Measurements of Directional Wave Spectra and Wind Stress from a Wave Glider Autonomous Surface Vehicle
1. Introduction
The Wave Glider is an autonomous surface vehicle that uses wave motion for propulsion. A surface float is connected by a tether, typically 8 m in length, to a subsurface body with a series of six wings. With the passage of each wave, the subsurface float glides forward but not backward because the wings feather to prevent it. A rudder on the subsurface body controls navigation. The subsurface body tows the surface float, such that the forward motion is in any desired direction (i.e., propulsion is achieved both upwave and downwave, or across-wave). The surface float contains the main electronics for telemetry, command/control, and scientific instrumentation. When prepared for deployment, as in Fig. 1, the surface float and subsurface body are bundled together; a mechanical release separates them once in the water. The Wave Glider is commercially produced by Liquid Robotics, Inc., based in Sunnyvale, California. The current version is the SV3, of which over 150 units have been produced for a range of applications, from oceanographic surveying to port security.
Wave Glider SV3–153 being deployed from the R/V Laurence M. Gould, an Antarctic research and supply vessel, near the Antarctic Peninsula.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
The following work describes and evaluates methods to make scientific-grade measurements of waves and winds from the Wave Glider. For waves, the challenge is that the surface float is not truly surface following, at least not in terms of the pitch–roll–heave signals used by traditional wave buoys, and also that the vehicle is extracting propulsion from the waves. The solution herein is to use global positioning system (GPS) measurements of horizontal motion as the raw wave data signal, instead of pitch–roll–heave, in a method termed GPSwaves (Herbers et al. 2012). This method is agnostic to the orientation of the surface float as well as the details of the vehicle response to surface slopes. For wind stress, the challenge also is motion contamination along with potential biases of measuring at low heights above the water, such that the measurements may be within the wave-coherent boundary layer (e.g., Grare et al. 2013; Edson et al. 2013; Hara and Sullivan 2015). The solution herein is the use a fast sampling sonic anemometer (Gill Instruments WindMaster) to observe the inertial subrange of wind turbulence at frequencies greater than those of motion contamination (Edson et al. 1991).
These methods are assessed in a series of evaluation datasets, using the commercially produced Datawell wave sensor (Datawell BV, the Netherlands) and Airmar ultrasonic anemometer (Airmar Technology Corp., Milford, New Hampshire) as reference data. The wind datasets are limited, relative to the wave datasets, and model reanalysis products are used to bolster the validation of this portion.
There have been several previous investigations of wave and wind measurements from the Wave Glider, particularly using the earlier SV2 model. Focusing on waves only, Wang and Allard (2012) find that the measurements are in good agreement with nearby National Data Buoy Center (NDBC) measurements. They note that wave spectra measured with the Wave Glider are slightly broader with some bias at low frequencies. More recently, Lenain and Melville (2014) used a Datawell MOSE-G sensor mounted on board a Wave Glider to measure wave heights up to 10 m and winds up to 37 m s−1 in Tropical Cyclone Freda (2012). These measurements agreed well with hindcast models of the storm conditions with adjustment of the winds to the standard 10-m reference height. Lenain and Melville (2014) also include an appendix comparing results from the on board Datawell unit with an independently moored Datawell Waverider buoy from the Coastal Data Information Program (CDIP). Although the comparison dataset is quite limited (2 days with a range of wave heights from 0.7 to 1.4 m), Lenain and Melville (2014) conclude that the Wave Glider measurements are in good agreement with the reference. Very recently, Mitarai and McWilliams (2016) presented measurements of winds up to 32 m s−1 during Typhoon Danas and suggested that the 10-min averaged wind speeds were in qualitative agreement with model reanalysis winds, despite the known complexities of the atmospheric boundary layer in the presence of surface waves (e.g., Hara and Sullivan 2015).
The present study expands upon these previous efforts using larger evaluation datasets covering full ocean conditions. The present work also describes and evaluates newly implemented methods that run on board the Wave Glider as directly integrated sensors and software packages (as opposed to third-party sensors with their own processing, such as the Datawell unit or the Airmar weather station). The wave spectral quantities and bulk wave parameters are compared using standard skill metrics (O’Reilly et al. 1996; Krogstad et al. 1999; Collins 2012). The wind stress results are compared to bulk parameterizations (i.e., Smith 1980; Fairall et al. 2003). Details of wave directional spectra will be difficult to compare (Collins 2012), even with standards such as the Wave Eval Tool (WET; Coastal Data Information Program 2009), but specific examples will demonstrate the more subtle results. It is worth noting at the outset that differences of 5%–10% in bulk wave parameters are common, even from sensors on the same platform (Bender et al. 2010).
