Surface Directional Wave Spectra Research Articles

A method for constructing directional surface wave spectra from ICESat-2 altimetry

Abstract. Sea ice is important for Earth's energy budget as it influences surface albedo and air–sea fluxes in polar regions. On its margins, waves heavily impact sea ice. Routine and repeat observations of waves in sea ice are currently lacking, and therefore a comprehensive understanding of how waves interact with sea ice and are attenuated by it is elusive. In this paper, we develop methods to separate the two-dimensional (2D) surface wave spectra from sea-ice height observations made by the ICESat-2 (IS2) laser altimeter, a polar-orbiting satellite. A combination of a linear inverse method, called generalized Fourier transform (GFT), to estimate the wave spectra along each beam and a Metropolis–Hastings (MH) algorithm to estimate the dominant wave's incident angle was developed. It allows us to estimate the 2D wave signal and its uncertainty from the high-density, unstructured ATL03 ICESat-2 photon retrievals. The GFT is applied to re-binned photon retrievals on 25 km segments for all six beams and outperforms a discrete Fourier transform (DFT) in accuracy while having fewer constraints on the data structure. The MH algorithm infers wave direction from beam pairs every 25 km using coherent crests of the most energetic waves. Assuming a dominant incident angle, both methods together allow a decomposition into 2D surface wave spectra with the advantage that the residual surface heights can potentially be attributed to other sea-ice properties. The combined GFT–MH method shows promise in routinely isolating waves propagating through sea ice in ICESat-2 data. We demonstrate its ability on a set of example ICESat-2 tracks, suggesting a detailed comparison against in situ data is necessary to understand the quality of retrieved spectra.

Coastal Data Information Program: advances in measuring and modeling wave activity, climate, and extremes

ABSTRACT The Coastal Data Information Program (CDIP) provides wave data to the public in near real-time, maintains an operational wave model for the California coast, and is engaged in ocean wave research on a global scale. CDIP’s array of moored wave buoy stations are instrumented with Datawell Waveriders. CDIP’s recent work to improve monitoring capabilities for directional surface wave spectra, surface current, and temperature is described. This includes data quality assurance and control, real-time alerts, telemetry and dissemination information technology infrastructure and methodology, data visualization tools, and mooring and instrumentation innovation. CDIP’s goal is to maximize data reliability, availability, accuracy, and precision. Validation of commonly used wave models – operational, hindcast, and forecast – with CDIP data is automated to provide assessments of relative skills at a variety of coastal locations and wave conditions. Wave heights measured by the buoys typically exceed modeled heights during the most energetic events, such as hurricanes, nor’easters, and bomb cyclones. In a practical validation example, the global wave model used to drive CDIP’s California coastal wave forecasts was recently changed, based on comparisons against buoy data. Forecast performance has improved for swell events, which are a challenge to model accurately in the Southern California Bight.

Using Axial Base cabled array sensor data to study the prediction of second-order pressures from nonlinear surface wave interactions associated with microseisms

There are currently no published experimental measurements of second-order pressures in the water column from nonlinear surface wave interactions. Microseism researchers have focused on predicting and measuring microseisms directly without measuring second-order pressures in the water column. We considered several Ocean Observatory regional cabled arrays as sources for water column measurements to compare with analytical model second-order pressure predictions based on hindcast directional wave spectra. We selected the Axial Base cabled array for its location and suite of instruments including two hydrophones, 3D velocity sensor, and seismometer near the seafloor. Here we present results for predicted second-order pressures along with hydrophone measurements at the Axial Base site over different times of a year (2019–2020) to demonstrate a correlation. Validating a prediction model for second-order pressures based on directional surface wave spectra using the OOI cabled array sensor data could spur development of wave energy harvesting devices in the deep ocean and other applications.

