1. Introduction
The breaking of ocean surface waves generates strong turbulence and energy dissipation. In deep water, breaking participates in air–sea exchange and limits wave growth (Banner and Peregrine 1993; Melville 1996). In shallow water, breaking suspends sediment, forces currents, and drives coastal morphology (Battjes 1988). Although the mechanisms differ, both types of breaking are effective at dissipating wave energy in the form of turbulent kinetic energy (Herbers et al. 2000; Gemmrich and Farmer 1999).
Field observations of deep water breaking (i.e., whitecaps) have shown that the turbulent dissipation rate is a function of wave steepness and is correlated with wind stress (Terray et al. 1996; Gemmrich and Farmer 1999, 2004; Gerbi et al. 2009; Thomson et al. 2009; Gemmrich 2010). Field observations of shallow water breaking (i.e., surf) have shown that the turbulent dissipation rate is a function of water depth and is correlated with the energy flux gradient of shoreward swell (Trowbridge and Elgar 2001; Bryan et al. 2003; Feddersen 2012). These observations typically are made using fixed instruments mounted below the mean (still) water level. Thus, it has been difficult to estimate turbulent dissipation rates near the time-varying wave surface. Recently, Gemmrich (2010) used up-looking Doppler sonars to estimate dissipation within breaking wave crests and found dissipation rates 10 times higher than those measured below the mean water level.
Here, the method of Gemmrich (2010) is adapted to wave-following reference frame using a new Lagrangian drifter. The drifter, which is termed a Surface Wave Instrument Float with Tracking (SWIFT), is designed to follow the time-varying free surface while collecting high-resolution profiles of turbulent velocity fluctuations. The velocity fluctuations are used to estimate the turbulence dissipation rate following Wiles et al. (2006). Thus, the SWIFT measurements can be used to estimate both wave spectra (from the drifter motions) and wave-breaking dissipation (from the Doppler velocity profiles). Previously, drifters have been used in the nearshore to observe currents (Schmidt et al. 2003; MacMahan et al. 2009), as well as particle dispersion (Spydell et al. 2007). Drifters also have been used in the open ocean to observe wave breaking and air–sea exchange (Graber et al. 2000; Pascal et al. 2011). In addition to a Lagrangian reference frame, drifters have the advantage of measurement in the absence of ship interference (e.g., wave reflections from the hull).
The SWIFT platform and raw data collection are presented in section 2. Then, processing methods for wave spectra and turbulent dissipation rates are described in section 3, with an emphasis on separating platform motion from turbulence. The processing steps are demonstrated with data from the following two field tests: (a) shallow water surf at the Field Research Facility (FRF) in Duck, North Carolina, and (b) deep water whitecaps on Lake Washington in Seattle, Washington. For each field deployment, the methods are compared between “bursts” with weak wave breaking and with strong wave breaking, as quantified by a breaking rate from surface video data. For the Lake Washington tests, an independent measurement of the wave-breaking turbulent dissipation rate at one point in the vertical profile is obtained using an acoustic Doppler velocimeter (ADV) on board the SWIFT. In section 4, all bursts are aggregated to examine overall patterns in wave-breaking dissipation during the field testing. Discussion of the test results and data quality follow in section 5, and conclusions are given in section 6.
2. Measurements
SWIFT is shown in Fig. 1. The purpose of the SWIFT is to make measurements in a wave-following reference frame. The primary dimensions are a 2.15-m length overall (1.25-m draft + 0.9-m mast) and a 0.3-m-diameter hull. Onboard instruments include a GPS logger (QStarz BT-Q1000eX), a pulse-coherent Doppler velocity profiler [Nortek Aquadopp (AQD) HR], an autonomous meteorological station (Kestrel 4500), and a digital video recorder (GoPro Hero). The SWIFT location is tracked in real time with a radio frequency transmitter (Garmin Astro). SWIFT missions typically last several hours up to a full day, and data are collected in 5-min bursts. Upgrades are ongoing to swift including extending mission life, and integrating an ultrasonic anemometer (AirMar PB200) and data telemetry (Iridium).
(a) Dimensional drawing and (b) picture of a SWIFT. Drawing and design by J. Talbert, Applied Physics Laboratory, University of Washington.
