Spectral wave parameters from 11 platforms, measured during the recent Impact of Typhoons on the Ocean in the Pacific (ITOP) experiment, are intercompared. Two moorings, separated by ~180 km, were deployed in a section of “typhoon alley” off the coast of Taiwan for 4 months. Each mooring consisted of an Air–Sea Interaction Spar (ASIS) buoy that was tethered to a moored Extreme Air–Sea Interaction (EASI) buoy. EASI, the design of which is based on the hull of a 6-m Navy Oceanographic Meteorological Automatic Device (NOMAD) buoy, is validated as a 1D wave sensor against the established ASIS. Also, during this time three drifting miniature wave buoys, a wave-measuring marine radar on the Research Vessel Roger Revelle, and several overpasses of Jason-1 (C and Ku bands) and Jason-2 (Ku band) satellite altimeters were within 100 km of either the northern or southern mooring site. These additional measurements were compared against both EASI buoys. Findings are in-line with previous wave parameter intercomparisons. A corroborated measurement of mean wave direction and direction at the peak of the spectrum from the EASI buoy is presented. Consequently, this study is the first published account of directional wave information that has been successfully gathered from a buoy with a 6-m NOMAD-type hull. This result may be applied to improve operational coverage of wave direction. A high level of confidence is established in the ITOP wave data. Advantages and disadvantages of the different sensor types are discussed, which may be useful for the design of future field experiments.
The Impact of Typhoons on the Ocean in the Pacific (ITOP) field campaign took place in late 2010 within the Philippine Sea and was sponsored by the U.S. Office of Naval Research. ITOP included measurements made by moored buoys, drifters, gliders, aircraft, satellites, and research vessels, as well as extensive modeling efforts. Wave spectra and spectral parameters were derived from data recorded by several of these platforms. The platforms included three drifting miniature wave buoys (MWBs 41, 42, and 43), a dedicated X-band marine radar (MR) on the Research Vessel (R/V) Roger Revelle, Jason-1 (Ku and C bands) and Jason-2 (Ku band) satellite altimeters, and a pair of Extreme Air–Sea Interaction (EASI) (Drennan et al. 2014) and Air–Sea Interaction Spar (ASIS) (Graber et al. 2000) buoys at two mooring sites. The EASI and ASIS buoys at the northern and southern moorings will be referred to as EASI-N/ASIS-N and EASI-S/ASIS-S, respectively.
One of the scientific objectives of ITOP was to better understand the surface wave field under the forcing of typhoons. Toward this goal, this study critically evaluates wave sensors by intercomparison and by assessment against expectations based on previous studies. A thorough understanding of each sensor will support interpretation of the wave measurements and will therefore aid in subsequent analysis of tropical cyclone–generated wave fields.
Sensor comparison studies also play a critical role in advancing the state of wave science. The verification and validation of theoretical/empirical spectra and directional distributions, wave models, and remote sensing techniques depend on evaluation against in situ sensors. As such, all areas of wave science benefit from progress in understanding of wave measurements and differences among in situ sensors.
This study is compelling because of four unique factors: (i) We present evaluations of two new platforms: EASI buoys (Drennan et al. 2014) and MWBs (e.g., Herbers et al. 2012), and the MR (e.g., Nieto Borge et al. 1999; Reichert et al. 1999) under untested conditions (i.e., mobile MR). These platforms have not yet been extensively documented. (ii) There have been relatively few wave studies in the Philippine Sea. (iii) During the study period, variable environmental conditions were observed, including waves generated by tropical cyclones (TC) (e.g., Wright et al. 2001). (iv) It has been posited that the asymmetric Navy Oceanographic Meteorological Automatic Device (NOMAD) hull (boatlike shape), in which the pitch-and-roll response could be significantly different, would compromise any directional measurement (Teng 2002). In this paper we demonstrate a determination of mean direction and direction at the peak from the EASI buoys (which are based on NOMAD-type hulls) that agrees well with other platforms despite this prevailing wisdom. As far as the authors are aware, this is the first published account of retrieving directional information from a buoy with a NOMAD-type hull. Furthermore, this implies we might expect other buoys with NOMAD hulls to perform similarly.
The study presented here is based on the 2D frequency-direction spectrum E(f, θ). To derive spectra, different physical principles were applied to each platform. EASI buoys and the MWBs simultaneously measured three complementary properties of the sea surface and were therefore called single-point triplets (SPT) (Longuet-Higgins et al. 1963; Young 1999). In SPT analysis only a low-order estimate of E(f, θ) is derived; the first two directional moments are calculated directly from the cospectra and quadrature spectra as detailed in appendix A of Kuik et al. (1988). The MR analysis yields a wavenumber spectrum that is converted to the frequency-direction spectrum via the linear dispersion relation. In this study, ASIS measured only the 1D spectrum through the combination of a platform motion sensor and a capacitance wave gauge.
There is an established body of literature for wave sensor comparisons (Allender 1989; Anctil et al. 1993; O’Reilly et al. 1996; Graber et al. 2000; Wyatt et al. 2003; Pettersson et al. 2003; Hauser et al. 2005a; Collins 2012). To summarize, there has been relatively good agreement on the 1D variance spectra for the energy-containing range 0.1–0.2 Hz. Agreement outside this range of frequencies has been generally poorer (Allender et al. 1989), and mean spectral ratios have shown disagreement in excess of sampling variability (Krogstad et al. 1999). Bulk parameters derived from 1D spectra have compared well (bias <10%) within the available range of sea states (up to 10 m). While mean direction at the peak has usually agreed within 10°, sensors do not agree on mean direction across the entire frequency range. This is the standard upon which we will evaluate the differences seen in this study.
