Observations of strongly modulated surface wave and wave breaking statistics at a submesoscale front

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1 Observations of strongly modulated surface wave and wave breaking

2 statistics at a submesoscale front

3 Teodor Vrećica, Nick Pizzo, and Luc Lenain

4 Scripps Institution of Oceanography, University of California, San Diego

5
 ∗

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ABSTRACT

 6 Ocean submesoscale currents, with spatial scales on the order of 0.1 to 10 km, are horizontally

 7 divergent flows, leading to vertical motions that are crucial for modulating the fluxes of mass,

 8 momentum and energy between the ocean and the atmosphere, with important implications for

 9 biological and chemical processes. Recently, there has been considerable interest in the role of

10 surface waves in modifying frontal dynamics. However, there is a crucial lack of observations

11 of these processes, which are needed to constrain and guide theoretical and numerical models.

12 To this end, we present novel high resolution airborne remote sensing and in situ observations

13 of wave-current interaction at a submesoscale front near the island of O’ahu, Hawaii. We find

14 strong modulation of the surface wave field across the frontal boundary, including enhanced wave

15 breaking, that leads to significant spatial inhomogeneities in the wave and wave breaking statistics.

16 The non-breaking (i.e. Stokes) and breaking induced drifts are shown to be amplified at the

17 boundary by approximately 50% and a factor of ten, respectively. The momentum flux from the

18 wave field to the water column due to wave breaking is enhanced by an order of magnitude at the

19 front. Using an orthogonal coordinate system that is tangent and normal to the front, we show

20 that these sharp modulations occur over a distance of several meters in the direction normal to the

21 front. Finally, we discuss these observations in the context of improved coupled models of air-sea

22 interaction at a submesoscale front.

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23 1. Introduction

24 Submesoscale fronts, jets, and eddies in the ocean are defined as currents with scales ranging

25 from one-tenth to tens of kilometers (McWilliams 2016). These currents provide a pathway from

26 quasi two dimensional mesoscale eddies, the main reservoir of kinetic energy in the ocean, to the

27 fully three dimensional dissipation scales (McWilliams 2016). Submesoscale variations have been

28 shown to modulate mean heat fluxes at mid-latitudes between the ocean and atmosphere (Su et al.

29 2018), potentially more than the change of air-sea heat fluxes due to climate change (Yu and Weller

30 2007). Furthermore, submesoscale motion can have strong horizontal divergences, which through

31 mass conservation leads to upwelling and downwelling flows - facilitating exchanges between the

32 atmosphere and the ocean. This has important biological implications through modulations to

33 the both the production of phytoplankton and plankton biodiversity (Mahadevan 2016; Lévy et al.

34 2018). Submesoscale currents are also important for the dispersion of surface and near surface

35 pollutants, such as oil and plastics (Poje et al. 2014; D’Asaro et al. 2018). However, submesoscale

36 currents are also difficult to measure, as they are generally too large for ship-based sampling and

37 too small for orbital remote sensing products (McWilliams 2016). Therefore, there is a crucial

38 need to observe submesoscale processes and in particular their interaction with other important

39 features of the upper ocean.

40 High resolution simulations have explored the complex life cycle of submesoscale features

41 (Gula et al. 2014; McWilliams 2017; Sullivan and McWilliams 2018, e.g.). Recently, the role of

42 surface wave averaged effects, in particular the Stokes drift, have been explored in these models

43 (Hamlington et al. 2014; Suzuki et al. 2016; McWilliams 2018). Wave breaking also generates

44 currents (Rapp and Melville 1990; Melville et al. 2002; Pizzo et al. 2016; Deike et al. 2017) and the

45 vertical vorticity induced by these finite crest breaking events (Peregrine 1999; Pizzo and Melville

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46 2013) may lead to strong downwelling events through the so-called vortex force (Sullivan et al.

47 2007). However, the prescribed Stokes drift and breaking statistics are not well-constrained in these

48 models (Sullivan et al. 2007). Furthermore, the spatial variability of the momentum flux is not

49 necessarily realistic in these models, which often do not include the two way coupling between the

50 waves and underlying currents. This is particularly significant, as the spatial horizontal distribution

51 of momentum flux is important for frontogenesis and stability properties of submesoscale features

52 (Hoskins and Bretherton 1972; Thomas and Lee 2005). These studies highlight the need to conduct

53 high resolution observations of the surface wave field and wave breaking statistics, including their

54 spatial distribution, at submesoscale currents.

55 Surface waves can be strongly modulated by currents in the upper ocean, in particular near

56 submesoscale fronts (Romero et al. 2017) where large horizontal gradients in the currents lead

57 to strong wave refraction. A striking example is given by the recent study of Lenain and Pizzo

58 (2021) that characterizes the intense modulation of surface waves by the currents induced by an

59 internal wave train. Classical geometrical optics and wave action theories (Longuet-Higgins and

60 Stewart 1964; Phillips 1966; Bretherton and Garrett 1968) show that it is mostly shorter wave

61 components which are strongly modulated by submesoscale currents (McWilliams 2018) and that

62 their gradients drive wave refraction. Furthermore, WKB theory predicts that vertical vorticity is

63 responsible for creating ray curvature of these waves as they propagate over the currents (Kenyon

64 1971; Dysthe 2001), which has also been examined recently in the context of statistical theories

65 (Villas Bôas et al. 2020). However, it is still a topic of active debate as to the extent to which

66 these WKB solutions hold for currents with large gradients (Shrira and Slunyaev 2014; Lenain and

67 Pizzo 2021) or active two-way coupling with the currents (Pizzo and Salmon In review), and there

68 is an urgent need for more high resolution spatio-temporal observations to test the fidelity of these

69 theoretical and numerical predictions.

