The Competing Effects of Breaking Waves on Surfzone Heat Fluxes: Albedo Versus Wave Heating
Depth-limited wave breaking modifies the heat flux in the surfzone relative to the inner-shelf (where waves are not breaking). Surfzone wave breaking generates heat through viscous dissipation (wave heating), but also increases surface foam coverage and albedo, thereby reducing solar heating, that is, cooling relative to the inner-shelf. These two competing breaking wave effects are quantified with a yearlong experiment at the Scripps Institution of Oceanography Pier. Cross-shore averaged surfzone albedo estimates were more than three times higher than inner-shelf albedo, reducing the yearly averaged surfzone water-entering shortwave radiation by 41 W/m2 relative to the inner-shelf. Surfzone breaking wave dissipation added an additional yearly averaged 28 W/m2 relative to the inner-shelf. The albedo-induced solar heating reduction in spring, summer, and fall was usually greater than the wave heating. However, in winter, large waves and relatively weak shortwave solar radiation (due to both lower top of the atmosphere solar radiation and clouds) resulted in a nearly equal number of days of breaking wave-induced heating or cooling. These two heat flux terms are coupled via wave breaking dissipation. Averaged over the surfzone, the albedo-induced solar radiation reduction is linearly related to the downwelling solar radiation and is independent of wave height. Consequently, the albedo-induced cooling to wave heating ratio is a function of breaking wave height to the −3/2 power, allowing evaluation of the relative importance of these terms in other geographic regions.
- Surfzone breaking waves heat via dissipation; foam increases albedo, reducing solar radiation
- Over a year, the albedo-induced solar heating reduction was most significant
- The net effect depends on incident wave height, latitude, seasons, beach slope, and cloudiness
Plain Language Summary
Temperature variation in nearshore waters affects the local ecology, and is also used to study important physical processes. Wave breaking contributes to surfzone temperature variation in two ways. First, breaking waves dissipate their energy in the surfzone creating friction (heat) and foam. Surfzone foam reflects sunlight reducing solar warming of the surfzone, thus leading to cooling relative to no wave breaking. These two competing wave effects (addition of frictional heating and reduction in solar heating) are quantified with a yearlong experiment at the Scripps Institution of Oceanography pier (La Jolla, CA). On average, frictional wave heating added 28 W to each square meter of surfzone. At the same time, surface foam reduced the solar heating in each square meter of surfzone by 41 W on average. The relative contribution of these competing effects varied depending on the wave height and the available sunlight, which depended on seasons and clouds. Temperature variation caused by these two effects can be estimated at other locations if the wave height and the amount of sunlight are known.
The surfzone (region of depth-limited wave breaking) and adjacent offshore shallow inner-shelf (no depth-limited wave breaking) comprise the nearshore; a physically dynamic, economically important, and biologically diverse part of the ocean. Temperature is an important physical attribute here, as temperature variation affects growth rates, recruitment rates, and egg mass production rates of various species (e.g., Broitman et al., 2005;Fischer & Thatje, 2008;Phillips, 2005) as well as pathogen ecology (e.g., Goodwin et al., 2012). Pathogen mortality is related to both temperature (Surbeck, 2009) and exposure to solar shortwave radiation (e.g., Boehm et al., 2002; Sinton et al., 1999, 2002). In the nearshore, temperature can also be a tracer for nutrient delivery (e.g., Omand et al., 2012) or surfzone to inner-shelf water mass exchange (e.g., Hally-Rosendahl et al., 2014).
Consequently, quantitatively understanding physical mechanisms affecting the inner-shelf heat budget has been an active area of recent study. Inner-shelf heat budgets include upwelling (e.g., Fewings & Lentz, 2011;Lentz, 1987), wind stress (e.g., Austin, 1999), eddies (e.g., Wilkin, 2006), internal waves (e.g., Shroyer et al., 2010), and the passage of weather systems on time scales of days to weeks (e.g., Austin & Lentz, 1999). Heat transfer between the air-sea interface occurs through radiative solar shortwave heating, net long-wave heat flux, as well as net latent and sensible heat exchange and is often parameterized (e.g., Beardsley et al., 1998; Fairall et al., 1996, 2003) when applied to observational and modeling studies (e.g., Davis et al., 2011; Etter et al., 2004; Lentz, 1987; Wilkin, 2006).