The next section will describe the platforms, the conditions encountered during the experimental period, and the methods involved in the comparisons. This is followed by a section that presents and discusses the main results of graphical spectral comparisons and quantitative parameter comparisons. The last section will conclude the paper with a summary of the findings and a discussion of implications.
a. Wave parameter calculation
Except for the satellite altimeters, the calculation of wave parameters is based on the 2D frequency-direction spectrum, E(f, θ). From E(f, θ), all other statistical details can be calculated, including the following:
We have used the full, unweighted spectral integral to calculate these parameters, in contrast to other comparison studies [e.g., O’Reilly et al. (1996) compared band-averaged parameters using the range 0.06–0.14 Hz]. Although this has shown to improve comparisons by reducing noise (e.g., Anctil et al. 1993), our philosophy is that it is better to compare parameters that Krogstad et al. (1999) identified as most important in describing sea state and are routinely reported by monitoring agencies.1 Also, these parameters were not calculated for each wave system separated in frequency and/or direction (i.e., partitioned spectra); this will have a negative effect on the agreement when significantly multimodal seas are present, but, in our cases, not so much to warrant the additional analysis. Table 1 gives information on the availability of each parameter from each platform.
The ASIS buoys are pentagonal spar platforms that ride waves with periods longer than ~8 s, and are relatively stationary relative to waves with shorter periods. The spar platform allows for multiple scientific instruments, the exact configuration of which can be catered to the objectives of an experiment. A typical instrument payload includes a capacitance wave wire array, wind, temperature, and current sensors with an Argos satellite uplink to report mean measurements. The weight and dimensions of ASIS (~1500 kg and ~12-m length, respectively) result in difficult but feasible seagoing operations.
The ASIS buoy was designed to provide observations of high-resolution directional wave spectra and was isolated from vertical mooring forces to improve the buoy response. Previous studies show that ASIS compares very well against more common wave sensors [i.e., National Data Buoy Center (NDBC) 3-m discus or Datawell Directional Waverider (DWR)] under a variety of conditions (Collins 2012; Drennan et al. 1998; Drennan et al. 2003; Graber et al. 2000; Hauser et al. 2005b; Pettersson et al. 2003). ASIS senses the local sea surface elevation with an array of eight capacitance wave wires. The outer array forms a pentagon with sides of 0.93 m and is complimented with a triangular inner array with sides of about 9 cm. The local sea surface elevations at each wave wire are transformed to Earth-referenced sea surface elevations by accounting for buoy motions2 (which are low-pass filtered at 1 Hz to decrease noise) (Anctil et al. 1994). The directional resolution depends on the number of functioning wave wires and the shape of the directional distribution. With the proper configuration, a minimum of three wave wires is needed to provide directional resolution similar to SPTs (Collins 2012). Although this buoy is well suited to sense directional waves, the quality and resolution of the measured directional spectra hinge on the performance of the wave wires. During ITOP, multiple wave wire failures on both ASIS-S and ASIS-N prevented measurement of the 2D directional spectrum. The remaining wave wires produced good quality 1D wave data similar to previous studies (e.g., Pettersson et al. 2003). Therefore, an individual wave wire was used to calculate 1D spectral parameters in this study.
Raw data were recorded at 20 Hz and processed in 30-min blocks. The surface elevation time series was detrended and a Blackman–Harris window was applied. A low-frequency cutoff was applied at 0.05 Hz and 15 elementary frequency bands were averaged to improve the spectral estimate.
More robust wave wire setups and alternatives that may withstand TC-strength conditions are currently being considered. The occasional overtopping of the buoy (or exceedance of the wire’s dynamic range) has a negligible effect on integral parameters (Collins 2012). Although not explored in depth here, the ASIS buoy is also able to sense short waves down to about 10 cm, below which scattering off the 20-cm columns becomes important.
The National Oceanic and Atmospheric Administration’s (NOAA) NDBC and the Canadian Marine Environmental Data Service (MEDS) have routinely used buoys with NOMAD-type hulls for measuring wind, 1D wave spectra, and spectral wave parameters for several decades (Schwab and Liu 1985; Shey et al. 1998). Although the EASI buoy also utilizes a NOMAD hull design, the commonalities with other NOMAD buoys end there. The EASI buoys are fully customized, experimental buoys that differ from the other NOMADs in mass (and center of mass), moorings, instruments, data acquisition systems, and data analysis techniques.
The lack of in situ air–sea measurements in extreme conditions motivated the design and construction of the EASI buoys. To increase the chances of recording quality data in severe TC conditions, two redundant systems are housed in separate watertight compartments. As a metocean platform, EASI allows for flexible experimental objectives by hosting a variety of air–sea instruments with multiple redundancies. The buoys are weighty (~3900 kg) and cumbersome (6 m × 3 m × 3 m). Deployment and recovery are only possible during very calm conditions (Hs < 2 m) with a very large and stable vessel (e.g., R/V Roger Revelle). Further information on the EASI buoy’s design and configuration during ITOP may be found in Drennan et al. (2014).
To measure directional waves, the EASIs were treated as a SPT (Longuet-Higgins et al. 1963; Young 1999), where the triplet includes sea surface elevation, east–west slope, and north–south slope. Therefore, all 6 degrees of freedom were recorded with a motion pack3 (local buoy reference frame) along with compass heading. The heave acceleration was tilt corrected (Anctil et al. 1994) and double integrated to produce a time series of sea surface elevation. The compass heading was used to transform the pitch-and-roll rate output to an Earth-fixed coordinate frame, and the result is integrated to produce north–south and east–west slopes (Steele et al. 1998). This process was slightly different for EASI-N and EASI-S because of technical reasons as outlined in appendix A. Similar to ASIS, the signals were recorded at 20 Hz and split into 30-min analysis blocks. EASI time series were treated to the same spectral analysis as ASIS with the additional calculation of cross spectra (cospectra and quadrature spectra) from the triplets. More details on wave sensing with the EASI buoy, as well as wave statistics during ITOP, may be found in Collins et al. (2014).
The MWBs are part of a new generation of inexpensive, expendable GPS directional wave buoys of convenient weight (<20 kg) and dimension (~0.4-m diameter). These are deployed by hand and not meant to be recovered. Although convenient, the life span of these buoys during the ITOP deployment was relatively short (~3, ~8, and ~20 days for MWBs 41, 42, and 43, respectively). It is possible to envision an experiment where the life span of the instrument is less of a factor, such as mass deployment of these in the track of a TC to learn more about the wind waves generated in each region of a TC. The MWBs are not a stable platform for external instruments, so these were used exclusively for wave measurements.
