Two-dimensional Wave Spectra Research Articles

Accuracy verification of the 2D spectral AIS method by the hull monitoring data

Accuracy validation of the 2D spectral AIS method (AIS method using two-dimensional wave spectrum; 2D-AIS method) using hull monitoring data of a large ore carrier is discussed. The AIS method predicts the response of actual ships using AIS-based ship position data, hindcast wave data, and response characteristics data. The conventional AIS method uses representative parameters(H, T, θ) from wave spectrum modeling. The modeling involves many uncertainties. By using the 2D wave spectrum as it is, the effect of uncertainties associated with wave spectrum modeling is investigated. Compared to the analysis of the monitoring data conducted in this study, it was found that the 2D-AIS method improves the accuracy to about 15 %, while the conventional AIS method shows an error of up to about 35 % compared to the actual measurements in the long-term maximum expected values. This enhancement is attributed to the inability of the modeled wave spectrum to accurately represent the two-peak wave spectrum observed in extreme sea states, leading to a deficiency in reproducing wave frequency components corresponding to peak frequencies of the response. The findings underscore the effectiveness of the 2D-AIS method in refining long-term hull stress estimations, thus offering valuable insights for enhancing the safety and performance of hull structures.

Optimal Configuration of Omega-Kappa FF-SAR Processing for Specular and Non-Specular Targets in Altimetric Data: The Sentinel-6 Michael Freilich Study Case

In this study, the full-focusing (FF) algorithm is reviewed with the objective of optimizing it for processing data from different types of surfaces probed in altimetry. In particular, this work aims to provide a set of optimal FF processing parameters for the Sentinel-6 Michael Freilich (S6-MF) mission. The S6-MF satellite carries an advanced radar altimeter offering a wide range of potential FF-based applications which are just beginning to be explored and require prior optimization of this processing. In S6-MF, the Synthetic Aperture Radar (SAR) altimeter acquisitions are known to be aliased in the along-track direction. Depending on the target, aliasing can be tolerated or may be a severe impairment to provide the level of performance expected from FF processing. Another key aspect to consider in this optimization study is the unprecedented resolution of the FF processing, which results in a higher posting rate than the standard SAR processing. This work investigates the relationship between posting rate and noise levels and provides recommendations for optimal algorithm configurations in various scenarios, including transponder, open ocean, and specular targets like sea-ice and inland water scenes. The Omega–Kappa (WK) algorithm, which has demonstrated superior CPU efficiency compared to the back-projection (BP) algorithm, is considered for this study. But, unlike BP, it operates in the Doppler frequency domain, necessitating further precise spectral and time domain settings. Based on the results of this work, real case studies using S6-MF acquisitions are presented. We first compare S6-MF FF radargrams with Sentinel-1 (S1) images to showcase the potential of optimally configured FF processing. For highly specular surfaces such as sea-ice, distinct techniques are employed for lead signature identification. S1 relies on image-based lineic reconstruction, while S6-MF utilizes phase coherency of focalized pulses for lead detection. The study also delves into two-dimensional wave spectra derived from the amplitude modulation of image/radargrams, with a focus on a coastal example. This case is especially intriguing, as it vividly illustrates different sea states characterized by varying spectral peak positions over time.

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.

Investigation on the Utilization of Millimeter-Wave Radars for Ocean Wave Monitoring

The feasibility of using millimeter-wave radars for wave observations was investigated in this study. The radars used in this study operate at a center frequency of 77.572 GHz. To investigate the feasibility of wave observations and extract one-dimensional and two-dimensional wave spectra, arrays consisting of multiple radar units were deployed for observations in both laboratory and field environments. Based on the data measured with the millimeter-wave radars, one-dimensional wave spectra and two-dimensional wave directional spectra were evaluated using the periodogram method and the Bayesian directional spectrum estimation method (BDM), respectively. Meanwhile, wave parameters such as the significant wave height, wave period, and wave direction were also calculated. Via comparative experiments with a capacitive wave height meter in a wave tank and RADAC’s WG5-HT-CP radar in an offshore field, the viability of using millimeter-wave radars to observe water waves was validated. The results indicate that the one-dimensional wave spectra measured with the millimeter-wave radars were consistent with those measured with the mature commercial capacitive wave height meter and the WG5-HT-CP wave radar. Via wave direction measurement experiments conducted in a wave tank and offshore environment, it is evident that the wave directions retrieved with the millimeter-wave radars were in good alignment with the actual wave directions.