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
A series of field tests have been conducted to refine the SWIFT design and data processing algorithms. To date, six SWIFTs have been fabricated and approximately 1300 h of SWIFT data have been collected. Select data and results from tests are used to demonstrate the data collection and processing steps. For each field test, individual burst data and processing are compared between weak and strong breaking conditions (as determined from the onboard video recordings), and then patterns from aggregate results using all bursts are examined.
First, a shallow water test deployment was conducted over 4 h on 15 September 2010 at the U.S. Army Corps of Engineers (ACE) Field Research Facility in Duck. Conditions, as measured by FRF instruments, were onshore 2–5 m s−1 winds and 10-s period swell, with 0.6-m significant wave height. The FRF uses a local coordinate system, in which x is increasing offshore and y is increasing alongshore. For these mild conditions and neap tides, the surf zone was contained with 75 < x < 175 m. SWIFTs were released from a small boat outside of the surf zone (cross-shore distance x ~ 250 m, water depth h ~ 4 m) and were allowed to drift into the surf zone. SWIFTs eventually grounded on the beach and were recovered there. An early version of the SWIFT was used, which differed slightly from the version in Fig. 1. The earlier version used a 90° transducer head on the Aquadopp HR, which was mounted across the lower hull to achieve approximately the same beam geometry as the version in Fig. 1.
Second, a deep water test deployment was conducted over 6 h on 12 November 2011 on Lake Washington in Seattle. Conditions, as measured by nearby meteorological station (King County buoy) and a Datawell Waverider buoy, were southerly 8–10 m s−1 winds and 3-s-period fetch-limited waves, with 0–1-m significant wave height. The wave age was approximately cp/U10 = 0.4, where cp is the deep water phase speed and U10 is the wind speed at a 10-m reference height. SWIFTs were released from a small boat just north of the I-90 floating bridge in the middle of the lake and allowed to drift north along a fetch distance x, where x = 0 is the location of the floating bridge. SWIFTs were in deep water (h > 30 m) at all times, as confirmed via postprocessing of GPS positions with bathymetry in Google Earth. As shown in Fig. 1, this version of SWIFT included an acoustic Doppler velocimeter [Nortek Vector (VEC)] sampling at a single bin in the middle of the Aquadopp HR profile.
a. Platform motion
The SWIFT wave-following motion is measured via GPS logger (QStarz BT-Q1000eX) at 5 Hz, following Herbers et al. (2012). Although the absolute horizontal accuracy of the differential GPS (DGPS) positions is only 10 m, the relative horizontal velocity resolution is much higher (0.05 m s−1) and suitable for the orbital motions of most ocean waves. This velocity resolution is possible by Doppler phase processing the raw GPS signals. The GPS vertical elevation accuracy is not sufficient to track wave-following motion; however, relative (i.e., in the wave-following reference frame) vertical information is available from the pressure and orientation sensors in the Nortek Aquadopp HR. The Aquadopp pressure is equivalent to the SWIFT surface tracking, and pitch and roll are equivalent to the components of the SWIFT vertical tilting. (Constant values from these sensors indicate good wave-following behavior.) The GPS and Aquadopp orientation data are processed to determine the wave-height spectra and the quality of wave following, respectively.
In addition to wave-following motions, the SWIFT oscillates, or “bobs,” at a natural frequency. The SWIFT has 12.7-kg buoyancy in the main hull (0.3-m diameter, see Fig. 1) and 2.6 kg of lead ballast at the bottom of the lower hull (i.e., 1.25 m below the surface). Following Middleton et al. (1977), the corresponding theoretical natural period is Tn ≈ 1.3 s, which is intentionally shorter than most ocean waves. This natural oscillation is damped by a heave plate at the bottom of the lower hull (see Fig. 1).