Like the EASI buoys, the MWBs were treated as SPT surface followers, but here a GPS sensor reported the vertical, north–south, and east–west displacement. Data analysis was performed on board the MWBs, and spectra and spectral parameters were transmitted via telemetry. The spectrum was reported from 0.000 to 0.398 Hz with irregular bandwidths. We compared the spectral parameters as reported, but we also recalculated Hs and Tm from the spectra to investigate discrepancies. Herbers et al. (2012) and the references within provide an introduction and verification of GPS technology as applied to ocean waves.
The X-band MR has been used for the retrieval of information related to oceanographic phenomena (e.g., surface waves, internal waves, winds, rain, currents, and bathymetry). MR works by transmitting microwave pulses and recording the backscatter intensity. The backscatter intensity is dominated by the Bragg scattering resonance mechanism. Bragg resonances are associated with short wind waves (~1.5 cm), which are about half the wavelength of the electromagnetic wavelength at grazing incidence. These systems can be based on preexisting ship navigation radars, but it is preferable for the radar to be dedicated for wave oceanographic purposes because of the differences in setup.
During ITOP, the MR data were acquired from the R/V Roger Revelle using a standard Furuno marine X-band radar operating at 9.4 GHz, horizontal-transmit horizontal-receive (HH) polarization, and grazing incidence. Radar images were sampled every 1.5 s, covering a range from 240 to 2145 m. Radar data were acquired with a grid size of 7.5 m in range and approximately 0.3° in azimuth. The MR’s range resolution was 10.5 m, which implies that surface waves must have a minimum length of ~20 m to be imaged by the MR. Since conventional MRs are not radiometrically calibrated, backscatter intensities were stored as values ranging from 0 (no backscatter) to 4095 (very strong backscatter). The commercially available Wave and Surface Current Monitoring System (WaMoS) II system served as the data acquisition system for the X-band MR on the R/V Roger Revelle. Data processing was performed separately with software developed at the University of Miami. More information on the MR and the WaMoS II system may be found in Nieto Borge et al. (1999) and Reichert et al. (1999).
The main advantage of the MR is the high-resolution, spatiotemporal measurement. The MR is able to derive a wavenumber spectrum about once every minute. To retrieve this information from MR data, a sequence of radar images is Fourier transformed, and the resulting 3D spectrum is filtered using the linear (small amplitude) dispersion relation and integrated over the frequency domain. The wavenumber spectrum of wave energy is calculated by applying an inverse modulation transfer function (Ziemer and Rosenthal 1993) to the image spectrum. A wavenumber spectrum is transformed to frequency-direction space through the dispersion relation (Young et al. 1985). In contrast to SPT systems, the directional resolution is much higher, so the MR is capable of resolving multimodal seas without data-adaptive methods. The Hs is retrieved by empirically fitting the signal-to-noise ratio (SNR) to in situ data; this process also provides scaling to the wavenumber spectra. Since our MR was installed on a ship, the most intense sea states are typically missed because of safety precautions.
The primary focus of previous MR studies has been to evaluate X-band radar capabilities from stationary platforms (Wyatt et al. 2003). Retrieval of wave parameters is sensitive to local conditions (i.e., low wind, low wave height, and rain) (Nieto Borge et al. 1999). Wave parameter retrieval from the MR on a moving platform presents additional challenges—in particular, horizontal ship motion and course changes during the radar image acquisition, image jitter due to compass or synchronization errors, and the dependency of wave and surface current estimates on the relative angle between look direction and wave direction as well as range (Lund et al. 2013, 2014). The SNR and mean period are acutely sensitive to these issues, which is why we only compare the MR retrieval of fp and θp. Solutions to moving platform issues are in development, and an evaluation of the full frequency-direction spectrum is planned as part of a future study. Although limited (see Table 1), this paper provides a needed evaluation of nonstationary MR wave parameter retrieval.
5) Satellite altimeter
Jason-1 and Jason-2 satellites flew nearly the same non-sun-synchronous, 66° inclined, 10-day orbits but on opposite sides of the Earth (5 days apart). Both Jason-1 and Jason-2 utilized versions of the Poseidon (2 and 3, respectively) radar altimeter, which operated in the Ku band (13.6 GHz) and C band (5.3 GHz) of the electromagnetic spectrum. The gradient of the radar echo return’s leading edge is physically related, though empirically fit, to Hs (Ménard et al. 2003). In this study we compare the average of Hs values sampled at 1 Hz along a 40-km track centered at the point of closest approach, which was typically six values (ground speed of 5.8 km s−1).
Thorough evaluation studies have previously been performed. For examples, see Durrant et al. (2009), Queffeulou (2004), Ray and Beckley (2012), and Zieger et al. (2009), and the references within. The satellite altimeters sample over a footprint that ranged from 2 to 12 km for seas of 0–15-m Hs. It is estimated that the accuracy (root-mean-square error) is about 0.25 m (Ray and Beckley 2012; Zieger et al. 2009). The obvious advantage of satellite altimeter measurements is worldwide spatial coverage, but this is at the cost of temporal resolution and, currently, only the retrieval of Hs is possible.
c. Study design
During ITOP there were two mooring sites, each of which hosted an EASI–ASIS pair. A 60-m-long, 13-mm-diameter wire rope tethered ASIS to EASI, which was moored to the seabed. Both mooring sites were located at a depth of ~5500 m. A single-point inverse catenary-style mooring system was employed with a scope (i.e., ratio of mooring length to water depth) of 1.26, which allowed EASI to follow the surface relatively unobstructed. The attachment point was a stainless steel yoke, the purpose of which was to further isolate EASI from mooring forces. A map of the area is shown in the left panel of Fig. 1, with the comparison area detailed in the right panel of Fig. 1. The ~3100-kg mooring anchors (locomotive wheels) were located at 19.63°N, 127.25°E and 21.23°N, 126.96°E (black triangles) approximately 740 km east of southern Taiwan. This amounts to a separation between moorings of ~180 km. Further details of the mooring components may be found in Drennan et al. (2014).