Closer to shore, rip currents (narrow wave-driven ejections from the surfzone) have been associated with strong temperature variation on the inner-shelf (Hally-Rosendahl et al., 2014; Smith & Largier, 1995), interacting with and adjusting the vertical temperature profile and influencing the inner-shelf cross-shore heat flux (Kumar & Feddersen, 2017). Thus, surfzone temperature (relative to the stratified inner-shelf) is an important determining factor for how this transport mechanism is established and evolves. Additionally, the presence of fecal indicator bacteria (FIB) near the Southern California coast varies with temperature (Boehm et al., 2004), and predictive models for pathogen transport in the surfzone include temperature and shortwave radiation (e.g., Boehm, 2003). In addition, solar radiation-induced Enterococcus (FIB) mortality contains cross-shore variation, and modeled FIB concentrations and decay rates were best predicted when cross-shore mortality gradients were included (Rippy, Franks, Feddersen, Guza, & Moore, 2013). Thus, cross-shore variation of temperature and solar radiation affects many important biological processes, motivating a more complete understanding of surfzone to inner-shelf temperature and solar radiation differences.
Many aspects of the surfzone heat budget are similar to the inner-shelf heat budget, although surfzone wave breaking modifies terms and creates a new term. The new wave heating term is generated by surfzone wave breaking, which through viscous dissipation, generates heat. Also, breaking wave-induced foam increases the surfzone albedo and thereby reduces the water-entering solar shortwave radiation relative to the inner-shelf. Further, surfzone wave breaking affects the sensible (MacMahan et al., 2018) and potentially the latent air-sea fluxes. Here the wave heating and surfzone foam albedo effects are explored.
The wave heating contribution to the surfzone heat budget results from mechanical wave energy being converted to heat (internal energy) through viscous dissipation. Waves outside the surfzone shoal and break in the shallow surfzone, generating turbulent kinetic energy. Some wave energy is reflected from the shoreline, however on shallow sloping beaches (such as in this study) the percentage of reflected wave energy is typically small (<3%; Elgar et al., 1994). Other surfzone processes driven by wave breaking are frictionally balanced with energy pathways still leading to viscous heating. For example, breaking wave-driven alongshore currents are frictionally balanced (Feddersen et al., 1998). Similarly, surfzone wave breaking can suspend sediment or inject bubbles into the water column, yet their fall or rise is also frictionally balanced. Acoustic noise energy generated by wave breaking does radiate away but noise generation is negligible (6–10 orders of magnitude smaller) relative to breaking wave dissipation (e.g., Kennedy, 1992; Klusek & Lisimenka, 2013). Additional export of mechanical energy from the surfzone (via rip currents or undertow, e.g.) has been estimated to be many orders of magnitude smaller than incident wave energy flux on similar beaches (Sinnett & Feddersen, 2014). Thus, the bulk of the incident wave energy is dissipated in the surfzone through turbulence throughout the water column, and eventually converted to heat. Wave heating heats the surfzone relative to the inner-shelf.
Solar heat flux is a major surfzone heat budget term (Sinnett & Feddersen, 2014), so changes to the albedo, and thus the amount of absorbed solar radiation, are consequential. The surfzone surface is a combination of foam-free and foam-covered areas due to the recent passage of breaking waves (e.g., Frouin et al., 1996). As foam has a higher albedo (α ≈ 0.55; Whitlock et al., 1982) than foam-free water (α ≈ 0.06; Payne, 1972), the average albedo is higher in the surfzone than in the relatively foam-free inner-shelf (Frouin et al., 1996). Deep-water albedo parameterizations have been developed for wind-generated whitecapping (e.g., Frouin et al., 1996; Jin et al., 2011; Koepke, 1984). However, surfzone foam is due to depth-limited wave breaking and does not require wind, making these parameterizations inappropriate for the surfzone. Recently, a surfzone albedo parameterization has been developed that uses offshore wave conditions, bathymetry, and a surfzone wave model (Sinnett & Feddersen, 2016).
The breaking wave-related surfzone albedo increase can be large (as much as 8× the inner-shelf albedo; Sinnett & Feddersen, 2016), and the subsequent decrease in solar radiation is significant. Thus, elevated surfzone albedo results in surfzone cooling relative to the inner-shelf. Similarly, the wave heating term can be a significant source of heat as including wave heating improved a surfzone heat budget (Sinnett & Feddersen, 2014). However, breaking wave albedo effects were not included, although a residual net surfzone cooling was inferred. Thus, the relative importance of these two competing effects is unknown, as is how parameters such as wave height, beach slope, or latitude affect relative heating or cooling.