While wave following, the SWIFT also drifts with mean currents and wind. Tests in Puget Sound, under a range of tidal currents from 0.4 to 2.2 m s−1, indicate drift velocities are consistent with fixed ADCP observations (not shown). Wind drag causes the SWIFTs to drift with the wind, which is measured on board the SWIFT at 0.9 m above the surface, at about 5% of the wind speed (as empirically determined from tests in 0–14 m s−1 winds). While drifting, a subsurface vane on the lower hull (see Fig. 1) provides additional drag to maintain an orientation such that the video and Aquadopp beam 1 look upwind (or upwave, for locally generated wind waves). Under strong winds, the drag of the 0.9-m mast causes a steady tilt of the SWIFT relative to the vertical of approximately 5°–10° (see picture in Fig. 1). This mean tilt changes slightly the vertical projection of subsurface velocity profiles (next section), but otherwise has negligible effects.
b. Turbulence profiles u′(z)
Turbulent velocity profiles u′(z) are obtained with a 2-MHz Nortek Aquadopp HR (pulse coherent) Doppler profiler, where z is the distance below the wave-following surface at z = 0. The Lagrangian quality of the drifter is motivated, in part, by range and magnitude limitations in the Doppler measurements of u′(z) and the goal of measuring turbulence within the crests of breaking waves (i.e., above the still water level). The Aquadopp is mounted in the lower hull and collects along-beam velocity profiles at 4 Hz with 0.04-m vertical resolution along a 0.8-m beam. Bursts of 1024 profiles (=256 s) are collected at 300-s intervals. The beam is orientated up- and outward at an angle of 
The along-beam velocities are mapped, but not projected, to a vertical coordinate z for subsequent processing and plotting (i.e., each value of u′ is unchanged, but is assigned a z location). The z location is defined as the distance beneath the instantaneous free surface (z = 0) and the Aquadopp pressure gauge (also sampled a 4 Hz) is used to correct for any changes in the waterline level at the SWIFT. This correction is small (a result of the wave-following nature of the platform), and never shifts the observed profile up or down more than one profile bin (i.e., ±0.04 m).
Figure 2 show examples of raw Aquadopp data for selects bursts (4 Hz for 5 min) from outside and inside of the surf zone at Duck (left versus right panels). Figure 3 shows examples of raw Aquadopp data for selects bursts with mild breaking at short fetch and strong breaking at long fetch (left versus right panels). The surface elevation (z = 0) appears constant in the lower panels because the SWIFT is following the free surface. The depth profiles of u′(z) do not show any strong trends. However, in shallow water, the backscatter amplitude is uniformly increased in the surf zone example (a ~ 200 counts, Fig. 2l) compared with the offshore example (a ~ 150 counts, Fig. 2i), consistent with the presence of bubbles in the surf zone. In deep water, the amplitude increases slightly near the surface for both examples (Figs. 3i,l), consistent with bubble injection by wave breaking (whitecaps).
Example raw SWIFT burst data collected in shallow water at the Duck FRF. (left) Nonbreaking conditions outside of the surf zone, and (right) breaking conditions within the surf zone are shown. (a),(b) Onboard video images with rectified 1-m2 regions for counting breakers (red outline). (c),(d) Quality-controlled velocity data using a pulse-to-pulse correlation cutoff c > 50 (red lines). (e),(f) Comparisons of extended velocity range measurements with midprofile velocity measurements. (g),(j) Vertical profiles of turbulent velocity u′(z). (h),(k) Vertical profiles of correlation c(z). (i),(l) Vertical profiles of backscatter amplitude a(z). Mean values (thick black lines) and ±one standard deviation (dashed black lines) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
Example raw SWIFT burst data collected in deep water on Lake Washington. (left) Moderate breaking conditions at a short fetch distance, and (right) strong breaking conditions at a larger fetch distance. (a),(b) Onboard video images with rectified 1 m2 regions for counting breakers (red outlines). (c),(d) Quality-controlled velocity data using a pulse-to-pulse correlation cutoff c < 50 (red lines). (e),(f) Comparisons of extended velocity range measurements with midprofile velocity measurements. (g),(j) Vertical profiles of turbulent velocity u′(z). (h),(k) Vertical profiles of correlation c(z). (i),(l) Vertical profiles of backscatter amplitude a(z). Mean values (thick black lines) and ±one standard deviation (dashed black lines) are shown.