2. Methods
a. Wave measurements and processing
The approach to measuring waves from the Wave Glider follows closely the work of Herbers et al. (2012), as applied to other nonspherical surface objects, such as the Surface Wave Instrument Float with Tracking (SWIFT) drifter (Thomson 2012). The primary raw data for this method are GPS-measured horizontal velocity components: u (east) and υ (north). By using the phase of the GPS carrier wave to determine a Doppler-shifted velocity, the latest generation of GPS receivers reports velocities with a precision of a few centimeters per second (cm s−1). These velocities are used to measure the wave orbital motions. The approach is agnostic to the orientation (pitch, roll, heading) of the surface float, and it requires only that the float move laterally with the orbits of the waves. Supplemental inertial motion unit (IMU) data are include to help resolve wave direction, by calculating the phase of vertical acceleration a relative to the lateral velocity components u and υ.
1) Raw wave data collection
The raw wave data are collected using a Microstrain 3DM GX3-35 sensor mounted on a mast 0.65 m above the Wave Glider float. The GX3 sensor integrates GPS and IMU data into a single serial output. No postprocessing or real-time corrections [i.e., postprocessing kinematic (PPK) or real-time kinematic (RTK)] are made on the raw GPS data. Data are collected at a sampling frequency 
2) Raw wave data preprocessing
Next, the raw data are despiked by removing any points that are more than N standard deviations from the mean, where the N is an input to the routines, with a default setting of 
3) Spectral processing
4) Spectral wave energy
For efficiency of telemetry, only the first 49 frequency bands of this result are retained, and thus the frequencies reported are 
5) Antenna height corrections
6) Spectral wave directions
Directional information is obtained from the cross spectra, in particular the phasing of the signals (which is related to the real vs imaginary parts of the cross spectra). Following the methods of Kuik et al. (1988) and the adaptations similar to Herbers et al. (2012), the directional moments 
7) Quality control of spectral results
The scalar energy spectra obtained by these methods are often contaminated by spurious energy at swell frequencies, nominally at 
8) Doppler correction for vehicle navigation
Implementing a Doppler correction on board the GPSwaves routine would be an iterative process, as was done in Zippel and Thomson (2017), wherein the spectral wave directions would be estimated to get 
9) Determination of bulk wave parameters
10) Evaluation datasets (wave)
Several datasets have been collected to evaluate and characterize the wave measurements and the onboard processing routines. There are five datasets:
Southern Ocean (Drake Passage), winter 2017
Astoria Canyon (offshore Oregon), winter 2017
Hawaii, autumn 2016
Monterey Canyon (offshore California), spring 2015
Hawaii, spring 2014
Time series of wave bulk parameters during the (a)–(c) Southern Ocean and (d)–(f) Astoria Canyon missions. Values are from the GPSwaves method (blue) and ground truth from the Datawell (red).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
b. Wind measurements and processing
The approach to estimating wind stress from the Wave Glider follows closely the work of Edson et al. (1991) and Yelland et al. (1994), in which fast-sampling three-axis sonic anemometers are used to measure turbulent fluctuations of the wind velocity components in the inertial subrange of the turbulent length scales. The essential point is that the inertial subrange is observed at frequencies beyond the influence of platform motion. After using this portion of the frequency spectrum to estimate the turbulent dissipation rate ε, the wind friction velocity 
1) Raw wind data collection
Raw turbulent winds are collected with a Gill Instruments WindMaster three-axis ultrasonic anemometer (Hampshire, United Kingdom) mounted to the bow of the Wave Glider at 0.77 m above the sea surface. The Gill samples at 10 Hz continuously; the raw data of relative wind velocity components 
2) Adjustment to 10-m wind speed
Both measurements of the wind are adjusted to a 10-m reference height, assuming a logarithmic profile (e.g., Zedler et al. 2002). The Gill measurements of relative wind are first adjusted for burst-averaged vehicle heading and speed over ground to produce burst-averaged true winds. Raw motion correction is not attempted, because the raw data recording is not synchronized with the Microstrain GPS/IMU data recording. At moderate wind speeds, this height adjustment is approximately 
3) Turbulent wind spectra
Calculation of the turbulent wind frequency spectra follows closely the steps for spectral processing of the wave data but with 
4) Quality control of wind spectra
The turbulent wind spectra are used only when the Wave Glider is head to wind, such that the wind measurements are not in the wake of the other masts and antennas on the vehicle. This is determined by screening the burst-average components for cases when 
5) Wind stress from inertial dissipation
6) Evaluation datasets (wind)
The wind stress method was only recently implemented on the Wave Glider, so the Southern Ocean dataset is the only case available for evaluation. The dataset is 68 days in duration, and the burst-averaged true wind speeds range from 1 to 17 m s−1. Time series of wind magnitude and direction are shown in Fig. 3. The screening for head-to-wind conditions is severe in this dataset; only 30% of the 30-min bursts meet the criterion. These are mostly from the first half of the mission. During the second half of the mission, the vehicle was on a downwind crossing of the Drake Passage, and the winds were almost aways from astern. Note that this also corresponds to the poor estimates of wind direction from the Gill measurements in Fig. 3b.
