as a function of 10-m wind speed U10 for the γ values indicated. As explained in the text, in Eq. (6.5) F = 200 m, R = 30 m, S comes from Eq. (6.1), and W(U10) comes from Eq. (5.4).
Citation: Journal of Applied Meteorology and Climatology 55, 9; 10.1175/JAMC-D-15-0211.1
Although their geometry was somewhat different than for my observations on Mount Desert Rock, the γ = 1 and γ = 10 cases in Fig. 11 approximate the data that de Leeuw et al. (2000) and van Eijk et al. (2011) obtained downwind of far less energetic surf zones over sloping beaches. Even if the breakers on their beaches were not more effective spray producers than open-ocean whitecaps are—that is, assuming γ = 1—Fig. 11 suggests that the spray production would still be enhanced by a factor of 3 or 4 because of the increased whitecap coverage.
Meanwhile, according to Fig. 11, a γ value between 100 and 1000—which, according to my literature review, seems to be possible—would explain the observed spray concentrations and spray-generation function (Fig. 10), for which the Mount Desert Rock values are about three orders of magnitude larger than over the open ocean.
b. Parameterizing the spray
The second school of thought supposes that the shape of the droplet spectrum depends on the forcing variables; therefore, separating the size function and the forcing function as in Eq. (6.6) is not possible. Monahan et al. (1983) seemed to document this change in the droplet spectrum with wind speed when they observed enhanced droplet counts for large droplets at higher wind speeds. Miller and Fairall (1988) put this approach into practice when they synthesized from four datasets a spray-generation function for which the shape changed with wind speed. Andreas (1992), for example, was an early user of this Miller and Fairall function. Smith et al. (1993) and later Smith and Harrison (1998) likewise derived spray-generation functions for which the shape of the droplet spectrum changed with wind speed.
My observations, however, come down on the side of Eq. (6.6)—that the droplet spectrum does not change shape significantly with wind speed or other forcing variables for wind speeds between 5 and 17 m s−1. In view of Figs. 5–7, this conclusion is very robust.
I admit that the references cited in this section were all to open-ocean conditions. Hence, it is not clear that the data from Mount Desert Rock can be extended to the open ocean and, thereby, can add weight to either side of the argument on how to parameterize C0 and dF/dr0. I nevertheless felt it essential to interpret my data in the context of this debate.
c. Height profile of the spray
To continue with the calculation, readers can use their favorite algorithms for computing Vg and u*. As an alternative, they can retrieve online (at http://people.nwra.com/resumes/andreas/software.php) a bulk flux algorithm that Andreas et al. (2015) developed for computing u* over the ocean, among other fluxes, and a second algorithm for fast microphysical calculations that include computing Vg (Andreas 2005).
7. Conclusions
With increasing wind speed, the surf zone at the rocky shore of Mount Desert Rock became increasingly energetic. Active wave breaking, ubiquitous stage-A whitecaps, and continuous turbulent white water grew oceanward from the shoreline with increasing winds. A cloud-imaging probe placed a few tens of meters downwind from this surf zone counted the spray droplets generated there.
Because of the high energy in the surf zone and the fact that a footprint analysis suggests that the CIP focused preferentially on spray coming from the surf zone, the measured spray concentrations are from two to three orders of magnitude higher than those measured over the open ocean. Waves crashing against rocks also produce one to two orders of magnitude more spray than waves breaking on sloping beaches.
The spray-generation function derived from these near-surface concentration measurements reiterates how much more productive the surf zone is than is the open ocean. Figure 10 shows that, at least for droplets smaller than about 30 μm in r0, the surf zone at Mount Desert Rock was three orders of magnitude more productive than the open ocean.
For droplets above 100 μm in radius, on the other hand, the Mount Desert Rock spray-generation function is comparable to the open-ocean function. There are two possible explanations for this convergence for large radii. Either the joint Monahan et al. (1986) and Fairall et al. (1994) function overestimates the generation rate of the largest droplets or, at the CIP site on Mount Desert Rock, many of the larger droplets settled out of the airflow before the CIP could count them. Both explanations are plausible because the counting statistics for the CIP were best for the smaller droplets, while the joint Monahan and Fairall function for open-ocean spray generation shown in Fig. 10 is also most reliable for the smaller droplets. In summary, the orders-of-magnitude difference in spray concentration and in spray generation (Fig. 10) between Mount Desert Rock and the open ocean is robust for droplet radii less than 50–100 μm.
Because these observations on Mount Desert Rock are the first spray measurements at a rocky shoreline, I cannot say how general the results are. The footprint analysis in section 6a provides justification for presuming that production in the surf zone at a rocky shoreline should be 2–3 orders of magnitude higher than over the open ocean. Moreover, its correct order-of-magnitude prediction for spray production over a sloping, sandy beach provides validation for that analysis. Consequently, although Eqs. (4.5) and (5.1) may not be perfectly transferrable to other abrupt shores, they should be useful planning tools for evaluating how hazardous spray icing and sea salt might be for artificial islands currently built or planned for the high-latitude ocean.
Acknowledgments
I thank Kathy Jones of CRREL for help in the field, advice on the analysis, and comments on the manuscript. I also thank Captain Toby Stephenson of the MV Osprey for getting us and our equipment safely to and from Mount Desert Rock; Chris Tremblay, Alex Borowicz, Tanya Lubansky, and Lindsey Nielsen for logistics support and company on the Rock; and Chris Fairall, Dan Wolfe, and Sergio Pezoa of NOAA/ESRL for loaning me their cloud-imaging probe and instructing me in its use. Emily Moynihan of BlytheVisual created Fig. 1 from a similar image that Chris Tremblay provided. The U.S. Office of Naval Research supported me in this work with Awards N00014-12-C-0290 and N00014-11-1-0073.
APPENDIX
Obtaining Droplet Concentration from the CIP
The DMT CIP uses single-particle optical imaging with a linear array of 64 photodetectors to count and size droplets. The following equations that I used to process the raw CIP data come from the user’s manuals (DMT 2009, 2013) and from software that C. Fairall (2012, personal communication) shared with me.
The CIP uses a red laser; the wavelength is λ = 0.660 μm. The resolution in size bins is R = 25 μm: that is, the CIP counts droplets in size bins that increase from zero in steps of 25 μm in diameter. The CIP has a linear array of 64 (=ND) diode detectors; it thus can sort droplets into 62 (=NB) bins, each 25 μm wide.
I do the analysis, however, in terms of droplet radius; thus, the radius resolution is Δr = R/2 = 12.5 μm. With 62 CIP bins of width Δr, the upper radius limit for each bin BinHi increases as 12.5i, where i = 1, 62. Hence, BinHi = 12.5, 25, 37.5, 50, …, 762.5, and 775 μm. Likewise, the lower limit on each radius bin BinLo goes as 12.5(i − 1), where i = 1, 62. That is, BinLo = 0, 12.5, 25, 37.5, …, 750, and 762.5 μm. My convention is to use the center radius of each bin to denote droplets counted by the CIP at a given radius. The center radius of a bin (in micrometers) is Bincent = 6.25 + 12.5(i − 1), where i = 1, 62.
On Mount Desert Rock, the counting statistics for 30 min of sampling were poor for droplets beyond the bin centered at 143.75 μm. Hence, my plots show only droplets centered in the 12 bins 6.25, 18.75, 31.25, 43.75, …, 131.25, and 143.75 μm.
The final dimension for calculating the volume V in Eq. (A.2) is related to the flow of air through the laser array. This is just 
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