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70 In recent years, the use of airborne remote sensing has enabled the detailed characterization of

71 ocean surface properties, such as the directional properties of the wave field and wave breaking

72 statistics (e.g. Lenain and Melville 2017a,b; Lenain et al. 2019), at resolutions down to O(0.1)

73 meters. In Romero et al. (2017), airborne observations of the rapid evolution of the spectral

74 properties of the surface wave field across the boundary of the submesoscale front were presented.

75 They found that both wave and breaking statistics are strongly modulated through wave-current

76 interaction processes. More recently, using a combination of in situ, airborne and orbital remote

77 sensing approaches, Rascle et al. (2020) showed that submesoscale fronts can be very sharp (

93 2. Background and definitions

 94 a. The sea surface wave spectrum

 95 To analyze the properties of ocean surface waves, the surface elevation can be approximated

 96 to first order as a linear superposition of sinusoidal waves, and can be characterized statistically in

 97 terms of the directional ( ) and omnidirectional ( ) spectra, defined here as

 ∫ , ∫ , ∫ 
 2
 h i = ( , )d d = ( )d , (1)
 − , − , 

 98 where hi represents an averaging operation over the area for which the spectra are computed, 

 99 and are the wavenumbers in the and -axis direction, and the modulus of the wavenumber,

100 i.e. k = ( , ). The terms ( , = , = , ) are the highest and lowest wavenumbers

101 resolved in the present study, respectively.

102 Irrotational deep-water surface gravity waves have particle trajectories that are not closed, which

103 leads to a net drift in the direction of the wave propagation, known as the Stokes drift (Phillips

104 1966). Following Kenyon (1969), the Stokes drift U at the surface is computed from the directional

105 wave spectrum ,
 ∫ p
 U = 2 (k) kdk, (2)

106 assuming a linear deep water dispersion relation. Note, Breivik et al. (2016), Pizzo et al. (2019a)

107 and Lenain and Pizzo (2020) have examined the contribution of various ranges of the spectrum

108 (e.g. the equilibrium and saturation ranges - see Phillips 1985 and Lenain and Melville 2017b)

109 to the Stokes drift. There, they found that the saturation range (i.e. shorter waves) can contribute

110 significantly to the total Stokes drift, highlighting the importance of high resolution measurements

111 of the surface wave field to properly resolve this important bulk scale quantity.

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112 b. Wave breaking statistics

113 To characterize properties of wave breaking near the front, following Phillips (1985) we define

114 the breaking distribution, as the average length of breaking crests with speed cb in the range

115 (cb − Δcb /2, cb + Δcb /2) per unit surface area , such that (Kleiss and Melville 2010)

  
 1 Õ Δcb Δcb
 Λ(cb ) = |cb − < cb,n < cb + (3)
 Δcb 2 2

116 where is the length of actively breaking crest element, and cb,n is the velocity of the breaker

117 element under consideration.

118 The strength of Phillips’s approach is that the spectral moments yield physically important

119 variables. For example, the fourth moment of Λ(cb ) yields the momentum flux induced by

120 breaking waves, M, defined as

 ∫
 
 M= 3 cb Λ(cb )dcb , (4)
 
121 where is the water density, is the gravitational constant, and is a parameter determining the

122 strength of wave breaking (Drazen et al. 2008; Romero et al. 2012). To compute we follow the

123 procedure outlined in Romero et al. (2012). Note, Sutherland and Melville (2013) and Sutherland

124 and Melville (2015a) used this formulation to compare the momentum flux from the wind to the

125 water column with the momentum flux lost by the wave field and found that for young waves the

126 budget was approximately closed. Furthermore, these authors examined the energy dissipation rate

127 through this formulation and compared the results to subsurface measurements of the dissipation

128 rates, finding relatively good agreement.

129 Next, Pizzo et al. (2019b) showed that the breaking induced drift (Deike et al. 2017; Lenain

130 et al. 2019) is computed from the third moment of the Λ( ) distribution. The value of the drift at

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131 the surface is defined as
 2 
 ∫
 Ub = ( − 0 )cb Λ(cb )dcb , (5)
 
132 where is the characteristic slope of the wave packet, 0 the breaking threshold, the wave phase

133 velocity, and = 9 is a constant found from the numerical simulations of Deike et al. (2017) and

134 corroborated by the laboratory experiments of Lenain et al. (2019).

135 Pizzo et al. (2019b) examined the speed of the breaking induced drift versus the Stokes drift

136 over a range of environmental conditions. For wind speeds ranging from 1.6 to 16 / , significant

137 wave heights in the range of 0.7 − 4.7 m, and wave ages ranging from 16 to 150, the author’s found

138 that the breaking induced drift may be up to 30% of the Stokes drift.

139 Finally, the relationship between breaking crest velocity and wave phase velocity has been

140 explored in numerous studies (see for example Stansell and MacFarlane 2002). Following Romero

141 et al. (2012), we assume here that the breaking crest velocity is equal the wave phase velocity (see

142 also Sutherland and Melville 2013, 2015a).