Time series of (a) burst-averaged wind magnitude and (b) direction adjusted to 10-m reference height. Values from the Gill three-axis ultrasonic anemometer (green points) and the Airmar two-axis ultrasonic anemometer (magenta points), and NCEP reanalysis winds (black lines).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
The Southern Ocean dataset lacks a fully independent wind measurement, such as a nearby moored buoy, to evaluate the application of the inertial dissipation method on the Gill data. There are 2 h of validation data available from a test mission on the Washington coast, in which results from a nearby direct covariance wind system (Edson et al. 1998) on the R/V Jack Robertson at 6-m height will be compared with the Wave Glider methods. Otherwise, reference data will use the bulk drag formula applied to the Airmar wind measurement and a wind reanalysis product from the U.S. National Centers for Environmental Prediction (NCEP; Saha et al. 2010). Finally, the wind-wave equilibrium stress [Eq. (1)] will be used as another reference and as a demonstration of the combined wave and wind stress results.
3. Results
a. Wave results
1) Wave spectra
Since the determination of wave spectra is a precursor to the determination of bulk wave parameters in the method, the wave spectra results are also presented first. Average spectra are shown for the Southern Ocean and Astoria Canyon datasets. These averages are not valid wave spectra, in the sense of having stationary statistics over such a wide range of wave conditions; however, they are illustrative of the signal characteristics and overall quality. Averages of the ratios between energy spectra are also presented; these are more robust, as they are relative metrics that are calculated for each 30-min burst of data (and then averaged over the whole dataset).
2) Spectral wave energy
The averaged wave energy spectra in Fig. 4 show good agreement between the GPSwaves method and the Datawell reference. There is some bias in the range of approximately 
(a),(c) Average wave energy spectra and (c),(d) ratios during the (a),(b) Southern Ocean and (c),(d) Astoria Canyon missions. Values are from the Wave Glider GPSwaves method (blue) and ground truth from the Datawell (red). Shown in (b) and (d) are ratios equal to one (thin dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
The bias in spectral energy is likely related to wave propulsion, which would contribute nonorbital motion to the raw velocity signals. Removal of this signal would require detailed knowledge of the vehicle motion to develop a transfer function that could correct for these contaminations. Alternatively, an empirical spectral correction factor 
3) Spectral check factors
A commonly used quality metric for wave energy spectra is the “check factor,” which is the ratio of vertical motion to horizontal motion at each frequency band (e.g., Thomson et al. 2015). In deep water, this value is theoretically equal to one, because wave orbits are circular. Figure 5 shows the average check factors from the Astoria Canyon dataset. Reference check factors are not shown for the Southern Ocean dataset, because they are produced only for the CDIP Datawell buoys and not from the Datawell units on board the vehicle (so there are no reference check factors for the comparison in the Southern Ocean dataset). As expected, the Datawell reference check factors are close to one for the frequencies dominated by wave energy, and deviations from one are seen only at the very lowest or highest frequencies. The GPSwaves results, by contrast, are less than one at most wave frequencies. This indicates that horizontal motions exceed vertical motions, consistent with the mechanism listed above for a bias high in spectral energy: wave propulsion. Again, it is tempting to use the spectra check factor to correct for the bias, much as with the 
Average spectral check factors during the Astoria Canyon mission. GPSwaves method (blue) and ground truth from the Datawell (red). Theoretical value of one across all frequencies (thin dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
4) Spectral wave directions
The averaged spectral wave directions in Fig. 6 show excellent agreement between the GPSwaves method and the Datawell reference. The only deviations are at the lowest frequencies, where the wave signals are generally very small. The average ratio between the individual estimates is close to one, except at the higher frequencies. This suggests that the directional wave estimates from Wave Glider may actually be better than the scalar energy estimates—at least there is no obvious bias. This is likely because the directional moments are normalized quantities (see the appendix), and the fidelity of the estimates comes from the quality of the relative phases of the raw signals.