Observations of Extreme Waves and Wave Spectra during Hurricane Dorian (2019)

Due to the sparse distribution of buoys in the ocean, direct observations of extreme wave activity as excited by tropical cyclones (TCs) are few; but nonetheless, these buoys provide rare opportunities to learn more about how weather systems interact with the ocean wave field. In this study, National Oceanic and Atmospheric Administration National Data Buoy Center buoy observations of one-dimensional (1D) and two-dimensional (2D) wave spectra during the translation speed of Hurricane Dorian (2019) through the Atlantic Ocean were used to examine extreme wave events in the days before and after its September 1, 2019 landfall in The Bahamas. Observations of wave properties during storm intensification and decay showed that although significant wave height naturally rose and fell, the dominant wave period remained virtually constant. At the height of the storm, a lethal combination formed, with the highest significant wave heights being recorded at over 8 m (more than four times the mean) and dominant wave periods exceeded 12 s. Wave direction also varied widely as wave regimes shifted from wind-sea to swell, with spectral wave energy peaking at over 120 m2/Hz, six times higher than pre-Hurricane Dorian wave states. This study provides the first in situ characterization of extreme wave heights as induced by Hurricane Dorian. The study recommends that a number of observational platforms be funded, developed, and deployed throughout the Lucayan Archipelago.

A Novel Partition Method Based on 2-D Ocean- Wave Spectra of CFOSAT SWIM

Two-dimensional wave spectra describe the distribution of wave energy in terms of frequency and direction. For unimodal seas (i.e., single peaked), wave spectra can describe the wave component accurately. However, they fail to describe wave components properly in more complex situations. The simultaneous existence of wind sea and one or more swell systems is a situation that occurs very often. Therefore, for convenient application, these wave components should be distinguished by partitioning, which often relies on the watershed algorithm. However, the watershed algorithm has some problems, such as oversegmentation, as its first step takes many small partitions and the elements of these small partitions cannot be separated in the subsequent steps. A new method called merging and expanding (ME) method that involves two main steps (i.e., element merge and partition expansion) based on the 2-D slope spectrum product of surface waves’ investigation and monitoring (SWIM) is presented in this article. The step called element merge and the principle of regional consistency (PORC) are adopted to avoid oversegmentation and to make partitions possess physical meanings while the step called partition expansion is implemented to decrease filter dependence. The result indicates that the ME method can suppress excessive segmentation and the partitioned wave parameters of the ME method are closer to that of WAVEWATCH III (WW3) data than SWIM products.

Approach for Preservation and Reconstruction of Two-Dimensional Wave Spectra and Its Application to Boundary Conditions in Nested Wave Modeling

Typically, storing a two-dimensional wave spectrum could occupy more than one thousand storage units, making saving and reading boundary spectra computationally burdensome in nested wave simulations. This paper proposes a new approach for preservation of a wave spectrum that can reduce the required number of storage units to dozens. Using a corresponding reconstruction approach, the spectrum can then be rebuilt with intact spectral characteristics. Experimental application confirmed that the reconstructed spectra could be adopted as boundary conditions in nested wave modeling. The newly proposed approach for preservation and reconstruction of spectra allows long-term spectral information covering the entire simulated domain to be saved with more acceptable storage consumption, and such information can then be adopted as nesting conditions for nested-child simulations without the limitations of predefined boundaries. The above-mentioned properties of the new method could help support engineering projects concerning wave environments, research focused on wave climatology, and studies associated with wave energy assessment.