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
A major concern with up-looking Doppler measurements is interference from surface reflections. This is especially significant for coherent systems. Profiles of along-beam backscatter amplitude and coherence (e.g., Figs. 2h–l and 3h–l) are used to look for interference, which would appear as a peak in amplitude and reduction in coherence at specific location in the profile (corresponding to a returning pulse interfering with an outgoing pulse). These and other profiles of amplitude and correlation do not show any sharp features that would indicate interference from surface reflections. Using a pulse distance of 0.8 m, which is similar to actual distance to the surface, is the minimum value that can be used.
The velocity data are quality controlled using a minimum pulse correlation value of c > 50 (out of 100) and a minimum backscatter amplitude a > 30 counts, which were empirically determined to be the maximum values associated with spurious points and with bins out of the water. Nortek notes that a canonical value of c > 70 is often overly restrictive, and recommends c > 50 as a more useful cutoff (Rusello 2009). For ADV measurements, an accepted threshold is 
For the Duck measurements shown in Fig. 2, there is a notable decrease in scatter for velocity measurements above the chosen correlation cutoff c > 50 (Figs. 2c,d). For the Lake Washington measurements shown in Fig. 3, the scatter for velocity measurements is similar above and below the chosen correlation cutoff c > 50 (Figs. 3c,d). Observations with c > 50 or a < 30 are assigned NaN velocity values and ignored during subsequent analysis (i.e., no interpolation). At worst, the quality control ratio of points removed to total points is 1:2, or half of the data in a given burst. At Duck, the burst data outside of the surf zone include a brief period (~20 s) with the instrument out of the water for repositioning, and this results in a much higher quality control ratio (i.e., more points are removed from the velocity data prior to processing). Even in these cases with significant data removal, there are at least 512 profiles remaining with which to determine the average structure of the turbulence. More often, the quality control ratio is less than 1:10.
The velocity data also are quality controlled by examining the extended velocity range (EVR) data in the HR mode, which uses a second, shorter pulse lag to obtain a wider velocity range at point in the middle of the profile (z = 0.3 m). Here, the pulse distances are 0.8 and 0.26 m, and the along-beam velocity range is 0.5 m s−1. Comparing the profile and EVR data is essential to confirm that phase wrapping has not occurred. Comparing the profile and EVR data also is useful to evaluate quality control via coherence and amplitude thresholds (i.e., for data within the velocity range, points with low correlations c or amplitudes a should be the only points that do not compare well). For the Duck measurements shown in Fig. 2, there is improved agreement between the profile data and the EVR data for velocity measurements above the chosen correlation cutoff c > 50 (Figs. 2e,f). For the Lake Washington measurements shown in Fig. 3, there is no significant difference in the EVR agreement for quality-controlled data (Figs. 3e,f).
The pulse-coherent measurements from the Aquadopp HR do not have a nominal Doppler uncertainty, or “noise,” value. Zedel et al. (1996) show that noise is a function of the coherence of each pulse pair, as well as sampling parameters (i.e., rate, number of bins) that control Doppler phase resolution. Still, a nominal value is useful when interpreting results. Here, a nominal velocity uncertainty (standard error) of 
c. Surface images
Time-lapse images of the surface are collected at 1 Hz from a GoPro Hero camera mounted to the mast at an elevation of 0.8 m above the surface and an incidence angle of 35° relative to nadir. Recording in mode “r4,” the horizontal field of view is 170° and the images are 2592 × 1944 pixels. Example images are shown in Figs. 3a,b. The shallow water testing at the FRF used a ruggedized Sanyo video camera recording at 30 Hz with a much reduced field of view, as shown in Figs. 2a,b. The images are processed to estimate the frequency of wave breaking fb, which is used as context for the turbulent dissipation rate estimates.
3. Methods
The wave-following behavior of the SWIFTs, which separates wave orbital velocities 
a. Frequency spectra S(f)
Frequency spectra S(f) are used to evaluate the motion of the SWIFT and to quantify the wave conditions. Spectra for each 5-min burst are calculated as the ensemble average of the fast Fourier transform (FFT) of 16 subwindows with 50% overlap, which resulting in 32 degrees of freedom and a frequency bandwidth df = 6.25 × 10−2 Hz. Figures 4 and 5 show example spectra from Duck and Lake Washington, respectively, using the same example bursts (showing weak and strong wave breaking) discussed in the previous section (section 2).