The area covered by the experiment was split into two zones, referred to as the northern zone (NZ) and the southern zone (SZ), formed by 100-km radii centered at each mooring location. The two zones are shown in Fig. 1 with dashed and dashed–dotted lines, respectively. Also in Fig. 1, MWB 41 (cyan dots) was deployed ~4 km south of the southern mooring. It drifted southeast, where it failed ~75 km from the southern mooring. MWB 42 (red dots) was deployed ~4 km southwest of the northern mooring. It drifted south, with the track forming an arc that bends toward the west. It eventually failed ~13 km southwest of the southern mooring. MWB 43 (green dots) was deployed ~10 km southwest of the southern mooring. It initially drifted west out of the SZ, and then north and entered the NZ, where it continued a counterclockwise path, coming within 16 km of the northern mooring before exiting the southeast side of the NZ. The R/V Roger Revelle’s ship track (magenta line) was dictated by daily experimental objectives; this included sensor deployment/recovery and ship courses designed to keep personnel safe in rough conditions. The vessel was very active, made many passes through the SZ, and made relatively fewer observations in the NZ. The satellite altimeter estimates of closest approach associated with different passes are shown with squares. We include a pass of Jason-1 in the comparison that is just outside the east-southeast NZ border. The average distance from the moorings to each of the mobile platforms can be found in Table 2.
In both the NZ and SZ, the EASI buoys operated continuously for approximately 4 months [described in full by Drennan et al. (2014)], endured the relatively close passages of four major TCs with significant wave heights up to 11 m, and received significant swell that radiated from a fifth TC. Figure 2 displays all of the comparison data from the NZ. The five major TCs that were observed by EASI-N (black dots in Fig. 2a) were the following: severe Tropical Storm Dianmu around 8 August [year day (YD) ~220], Typhoon Fanapi around 18 September (YD ~260), Typhoon Malakas around 28 September (YD ~270), Super Typhoon Megi on 17 October (YD ~290), and Typhoon Chaba around 27 October (YD ~300). The dates refer to the peak of the sea states recorded at the mooring sites as a result of the various storms, not the peak of storm intensity. ASIS-N (blue dots) was deployed following Dianmu. After ~40 days, during the pass of Fanapi, the tether linking ASIS-N to EASI-N failed. Initially, ASIS-N drifted freely to the northeast, but it eventually returned to the southwest, where it was recovered near the southern mooring. MWB 42 (red dots) was deployed on 11 August (YD 221) during the last part of Dianmu and was operational in the NZ for a little over 4.2 days. During this time the wave field was switching from the decaying wind sea, which emanated from Dianmu, to an underling swell system coming from the east, best seen in Tp and θp. MWB 43 (green dots) drifted into the NZ around 11 August (YD 229) and was active for 4.5 days during relatively mild sea states. The MR (magenta dots) recorded conditions during Dianmu and after the peak of Chaba. The maximum Hs measured by the altimeters (squares and diamonds) was 5.9 m as a result of the timing of the passes, which missed the peak storm periods. All measurements appear consistent with the exception of the MWB measurements of Tm, which clearly show longer periods than those of ASIS-N and EASI-N.
In Fig. 3, the comparison data for the SZ is displayed and the TCs observed by EASI-S (black dots) are noted in Fig. 3a. ASIS-S (blue dots) was deployed right before Dianmu and recorded for over 72 days when on 22 October (YD 295), during Megi, it broke free of its tether and required recovery. MWB 41 (cyan dots) was deployed 4 August (YD 216) just as the seas from Dianmu were increasing. It was operational just under 3 days and failed just before the peak of Dianmu. MWB 43 (green dots) was deployed just before the peak of Dianmu and drifted out of the SZ about 1.5 days later. MWB 42 (red dots) drifted in from the NZ around YD 226 and observed relatively mild conditions for the nearly 3 days it was operational in the SZ. The MR (magenta dots) collected measurements during (but not during the peaks of) Dianmu, Fanapi, Megi, and Chaba. The MR measurements captured a clear shift in peak wave systems at the start of Fanapi on YD 257. Again, the altimeter passes (squares) miss the peak of the storms, but Hs up to 3.8 m was measured. Higher wave heights were involved in the comparison for both ASIS-S and the MWBs relative to the NZ. Measurements appear consistent save the higher Tm as reported by the MWBs.
The length of 100 km is a relatively large separation distance for wave comparisons, but the mean EASI-MWB difference in Hs was found to be independent of separation distance up to 100 km (not shown). In fact, the mean distance between sensors (Table 2) was actually much less than 100 km. The study site was well suited to minimize these potential differences. The experiment took place in the open ocean in very deep water. The longest surface waves would not be affected by the bottom, thus improving the chance of spatial homogeneity. Using the method of Ambe et al. (2004), it was determined that the currents at the mooring locations were mild with a mean (σ) current speed of ~0.1 (~0.1) m s−1, so that the spatial variability of wave conditions due to wave–current interaction is much less than it would be along a coast, continental shelf, or in a strong western boundary current. So, the dominant processes responsible for spatial variability noted in other studies (Ashton et al. 2013) are not at play here. Therefore, spectra and spectral wave parameters are directly compared with homogeneity implicitly assumed. We acknowledge this assumption was questionable during TC forcing when there may have been strong spatial dependence of wave parameters. However, only the comparisons with MWB 41 and MWB 43 in the SZ are affected by TCs at distance to the moorings, which is discussed further in the results.
d. Analysis: Sensor intercomparison techniques
The ASIS buoy would have acted as the wave measurement standard, but it was not active for the entire duration of the experiment. So, we rely on EASI as the ground truth for comparison. To justify this, we present comparisons between EASI and ASIS before other comparisons. Given a high level of agreement, differences between other platforms and the EASI buoys will be interpreted as errors. Additionally, ASIS did not resolve directional wave fields, and EASI has never been verified as a directional sensor. Therefore, differences in θm and θp are interpreted with caution.