Winds, Waves, and Turbulence on a Shallow Continental Shelf during Passage of a Tropical Storm

AbstractMeasurements of collocated fields of atmospheric forcing, surface waves, and mean and turbulent velocities associated with passage of Tropical Storm (TS) Barry over the U.S. Navy Tower R2 on the Georgia continental shelf are presented. A vertical-beam ADCP enables computation of directional surface wave spectra and hence of directional Stokes functions of depth and time, as well as mean (including tidal) and turbulent velocities throughout the water column. Full-depth turbulent velocity and backscatter structures observed during TS Barry are determined to be Langmuir supercells (LS). The LS appear in the present observations and in similar observations from a shallower site only when a surface growth rate g* exceeds a critical value, providing a means of predicting how deep an unstratified water column must be before LS will not be expected. When observed, LS structures at Tower R2 are less organized than archetypical LS structures: we suggest that this result is due primarily to smaller near-bottom growth rate in the deeper water column. Despite g* values above the critical value, and appropriate values of Langmuir and Rayleigh numbers, full-depth velocity/backscatter structures disappear completely for a time between the two wind maxima associated with the TS, as wind veers rapidly clockwise with eye passage to the west of Tower R2. From the observations, the most likely explanation for this hiatus is decreased wave breaking during the period of wind veering, reducing surface supply of “effective” vertical vorticity that dominates generation of Langmuir circulation (LC). This result has significant implications for LES modeling of LC.

Directional Surface Wave Spectra from Point Measurements of Height and Slope

AbstractWe describe here a method for recovering directional ocean surface wave spectra obtained from height and slope measurements made over a small area, the iterative deconvolution method (IDM). We show that IDM is a more reliable method for estimating directional wave spectra than more common spectral estimation techniques by comparing it with the widely used maximum entropy method (MEM). IDM is based on the observation that pitch–roll buoys produce directional spectra that are the true spectra convolved with an angular windowing function and are therefore much broader than the true spectra. We test IDM against simulated data and find that it does a better job of retrieving the known input spectra than does MEM, which often produces false double peaks or incorrect angular widths. We compare IDM recoveries to spectra obtained using a nonstandard processing technique, the wavelet directional method (WDM) on data from a compact array of wave staffs on Lake Ontario. We find that IDM produces directional wave spectra very nearly identical to those obtained using WDM, verifying both techniques. Finally, we processed standard NDBC buoy directional spectra and showed that IDM recovers ocean wave spectra that narrow in the Strait of Juan de Fuca and that follow a changing wind in the expected manner. Neither of these phenomena are reliably obtained using MEM due to its tendency to produce false bimodal peaks and peaks that are too narrow.

Assessment of the temporal and spatial dependence of reverberation mechanisms for KOREX-17

Mid-frequency reverberation data were obtained over a 9-day period off Geoje Island, Republic of Korea, complemented by transmission loss and backscatter measurements. The reverberation data were collected using the Autonomous Reverberation Measurement System (ARMS), a benthic lander with a source and receive array mounted on a rotation stage in order to collect reverberation data as a function of bearing angle. The ARMS was repeatedly deployed in roughly the same location over the course of the experiment. The surficial sediments close to the ARMS are known to be composed primarily of mud with occasional rock outcrops. Beyond a range of 2 km, the sediment composition is uncertain and a geoacoustic measurement survey has been planned to collect additional data in this region. Using contemporaneous measurements of the sea surface directional wave spectrum and the currently limited geoacoustic data, modeling is used to estimate the relative importance of sea bottom and surface reverberation. [Work supported by of the Office of Naval Research.]