Example frequency spectra calculated from burst data in shallow water at the Duck FRF. (left) Nonbreaking conditions outside of the surf zone, and (right) breaking conditions within the surf zone. (a),(b) SWIFT platform orientation spectra (pitch, roll, and heading). (c),(d) Wave energy spectra (from independent FRF measurements) and SWIFT pressure spectra (from the Aquadopp). (e),(f) Velocity spectra, including wave orbital motion (from independent FRF measurements), SWIFT turbulence at one selected vertical position, and turbulence difference between selected vertical positions.
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
Example frequency spectra calculated from burst data in deep water on Lake Washington. (left) Moderate breaking conditions at a short fetch distance, and (right) strong breaking conditions at a larger fetch distance. (a),(b) SWIFT platform orientation spectra (pitch, roll, and heading). (c),(d) Wave energy spectra (from SWIFT GPS measurements) and SWIFT pressure spectra (from the Aquadopp). The theoretical equilibrium range is shown (green dashed lines). (e),(f) Velocity spectra, including wave orbital motion (from SWIFT GPS measurements), SWIFT turbulence at one selected vertical position, and turbulence difference between selected vertical positions.
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
Spectra from Aquadopp orientation data (i.e., pitch, roll, and heading), Sθθ(f), are used to assess the tilting and turning of the SWIFT during wave following. In Figs. 4a and 5a, example orientation spectra Sθθ(f) show broad peaks at the natural period of the platform and at the period of the waves. The weak response at wind sea frequencies (0.4–0.5 Hz) indicates some rotation and tilting during wave following. However, the more prominent signals are the trends caused by shifting winds and surface currents (i.e., low frequencies). These platform motions shift the entire Aquadopp profile u′(z) with an offset Δuθ, which has a negligible effect on the structure of u′(z) − u′(z + r).
Spectra from the Aquadopp pressure data (i.e., relative distance below the surface), Spp(f) are used to assess the surface tracking of the SWIFT during wave following. In Figs. 4b and 5b, the natural frequency (~0.7 Hz) is the dominant peak in the pressure spectra Spp(f), and wave peaks are negligible (i.e., pressure fluctuations from waves are absent in the wave-following reference frame). Integrating Spp(f) around the natural frequency estimates the variance in the surface tracking owing to bobbing of the platform. In field testing, this variance is typically O(10−4 m2), or a vertical standard deviation of σz ~ 0.01 m.
In contrast, the SWIFT horizontal velocity data from the phase-resolving GPS contain the wave orbital motions relative to the earth reference frame. Following Herbers et al. (2012), the wave orbital velocity spectra 
Finally, spectra of the Doppler turbulent velocity profiles 
The velocity differences (i.e., the turbulence) along a profile are much less susceptible to motion contamination, because platform motion contaminates the entire profile (i.e., an offset). Thus, spectra of velocity differences at selected points along the profile are used to evaluate the motion contamination for the purpose of turbulence calculations. Figures 4c and 5c show spectra two selected velocity differences (between depths [z, z + r1] and [z, z + r4]) for the example bursts, and the velocity difference spectra all lack the peaks associated with motion contamination. Moreover, the velocity difference spectra show an expected increase in energy density between smaller (r1 = 0.4 m) and larger (r4 = 0.16 m) lag distances (i.e., eddy scales), consistent with a turbulent cascade.
b. Turbulence structure function D(z, r)
Figures 6 and 7 show examples of the structure functions D(z, r) calculated outside and inside of the surf zone (Fig. 6a versus Fig. 6b) and during mild and strong whitecapping (Fig. 7a versus Fig. 7b). In each example, there are trends for increased velocity differences with increasing lag distances r, and the slopes of these trends differ by vertical location beneath the wave-following surface (color scale of z in the figures). These trends are consistent with a cascade of turbulent kinetic energy from large to small eddies.