(a),(c) Average spectral wave directions and (b),(d) ratios during the (a),(b) Southern Ocean and (c),(d) Astoria Canyon missions. Values are from the GPSwaves method (blue) and ground truth from the Datawell (red). Shown in (b) and (d) are ratios equal to one (thin dashed line).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
The directional spread also agrees well across all frequencies (not shown). When compared with the independently moored Datawell, as in the Astoria Canyon dataset, the GPSwaves results have spreads that are biased high by 5°–10°. This bias is not observed when comparing with the Datawell unit on board the vehicle, as in the Southern Ocean dataset, and the implication is that vehicle motion broadens the directional estimates slightly.
An example of the directional moments (
Examples of (a),(d) scalar spectra, (b),(e) mean direction, and (c),(f) directional moments for a randomly selected 30-min burst of data from the Astoria Canyon dataset at 0000 UTC 29 Jan 2017. (a)–(c) GPSwaves method; (d),(f) Datawell moored at CDIP station 172.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
Examples of full directional spectra estimated with MEM for a randomly selected 30-min burst of data from the Astoria Canyon dataset at 0000 UTC 29 Jan 2017. (top) GPSwaves method on board the vehicle; (bottom) Datawell CDIP station 172. Frequency increases radially outward from the center of each plot, and color scale is the log of the energy density.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
5) Bulk wave parameters
The bulk wave parameters 
Comparison of wave bulk parameters from GPSwaves vs Datawell during the (a)–(c) Southern Ocean and (d)–(f) Astoria Canyon missions. Shown are the 1:1 correspondence (dashed lines). Energy periods (green) are included in (b) and (e), which are more robust than the peak periods.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
Comparison of significant wave heights 
Comparison of peak wave period 
Comparison of peak wave direction 
6) Wave height comparison
The significant wave heights are generally in agreement between the onboard GPSwaves result and the Datawell reference. This is expected from the wave energy spectra comparisons, since the wave height is simply 4 times the square root of the integrated spectra [Eq. (12)]. Both the bias and the error are larger for the datasets with larger waves. The relative skills are, conservatively (worst case), 2% bias and 5% symmetric error. For full ocean conditions, this indicates that the GPSwaves method running on board the Wave Glider provides wave height estimates to within 
7) Wave period comparison
There is a strong negative bias in the estimates of peak wave period from the GPSwaves method on the Wave Glider. This is a direct result of the bias in the wave energy spectra, which has more energy at higher frequencies than the Datawell reference spectra. The negative bias is up to 25% of the range, while the symmetric error is up to 30%. These errors are exacerbated by the noisy nature of the peak period metric itself and are further enhanced by the inverse relation of period to frequency (i.e., the uniform frequency bands from the FFT give nonuniform spacing of the wave period with especially poor resolution at low frequencies).
Many researchers prefer an energy-weighted wave period [Eq. (13)] because it is a more stable estimator. These values compare much more favorably between the GPSwaves results and the Datawell reference. For the case of the Southern Ocean, the wave period bias reduces from −1.5 to 0.1 s, and the rms error reduces from 2.1 to 0.8 s. Thus, a more stable measure of the wave period can be reproduced by GPSwaves with less than 1% bias and 5% symmetric error.