Airborne Rain-Rate Measurement with a Wide-Swath Radar Altimeter

Abstract The NOAA Wide-Swath Radar Altimeter (WSRA) uses 80 narrow beams spread over ±30° in the cross-track direction to generate raster lines of sea surface topography at a 10-Hz rate from which sea surface directional wave spectra are produced. A ±14° subset of the backscattered power data associated with the topography measurements is used to produce independent measurements of rain rate and sea surface mean square slope at 10-s intervals. Theoretical calculations of rain attenuation at the WSRA 16.15-GHz operating frequency using measured drop size distributions for both mostly convective and mostly stratiform rainfall demonstrate that the WSRA absorption technique for rain determination is relatively insensitive to both ambient temperature and the characteristics of the drop size distribution, in contrast to reflectivity techniques. The variation of the sea surface radar reflectivity in the vicinity of a hurricane is reviewed. Fluctuations in the sea surface scattering characteristics caused by changes in wind speed or the rain impinging on the surface cannot contaminate the rain measurement because they are calibrated out using the WSRA measurement of mean square slope. WSRA rain measurements from a NOAA WP-3D hurricane research aircraft off the North Carolina coast in Hurricane Irene on 26 August 2011 are compared with those from the stepped frequency microwave radiometer (SFMR) on the aircraft and the Next Generation Weather Radar (NEXRAD) National Mosaic and Multi-Sensor Quantitative Precipitation Estimation (QPE) system.

Properties of the Umov vector in shallow water and its dependence on sea surface conditions

In this work, the effects of a rough sea surface on shallow water acoustic propagation are examined using experimental data collected during the ONR sponsored Target and Reverberation Experiment (TREX) off of the coast of Panama City, Florida, in May 2013. The acoustic data were collected from a bottom deployed recording tower that coherently recorded data on a horizontal line array (HLA), a vertical line array (VLA), and on an accelerometer-based vector sensor which was combined with a co-located hydrophone to formulate the Umov vector, or instantaneous intensity vector. The source was lowered from the stern of a research vessel to a depth one-third and two-thirds of the water depth (18 m), and transmitted a multi-frequency pulse from 1 to 4 kHz. These measurements were repeated at positions approximately 10, 20, and 40 water depths away from the tower, along a bearing perpendicular and parallel to the surface wave-crests. During the experiment, the sea surface directional-wave spectrum was measured by a Datawell Waverider buoy moored at the experimental site. Properties of the Umov vector are shown to relate to roughness and directional characteristics of the sea surface. The Umov vector is also studied in relation to the HLA and VLA measurements.

Directional surface wave spectra from acoustic Doppler current profiler data in sheared and stratified flows

Methods for estimating directional energy spectra of surface water waves from acoustic Doppler current profiler (ADCP) data are presented in cases of (1) waves on arbitrary, horizontal mean flows and (2) waves on a two-layer, density stratified fluid with finite water depth. An existing perturbation expansion method is employed up to second order to compensate for the effect of arbitrary mean velocity profiles. Equations describing characteristics of random waves on a two-layer fluid are utilized to allow determination of directional surface and interfacial wave spectra. Wave-induced velocities based on model wave spectra were synthesized for simulating ADCP measurement schemes to verify the new method, and to investigate misestimation when the two-layer condition was neglected. Errors are typically smaller than other measurement uncertainties but depend greatly on the relationship among wave characteristics, interface depth, relative densities, and measurement locations.

A wave parameters and directional spectrum analysis for extreme winds

In this research a comparison between two of the most popular ocean wave models, WAVEWATCH III™ and SWAN, was performed using data from hurricane Katrina in the Gulf of Mexico. The numerical simulation of sea surface directional wave spectrum and other wave parameters for several parameterizations and its relation with the drag coefficient was carried out. The simulated data were compared with in-situ NOAA buoy data. For most of the buoys, WAVEWATCH III™ presented the best statistical comparisons for the main wave parameters, such as significant wave height and peak period. The SWAN model tends to overestimate the maximum values for significant wave height for some buoys and the peak period for almost all the buoys. Both models tend to overestimate the value of peak direction, presenting an area of greater energy to the south. The WAVEWATCH III™ model performs best for buoys located in right forward quadrant, which generally has higher winds and waves. This indicates a better spatial representation of wave parameters in the higher energy areas for the WAVEWATCH III™ model. Results based on the quadrant location for most of the analyzed cases, are in agreement with the results from other sources such as the Scanning Radar Altimeter (SRA).