Example SWIFT burst results from in shallow water at the Duck FRF. (left) Nonbreaking conditions outside of the surf zone, and (right) breaking conditions within the surf zone. (a),(b) Velocity structure functions D(z, r) [Eq. (2), dots] and associated fits Ar2/3 + N [Eq. (4), lines]. Colors indicate distance beneath the wave-following surface, and the predicted noise intercept 
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
Example SWIFT burst results from deep water on Lake Washington. (left) Moderate breaking conditions at a short fetch distance, and (right) strong breaking conditions at a larger fetch distance. (a),(b) Velocity structure functions D(z, r) [Eq. (2), dots] and associated fits Ar2/3 + N [Eq. (4), lines]. Colors indicate distance beneath the wave-following surface, and the predicted noise intercept 
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
The offset N is expected to be 
c. Dissipation rate profiles 
Examples of the resulting dissipation rate profiles 
This integral is limited by the lowest depth (z ≈ 0.5 m) below the wave-following surface (z = 0 m). For some wave conditions, this limitation will be severe given the expectation that the depth-breaking turbulence scales with wave height (Babanin 2011) or water depth (Feddersen 2012). However, for the examples shown, dissipation rates are observed to decrease sharply beneath the wave-following surface, and linear extrapolation below z = 0.5 would rarely increase 
Finally, for the Lake Washington deployments, another method to estimate the dissipation rate is incorporated to provide an independent comparison with the structure function method. The second method uses the common approach of rapidly sampled (32 Hz) ADV data to calculate frequency spectra of turbulent kinetic energy (Lumley and Terray 1983; Trowbridge and Elgar 2001; Feddersen 2010). The frequency spectra are converted to wavenumber spectra by assuming the advection of a frozen field (i.e., Taylor’s hypothesis), and the dissipation rate is obtained by fitting an amplitude B to the inertial subrange of the spectra SADV (f) = Bf−5/3, and taking 
As shown in the example of Fig. 7, and later for all bursts, the estimates from the ADV at z = 0.25 m are consistent with structure function estimates at the same depth below the wave-following surface [although it must be noted that the largest values of 
d. Frequency of breaking fb
The frequency of breaking is the number of waves breaking at a given point per unit time and is a useful quantity in interpreting the dissipation results. Previous work has linked the frequency of breaking to the energetics of breaking, either directly (Banner et al. 2000) or as the first moment of the crest-length distribution by speed Λ(c) (Phillips 1985). Video recordings of the surface collected on board the SWIFT are rectified following Holland et al. (1997), such that pixels sizes and locations are corrected for distortion and perspective. After rectification, breaking waves within a 1 m × 1 m square region immediately in front of the SWIFT are counted manually for each 5-min burst to obtain a burst-averaged frequency of breaking fb. Restriction to 1 m2 is consistent with the normalization used in Λ(c) studies (e.g., Thomson et al. 2009). Examples of this region are overlaid on the video images in Figs. 2 and 3, and the manually calculated frequencies of breaking are shown. The crest-length distribution by speed Λ(c) is not estimated, because the pixel resolution is insufficient over the larger areas needed to observe crest propagation.
4. Results
In this section the methods are applied to all burst data collected during testing, and the results are aggregated to assess spatial patterns, dynamic range, and sensitivity.
a. Surf zone testing
Figure 8 shows cross-shore bathymetry (Fig. 8a) and the aggregated results of all SWIFT bursts on 15 September 2011 (Figs. 8b–d), plotted as a function of cross-shore distance in the local FRF coordination system. With small incident waves and a weak (neap) low tide, the surf zone is at approximately 75 < x < 175 m. (With larger waves and lower tides, the surf zone typically is farther offshore.) The frequency of breaking is maximum in the surf zone (fb ~ 40 h−1 at x ~ 130 m in Fig. 8b), as is the vertically integrated total dissipation rate (
Aggregated results of SWIFT drifts at the Duck FRF vs cross-shore position. (a) Nearshore bathymetry (shaded region) and the still water level (dashed line). (b) Frequency of breaking calculated from the video images on board the SWIFT. (c) Depth-integrated total dissipation 
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
b. Whitecap testing
Figure 9 shows the aggregated results of all SWIFT bursts on 12 November 2011, plotted as a function of north–south fetch distance x along Lake Washington. Wave heights, as estimated from the SWIFT GPS spectra, increase along the fetch from 0.2 m to 0.9 (Fig. 9a). The frequency of breaking fb increases along fetch from 
Aggregated results of SWIFT drifts on Lake Washington vs fetch x. (a) Significant wave height estimated from the SWIFT GPS spectra as 
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
5. Discussion
In this section the magnitude and depth dependence of the dissipation rates during field testing are compared with literature values and simple models. Then, errors and uncertainties in the dissipation rates are discussed, as well as sensitivity to the correlation cutoff applied to the Doppler velocity measurements.