143 3. Experiment and instrumentation

144 The experiment was conducted near the island of O’ahu, Hawaii, in April 2018. The Scripps

145 Institution of Oceanography (SIO) Modular Aerial Sensing System (MASS, see Melville et al.

146 2016) airborne instrument was installed on a Cessna 206 operated by Williams Aerial Inc. The

147 MASS was used to retrieve sea surface topography, and collocated georeferenced aerial imagery

148 (visible, infrared and hyperspectral). While the present study was not part of the scientific objectives

149 of the original project, a serendipitous observation of a line of a persistent enhanced breaking (see

150 figure 1) during one of the flights led us to dedicate a portion of a flight to observing the modulation

151 of surface wave properties across this front, on April 17 2018. Several years after conducting these

152 airborne observations, we discovered that the R/V Ka‘imikai-O-Kanaloa was also fortuitously

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153 present in the area, within a few hours of our flight time, while in transit to the Hawaii Ocean

154 Time-series (HOT) site, in support of a completely unrelated campaign (KOK1801, Rolling Deck

155 To Repository 2019). Data collected from the ship are included in the analysis.

156 The MASS is a portable airborne remote sensing instrument (MASS, see Melville et al. 2016)

157 developed in the Air-Sea Interaction Laboratory at the Scripps Institution of Oceanography. For this

158 experiment, the MASS was equipped with a Riegl VQ-820G bathymetric lidar. Note, although this

159 model is designed for bathymetric surveys, it is also capable of collecting sea surface topography

160 (multi-return waveform lidar). From the obtained georeferenced 3D lidar point clouds, datasets

161 were regridded, with a discretization step of = = 0.25 m. Aerial visible, hyperspectral, and

162 infrared imagery were obtained respectively with an IO Industries Flare 12M125-CL camera (4096

163 x 3072 pixel resolution, 10 bit, 5 Hz sampling rate), a Specim AisaKESTREL 10 hyperspectral

164 camera operating in the 400-1000 nm spectral range (1024 pixel cross-track resolution), and a

165 FLIR SC6700SLS longwave infrared (IR) camera (640 x 512 pixel resolution, 50 Hz sampling

166 rate). Portions of the visible band images affected by sun glint were discarded in the analysis.

167 Vignetting effects were corrected by equalizing mean background brightness intensity, and its

168 standard deviation. Finally, these images were georeferenced with a discretization step of =

169 = 0.2 m.

170 A Novatel SPAN LN200 Inertial Measurement Unit (IMU) coupled to a ProPak6 GPS receiver

171 was used to produce aircraft trajectory information (altitude and position) needed for georeferencing

172 the lidar point cloud and imagery. Trajectory information from the GPS-IMU was post-processed

173 using Novatel Waypoint Inertial Explorer software. Visible imagery was processed using the

174 Trimble INPHO software suite.

175 The R/V Ka‘imikai-O-Kanaloa (now retired) was a 221 foot long vessel, owned and operated

176 by the University of Hawaii Marine Center. It was equipped with a Seabird SBE-21 analog

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177 thermosalinograph and SeaBird SBE-3S remote temperature sensor to sample salinity and water

178 temperature at 4 m depth. The wind speed and direction were measured from a RM Young 5106

179 anemometer, mounted on a pole 13 m above the mean sea level. Finally, current profiles were

180 measured from a Teledyne Workhorse 300 kHz ADCP (Acoustic Doppler Current Profiler).

181 4. Observations

182 Figure 1 shows a line of enhanced breaking observed on April 17 2018, at 03:23 UTC from

183 the cockpit of the aircraft. During this flight, the plane was flying at an altitude of approximately

184 340 m above mean sea level, with a speed of about 58 m/s. Tracks of the aircraft and of the

185 research vessel (within one hour of the flight time) are shown in figure 2, overlaid over bathymetry

186 contours (50 meter horizontal resolution). At that time, the R/V Ka’imikai O-Kanaloa was traveling

187 approximately to the north, a few kilometers west of the flight track. Kaena Point (21.57515 N,

188 158.28174 W) is chosen as the origin for the data transformation into a Cartesian coordinate grid.

189 a. Shipborne observations

190 Observations of near-surface water temperature, salinity, current profiles, wind speed and direc-

191 tion are shown in figure 3 as a function of latitude, starting one hour prior to the flight time. The

192 latitude of Kaena Point and the submesoscale front observed by the aircraft are also shown. The

193 wind speed and direction (13 meter elevation) were relatively constant throughout the observation

194 period, with an average magnitude of approximately 12.9 m/s and mean wind direction of 55 ◦

195 (coming from true north). This implies that the line of breaking observed from the aircraft is not

196 associated with a rapid change in wind forcing that could occur in the wake of an island.

197 Both near surface observations (temperature and salinity) and current profiles show the presence

198 of a filament, about 1 km wide, in the vicinity of the latitude of the front observed by the aircraft.

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199 At the frontal boundary, we find sharp gradients of temperature (up to 0.5 C in less than 100

200 m), and currents reaching magnitudes of up to 0.4-0.5 m/s inside the filament. This jet current

201 and temperature front are likely associated with tidally driven flow as the structure extends to

202 significant depth. Note that the locations (latitude) of the front captured from the aircraft and the

203 ship do not precisely match, as the ship data near the front was collected a few kilometers away

204 from that of the plane, and approximately 45 minutes prior, and we expect some meandering of the

205 frontal boundary, as the Reynolds number of the flow associated with the jet implies fully turbulent

206 motion. The shedding of vortices from the island is also a topic of considerable interest (?), but

207 falls outside of the scope of the current manuscript.

208 b. Remote sensing of ocean surface properties

209 Figure 4 shows a subset of georeferenced infrared and visible imagery collected from the MASS

210 at the front. We find a sharp transition of sea surface temperature (SST) and wave breaking

211 conditions over a very short distance, i.e. a few meters, which is quite remarkable. The SST is

212 used to compute the frontal boundary using a 23.5 ◦ threshold, shown in both subplots.