波浪追算による2次元波スペクトルを利用した波浪荷重推定

波浪追算による2次元波スペクトルを利用した波浪荷重推定

Numerical Analysis of the Effect of Binary Typhoons on Ocean Surface Waves in Waters Surrounding Taiwan

The ocean surface waves during Super Typhoons Maria (2018), Lekima (2019), and Meranti (2016) were reproduced using hybrid typhoon winds and a fully coupled wave-tide-circulation modeling system (SCHISM-WWM-III). The hindcasted significant wave heights are in good agreement with the along-track significant wave heights measured by the altimeters aboard the SARAL (Satellite with ARgos and ALtiKa) and Jason-2 satellites. Two numerical experiments pairing Super Typhoons Maria (2018) and Meranti (2016) and Super Typhoons Lekima (2019) and Meranti (2016) were conducted to analyze the storm wave characteristics of binary and individual typhoons. Four points located near the tracks of the three super typhoons were selected to elucidate the effects of binary typhoons on ocean surface waves. The comparisons indicate that binary typhoons not only cause an increase in the significant wave height simulations at four selected pints but also result in increases in the one-dimensional wave energy and two-dimensional directional wave spectra. Our results also reveal that the effects of binary typhoons on ocean surface waves are more significant at the periphery of the typhoon than near the center of the typhoon. The interactions between waves generated by Super Typhoons Maria (2018) and Meranti (2016) or Super Typhoons Lekima (2019) and Meranti (2016) might be diminished by Taiwan Island even if the separation distance between two typhoons is <700 km.

Analysis of the Caribbean wave climate for wave energy harvesting

In this study, the design requirements for a regional wave energy converter are identified from the analysis of 10 years of spectral data provided by nine buoys located across the Caribbean. It indicated that the average significant wave height and wave period in the Caribbean is 1.62 m and 5.91 s, respectively, while the average total theoretical power capable of being absorbed from a wave energy converter is 7.4 kilowatts per meter of surface waves. Devices should be designed to withstand a significant wave height of 19.0 ± 2.8 meters (95% confidence) for a 1 in 100 year return wave. This was determined by performing various extreme wave analyses. Additionally, a design life of 30 years for a device would have a probability of exceedance regarding this return wave as 26%. Using two-dimensional wave spectra analysis for the resource study, the overall spectral width, directionality coefficient and direction of the maximum directionally resolved wave power for the region are determined to be 0.172, 0.74 and 42°, respectively. It is expected that the combination of these information would improve the viability of a wave energy industry in the Caribbean and advance technological development.

Wave energy resource characterization employing joint distributions in frequency-direction-time domain

Joint and marginal distributions in the frequency, direction, and time domain are employed to demonstrate their value for wave energy resource characterization when full spectra are available. Insights gained through analysis of these distributions support wave energy converter concept design, operation and maintenance. Spatial trends in the wave energy resource and contributing wave energy systems along the continental shelf of the West Coast of the United States are investigated using the most recent two-dimensional wave spectra measurements at four buoys over an eleven year period (2008 to 2018). Resource hot spots and dominant resolved energy resource bands in the frequency-direction-time domain are delineated. Resource attributes, including frequency and directional spreading, and seasonal variability, are characterized using joint distributions and marginal distributions of wave power spectra. North Pacific westerly swells in the winter season, augmented by Aleutian low-pressure southwesterly swells, are the principal suppliers of the dominant resource and main drivers influencing resource attributes. The modification of these systems southward, especially the North Pacific westerly swells, explains the observed spatial resource trends. The dominant resource wave period shifts two seconds to higher wave periods, thirty degrees in the dominant direction band to a more northward orientation, and forward by one month.

FUTURE CHANGES IN SPECTRAL WAVE CLIMATE AROUND JAPAN UNDER GLOBAL WARMING

Future projections of ocean wave climate related with global warming has been conducted for the assessment of climate change impacts on coastal disaster, beach morphology, and coastal structure design. In this study, we conduct the high-resolution future wave climate projection in the East Asia region and detail analysis on wave climate based on two-dimensional wave spectra in addition to conventional wave statistics (significant wave height). Future changes in wave height, period and direction can be discussed consistently owing to analysis on the mean wave spectra.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/FEYPZFRr5SQ