The comparisons in this study follow the recommendations made by Kuik et al. (1988) for comparing data based on SPT analysis. We also follow the recommendations of Krogstad et al. (1999) for the comparison and interpretation of directional and nondirectional wave data. Our comparisons include an estimate of the sampling variability, so that variability in excess of the sampling variability may be interpreted as real differences between sensors.
Quantitative comparisons were performed by linearly interpolating the EASI data to match the sampling schemes of the other platforms. The exception to this was the EASI–MR comparison, where the very dense MR data were linearly interpolated to the sampling scheme of EASI. Specific quality control measures can be found in appendix B. The maximum likelihood (ML) regression was chosen to produce a fit between the EASI data and the other platforms’ data because all platforms were assumed to suffer measurement errors (Krogstad et al. 1999). Tables 3–5, which describe comparisons for nondirectional data; report the number of data points the comparisons are based on (number of points); ML fit parameters of slope and intercept [i.e., EASI = (slope) × platform + intercept]; correlation coefficient (R2); mean difference (bias); standard difference (std); coefficient of variance (COV); percentage of data points that lie within a 90% confidence interval given the stated COV (P90) ignoring bias; and percentage of data points that lie within a 90% confidence interval given the stated COV including bias (P90b). COV was calculated from ASIS during a stable period by dividing the estimated mean by the standard error (σ). P90 and P90b are not estimated for altimeter data, where the data variance was different for every measurement and was not a monotonically increasing function of Hs. Table 6 describes comparisons of directional data and reports measures based on directional statistics (Berens 2009; Jones 2006a,b). These measures include the number of data points the comparisons were based on (number of points), mean directional difference (biasθ), directional standard difference (stdθ), and directional association measure (Rθ).
3. Results and discussion
a. Average S(f) and θ(f)
In this section we present average frequency spectra S(f) and mean direction θ(f), as measured concurrently by EASI, ASIS, and MWBs. Many case studies (CS) were performed, each with different wave heights, durations, MWB involved, and distances from MWB to either the northern or southern mooring (Table 7). Here we present three case studies, but these are representative cases, so the discussion that follows is quite general. All S(f) and θ(f) were averaged over short periods (3–14 h) when the spectral parameters were relatively stable. This reduced the differences due to sampling variability. This variability was represented by the standard error bars in Figs. 4b,c; 5b,c; and 6b,c.
First, some general remarks on the shape of S(f) in Figs. 4a,b; 5a,b; and 6a,b. The MWBs have a very low-frequency peak centered around 0.008 Hz that is on the same order as the wind-wave peak (CS I) or even more energetic (CS II). These are obviously spurious peaks (there has not been evidence for energy in this band on the order of the wind-wave band; e.g., Webb et al. 1991). It is apparently an artifact of GPS satellite motion that is mapped into the displacement spectrum (Doong et al. 2011). This artificial peak is a source of error and can be filtered (Waseda et al. 2011). We recalculated Hs and Tm from filtered spectra and compared it to the reported Hs and Tm. Evidently this peak was filtered during the MWB onboard analysis for Hs but not for Tm. This fact accounts for some of the observed bias in MWB Tm.
In CS I and CS III, EASI and/or ASIS exhibited low-frequency peaks, near 0.05 Hz, that are noise (most likely from the accelerometers). Typically in the band of 0.05–0.09 Hz, S(f) was stratified with ASIS > EASI > MWB. Although the MWB generally measured slightly less energy around the peak, there was good agreement in the spectral shape from all three buoys in the frequency range of 0.10–0.20 Hz. From around 0.22–0.30 Hz, the spectral energy in MWB tended to drop from near 100% of ASIS or more to ~30% of ASIS and stay at this level from 0.30 to 0.40 Hz. EASI tended to give slightly higher energy compared to ASIS in the 0.25–0.45-Hz band, at which point the energy in EASI falls off because of the size of the buoy. Most spectra are peaked, similar to the Joint North Sea Wave Project (JONSWAP) spectra (Hasselmann et al. 1973) and show an equilibrium range close to f−4. ASIS holds this near-f−4 equilibrium range from 0.13 to 4.00 Hz (not shown). Since the MWBs were apparently unable to accurately reproduce the spectral shape after 0.20 Hz, data from these buoys are not ideal for studies of the equilibrium range. The ±σ of the spectral estimates from the different buoys were of similar magnitude. Very few of the cases were pure wind seas. CS II (Fig. 5) clearly shows three simultaneous wave systems, and EASI and ASIS agreed on the location of all three peaks. MWB agreed on the location of the first two peaks, but the location of the third was downshifted.
Since a low-frequency cutoff was applied at 0.05 Hz to motion signals in EASI, its measurement of θ(f) and S(f) below this range is meaningless. Above 0.05, MWB and EASI tend to agree on the shape of θ(f) within the sampling variability. Near the peak of the spectrum, the agreement between the two tends to improve and the variability becomes minimal. The variability tends to increase as the frequency increases, particularly for the MWB.
Power transfer function (PTF) relationships for S(f) between EASI and ASIS were derived in Drennan et al. (2014), but we have chosen not to broadly apply these PTFs here for two reasons: (i) the PTF may be a function of sea state, environmental forcing, and unknown mooring forces; and (ii) any PTF will not significantly improve the spectral parameters (the current level of agreement is already high).
In the energy containing frequencies, typically 0.10–0.20 Hz, the sensors are in good agreement, but the agreement decayed outside of this band. This is not surprising, as it has been documented in previous experimental studies (Allender et al. 1989; Collins 2012). In addition, it has become evident that many operational in situ sensors report spectra with significant inconsistencies (Jensen et al. 2011). Presently, many different devices are able to produce an estimate of 1D and 2D wave spectra, but the exact accuracy of these measurements is unknown (Forristall 2000). The status quo for wave measurements is acceptable when only considering spectral parameters, but it is becoming more important to understand the accuracy of measured spectra. Although very consistent measurements have been made by stationary wave wires, ASIS buoys, and DWRs, there is no absolute reference for the wave frequency spectrum (let alone wavenumber or 2D directional spectra) (Jensen et al. 2011). Because of improvements in spectral models, theoretical models, and remote sensing techniques, the wave science community needs either to determine an absolute reference or to try to quantify the limitations of measuring wave spectra without an absolute reference. This way we will be able to better understand the accuracy of in situ (and remote) wave measurements.