213 An overview of temperature and whitecap coverage is given for the entire surveyed area in figure

214 5. The submesoscale front extends for more than 4.5 km, with the warmer side of the front to the

215 south, and the colder side to the north. Whitecap coverage is defined as the portion of the surface

216 exceeding a set brightness threshold (see Callaghan and White 2009; Kleiss and Melville 2010,

217 and the appendix for details). It is computed here using 40 by 40 meter segments of ocean surface

218 observed from the MASS visible imagery, small enough to characterize spatial variability near the

219 front (figure 5a).

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220 We find a rapid increase in whitecap coverage across the front, by up to an order of magnitude,

221 on the southern (warmer) side of the front along its entire length. Note, the largest values are found

222 near the frontal boundary ( −2400 ) and F2 (west, < −2400 ), are considered in the analysis.

226 The frontal boundary in the F1 area is oriented 115 from true north, while F2 is oriented 90 

227 from true north. Most of the subsequent analysis focuses on the F1 portion of the front where we

228 experienced the largest wave breaking enhancement. Note data close to shore, with depth less than

229 50 m are discarded in the analysis to avoid potential bathymetric effects (e.g. refraction, shoaling,

230 depth induced breaking).

231 To investigate the spatial evolution of SST and wave breaking near the front, we project these

232 observations into a new coordinate system ( , ) →
 − ( , ), where is the tangent and the normal

233 direction along the front. The spatial evolution of variables is defined as a function of distance

234 from the front, as illustrated in figure 4b. the south side of the frontal boundary (warm area)

235 corresponds to positive values.

236 Figure 6 shows whitecap coverage and SST averaged over both areas F1 and F2 using the new

237 coordinate system. The warmer side of the front exhibits enhanced breaking as compared to the

238 colder side, with the largest increase in whitecap coverage (by an order of magnitude) occurring

239 within approximately ten meters of the frontal boundary (for both F1 and F2 sections). Note the

240 sharp "step-like" temperature gradient (over less than 10 meters); such sharp transitions have only

241 very recently been observed (Romero et al. 2017; Rascle et al. 2020).

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242 c. Spectral analysis

243 To characterize the evolution of surface wave properties as a function of distance from the frontal

244 boundary, directional spectra are computed using two-dimensional fast Fourier transforms (FFT)

245 over data segments 62.5 m by 62.5 m with a horizontal resolution of 0.25 m. These segments are

246 defined along the entire flight trajectory, and are taken every 62.5 m in the along-track direction,

247 and every 10 m in the cross-track direction. The coordinate of the area is defined as the distance

248 from the center of these segments to the boundary. Note that the aircraft track was following the

249 direction of the frontal boundary during the flight. Before Fourier transforming, the mean was

250 removed and the data was tapered with a two-dimensional Hanning window and padded with zeros

251 (for details see Lenain and Melville 2017b; Lenain and Pizzo 2020, 2021).

252 The resulting spectra are then rotated into the mean wind direction ( = 55◦ ). Finally, the spectra

253 are sorted as a function of distance from the frontal boundary , then bin-averaged together for

254 specific ranges of . The spectral data above = 6 rad/m are discarded due to instrument noise.

255 Additionally, while this approach allows us to characterize the spatial variability of shorter waves

256 over small scales, we can not resolve the longer waves (> 62.5 m). As such, a mean spectrum (bulk

257 spectrum) is computed using larger segments of 522 m by 522 m.

258 5. Results

259 a. Wave field modulation

260 Omnidirectional spectra of the surface wave field, ( ), are shown in figure 7a computed

261 from areas south ( = +30 m), and north ( = −80 m) of the frontal boundary along with an

262 omnidirectional spectrum computed over the entire experimental domain (bulk spectrum) to resolve

263 the longer waves, as described in section 5c. We find that the the higher wavenumber portion of the

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264 spectra ( > 0.3 / ) to the south of the frontal boundary exhibit larger amplitudes as compared

265 to the background spectrum, while the ones computed on the north side shows a significant decrease

266 over the same range of wavenumbers. The transition from equilibrium to saturation ranges (Lenain

267 and Melville 2017b) is observed in all three cases. Saturation spectra ( ) 3 are shown in figure

268 7b. We find the higher wavenumber portion of the spectra to be strongly modulated near the front,

269 by almost a factor two as compared to the background spectrum.

270 Spectrograms of omnidirectional and saturation spectra, as a function of distance from the front

271 boundary , are shown in figures 8b and 8c. For reference, SST as a function of is also plotted in

272 Figure 8a. The spectra remain mostly unchanged to the north of the boundary ( < 0 m). Closer

273 to the frontal boundary, especially on the south side ( > 0 m), we observe an increase in spectral

274 magnitude for the higher frequency components ( > 0.3 rad/m), reaching a saturation maximum

275 for ∈ (0, 50) m, corresponding to the area where wave breaking is enhanced. The steepening of

276 the wave field and amplification of wave breaking statistics is caused by the focusing of energy and

277 modulation of the wavenumber as waves and currents interact near the frontal boundary. Finally,

278 as waves propagate to the south of the boundary the spectral energy levels are reduced to nearly the

279 levels observed far north of the front ( = 125 m), in the unmodulated portion of the wave field.

280 b. Active wave breaking statistics

281 Details about the approach used to compute active wave breaking statistics can be found in the

282 Appendix. An example of sea surface imagery showing a large active breaking wave and the

283 corresponding breaking front velocities (red quiver) is shown in figure 9.