Here surfzone parameterizations of wave heating (Sinnett & Feddersen, 2014) and wave-induced albedo increase (Sinnett & Feddersen, 2016) are applied to yearlong observations quantifying the competing wave heating and albedo affects on surfzone heat fluxes. The experiment and analysis methods are detailed in section 2. Results quantifying the competing effects of wave heating and albedo-induced solar heating reduction are described in section 3. The implications of these competing effects for different parameter space (wave height, beach slope, latitude) is discussed in section 4.1. These competing wave-related heating and cooling effects are discussed relative to a previous heat budget at the same location (Sinnett & Feddersen, 2014) in section 4.2. Section 5 is a summary.
2.1 Instrumentation and Data Processing
A yearlong study was conducted at the Scripps Institution of Oceanography (SIO) pier (La Jolla California, 32.867N, 117.257W) between 25 October 2014 and 25 October 2015. The SIO pier extends 322 m west-north-west (288°) from Scripps beach into water depth h ≈ 7 m (Figure 1a). The roughly alongshore uniform shoreline extends 200 m north to 500 m south of the pier. Cross-shore bathymetry profiles were conducted along the pier at 0.5 to 1 month intervals as wave conditions allowed. The cross-shore profile slopes gently with yearly bathymetric changes less than 0.3 m at any location, causing slope variation of less than 5%. The average slope in depths h< 3.5 m (typically includes the surfzone) is s ≈ 0.023 (Figure 1b). A pier-end NOAA station (9410230) measured 6-min averaged tidal elevation η relative to the mean tide level. The cross-shore x coordinate is positive onshore, with the mean shoreline (x = 0) where mean tide level intersects the mean bathymetry. The alongshore coordinate y is positive toward the north, with y = 0 at the northern edge of the pier.
For the 365 days beginning 25 October 2014, hourly significant wave height Hs (zeroth moment of the hourly energy spectrum) and peak period Tp (period of the highest spectral energy density) were observed at the pier-end (square, Figures 1a and 1b) by the Coastal Data Information Program station 073 pier-mounted Paros pressure sensor. When the sensor was inoperative (<7% of the time), a spectral refraction wave model with very high skill and initialized from offshore buoys was used (O'Reilly & Guza, 1991, 1998; O'Reilly et al., 2016).
Concurrently, a Campbell Scientific NR01 four-way radiometer located midpier (triangle, Figures 1a and 1b) recorded 1-min averaged downwelling and reflected upwelling solar shortwave radiation (wavelengths 300 to 2800 nm) as described in Sinnett and Feddersen (2016). Although the radiometer was cleaned at regular intervals, rain or very dense fog caused water to accumulate on the glass optics. Additionally, rarely occurring extremely low tides moved the shoreline seaward of the radiometer location so that the sensors viewed sand rather than water. Data during these times were flagged and removed from the record (6% of all data). For this study, radiation data were hourly averaged onto the same temporal grid as the wave observations. These wave and radiation data were used to calibrate a parameterization relating offshore wave energy to surfzone albedo as described in section 2.2.3 and detailed in Sinnett and Feddersen (2016).
2.2.1 Wave Model
The model adapted here follows Church and Thornton (1993) with standard breaking parameters (B =0.9 and γ = 0.57).
An example cross-shore wave transformation over bathymetry is illustrated (e.g.) on 5 May 2015 at 14:00 PDT (Figure 2a). Observed offshore wave height Hs = 1.4 m slightly increases onshore before breaking (black, Figure 2b) due to the shallowing bathymetry. Wave set-up and set-down are ignored in the transformation model as these adjustments contribute to a negligibly small variation in shoreline location. As waves break, Hs decreases from the outer surfzone to the shoreline, also reducing the wave energy flux Fwave (red, Figure 2b).
For the example in Figure 2, xsz=−170 m and xsl = −22 m, making the effective surfzone width Lsz = 148 m.
2.2.2 Wave Heating
2.2.3 Solar Radiation
Thus, changes to either the available downwelling radiation or the albedo α affect the water-entering shortwave radiation and thus solar heating.