b. EASI versus ASIS
Measurements of Hs, Tp, and Tm from EASI were compared against ASIS in Fig. 7, and the accompanying statistics are in Table 3. This was the most comprehensive comparison performed with 5162 data points and Hs up to 5 m, and, crucially, the agreement is excellent. The combined percent bias, std, and R2 for Hs were ~3%, 0.1, and 0.99, respectively. Separately, the bias was negligible in the SZ and acceptable (~7%) in the NZ. For Tp, the combined percent bias was negligible, std was 1.3, and R2 was 0.71. The correlation was less strong in the NZ compared to the SZ. Although Tp is a commonly utilized parameter, it is not a very stable temporal metric of the sea state. This lack of stability was reflected in the relatively low correlation coefficients and higher standard differences (Tables 3, 5). The comparisons for Tm showed also excellent agreement with combined percent bias, std, and R2 at ~0%, 0.3, and 0.95, respectively. We can only speculate, but the differences between NZ and SZ may be associated with a combination of factors, including slightly different wave wire calibrations and differences in unknown mooring forces.
Because of the high level of agreement, it is appropriate to designate EASI as ground truth for comparisons against the other platforms, and the level of agreement between ASIS and EASI will act as the standard for evaluating these comparisons in the following sections.
c. Remaining platforms versus EASI
1) Significant wave height
The statistics for Hs may be found in Table 4, and the scatterplots for the NZ and SZ are the top-left and top-right panels of Fig. 8, respectively. The agreement between EASI and the various sensors was very good in general, with most R2 values greater than 0.90. The agreement declined slightly for the comparisons between the EASI buoys and some of the satellite passes. For our study, the Ku band on Jason-1 outperformed the C band in both zones. In the NZ Jason-2 outperformed Jason-1 but was the poorest performer in the SZ. This apparent poor performance is particularly dependent on one point (a pitfall of few data points) and the statistics are much improved when this point was removed from the comparison, as can be seen in EASI-S/Jason-2 Kub, Table 4. Since there was a limited number of data points for comparison, the quality of the comparison statistics was negatively impacted. The σ (the altimeter data) was variable, as shown by the wide range of error bar width (±σ) in Fig. 8.
The notable exception to good agreement was EASI-S versus MWB 43 with R2 = 0.40. This same comparison had the highest bias and a high std. The comparison period was during the peak of Dianmu. TCs are typically associated with strongly inhomogeneous wave fields, which are dependent on the storm quadrant (Black et al. 2007; Holthuijsen et al. 2012; Wright et al. 2001). As a result, it is likely that there was strong spatial variability in Hs as the MWB was forced eastward out of the SZ. However, the COV during the comparison, estimated for points where the mean was relatively stable, was 0.06 for EASI-S, whereas for MWB 43 it was 0.10. The COV for MWB 43, estimated from other times in the NZ, was more regular (~0.06). Furthermore, a look at the combined scatterplots, Fig. 8, shows the scatter increasing as a function of Hs and looking quite regular for all comparisons save the MWB 43 (green dots). The later comparison of EASI-N with MWB 43 during lower wave heights (<2 m) was much improved if still slightly biased. This was the highest Hs comparison for any MWB, so the low R2 and high std were a consequence of increased scatter associated with the larger wave heights. It may also be possible that the MWBs have increased error for wave heights greater than 2 or 3 m, but more data in wave heights over 3 m are needed for more definite conclusions.
2) Peak period
Table 5 shows the comparison statistics for Tp, and the scatterplots are in the second row in Fig. 8. The Tp is a highly variable metric, which manifests as lower values of R2 and higher values of std. Some of the variability was due to the discrete nature of the peak period parameter (i.e., each platform had different frequency resolutions that depend on the details of the spectral analysis and that became coarser as the period became longer). The P90 statistic was close to or greater than 80% (except MWB 43 in the NZ and MWB 42 in the SZ); as a result, most of the variability can be explained by the inherent sampling variability of the parameter. The comparisons of Tp were largely in-line with previous studies (Collins 2012).
There were two notable exceptions: (i) comparison of EASI-N with MWB 43 and (ii) EASI-S with MWB 42. If the spectra have multiple peaks in frequency space of nearly the same energy, then uncertainty in the spectral estimate causes the peak frequency to jump back and forth between these peaks. Bimodal seas of this nature occur sporadically throughout the experiment (e.g., Fig. 9), but these two comparisons are particularly affected. Furthermore, the two comparisons were over relatively short periods that were dominated by bimodal seas, which degraded agreement in a way unrelated to sensor performance.
3) Mean period
The Tm is a less variable temporal metric than Tp because it is an integral parameter and perhaps better suited for comparison. In contrast to EASI/ASIS comparisons, the agreement observed between the EASIs and MWBs was somewhat problematic (third row in Fig. 8). The MWBs were found consistently biased (~1-s combined average) high over the EASI measurements, but the stds were only slightly higher (not shown). This was the result of the persistent low-frequency peak in the MWB data around 0.008 Hz. Table 6 shows the results filtering out this low-frequency peak and repeating the comparison. The bias was much improved but still quite high (~0.4-s combined average). Remember Tm is an integral over the spectrum weighted by the frequency [Eq. (5)] (i.e., higher frequencies are more important). So, for the MWBs, this bias was most likely due to two combined factors: (i) the drop off in spectral energy after 0.20 Hz and (ii) the high-frequency cutoff at 0.38 Hz (see Figs. 4–6). Both of these attributes effectively shifted Tm toward longer waves. To this point, recalculation of Tm from EASI to match the frequency range of the MWBs further improved this bias (~0.1-s combined average). The poorest comparison was EASI-S/MWB 41a in Table 6. This was a result of the period (first six 30-min points) shortly after the deployment of MWB 41. Inspection of the spectra during this time showed a severe drop-off in energy in the high frequencies (not shown). The reason for this is currently not known. EASI/MWB 41b in Table 6 displays the Tm comparison statistics after removing the first six points in the MWB time series. The resulting statistics are more in-line with the other comparisons. After accounting for bias, almost all of the variability is due to sampling variability.