284 Omnidirectional Λ( ) distributions for elements just to the south of the frontal boundary

285 ( ∈ (0, 30) m) and further north ( ∈ (−200, −50) m) are shown in figure 10a. We find a significant

286 increase in the magnitude of Λ( ) between these two regions, by up to two orders of magnitude

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287 for < 6 m/s, while the distributions are approximately the same for higher velocities. These

288 distributions are collected in areas just a few hundred meters apart, again highlighting the sharpness

289 of the front, and the localized effects of the interaction of the waves with the front. Relatively little

290 wave breaking is observed for > 10 m/s, in line with observations from Kleiss and Melville

291 (2011).

292 Scaled Λ( ) 4 distributions, which is directly related to the momentum flux due to wave

293 breaking, as defined by equation (4), is plotted in figure 10b. We find a peak of the distribution

294 around = 4 m/s, which then decreases to negligible amounts for larger velocities. This decrease

295 in magnitude is more pronounced north of the frontal boundary, with negligible values for > 2

296 m/s. The position of this peak ( = 4 m/s) approximately aligns with the observed increase in

297 surface wave spectral magnitude around = 1 rad/m (see figure 7), corresponding to a phase

298 velocity of 3.1 m/s.

299 The evolution of wave breaking statistics, as a function of distance from the boundary , is shown

300 in figure 11, along with the observed SST. The whitecap coverage is shown in figure 11b and

301 the zeroth moment of the Λ( ) distribution in figure 11c. While their magnitude remain small

302 on the north side of the frontal boundary ( < 0 m), these measures of breaking rapidly increase

303 for > 0 m, with a maximum value found within 10 m of the frontal boundary, and in general

304 exhibiting larger magnitudes on the south side of the front. A spectrogram of Λ( ) is given in

305 figure 11d. The distributions are mostly uniform to the north of the boundary ( < 0 m), then

306 undergo a sharp order of magnitude amplification directly south of the boundary (for breaking

307 velocities lower than approximately 4 m/s) over just a few meters. Further south of the boundary,

308 Λ( ) remained elevated while slowly decreasing away from the front.

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309 c. Directional properties of the wave field

310 Directional wavenumber and saturation spectra at the same locations as the omnidirectional

311 spectra plotted in figure 7, north and south of the frontal boundary, are shown in figure 12. The

312 spectra have been rotated such that the x-axis is aligned with the mean wind direction, = 55◦

313 (coming from true north). Spectra computed north of the boundary are shown in figures 12a and

314 12b, while the spectra to the south of the boundary are shown in figures 12c and 12d.

315 The primary difference between the two spectra are the amplification of the higher wavenumbers

316 south of the front, which is shown most clearly by the saturation spectra. These modulations by

317 the front manifest themselves in both larger amplitudes of the saturation spectra, and a broader

318 directional distribution. In general, an opposing current will focus the wave field - decreasing its

319 directional spread (see the related discussion in Lenain and Pizzo 2021) and increasing its slope.

320 Here, we see that for ≈ 1 rad/m, the components south of the front remain relatively narrowly

321 spread. For larger wavenumbers, much larger directional spreading is found.

322 Directional Λ(cb ) distributions where cb = ( 1 , 2 ) for elements just to the south of the frontal

323 boundary ( ∈ (−30, 0) m) and to the north ( ∈ (0, 30) m) are shown in figure 14a and 14b.

324 These distributions are rotated into the mean wind direction (which is the same as the directional

325 spectra presented in figure 13). We find significantly more breaking on the south side of the front,

326 especially for 1 < 3.5 / and | 2 | < 1.5 / . We observe a larger number of breakers in the

327 crosswind direction for larger values of 2 (i.e. longer waves).

328 Following the approach of Kleiss and Melville (2011), a first order approximation of surface

329 currents can be obtained from the motion of non-breaking foam patches. In order for a patch to be

330 considered non-breaking, we require that at least 99 % of the elements of the boundary of the foam

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331 patch are classified as non-breaking. Surface current magnitudes are then computed by tracking

332 the velocity of the foam patches, and are indicated by white cross marks in figure 13b.

333 d. Surface wave induced mass transport

334 Stokes and wave breaking drift are computed according to equations 2 and 5, respectively, using

335 the directional wave spectrum and breaking distributions. They are then conditionally averaged

336 along-front (i.e. in the direction) for each section. Mean surface currents (see Kleiss and

337 Melville 2011, and previous subsection) are shown in figure 12a for the east (F1) section in the

338 front coordinate system ( , ). We find that surface currents are rapidly rotating close to the frontal

339 boundary, experiencing close to a 120 change in just 200 m. No surface current estimates were

340 computed on the north side, away from the front, due to limited whitecap coverage. Note, this is

341 an indirect way of inferring surface currents, and should be treated as a first order estimate.

342 The corresponding values of Stokes drift are shown in figure 12b. The magnitude of the Stokes

343 drift Us at the surface increases just south of the frontal boundary by nearly 50 %. The Stokes

344 drift direction is oriented in the mean wind direction north of the frontal boundary ( < 0 m), then

345 rotates in a clockwise direction near the boundary (by approximately 17 ). The wave breaking

346 induced drift Ub is given in figure 12c. We find that the magnitude of the wave breaking induced

347 drift rapidly increases near the frontal boundary by up to an order of magnitude. The direction of

348 the drift remains approximately constant across the front, aligned with the wind direction. Finally,

349 the ratio between wave breaking induced and Stokes drift is given in figure 12d, illustrating the

350 important contribution of the wave breaking induced drift (by up to 100% of the value of the Stokes

351 drift near the frontal boundary) to upper ocean processes in this type of scenario (Deike et al. 2017;

352 Pizzo et al. 2019b; Lenain et al. 2019).

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353 e. Modulation of the momentum flux near the frontal boundary

354 From the directional spectra of the surface waves and the Λ( ) distribution, we can also estimate

355 the wave-breaking induced momentum flux M. This is shown in figure 15b plotted as a function

356 of along front distance . The SST is shown in panel (a), for reference. The magnitude of the

357 wave-induced drift is plotted in Figure 15c. The momentum flux is small on the northern side of

358 the front ( < 0 m), on the order of what can be expected through wind forcing only. However,

359 near the frontal boundary, for 0 < < 50 m in particular, we find a rapid increase of the momentum

360 flux, by an order of magnitude, reaching a value of 1 N/m2 .