2.2.4 Inner-Shelf and Surfzone Albedo
In direct sunlight, standard nonwave breaking albedo parameterizations depend only on solar zenith angle θs (Briegleb et al., 1986; Payne, 1972; Taylor et al., 1996). In diffuse light (defined here when the ratio of atmospheric reduction in shortwave radiation to top-of-atmosphere shortwave radiation ), ocean surface albedo is near 0.06 and no longer depends on θs (Payne, 1972). Thus, here the inner-shelf albedo (where waves are not breaking) αθ is defined following Taylor et al. (1996) with specular reflection for (direct sunlight). In diffuse light ( ) α ≈ 0.06 (Payne, 1972). Latitude and local time define θs following Reda and Andreas (2008). This θs dependent parameterization works well for inner-shelf observations at this site (Sinnett & Feddersen, 2016),
(Figure 2d). Here the best-fit αf=0.465 (Sinnett & Feddersen, 2016) and αθ is the θs parameterized albedo of foam-free water (Taylor et al., 1996). Onshore of the outer surfzone limit (xsz, where waves begin to break) albedo increases above αθ due to surface foam. Generally, albedo increases as the surfzone depth decreases, with variations caused by undulations in bathymetry. In the very shallow inner-surfzone, nearly all waves are breaking and the surfzone is nearly saturated in foam, so that αsz ≈ αf.
Both the amount of available downwelling radiation and the albedo difference between the surfzone and inner-shelf affect . As 〈αsz〉>αθ, the surfzone has an albedo-induced cooling relative to the inner-shelf. Over the year, hourly is estimated with Hs and via 17.
At this quartz-sand beach, this albedo parameterization does not explicitly consider the albedo of the seabed and suspended sediment, which can be important for other regions such as coral reefs (e.g., Hochberg et al., 2003) and estuaries (e.g., Fogarty et al., 2017). At small θs, the albedo of wet sand is about 0.07 (e.g., Dickinson, 1983), thus seabed reflections are weak. Furthermore, due to breaking wave-generated turbulence suspending sediment, the surfzone optical depth is typically small (e.g., Rippy, Franks, Feddersen, Guza, & Warrick, 2013) such that little light penetrates to the seabed. Surfzone suspended sediment concentrations above 5 g/L are unusual except near the seabed (e.g., Beach & Sternberg, 1996), and thus near-surface sand reflectance that contribute to albedo is also expected to be weak. Colocated instantaneous surfzone albedo and video observations clearly show that breaking wave foam drives albedo time-dependence, and when no waves are breaking, observed albedo agrees with the Taylor et al. (1996) parameterization (Sinnett & Feddersen, 2016).
3 Observations and Results
3.1 Observed , Hs, Fwave, and Albedo
The top of the atmosphere varies with θs and Γ on diurnal and seasonal time scales, so that the daily maximum varies seasonally (red, Figure 4a). At the water surface available downwelling solar radiation primarily varied diurnally, but also varied at synoptic to seasonal time scales (black, Figure 4a). On clear days, atmospheric attenuation resulted in . Clouds decreased the available further (Figure 4b). In winter, cloudy periods usually lasted a few days (jagged peaks, Figure 4b) and were frequently accompanied by rain causing short data gaps. In the very late spring and early summer, coastal fog persisted for longer periods causing to remain elevated (Figure 4b). Early spring, late summer, and early fall were typically less cloudy.
Pier-end significant wave height Hs typically varied synoptically between 0.5 and 1.5 m, with generally larger waves in winter and spring, and smaller waves in summer and fall (Figure 4c). Pier-end peak wave period was usually between 7 and 13 s (not shown). The mixed barotropic tide typically varied ±1 m (not shown) inducing a roughly ±43 m variation in xsl. Wave and tide conditions, together with the evolving bathymetry, affected the surfzone width Lsz (Figure 4d). Average Lsz = 84 m, but was at times above 150 m during strong wave events and as small as 4 m when waves were small. Time periods were excluded from analysis when waves were very small and xsz was in less than 0.5 m depth (i.e.,Lsz<10, less than 0.2% of all data).
At the outer surfzone boundary, wave energy flux mean and standard deviation = 2,149 ± 1,826 W/m driven primarily by variable Hs through 3 on synoptic time scales (Figure 5a). Large wave events have an outsized contribution to Fwave due to the quadratic relationship between Fwave and Hs 3. Seasonal Hs variability generally elevated Fwave in wintertime and reduced Fwave in summertime. The cross-shore average surfzone albedo mean and standard deviation 〈αsz〉=0.28 ± 0.07 (Figure 5b) and was more than three times the mean inner-shelf albedo. Surfzone albedo 〈αsz〉 varied on tidal, diurnal, and seasonal time scales, and usually much more rapidly than Fwave.