The sea surface directional wave spectrum and forward scattering from the sea surface

An influence of the directional wave spectrum on acoustic forward scattering from the sea surface is difficult to measure. Here we present results of an experiment to measure vertical spatial coherence from an acoustic path interacting once with the sea surface at two different angles with respect to the wave direction. The measurements were part of the Shallow-Water 2006 program that took place off the coast of New Jersey in August 2006. An acoustic source was deployed at depth 40 m, and signals were recorded on a moored receiving system consisting of two, 1.4 m long vertical line arrays centered at depths 25 and 50 m. Measurements were made over four source-receiver bearing angles separated by 90°, during which sea surface conditions remained stable and characterized by an rms waveheight of 0.17 m and a mixed swell, and wind-wave field originating from different directions. The measurements show a statistically significant difference depending on source-receiver bearing when the acoustic frequency is less than about 10 kHz; a result not observed at higher frequencies. This paper will present field observations along with modeling based on a rough surface parabolic wave equation utilizing synthetic sea surfaces. [Research supported by ONR Ocean Acoustics].

Evidence of Doppler-shifted Bragg scattering in the vertical plane by ocean surface waves

A set of narrowband tones (280, 370, 535, and 695 Hz) were transmitted by an acoustic source mounted on the ocean floor in 10 m deep water and received by a 64-element hydrophone line array lying on the ocean bottom 1.25 km away. Beamformer output in the vertical plane for the received acoustic tones shows evidence of Doppler-shifted Bragg scattering of the transmitted acoustic signals by the ocean surface waves. The received, scattered signals show dependence on the ocean surface wave frequencies and wavenumber vectors, as well as on acoustic frequencies and acoustic mode wavenumbers. Sidebands in the beamformer output are offset in frequency by amounts corresponding to ocean surface wave frequencies. Deviations in vertical arrival angle from specular reflection agree with those predicted by the Bragg condition through first-order perturbation theory using measured directional surface wave spectra and acoustic modes measured by the horizontal hydrophone array.

Underwater acoustic measurements of Doppler-shifted Bragg scattering in the vertical plane from interaction with the ocean surface.

High resolution beamformer output in the vertical plane for received fields from narrowband acoustic tones transmitted at 280, 370, 535, and 695 Hz shows evidence of Doppler-shifted Bragg scattering by the ocean surface waves. The sidebands in the beamformer output are offset in frequency by amounts corresponding to ocean surface wave frequencies, while deviations in vertical arrival angle agree with those predicted by the Bragg condition through first-order perturbation theory using measured directional surface wave spectra and measured acoustic mode wave numbers. The acoustic measurements were made by a horizontal hydrophone array on the ocean bottom in a shallow water waveguide under a variety of ocean surface conditions. [Work supported by ONR, Code 321(US).]

Numerical simulation of sea surface directional wave spectra under typhoon wind forcing

Numercial simulation of sea surface directional wave spectra under typhoon wind forcing in the South China Sea (SCS) was carreid out using the WAVEWATCH-III wave model. The simulation was run for 210 h until the Typhoon Damrey (2005) approached Vietnam. The simulated data were compared with buoy observations, which were obtained in the northwest sea area of Hainan Island. The results show that the significant wave height, wave direction, wave length and frequency spetra agree well with buoy observations. The spatial characteristics of the signifciant wave height, mean wave period, mean wave length, wave age and directional spectra depend on the relative position from the typhoon center. Also, the misalignment between local wind and wave directions were investigated.