361 This is significant, as wave breaking balances the momentum flux from the wind for young waves

362 (Sutherland and Melville 2013, 2015a). That is - nearly all of the momentum that is transferred

363 from the wind to the waves goes into wave breaking once the sea surface has been modestly

364 deformed (Banner and Peirson 1998; Grare et al. 2013). Therefore, this localized breaking at the

365 front represents an important conduit for momentum to be transferred indirectly from the wind

366 to the water column. This applies to both the magnitude of the momentum flux as well as its

367 spatial distribution. The measurements provided here should be useful in providing realistic spatial

368 distributions of the momentum flux to be used in coupled air-sea models.

369 Note, the contribution of non-aerated breakers (i.e lower velocities) is not included here but could

370 also contribute significantly to the momentum flux (see Sutherland and Melville 2013).

371 6. Discussion and conclusions

372 In this study, we have presented novel high-resolution airborne remote sensing observations of

373 wave modulation in the vicinity of a submesoscale front near the island of O’ahu, Hawaii. This

374 work expands previous studies on this topic (e.g. Romero et al. 2017; Rascle et al. 2018), by

375 characterizing the modulation of surface properties at a much higher spatial resolution, in the area

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376 directly near the front (within less than a couple of hundred meters, and with submeter horizontal

377 resolution). Overall, we found that the surface wave field is strongly modulated by the front. This

378 in turn leads to significant spatial inhomogeneities in bulk scale properties of the wave field and

379 wave breaking statistics.

380 To capture the rapid spatial evolution of these features, especially within a few meters of the

381 frontal boundary, the present analysis was conducted in a "front reference frame". We found that

382 currents, breaking statistics, temperature and spectral properties varied significantly over very short

383 spatial scales (on the order of a few meters).

384 This in turn rapidly modulates the magnitude of Stokes and breaking induced drifts, that are

385 enhanced by around 50 % and an order of magnitude, respectively, within a distance of 50 m or

386 less, near the boundary of the front. The breaking induced velocity is particularly large near the

387 frontal boundary, exceeding locally the Stokes drift. This is important, as a significant portion

388 of wind stress is absorbed by the wave field (Banner and Peirson 1998; Grare et al. 2013), which

389 is then transferred to the upper ocean through wave breaking. This process is often assumed to

390 be spatially uniform, at least in the modelling community. This study shows that the distribution

391 of momentum flux due to breaking can vary significantly near fronts, and more broadly in the

392 presence of wave-current interactions. It is also shown that the total wave induced drift can vary

393 by nearly a factor of two over the same distance. As the momentum flux from the atmosphere

394 to the ocean and wave averaged effects (drift) can be key components governing the dynamics of

395 submesoscale fronts, this may have have significant implications for front stability and frontogenesis

396 (McWilliams 2016). This would in turn affect many other ocean processes (such as vertical flux

397 of nutrients, propagation of near-surface pollutants, and air-sea heat and gas fluxes), which are

398 strongly modulated by submesoscale features. Note that here the gradient of surface velocity

399 (figure 14a) across the front are found to significantly exceed , the Coriolis force, by more than

 19

400 a factor 400. While this is beyond the scope of this work, this hints at the intense, very localized,

401 upper ocean vertical transport and associated processes occurring at these submesoscale fronts.

402 The results presented in this paper are a step towards better understanding wave-current in-

403 teractions and wave breaking at a submesoscale front. They also highlight the need for broad

404 spatio-temporal measurements of the atmosphere-ocean boundary layer at these locations. A com-

405 bination of airborne measurements of sea surface and current measurements (and its depth profile),

406 performed by autonomous surface vehicles (Lenain and Melville 2014; Grare et al. 2021), would

407 establish the range of magnitudes of submesoscale currents and their spatial variability, which is

408 of crucial importance for the development of new wave models. This will be further examined by

409 the authors as part of the NASA S-MODE Earth Venture Suborbital III research program.

410 Acknowledgments. The authors are grateful to Williams Aerial inc. for providing flight resources.

411 We thank Nick Statom for making the initial observation of the enhanced breaking, and for georefer-

412 encing the visible light imagery. We thank Jules Hummon (University of Hawaii) for help with the

413 shipborne data. This research was supported by grants from the Physical Oceanography programs

414 at ONR (Grants N00014-17-1-2171, N00014-14-1-0710, and N00014-17-1-3005) NSF (OCE;

415 Grant OCE-1634289), and NASA (Grant 80NSSC19K1688). Data availability: All presented data

416 are available at the UCSD Library Digital Collection (https://doi.org/10.6075/J0FN162S)

417 and the Rolling Deck to Repository (R2R) for the shipborne data (KOK1801, Rolling Deck To

418 Repository 2019).

419 APPENDIX

420 Active wave breaking statistics

 20

421 Our approach to computing Λ(cb ) is based on Kleiss and Melville (2011). Observing wave

422 breaking statistics is a notoriously difficult problem, as differentiating foam and actively breaking