The daylight variation of 〈αsz〉 and αθ is examined with ensemble averages. Albedo estimates are removed when solar zenith angle is large (|θs|> 80°) to remove near-horizon effects. For each day, the daylight albedo estimates are normalized onto a standard 12 hr time-period removing seasonal daylight variations. These are subsequently binned over all the days in the year, allowing interday surfzone and inner-shelf albedo comparison. Daily ensemble averaged αθ (blue line, Figure 6) has strong solar zenith angle θs dependence, with elevated albedo at low sun angles near sunrise and sunset. Seasonal variation in θs and cloud cover variation account for the relatively small αθ deviation from the mean (blue shaded). As the surfzone has fractional foam coverage, 〈αsz〉 retains some θs dependance, although weaker than αθ, with elevated 〈αsz〉 at larger |θs| (red line, Figure 6). However, surfzone foam elevates 〈αsz〉 above αθ, with midday ensemble averaged 〈αsz〉 elevated by 0.19 over αθ. Wave, tide, and bathymetry variability influence 〈ζ〉 and thus contribute to the relatively large 〈αsz〉 variability (red shaded).
3.2 Competing Wave Effects: and Qwave
Breaking wave energy dissipation leads to surfzone wave heating Qwave 7. Wave breaking also increases albedo, thereby reducing the water-entering shortwave solar radiation relative to the inner-shelf by an amount 17. Here these two competing effects are examined. Variability in Qwave and occur on seasonal, synoptic, diurnal, and semidiurnal time scales through variation in Hs, θs, , and Lsz. Here Qwave and are daily (24 hr) averaged to examine their relative effects on synoptic and seasonal time scales. Henceforth, all Q variables will be daily averaged.
Breaking wave-related heat flux contributions varied over the year (Figure 7) with Qwave always increasing (positive) surfzone heat flux and always reducing (negative) surfzone heat flux relative to the inner-shelf. Over the year, the mean and standard deviation of the daily averaged Qwave = 28 ± 11 W/m2 (red) and = −41 ± 16 W/m2 (blue). Thus, at this location, the combined effect of Qwave and typically reduced the surfzone heat flux relative to the inner-shelf. Both daily averaged Qwave and varied on synoptic to seasonal time scales. However, daily averaged Qwave and were uncorrelated (r2 = 0.04) as Qwave depends on incident Hs (Figure 4c) whereas depends also on clouds and . Throughout most of summer, clouds reduced and waves were small (Figures 4a–4c). Thus, the yearly maximum occurred in April when waves were larger and cloudiness lower, rather than at the summer solstice (21 June) when is maximum.
The relative effects of Qwave and have a seasonal dependance (Figure 8). In winter, is low and cloudiness can be high reducing . Wintertime waves are also relatively large with Qwave> 40 W/m2 about 20% of the time. The combined effect in winter heats the surfzone (to the right of the 1:1 line) relative to the inner-shelf 47% of the time (Figure 8a). In contrast, summertime waves were relatively small with Qwave> W/m2 only 5% of the time. The combined effect in summer cools the surfzone relative to the inner-shelf 96% of the time (Figure 8c).
Spring is characterized by a wide range of both Qwave and (Figure 8b). Spring had few clouds, with > 40% only a quarter of the time (compared to over half the time in summer). Spring also contained some of the largest Hs, resulting in the daily averaged Qwave> 50 W/m2 11% of the time. The fall distribution is slightly lower than in summer (Figure 8d). Fall is smaller than in summer (red, Figure 4a), yet fall skies were clearer (lower ) relative to summer such that mean was reduced by only 5%. Occasional large wave events in late fall (more typical of winter conditions) widened the fall Qwave distribution compared to summer. The seasonal variation in the Qwave and relationship demonstrates the effect of parameters such as the incident Hs, cloudiness, and .