High Frequency Radar Observing Systems in SEACOOS: 2002-2007 Lessons Learned

From 2002-2007, the Southeast Coastal Ocean Observing System (SEACOOS) deployed high frequency (HF) radars to overlook several venues stretching from the West Florida Shelf to the North Carolina Shelf. Based on extensive deliberations within SEACOOS, we decided to assess the two differing types of coastal ocean current radars within the southeast that were on the commercial market. The long-range SeaSondes (SS) were deployed to sense surface currents at hourly intervals and a 6 km resolution along the West Florida Shelf and the North Carolina Shelf. The medium and long-range Wellen Radars (WERA) were deployed along the Florida Straits and along the South Atlantic Bight with spatial resolutions of 1.2 to 3 km sampling at time scales of minutes. A common theme in these deployments was to sense the Loop Current, Florida Current and the Gulf Stream, which transport heat poleward as part of the gyre circulation.Several lessons were learned as part of these deployments, such as the need to protect against lightening strikes and the challenge of providing robust communication links between the remote sites and a central hub to make the data available in near real-time. Since states in the southeast and surrounding the Gulf of Mexico are prone to the passage of hurricanes, surface current and wave measurements during hurricanes are invaluable for improving storm surge and inundation models that are now being coupled to surface waves. In addition, significant wave heights (and directional surface wave spectra) are critical in the model assessment. Data quality and accuracy of the surface current and wave fields remain a central issue to search and rescue and safe maritime operations and to understanding the limitations of these radar systems. As more phased array systems (i.e., WERAs) are deployed for surface current and wave measurements, more attention needs to be placed on the interoperability between the two types of systems to insure the highest quality data possible is available to meet applied and operational goals. To insure the highest quality data possible, a full-time technician and a half-time IT specialist are needed for each installation as well as access to spares to keep these systems running consistently and to make quality observations available in near real-time.

Temporal variability of narrow-band tones in very shallow coastal waveguides

During an experiment near San Clemente, CA, a source moored on the bottom just outside the surf zone (500 m offshore, approximately 9-m depth) transmitted eight tones between 70 and 700 Hz to two nearly perpendicular, 64-element bottom-lying hydrophone arrays located approximately 1.2 km downcoast and 1 km further offshore (approximately 12-m depth). The acoustic tones were transmitted for 5 min every half hour over a 22-h period. Surface wave data obtained from a depth sensor array located approximately 40 km upcoast, as well as data from a PUV sensor data deployed during the experiment, are used to compute concurrent directional surface wave spectra. Long fast Fourier transforms of the acoustic recordings reveal temporal and spatial variability of the width and shape of the received tones in temporal frequency space. Surface-wave-related mechanisms of acoustic frequency distortion are proposed and their relative significance is investigated through the comparison of the data with results from physics-based models that use the measured surface wave properties as input parameters.

Relating ocean dynamics and sea state to time-angle variability of HF waveforms

One of the objectives of the Kauai experiment was a better understanding of the ocean dynamics effects on the propagation of high-frequency acoustic signals. Due to a unique oceanographic feature of the shallow water region near the Pacific Missile Range Facility in Kauai, a bottom mounted vertical line array containing eight elements was deployed with sufficiently small element spacing to measure the acoustic energy near the bottom. Simultaneous environmental parameters including current, temperature and salinity profiles, directional surface wave spectra, as well as the wind speed and direction above the sea surface were measured. High correlation between the environmental variability and the received acoustic signals is observed. To interpret the results broadband PE and Gaussian beam ray tracing models were utilized. Arrival time-angle statistics are correlated with the environmental variability due to ocean dynamics in this region. It is shown that variations of the sea surface dynamics exhibit different statistical effects than those occurring within the water column. [Work supported by ONR-321OA.] a)Paul Hursky, Martin Siderius (SAIC), Jerald Caruthers (USM), William S. Hodgkiss, Kaustubha Raghukumar (SIO), Dan Rouseff, Warren Fox (APL-UW), Christian de Moustier, Brian Calder, Barbara J. Kraft (UNH), Keyko McDonald (SPAWARSSC), Peter Stein, James K. Lewis, and Subramaniam Rajan (SSI).