423 waves from the sea surface can be particularly challenging (Kleiss and Melville 2010, 2011;

424 Sutherland and Melville 2013, 2015a,b). First, a normalized complementary cumulative image

425 intensity distribution ( ) is computed for each georeferenced image where , the pixel intensity,

426 varies from 0 (black) to 1 (white). These distributions exhibits two regimes (see Kleiss and

427 Melville 2011), one dominated by foam and wave breaking patches, and the other corresponding

428 to the underlying unbroken sea surface. By identifying this transition, using a brightness threshold

429 ( ) defined in Kleiss and Melville (2011) and determined from the second derivative of the the

430 natural logarithm of ( ), we can characterize the contours of the foam and breaking waves. Here

431 the threshold ( = 0.021) was set to filter out most foam patches. Additionally, only contours of 5

432 pixels or more were considered in the analysis.

433 The motion of whitecaps can be tracked using PIV methods, with application of the optical flow

434 for small scale tuning of velocities Kleiss and Melville (2011). In order to improve accuracy for

435 areas highly saturated with whitecaps, and for tracking large scale breakers with variable velocities

436 along its breaking front a new method of estimating breaker velocities is utilized. The velocity

437 of each contour element is determined using optical flow methods of Liu (2009), using pairs of

438 successive images separated by = 0.2 seconds in this work. The method seeks to minimize the

439 energy, , of two subsequent images defined as

 ≡ | 1 − 2 | 2 + (|∇ | 2 + |∇ | 2 ), (A1)

440 where 1 and 2 are two subsequent images, is a regularization term, and are computed pixel

441 velocities, and the energy is summed over every pixel of the two images. The images are first

442 downsampled to determine large scale motions, and the resolution is gradually refined in order to

 21

443 determine smaller scale features. More details can be found in Liu (2009), Brox et al. (2004) and

444 Bruhn et al. (2005).

445 A multi channel image approach is used to include brightness gradient in the analysis. The

446 energy is minimized for the image defined as I = ( , 0.5 , 0.5 ), where is the original grayscale

447 image, and and are its spatial derivatives. The values of derivatives are constrained to be real

448 and positive by subtracting their smallest negative value, and a factor of 0.5 is applied to equalize

449 the weight of the original image and its gradients. The value of the upsampling rate was set to 0.85

450 and the value of the regularization parameter ( ) was chosen to take values from 60 to 150 in order

451 to minimize outliers in the obtained velocity (( , ) > 12 / ), or outliers in velocity gradients

452 (|∇ | > 6 Hz or |∇ | > 6 Hz).

453 The following criteria were used to differentiate active breaking from foam:

454 • The brightness gradient of the image is above a set threshold.

455 • The difference of brightness for the same pixel in two subsequent images is above a set level.

456 • The direction of the velocity of each contour element is ±110◦ from the mean wind direction.

457 • The direction of the normal to the contour element is ±110◦ from the mean wind direction.

458 • The area of the considered patch needs to increase in each subsequent image. This criteria is

459 applied uniformly for each element of the contour.

460 It was required that each contour element passes four out of five criteria in order to be considered

461 an active breaker. Furthermore, if any element was found to be propagating into the interior of the

462 foam patch, or if they had no direct neighboring elements which were also registered as actively

463 breaking, they were discarded.

 22

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600 LIST OF FIGURES
601 Fig. 1. An observation of enhanced wave breaking along a submesoscale ocean front, as recorded
602 by a handheld DSLR camera on 17/04/2018 near Kaena Point, O’ahu, Hawaii. Notice the
603 abrupt change between non-breaking and breaking waves. The horizontal and vertical scales
604 of this photograph are a few hundred meters. . . . . . . . . . . . . . . 33

605 Fig. 2. An overview of the experiment site near O’ahu, Hawaii. The white rectangle indicates the
606 measurement area and is shown in more detail in the subfigure. The dashed yellow line
607 indicates the research vessel track - with the vessel crossing Kaena Point approximately 1
608 hour prior to the planes arrival. The subfigure also shows the flight track in black, overlaid
609 over bathymetry contours, with = = 50 m resolution. . . . . . . . . . . 34

610 Fig. 3. Ocean and wind data measured by the R/V Ka’imikai-O-Kanaloa, as a function of latitude.
611 The vertical line indicates position of Kaena Point (21.575◦ latitude), and the dashed vertical
612 line indicates the position of the observed submesoscale current jet. a) Water temperature,
613 b) salinity, c) wind speed (black line), and mean wind direction (red points, meteorological
614 direction convention). The empty portion of data corresponds to a fast change of course by
615 the ship, which contaminated that portion of data. We also show zonal (d) and meridional
616 (e) velocities as a function of depth. The shallowest resolved depth is = 12 m. . . . . . 35

617 Fig. 4. a) A georeferenced portion of the monochrome 16 bit image, recorded by the downward
618 looking MASS camera. The white line represents the boundary of the temperature front.
619 The whitecap coverage (due to air-entraining breaking waves) is undergoing a substantial
620 amplification, coinciding with the change in SST. b) A georeferenced infrared image for the
621 same area as (a). Note the sharpness of transition between the warm and cold areas. The
622 white area in the upper right corner represents a region for which no infrared imagery was
623 available. . . . . . . . . . . . . . . . . . . . . . . . 36