4) Peak direction
Table 8 shows the statistics for the comparison of θp. The level of agreement was surprising considering the supposed difficulties in determining the parameter with a NOMAD-type hull. In the NZ, the bias found was well within the ±10° demonstrated in previous studies (Allender 1989). The bias for the comparisons between EASI-S and MWB 43 and MR was just outside of the range, but it was still reasonably modest (17.3° and −11.5°, respectively) given the much higher sea states recorded and the degree of spatial separation. The directional associations were very high; five out of the seven comparisons produced Rθ greater than 0.90.
The comparison between EASI-N and MWB 42 (Table 8, EASI-N/MWB 42a) produced the lowest Rθ value (0.66) and the highest stdθ value (47.1°). The disagreement is due to seas that were changing direction from a decaying system from the southwest and to another system from the northeast over the course of 1.5 days from YD 221.5–223.0. In Fig. 9, the top panel shows the evolution of S(f) from EASI (color indicating energy on a natural log scale) with Tp from EASI (black dots) and MWB 42 (red dots). The bottom panel shows evolution D(θ) calculated by integrating E(f, θ)4 over frequency space and is shown on a natural log scale with θp from EASI (black dots), θp from MWB 42 (red dots), and wind direction (Drennan et al. 2014; Potter et al. 2014, manuscript submitted to J. Atmos. Sci.) (white dots). The two systems are separated direction space; however, except for a short period around YD 222.5, the systems are not as separated in frequency space. Hence, the comparison for Tp during this time remained relatively unaffected by these conditions. On the other hand, if θp from YD 221.5–223 is removed from the comparison, then the statistics are much improved with Rθ = 0.90 and stdθ = 25.0° (Table 8, EASI-N/MWB 42b). The bottom two rows in Fig. 8 show the combined scatterplot for the NZ and SZ. Most of the data are well behaved; the gray dots correspond to the times with bimodal seas. The effects of bimodal seas were also evident in the SZ (see Figs. 2d, 3d). Again, the statistics calculated during multimodal seas spuriously detract from agreement.
4. Concluding remarks
Spectra and spectral wave parameters from various platforms are reported from the 2010 ITOP experiment. The measurements from two EASI buoys, at separate moorings, were compared against other sensors within 100 km, including two ASIS buoys, three MWBs, the X-band MR, and Jason-1 (Ku and C bands) and Jason-2 (Ku band) satellite altimeters. The experimental setup was not ideal for comparing wave sensors. The EASI and ASIS pairs were stationary within the scope of the mooring line with minimal separation (≤60 m), but the MWBs were drifting at the mercy of the wind, waves, and currents; the MR was bound to the ship track; and the satellite pass locations were predetermined. The spatial separation between sensors was at times large, which increased the likelihood of spatial inhomogeneity, and we suspect especially increased spatial variability during comparisons that occurred during the passage of Dianmu. The EASI buoy was not designed as a directional wave sensor. Multimodal seas in frequency and direction space occurred throughout the comparison periods. Given all this, fair agreement was posited tentatively. Defying expectations, the agreement observed may be characterized as good and in accordance with previous comparison studies (Allender 1989; Collins 2012).
Measurements of Hs, Tp, Tm, and θp were consistent and within the range of differences found in previous studies (bias <10%) (Allender 1989; Collins 2012), but there were a few exceptions. These exceptions were most likely due to natural complications, such as increased spatial variability and the presence of multimodal seas for Hs and θp, respectively, not sensor errors. The correlation coefficients for Tp were not high, but this was due to the innate sampling variability of the parameter. The agreement was much improved using the mean period parameter, although the MWBs exhibited high bias. This bias was mostly due to a low-frequency peak in the spectra, and when the low-frequency peak was removed, the bias was improved by ~0.6 s on average. Most of the remaining bias was due to a drop-off in high-frequency energy around 0.25 Hz and a high-frequency cutoff at 0.38 Hz.
Although we have found good agreement on spectral wave parameters, we simultaneously compared spectra reported by EASI, ASIS, and MWB sensors to reveal good agreement on S(f) only within energetic bands of the 1D wave spectrum, not across the entire range of frequencies. Unresolved discrepancies in the spectral shape call for renewed attention to the general accuracy of in situ spectral measurements. The authors believe mooring forces may play a role. In the future, it would be useful to measure mooring forces and to better understand their influence on buoy response and in turn wave measurements.
Although neither EASI encountered the heaviest seas from the ITOP TCs, both endured quite extreme conditions (Hs in excess of 10 m and winds up to 28 m s−1, with instantaneous gusts near 40 m s−1) with negligible structural damage. On the basis of robustness alone, these buoys can be said to have been successful. But the main result here is that the robust design of EASI did not compromise the quality of the compared wave parameters. In particular, θm was consistent with the MWBs and θp compared well despite the asymmetric hull. We interpret the good agreement between EASI and the other sensors as a validation of the EASI buoys’ capability to resolve θp, at least within the expected range of error (±10°) (Allender et al. 1989). It may be advised to start reporting θp from all operational NOMAD stations. This may immediately increase the coverage of wave directions around the world. At NDBC alone, there are 17 NOMAD buoys, which could nearly double the number of operational buoys that report wave direction (23) (http://www.ndbc.noaa.gov/wstat.shtml). Furthermore, we have established confidence in the in situ wave measurements during the ITOP experiment and look forward to further analysis of data from the EASI buoys.
From the comparisons, we can conclude that this was an encouraging sea trial for the MWBs. Their performance in high sea states needs to be investigated further, and the spectral shapes do not agree with EASI and ASIS, which lead to significant bias in Hs and Tm. The agreement varied between each MWB, which may be a result of the different separation distances and different conditions encountered. The disagreement was especially poor for MWB 41, and it is not possible to rule out individual sensor-dependent differences. More comprehensive comparisons are needed to draw firm conclusions.