Numerical Simulation of Sea Surface Directional Wave Spectra under Hurricane Wind Forcing

Abstract Numerical simulation of sea surface directional wave spectra under hurricane wind forcing was carried out using a high-resolution wave model. The simulation was run for four days as Hurricane Bonnie (1998) approached the U.S. East Coast. The results are compared with buoy observations and NASA Scanning Radar Altimeter (SRA) data, which were obtained on 24 August 1998 in the open ocean and on 26 August when the storm was approaching the shore. The simulated significant wave height in the open ocean reached 14 m, agreeing well with the SRA and buoy observations. It gradually decreased as the hurricane approached the shore. In the open ocean, the dominant wavelength and wave direction in all four quadrants relative to the storm center were simulated very accurately. For the landfall case, however, the simulated dominant wavelength displays noticeable overestimation because the wave model cannot properly simulate shoaling processes. Direct comparison of the model and SRA directional spectra in all four quadrants of the hurricane shows excellent agreement in general. In some cases, the model produces smoother spectra with narrower directional spreading than do the observations. The spatial characteristics of the spectra depend on the relative position from the hurricane center, the hurricane translation speed, and bathymetry. Attempts are made to provide simple explanations for the misalignment between local wind and wave directions and for the effect of hurricane translation speed on wave spectra.

Numerical Simulation of Sea Surface Directional Wave Spectra under Hurricane Wind Forcing

Numerical simulation of sea surface directional wave spectra under hurricane wind forcing was carried out using a high-resolution wave model. The simulation was run for four days as Hurricane Bonnie (1998) approached the U.S. East Coast. The results are compared with buoy observations and NASA Scanning Radar Altimeter (SRA) data, which were obtained on 24 August 1998 in the open ocean and on 26 August when the storm was approaching the shore. The simulated significant wave height in the open ocean reached 14 m, agreeing well with the SRA and buoy observations. It gradually decreased as the hurricane approached the shore. In the open ocean, the dominant wavelength and wave direction in all four quadrants relative to the storm center were simulated very accurately. For the landfall case, however, the simulated dominant wavelength displays noticeable overestimation because the wave model cannot properly simulate shoaling processes. Direct comparison of the model and SRA directional spectra in all four quadrants of the hurricane shows excellent agreement in general. In some cases, the model produces smoother spectra with narrower directional spreading than do the observations. The spatial characteristics of the spectra depend on the relative position from the hurricane center, the hurricane translation speed, and bathymetry. Attempts are made to provide simple explanations for the misalignment between local wind and wave directions and for the effect of hurricane translation speed on wave spectra.

Hurricane Directional Wave Spectrum Spatial Variation at Landfall

The NASA Scanning Radar Altimeter (SRA) flew aboard one of the NOAA WP-3D hurricane research aircraft to document the sea surface directional wave spectrum in the region between Charleston, South Carolina, and Cape Hatteras, North Carolina, as Hurricane Bonnie was making landfall near Wilmington, North Carolina, on 26 August 1998. Two days earlier, the SRA had documented the hurricane wave field spatial variation in open water when Bonnie was 400 km east of Abaco Island, Bahamas. Bonnie was similar in size during the two flights. The maximum wind speed was lower during the landfall flight (39 m s−1) than it had been during the first flight (46 m s−1). Also, Bonnie was moving faster prior to landfall (9.5 m s−1) than when it was encountered in the open ocean (5 m s−1). The open ocean wave height spatial variation indicated that Hurricane Bonnie would have produced waves of 10 m height on the shore northeast of Wilmington had it not been for the continental shelf. The gradual shoaling distributed the wave energy dissipation process across the shelf so that the wavelength and wave height were reduced gradually as the shore was approached. The wave height 5 km from shore was about 4 m. Despite the dramatic differences in wave height caused by shoaling and the differences in the wind field and forward speed of the hurricane, there was a remarkable agreement in the wave propagation directions for the various wave components on the two days. This suggests that, in spite of its complexity, the directional wave field in the vicinity of a hurricane may be well behaved and lend itself to be modeled by a few parameters, such as the maximum wind speed, the radii of the maximum and gale force winds, and the recent movement of the storm.