624 Fig. 5. An overview of the area. a) Whitecap coverage, calculated in 40 by 40 meter cells, and
625 b) a mosaic of IR images are shown. The dashed vertical line indicates separation of front
626 into two different areas at = −2400 m (F1 and F2). The white (a) and black (b) lines
627 indicate the position of the front, where dashed lines represent areas with no IR images
628 (linear interpolation is used to draw these dashed lines). Due to its spatial variability, the
629 front is divided into two areas F1 to the east, and F2 to the west. . . . . . . . . . 37

630 Fig. 6. Sea surface parameters as a function of distance from the front boundary, shown for F1
631 ( < −2400 m) by a solid line, and for F2 by a dashed line. Results are presented for a)
632 whitecap coverage (fraction of surface covered by whitecaps), and b) mean temperature. Our
633 natural coordinate system, based on tangent and normal directions to the front, are such that
634 > 0 indicates the south side of the front, and vice versa. Both sides of the front show
635 similar properties - characterized by a sharp transition at the frontal boundary - although the
636 amplification of whitecap coverage is more severe for the F1 portion. Change of temperature
637 and of whitecap coverage are found to be well correlated at the frontal boundary. . . . . . 38

638 Fig. 7. Averaged omnidirectional spectra, (a) and saturation spectra (b) for the F1 front. The red
639 line represents spectra for the area on the south side of the front ( = 30 m), while the blue
640 line represents spectra for the north side of the front ( = −80 m). As it is not possible to
641 properly resolve lower wavenumbers ( < 0.3) with our window size, they are represented
642 using bulk spectrum, which is a mean spectrum for the whole area under consideration
643 (black straight line). Note the amplification of higher spectral components ( > 0.3 rad /m)
644 by approximately a factor of two. . . . . . . . . . . . . . . . . . 39

 30

645 Fig. 8. Evolution of wave spectral properties as a function of distance from the front (temperature is
646 also shown for reference in subfigure a). A spectrogram of omnidirectional spectra (b) and
647 saturation spectra (c) are calculated for the F1 portion of the front. The positive side of the
648 abscissa denotes the south side of the front ( > 0), and vice versa. The saturation spectra
649 ( > 0.3 rad/m) undergoes strong amplification to the south of the front boundary ( > 0)
650 with peaks at = 1 and = 6 rad/m, with some amplification over tens of meters leading up
651 to it from the northern side ( < 0) . . . . . . . . . . . . . . . . . 40

652 Fig. 9. A georeferenced large scale breaking wave obtained from the aerial imagery. Actively
653 breaking waves, and their associated velocities (determined using the optical flow method),
654 are plotted by the red arrows. A large number of such images is used to define the Λ( )
655 distribution, which provides a statistical description of wave breaking for the given area. . . 41

656 Fig. 10. a) Λ( ) distributions for the F1 portion of the front. Results are shown for the area just to
657 the south of boundary (0 < < 30 m), and further away to the north of it (−50 > > −200
658 m). b) Same as (a), except the distribution is multiplied by 4 (giving a quantity related
659 to the integrand of the momentum flux). Note that while the greatest amplification of the
660 distribution is for lower velocities (two orders of magnitude), the dynamically most significant
661 section of the distribution is around = 4 m/s (with amplification by a factor of 5). . . . . 42

662 Fig. 11. Wave field parameters as a function of distance from the front. a) Temperature, b) whitecap
663 coverage, c) total Λ distribution, d) and spectrogram of Λ( ) distribution are shown for
664 the F1 portion of the front. Results are shown as a function of distance from the frontal
665 boundary, with the positive abscissa ( > 0) indicating a region south of the front. The
666 breaking statistics are well correlated with the change of SST, and the amplification of Λ( )
667 distribution (for intermediate and lower velocities), occurs over the distance of a few meters. . 43

668 Fig. 12. a) Directional ( , ) spectra, and b) ( , ) 3 saturation spectra for north portion of
669 the front. c) to d) show the same quantities, except for south portion of the front. All results
670 are shown for F1 portion of the front (east of = −2400 ). The spectra have been rotated
671 into the wind reference frame (235◦ ), with the x axis representing mean wind direction. Note
672 the strong refraction (and amplification) of the spectra in Figures c and d. . . . . . . 44

673 Fig. 13. Directional Λ( 1 , 2 ) distributions for area north from the boundary (0 < < −30, is
674 distance from boundary in meters), and just to the south of it (0 > > 30). The distribution
675 has been rotated into the wind reference frame (235◦ ), with the 1 representing velocities in
676 the mean wind direction. The white cross marks indicate the mean inferred surface currents
677 for the area based on the motion of foam patches. In addition to amplification in magnitude,
678 a change of directional properties can be observed to the south of the front. . . . . . . 45

679 Fig. 14. Observed and derived surface velocities for the F1 portion of the front ( > −2400 ).
680 Results are shown in the approximate reference frame of the front (rotated by 25 degrees),
681 where the vertical components of velocities indicate crossfront velocities, and the horizontal
682 components of velocities indicate alongfront velocities. a) Total surface velocities (black
683 arrows) obtained from whitecap motion. b) Stokes drift. c) Breaking induced drift. d) Ratio
684 of breaking induced and Stokes drifts. All results are shown as a function of distance from
685 the front boundary, with positive abscissa ( > 0) indicating south side. The total surface
686 currents show a strong modulation at the frontal boundary, and the value of both drifts is
687 significantly amplified, with the breaking induced drift approaching the magnitude of the
688 Stokes drift. . . . . . . . . . . . . . . . . . . . . . . . 46

689 Fig. 15. Distributions of a) sea surface temperature, b) momentum flux to the oceans upper layer
690 due to wave breaking, c) and wave induced (total, Stokes, and breaking) drifts as a function

 31