On the Nonlinear Mapping of an Ocean Wave Spectrum into a New Polarimetric SAR Image Spectrum

AbstractA new nonlinear transformation relation is derived to describe the mapping of a two-dimensional ocean wave spectrum into a new polarimetric synthetic aperture radar (SAR) image spectrum. It is a further expansion and improvement of Hasselmann’s work. First, the nonlinear mapping relation proposed is derived on the basis of a new polarimetric SAR image instead of the conventional single-polarization SAR image. Second, the nonlinear mapping relation no longer includes the complex hydrodynamic modulation transfer function (MTF). Third, the traditional tilt MTF, which is not accurate enough for the retrieval of sea wave spectrum, is replaced by an empirical tilt MTF derived on the basis of the C-band geophysical model function [i.e., C-band synthetic aperture radar (CSAR) normalized radar cross section (NRCS) model]. A sea wave spectrum retrieval algorithm is then proposed that is based on the new nonlinear mapping and the empirical tilt MTF. The retrieved spectra from C-band polarizedRADARSAT-2SAR images are compared with the results obtained by the ECMWF Ocean Wave Model (ECWAM) and buoy measurements.

Virtual hull monitoring of a naval vessel using hindcast data and reconstructed 2-D wave spectra

A novel virtual hull monitoring approach is assessed using full-scale measurements from a naval vessel trial to address two questions. First: Can this technique accurately reproduce stress spectra from measured strains? Second: Are responses calculated using reconstructed two-dimensional wave spectra from hindcast data more accurate than those using simpler wave representations? Stresses calculated using wave hindcast data, ship track information, and stress transfer functions compare favorably to those derived from strain gauge measurements at five structural locations. Wave conditions are represented using a spectrum model along with bulk spectral parameters (significant wave height, peak period, and primary direction) from hindcast datasets and by reconstructing two-dimensional spectra from hindcast partition data. Both approaches give good agreement with strain measurements but using the more-detailed reconstructed two-dimensional wave spectra yields better results. Results suggest that wave hindcast data are sufficient for accurate structural calculations, encouraging further study of virtual hull monitoring using wave hindcast data.

Spectral Wave Characteristics over the Head Bay of Bengal: A Modeling Study

Information on spectral wave characteristics is an essential prerequisite for ocean engineering-related activities and also to understand the complex wave environment at any given location. To the best of our knowledge, there are no comprehensive studies attempted so far to study the wave spectral characteristics over the head Bay of Bengal, a low-lying deltaic environment. The present study is an attempt to describe the spectral characteristics of wave evolution across different locations over this deltaic region based on numerical simulations. Therefore, it implements a multi-scale nested modeling approach using two state-of-art wave models, WAM and SWAN, and forced with ERA-Interim winds spanning the year of 2016. Model-computed integrated wave parameters are validated against wave rider buoy data as well as remotely sensed SARAL/AltiKa and merged altimeter data. Analysis of the monthly averaged one-dimensional spectrum reveals a single peak during the southwest monsoon and existence of double peaks from November to January, and occasionally up to March. Variance energy density undergoes inter-seasonal variation and attains its maxima during the month of July. Transformation of swell wave energy as a function of depth is found to be mostly associated with physical processes such as wave-bottom interaction and attenuation by opposing winds during the northeast (NE) monsoon. Fetch restriction for the evolution of wind seas (from the NE), modification in wind shear stress by opposing swells, and bottom effects remarkably contribute to the reduction in wind sea energy at shallow water depths. This study indicates that the influence of swells is higher along the eastern side of the basin as compared to the western side, and marginally higher variance is also observed over the east except during February–April. The two-dimensional wave spectra exhibit differential wave systems approaching from various directions attributed to a reflected swell system from the south-southeast throughout the year, southwest swells, reversing wind seas following local winds, and reflected wind seas from the land boundary.