a. Scaling of dissipation rates
The dissipation rate profiles observed at both the Duck FRF (surf breaking) and on Lake Washington (whitecap breaking) decrease with depth beneath the free surface (i.e., Figs. 6c,d and 7c,d). In the absence of wave breaking (i.e., offshore of the surf zone at the Duck FRF or at very short fetch on Lake Washington), the linear decrease is qualitatively consistent with the well-known wall-layer dependence 
The frequency of breaking and the total dissipation rates observed at the Duck FRF can be compared to a simple budget for the incoming swell. Requiring every incident 10-s period wave to break gives a predicted frequency of breaking fb = 0.1 Hz = 360 h−1, which is 8 times larger than the fb ~ 40 h−1 obtained from the SWIFT in the surf zone (Fig. 8b). Similarly, requiring the energy flux per crest length 
Related to SWIFT propagation, another significant bias may be the 5-min burst averaging, because the dissipation rates in the surf zone are event driven and unlikely to be normally distributed. Alternate averaging (e.g., lognormal) in Eq. (2) produces similar results for these field tests, suggesting that intermittence cannot be simply treated. The breakpoint of an irregular wave field on a natural beach is not well defined; some waves may break further shoreward and some may break further seaward. Thus, even for a 5-min burst when the SWIFT is drifting within 10 m (cross-shore distance) of the nominal breakpoint, breaking (and presumably maximum dissipation) may only be observed for a few waves. This demonstrates the need for fixed instruments (Eulerian measurements) to interpret the SWIFT estimates. In contrast, whitecapping is more regular, and 5-min burst averages of 
The frequency of breaking and total dissipation rates observed on Lake Washington can be compared to a simple budgets for wind forcing. Under equilibrium conditions (i.e., steady-state, fetch-limited wave field), the frequency of breaking is controlled by the wave steepness at the peak of the spectrum, and the wind input rate W equals the total dissipation rate 
Finally, it must be noted that there are many sources of turbulent dissipation at the air–sea interface. The SWIFT-based estimates are the total dissipation rate in the upper 0.5 m of the ocean, and the above energy budgets attribute all of this dissipation to breaking waves. This assumption is supported by the frequency of breaking measurements, which are well correlated with the dissipation rates. However, to successfully isolate the breaking contribution, it may be necessary to remove a nonbreaking offset, which is estimated a priori, measured independently, or assumed to be the lowest value in the profile.
b. Errors and uncertainty in dissipation rates
There are three interrelated potential sources of error in the dissipation estimates: 1) errors introduced by SWIFT motion, 2) errors in the fit to the spatial structure of an assumed turbulence cascade, and 3) errors in the pulse-coherent Doppler velocity measurements.
Motion contamination is quantified using frequency spectra and corrected with an offset to the lag distances [Eq. (3)] used in the structure function [Eq. (2)]. There are no observed spectral peaks in the difference between velocity bins, although there are SWIFT motion peaks for individual velocity bins (see Figs. 4 and 5). Thus, motion contamination the structure function can be treated as an offset Δr, rather than a wave-dependent quantity.
Errors in the fit to an assumed eddy cascade are quantified by an uncertainty σε±, the propagated RMSE of the fit, and by N, the noise intercept of the fit. In general, 
Errors from the pulse-coherent Doppler velocity measurements are more difficult to quantify, although they are implicit to the values of σε± and N discussed above. A threshold for pulse correlation commonly is used to remove spurious points (e.g., Rusello 2009; Feddersen 2010), and the choice of c > 50 (out of 100) is evaluated relative to the implicit error N. Figures 10 and 11 show the distributions of N over all bursts and all vertical positions for four different values of correlation cutoffs. Also shown are vertical lines for the predicted 
Distributions of noise intercepts N from all bursts at Duck FRF using four different pulse correlation c cutoffs for quality control of velocity data. (a) c > 0, (b) c > 25, (c) c > 50, and (d) c > 75. Colors indicate distance beneath the wave-following surface, as in Fig. 6. Predicted value for N, given a Doppler velocity uncertainty of σu = 0.025 m s−1 (dashed lines).