Parameters derived from the MR were much less variable than the other in situ platforms (this is most obvious in Figs. 2b, 3b). For the two parameters considered, the comparisons with the EASI buoys were fair for Tp (combined percent bias of −5% and std of 1.2) and good for θp (combined biasθ of 9° and stdθ of 33°). Peak parameters may be reliably retrieved, even while the spectral shape and SNR have strong range and azimuthal dependency (Lund et al. 2014).
Our conclusions on satellite performance are limited by the small number of data points and the degree of separation for some of the passes. It is evident that the satellite-derived Hs is more variable than the in situ sensors and that it may appear inconsistent if only a few points are available. A proper comparison with altimeter Hs requires a long-term in situ sampling at multiple locations.
Comments from several anonymous reviewers very much improved the manuscript, and their time and attention are very much appreciated. This work would not have been possible without the expert technical support of Mike Rebozo (RSMAS). Big thanks to Neil Williams for comments on an early draft of this manuscript and for the many hats he wore throughout ITOP. We are indebted to Eric Terrill (SIO) for mini wave buoy data, Hitoshi Tamura (RSMAS/JAMSTEC) for current estimations, Mike Caruso (CSTARS) for satellite data, and Joe Gabriel (EC) for technical services. Thanks to the NTU crew on the ground in Kaohsiung. Thanks to Mike Ohmart and Avery Snyder (APL-UW) for the tremendous help with two ASIS recoveries. Thanks to the captains and crew members of the R/V Roger Revelle, and the WHOI mooring operations team. Funding provided by U.S. Office of Naval Research Grant N00014-09-0392.
Transformation to Earth Reference Slope
The method is based off the work of Steele et al. (1998) and Teng et al. (2004). According to these references, integrated pitch and roll from angular rate sensors are only a convenient approximation to the true system mentioned above. Pitch P and roll R in the buoy coordinates are related to three signals from strapped-down orthogonal angular rate sensors—ω1, ω2, and ω3—by the following system of equations:
One may apply a small angle approximation to get
An improvement would be solving the system of equations for and , but there are two equations and four unknowns (P, R, , and ). Steele et al. (1998) advocates an iterative method where one would (i) start with the small angle approximation (A6) and (A7), (ii) integrate via FFT to get an approximation for P and R, (iii) plug into (A4) and (A5), and repeat (ii) and (iii) until the correlation with the previous results changes very little (they claim that three iterations worked well). We found that the FFT integration of the signals amplified low-frequency noise and that iteration exacerbated the problem. We opted to forego the iterative process and use the small angle approximation directly.
To convert from buoy reference P, R, and azimuth (compass heading) A to sea surface slope in the east–west direction ηx and sea surface slope in the north–south direction ηy one applies the following geometric conversion:
For EASI-N, we use the process given above, but in EASI-S there was a loss of one component of the compass signal. Luckily, there were redundant compass component signals recorded on a different data acquisition system. Because of a nonlinear clock drift between the two data acquisition systems, a high-frequency compass signal could not be recovered, but a 30-min average azimuth was found to be accurate. Therefore, we skipped the steps in this appendix altogether and proceeded to the processing detailed in appendix A of Kuik et al. (1988). Afterward, the direction at the peak was adjusted by the azimuthal direction. Processing in this way assumes that there is very little azimuthal drift over the course of the 30-min processing time, which we found to be an appropriate assumption for an EASI buoy. By processing EASI-N with both methods and comparing, we found that calculating direction at the peak was not sensitive to the method chosen.
Platform-Specific Quality Control Measures
During mild sea states (Hs ≤ 1.5 m), spectra may exhibit several unrealistic peaks due to low signal-to-noise ratio. We have avoided discarding data points below a minimum Hs threshold. As a result, there were some isolated Tp data points that needed to be addressed (the integral parameters remain unaffected). We interpolated through very high period (Tp ~18 s) points, as reported by EASI-N (7 of 5481 points). All cases involved very mild sea states (accelerometer buoys have low fidelity for long, low waves).
There is also some intermittent high-frequency noise in the ASIS-S spectra. High-frequency noise affects the calculation of Tm much more than Hs and Tp, which typically remain unaffected. We only treat the extreme cases (28 of 3383 points) in which the difference between EASI and ASIS was greater than 4 times the standard deviation of the mean difference.
MWB 41 reported an extremely high Tp of ~25 s, which was probably an instrument error (1 of 56 points) for reasons as follows. Although it is possible to find high periods in the Pacific (~20 s), the aforementioned value is an extreme measurement for this buoy (i.e., neglecting this point the range is 5.7–10.7 s, with a mean of 9.5 s and a σ of 2.4 s, making the point outside 6.9σ). ASIS-S twice reported very high Tp values that are difficult to explain. They are likely due to some errors after considering 1) surrounding values are much lower and 2) EASI-S reported negligible spectral energy at those frequencies (2 of 3383 points).
Retrieval of MR wave parameters is sensitive to rain among other factors (e.g., low wind speed, low wave heights, ship movement). Although preprocessing techniques have been developed to identify most of the erroneous data points (Lund et al. 2012), three 30-min measurements of Tp and θp (3 of 503) were discarded because the values were unreasonably far (>10 standard deviations, σ) from adjacent measurements. In all, a total of 47 values, each lasting 30 min, were deemed defective and therefore replaced by a linearly interpolated value.
Current affiliation: Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi.
Current affiliation: Woods Hole Group–Houston, Stafford, Texas.
For example, the U.S. National Oceanic and Atmospheric Administration’s National Data Buoy Center, the Canadian Marine Environmental Data Service, the Coastal Data Information Program, the Joint Technical Commission for Oceanography and Marine Meteorology, etc.
The motion package consisted of Columbia Research Laboratories, Inc. SA-307HPTX triaxial linear accelerometers, three orthogonally oriented Systron Donner Inertial Division GCI-00050–100 rate gyroscopes, and a PNI Sensor Corporation TCM-2 compass.
The motion packages on the EASI buoys were essentially identical to the setup on the ASIS buoys with the exception of the rate gyroscope models, which were model SDG1000 in the south and model QRS-11 in the north.
Estimated using the maximum entropy method (Lygre and Krogstad 1986).