3.3 Surfzone Adiabatic Temperature Change
Over the year, the daily adiabatic ΔT (18) was negative 75% of the time (black dots, Figure 9), with a mean and standard deviation of ΔT = −0.5 ± 0.6 °C. The 30-day ΔT mean and standard deviation also varied seasonally (red dots and red lines, Figure 9). Wintertime mean and standard deviation ΔT = 0.0 ± 0.4 °C as wintertime Qnet is near zero. Beginning in early spring, ΔT typically becomes negative, with mean and standard deviation ΔT = −0.7 ± 0.5 °C between March and September. In late summer and early fall with low clouds and small waves, ΔT can be as low as −1.9 °C. Daily ΔT variability was largest in spring and late summer when was high, but intermittent clouds or coastal fog caused large changes in . The late fall reduction and overall Hs increase (Figures 4a and 4c) prompted a return to winter conditions. In the adiabatic limit, net surfzone heat flux changes induced by Qwave and are substantial and can induce significant ( (1 °C)) temperature changes.
4.1 Scaling for an Idealized Surfzone
The linear relationship between daily averaged and (Figure 10, has squared correlation r2 = 0.48 (p < 0.01)) with best-fit slope −0.19 (red line). This implies that the daily averaged surfzone albedo is on average 0.19 larger than the inner-shelf. With an idealized (constant) bathymetric slope s = 0.023, daily averaged clear-sky inner-shelf albedo (e.g., Payne, 1972), and foam albedo αf=0.465 as in section 2.2.4, the surfzone averaged foam fraction 20 applied to 21 yields a theoretical slope (dashed black line, Figure 10) which is less than 1% different from the best-fit slope to observations. Deviations from the scaling 21 are potentially due to tidal and incident Hs variation together with the realistic and variable nonplanar bathymetry. The linear relationship correlation between and (Figure 10) that matches the scaling 21 demonstrate the suitability of 20 and 21 to effectively scale on gently sloping and alongshore uniform beaches.
The scaling for an idealized surfzone 22 is compared with observations (Figure 11), illustrating how clouds, , and Hsb affect the ratio. The observed ratio is largest for small Hsb and decreases for larger Hsb consistent with the scaling. For Hsb> 1.5 m, the observations and scaling have (relative heating) at this location. For a clear sky (no clouds or constant atmospheric attenuation), in 22 depends only on , varying only by season and latitude. At a latitude of 33°N (near the SIO pier) for the clear-sky summer solar maximum, the scaling 22 bounds the upper limit on the observed for a particular Hsb (Figure 11, solid black). For the 33°N clear-sky winter solar minimum, the scaling intersects the observations (Figure 11, black dashed). Without clouds, observations are expected to fall between the black solid and dashed curves. However, the presence of clouds lower the observed (and subsequently the ) for a particular Hsb. Thus, the scaling 22 sets an upper bound.
The scaling for 22 can be used to estimate the relative importance of to Qwave at other locations with variable latitude and seasonal top of the atmosphere , cloud, beach slope, and wave conditions. At the equator (0°N) seasonal variation in is very small, resulting in a similar clear-sky and Hsb relationship year-round (red solid and dashed curves in Figure 11). At high latitudes, the seasonal difference in is large, expanding the summer to winter difference. At 66°N, the summer clear-sky to Hsb relationship (Figure 11, blue solid ) is nearly the same as at 33°N (the experiment site). However, for wintertime clear skies, for any Hsb > 0.4 m (Figure 11, blue dashed) indicating wave heating nearly always dominates at any beach exposed to the open ocean (not iced in). In contrast at 33°N, wintertime clear-sky only for Hsb> 1 m. These significant latitude and seasonal differences in clear-sky will have implications for surfzone heat budgets from equator to Arctic. Note that carbonate sands or coral reef surfzones, which often have high optical clarity, may have additional albedo affects due to seabed reflections (e.g., Hochberg et al., 2003).
4.2 Wave heating Qwave and Albedo-Induced Solar Radiation Reduction in Context
At the La Jolla, CA, experiment site, the parameters Hs, h(x), , , and cloudiness ( ) contribute to the breaking wave-induced positive or negative surfzone heat flux relative to the inner-shelf. Here the two terms Qwave and are placed in the context of a previous surfzone heat budget. Including wave heating (Qwave) but not improved a summertime binned mean surfzone heat budget on diurnal and longer time scales (Sinnett & Feddersen, 2014). However, here the summertime was usually greater than |Qwave| (Figure 8c). However, Qwave and are uncorrelated (r2 < 0.04). Thus, including Qwave but not still improved the binned mean heat budget slope by reducing the unexplained variance. Sinnett and Feddersen (2014) also inferred a net surfzone cooling of ≈ 5,200 W/m (or ≈ 90 W/m2 over the average Lsz for the same period) required to balance the surfzone heat budget. Here the summer-averaged = 44 W/m2 (compare to the yearly averaged = 41 W/m2) may account for nearly half the Sinnett and Feddersen (2014) inferred required net cooling. Advective processes, such as transient rip currents (e.g., Hally-Rosendahl et al., 2015) or nonlinear internal wave run up (e.g., Sinnett et al., 2018) may also contribute to the required relative surfzone cooling.