8) Wave direction comparison
Peak wave directions agree well between the GPSwaves method on the Wave Glider and the Datawell reference with small bias. There is, however, large scatter, reflected in rms errors up to 34°. Much of this scatter is derived from disagreements in the peak wave period, which sets the frequency 
b. Wind results
1) Bulk wind speed and direction
The bulk wind speed and direction agree well, although the direction from the Gill is error prone if the Wave Glider is not pointed into the wind (see right half of Fig. 3b). As the Airmar is on the tallest mast, above all obstructions, it does not have this limitation. The adjusted 10-m wind speeds from the two instruments are directly compared in Fig. 10, with a bias of −0.2 m s−1 and a symmetric error of 1.3 m s−1 reported in Table 4. The wind speeds are a relative bias of 1% and relative error of 8%. This agreement in 
Height-adjusted wind speeds from the Gill measurements, the Airmar measurements, and the NCEP reanalysis product. Legend is reported as vertical vs horizontal axes. Shown are the 1:1 correspondence (dashed line) and the bin average results of the Gill vs Airmar comparison (large black symbols).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
Comparison of wind speeds 
2) Turbulent wind spectra
The turbulent wind spectra are shown in Fig. 11, using wind speed bin averages. As expected, the spectral levels are sorted according to the bulk wind speed. All wind spectra show a motion-contaminated region from 
Turbulent kinetic energy spectra of horizontal wind components vs frequency f. Colored lines are averages in wind speed bins with the bin center annotated at the right terminus of the line. Frequency range of 
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
3) Wind stress
The wind friction velocity estimates are shown in Fig. 12 and Table 4, with a comparison to a standard drag law (Smith 1980) and to the wave equilibrium estimates [Eq. (1)]. The wind stress is simply the square of these estimates [Eq. (16)]. There is good agreement with 0.01 m s−1 bias (1%) and 0.03 m s−1 symmetric error (4%) relative to the drag law. There is also good agreement for two additional validation points; these compare with the direct covariance system on the R/V Jack Robertson during a test mission on the Washington coast in July 2016. There is increased variability in the 
Wind friction velocities vs adjusted height wind speeds for the inertial dissipation method (green points), a bulk drag law (magenta curve), and wind-wave equilibrium (blue open circles). Two points from a nearby shipboard direct covariance system are also included (black squares), and the corresponding Wave Glider dissipation estimates are indicated (black circle around the relevant green point). Only measurements passing the criteria of winds aligned within 
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
A stability correction can be made between Eqs. (14) and (15), but the effect is typically only a few percent change in 
4. Discussion
a. Lack of propulsion contamination
As noted, the wave height bias is likely related to wave propulsion, which raises the question: How can a Wave Glider measure waves to within 5% while simultaneously using the waves for propulsion? The heuristic answer is in the relative scales of motion and the inefficiency of the propulsion. First, the Wave Glider advances forward only a few meters with the passage of each wave, such that the raw signal of the horizontal motion (and the variance) is dominated by the natural wave signal. Second, the surface float is towed by the sub, not the other way around (i.e., the sub is the part that is restricted from moving backward after a wave passes and thus gives propulsion). This means that the surface float is free to track with the wave orbitals at the surface with the weak constraint of being pulled along by the sub. This is not all that different from a mooring tether keeping a CDIP buoy on station in a strong ambient current (although CDIP moorings often employ a rubber cord to soften this constraint). The same is true for moored air–sea flux buoys that estimate wind stress while moving with passing waves.
b. Natural wave variability
For the datasets at Astoria and Monterey Canyons, which have moored CDIP buoys as the Datawell reference, it is important to note the known natural spatial variations in wave fields. This would be a secondary explanation for the difference in wave results. As shown in Gemmrich et al. (2016), the separation of up to 10 km between the CDIP mooring and the Wave Glider can result in a 5% difference in wave heights. Similarly, there is significant uncertainty in determining bulk wave parameters from finite-length records. Drazen et al. (2016) show that the degrees of freedom typical for processing 30-min bursts of wave data can result in significant wave height uncertainties of up to 20%. Although these combined effects can account for the errors in the comparisons, they are less likely to account for the biases.
c. Alternative approaches to wind stress estimation
Following the work of Edson et al. (1998), many researchers now use a direct covariance method to calculate the wind friction velocity as 
5. Conclusions
Datasets spanning full open ocean conditions demonstrate that measurements of wave directional spectra and wind stress, along with bulk wave parameters and bulk winds, can be accurately made from the Wave Glider platform. In an ongoing upgrade, raw GPS and IMU data will be collected with a Microstrain GX4 sensor, rather than a Microstrain GX3 sensor, and a subset of the data confirms that a new sensor will supply raw data of similar quality for the GPSwaves algorithm. Future work on this topic would develop a spectral transfer function for the Wave Glider, such that the platform response and propulsion could be directly removed from wave and wind spectra.
Acknowledgments
Thanks to APL field engineers Alex de Klerk, Avery Snyder, and Joe Talbert for their help with the preparation, testing, and deployment of the Southern Ocean Wave Glider. Thanks to the captains and crews of all ships involved in these tests. Thanks to CDIP for providing excellent ground truth data from a consistently maintained database with publicly available software and documentation. Thanks to Liquid Robotics for integration and general support. Thanks to Seth Zippel and two anonymous reviewers for comments that improved the manuscript. Funding for the Southern Ocean work was provided by the National Science Foundation (PLR1558448). Funding for the other datasets provided by Liquid Robotics, Inc. (producers of the Wave Glider). Data are available online (http://faculty.washington.edu/jmt3rd/Waveglider/).
APPENDIX
Directional Moments from Cross Spectra
Diagram of the 
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
Diagram of the 
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0091.1
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