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
Distributions of noise intercepts N from all bursts on Lake Washington using four different pulse correlation cutoffs for quality control of velocity data. (a) c > 0, (b) c > 25, (c) c > 50, and (d) c > 75. Colors indicate distance beneath the wave-following surface, as in Fig. 7. Expected range for N, given a Doppler velocity uncertainty of σu = 0.025 m s−1 (dashed lines).
Citation: Journal of Atmospheric and Oceanic Technology 29, 12; 10.1175/JTECH-D-12-00018.1
For c > 50, the shallow water tests show N < 2σ2 for all bursts and all vertical positions (Fig. 10), and the deep water tests show N < 2σ2 for the majority of bursts and vertical positions (Fig. 11). The difference between tests may be related to the backscatter amplitude, which is also used in initial quality control (require a > 30) and is generally higher in the surf zone. The larger N values on Lake Washington may be the result of peak waves (fp = 0.33 Hz) that are closer to the natural frequency of the SWIFT (fn = 0.7 Hz) and may cause increased motion contamination relative to the peak waves during the Duck FRF testing (fp = 0.1 Hz). Within Lake Washington tests (Fig. 11), there also is a trend of larger noise intercepts N closer to the surface (z = 0), again suggesting motion contamination is more significant, because the bias to the structure function is more severe further from the Aquadopp [see Eq. (3)].
Although there is no known parametric dependence or clear empirical value, it is evident from the burst examples (Figs. 2 and 3) and full datasets (Figs. 10 and 11) that a higher correlation cutoff improves the quality of the dissipation rate estimates, at least within the constraint of removing too many points to obtain robust statistics. Testing selected values suggests that c > 50 is reasonable cutoff to give N < 2σ2 most of the time. For the SWIFT measurements, evaluation of pulse correlations above 50 may be more important in assessing the potential for surface reflections than in quality controlling individual points. Restated, a random distribution of low correlations will have only a small effect on the determination of dissipation rates, but a concentration of low correlations at particular depth indicates acoustic contamination via surface reflection that may severely deteriorate the quality of dissipation estimates using a structure function method.
Finally, the noise intercepts and uncertainties provide guidance on the minimum values of dissipation that may be obtained from the SWIFT observations. Using the σ = 0.025 m s−1 value, the minimum dissipation rate for N < Ar2/3 is 
6. Conclusions
A new wave-following platform, termed the Surface Wave Instrument Float with Tracking (SWIFT), is used to estimate the dissipation rate of turbulent kinetic energy in the reference frame of ocean surface waves. Pulse-coherent Doppler velocity data are used to determine the spatial structure of the near-surface turbulence and thereby estimate burst-averaged dissipation rates as a function of depth and time without assuming the advection of a frozen field (i.e., without using Taylor’s hypothesis). The approach is demonstrated in two field tests under markedly different conditions (shallow water surf breaking versus deep water whitecap breaking). In both cases, motion contamination is successfully minimized and error propagation indicates robust estimates of dissipation. The advantages of the wave-following reference frame, in particular, observations above the still water level and along a spatial gradient (e.g., depth or fetch), are evident in the field tests. Limitations are also evident, in particular the lack of dwell time moving through regions of strong gradients.
Acknowledgments
Thanks to APL-UW Field Engineers J. Talbert and A. deKlerk for tireless efforts in the design, assembling, testing, deployment, and recovery of the SWIFTs. Thanks to the US-ACE Field Research Facility (FRF) staff J. Hanson and K. Hathaway for excellent logistical support, array data, and bathymetry surveys. Thanks to C. Chickadel, D. Clark, M. Haller, D. Honegger, A. Jessup, E. Williams, and G. Wilson for daily shore support during FRF tests, and to M. Schwendeman for help with Lake Washington tests. Thanks to F. Feddersen, G. Farquharson, J. Gemmrich, G. Gerbi, R. Holman, P. J. Rusello, and anonymous reviewers for many helpful discussions and comments on the manuscript. Funding provided by the National Science Foundation, the Office of Naval Research, and the University of Washington Royalty Research Fund.
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