Breaking wave-induced changes to the surfzone latent or sensible heat flux are also modified by wave breaking due to surfzone spray and aerosol generation, which may also contribute to the surfzone heat budget. Parameterized (COARE) surfzone sensible heat flux estimations required an additional spray contribution when compared to surfzone covariance measurements (MacMahan et al., 2018). For the average wave dissipation observed at this site, the additional sensible heat flux due to breaking wave spray is ≈ 5 W/m2, relatively small compared to Qwave and at Scripps Beach. Spray droplets produced by breaking are typically large (Andreas, 2016) and quickly fall back to the surface before exchanging latent heat (MacMahan et al., 2018; Veron, 2015). However, the enthalpy exchange coefficient may be larger for a foamy sea surface than a foam-free surface (Chickadel, 2018), potentially enhancing surfzone latent heat flux. Examination of all surfzone heat flux terms is warranted to properly understand all the ways that breaking waves can affect the surfzone heat budget.
Nearshore heat and solar radiation budgets typically overlook breaking wave effects, and the relative importance of this adjustment is unknown. Here the relative effects of wave heating due to viscous dissipation of breaking waves Qwave and albedo-induced solar heating reduction relative to the inner-shelf are studied with yearlong observations at the SIO (La Jolla, CA) pier. Wave energy flux at the outer surfzone boundary = 2,149 ± 1,826 W/m, which dissipated over Lsz yielding a daily averaged wave heating contribution Qwave = 28 ± 11 W/m2. Breaking waves partially covered the surfzone in foam, increasing albedo on average by a factor of 3 relative to the inner-shelf. The increased surfzone albedo subsequently created a solar heating reduction relative to the inner-shelf of = 41 ± 16 W/m2. Usually at this location, the net effect (Qwave+ΔQsww) together act to cool the surfzone relative to the inner-shelf. However, the combined (Qwave and ) effect had seasonal dependence, with a net heating roughly half the time in winter, but only 4% of the time in summer.
On a beach of constant slope, the average surfzone foam fraction can be scaled as a function of beach slope, resulting in a surfzone averaged albedo 〈αsz〉 that is independent of Hs. At the experiment site, and are linearly related and are in good agreement with the scaling. Scalings also are developed to the relative breaking wave surfzone heat flux contribution. The amount of additional surfzone cooling or heating relative to the inner-shelf is related to the ratio of to at the outer surfzone boundary. Clouds, , and Hsb affect the ratio and thus the relative surfzone cooling or heating. This scaling can be applied at other locations to determine the relative heating or cooling effects of surfzone breaking waves.
This publication was prepared under NOAA Grant NA14OAR4170075/ECKMAN, California Sea Grant College Program Project R/HCME-26, through NOAAS National Sea Grant College Program, U.S. Dept. of Commerce. Additional support for this work was provided in part by ONR (N00014-15-1-2117) and NSF (OCE-1558695). The radiometer boom arm was designed and manufactured by B. Woodward, B. Boyd, K. Smith, and R. Grenzeback. Deployment was aided by C. McDonald, R. Walsh, S. Mumma, G. Boyd, L. Parry, and many San Diego lifeguards. Wave data from the Coastal Data Information Program (CDIP) were provided with assistance from W. O'Reilly and C. Olfe. Atmospheric conditions and tide data were from NOAA station 9410230 and Earth Networks. J. Norris, R. Clemesha, S. Giddings, A. Suanda, D. Grimes, G. Pawlak, K. Davis, and two anonymous reviewers provided helpful feedback. We sincerely thank these people and institutions. Data are available at iodlabs.ucsd.edu/falk/szheat
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In the originally published version of this article, a labeling error in Figure 11 switched “warming” and “cooling” above and below the y = 1 line. This error has been corrected, and this may be considered the authoritative version of record.