High-resolution wave climate hindcast around Japan and its spectral representation

A 34-year high-resolution ocean surface wave climate hindcast around Japan is presented, and the wave climate around Japan is examined from a spectral point of view. The spectral wave model is forced by the sea surface wind data obtained from the JRA-55 atmospheric reanalysis. The wave climate hindcast is validated by comparing it with buoy observations around Japan. The correlation coefficient of the significant wave height is 0.9. The correlation coefficient of the mean wave period is 0.8 for the Japan Sea and Pacific side of eastern Japan and 0.7–0.8 for the Pacific side of western Japan. The wave climate is represented by temporal-mean two-dimensional wave spectra. The characteristics of the spectral wave climate are investigated by classifying them into three types. Distinctive characteristics of the mean wave spectra along the Japan Sea are narrower band widths for both the period and direction. The mean wave spectra along the Pacific side of eastern Japan are characterized by swells with a spectral peak propagating from the northeast. The distinctive spectral features corresponding to the Pacific side of western Japan are bi-modal peaks with long-period components typically generated by typhoons. The variability in the monthly mean wave spectra is examined using an empirical orthogonal function (EOF) analysis. In the winter, it is found that the wave height variability (EOF 1st mode) is related to wave direction variability (EOF 2nd mode) at locations 1000 km apart via the sea level pressure variance over the North Pacific. In the summer, the EOF 1st mode corresponding to the Pacific side locations is dominated by the variability in typhoon-generated swells. The spectral wave climate representation provides new insight into the wave climate around Japan with clear relationships between the atmospheric conditions, the wave height, direction, and period.

Multi-directional wave spectra from marine X-band radar

The signal measured by heave–pitch–roll directional wave buoys yields the first four coefficients of a Fourier series. Data adaptive methods must be employed to estimate a directional wave spectrum. Marine X-band radars (MRs) have the advantage over buoys that they can measure “model-free” two-dimensional (2D) wave spectra. This study presents the first comprehensive validation of MR-derived multi-directional wave characteristics. It is based on wave data from the 2010 Impact of Typhoons on the Ocean in the Pacific (ITOP) experiment in the Philippine Sea, namely MR measurements from R/V Roger Revelle, Extreme Air–Sea Interaction (EASI) buoy measurements, as well as WAVEWATCH-III (WW3) modeling results. Buoy measurements of mean direction and spreading as function of frequency, which do not require data adaptive methods, are used to validate the WW3 wave spectra. An advanced MR wave retrieval technique is introduced that addresses various shortcomings of existing methods. Spectral partitioning techniques, applied to MR and WW3 results, reveal that multimodal seas are frequently present. Both data sets are in excellent agreement, tracking the evolution of up to 4 simultaneous wave systems over extended time periods. This study demonstrates MR’s and WW3’s strength at measuring and predicting 2D wave spectra in swell-dominated seas.

Validation of naval vessel spectral fatigue analysis using full-scale measurements

Full-scale measurements taken during a naval vessel sea trial are compared to calculated stress spectra and associated fatigue damage estimates using linear frequency-domain hydrodynamic and finite element analysis codes. Results were generated using four different wave spectrum models to better understand their influence on fatigue damage estimates. The results using measured two-dimensional wave spectra were most similar to measurements, but the agreement with measurements for each of the spectrum models was acceptable. Significant improvement in calculation accuracy was observed when adding a spreading function to longcrested wave spectra. The use of ±90° as the extent of wave spreading gave results with minimal differences from the use of measured spreading angles. The agreement between measurements and calculations using longcrested wave spectra with a constant spreading function is fortunate because available seaway data are commonly limited to wave height and period combinations. The results of this study suggest the spectral fatigue analysis method can be used to generate reasonable estimates of stress spectra and resulting fatigue damage for a naval vessel.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.

Analysis of the Global Swell and Wind Sea Energy Distribution Using WAVEWATCH III

Over the past several decades, an increasing number of studies have focused on the global view of swell and wind sea climate. However, our understanding of wind sea and swell is still incomplete as is the lack of an integrated description for all the wave components. In this paper, the European Centre for Medium-Range Weather Forecasts (ECMWF) Era-medium wind data is used to run the WAVEWATCH III model and the global wave fields in 2010 are reproduced. Using the spectra energy partition (SEP) method, two-dimensional wave spectra were separated and detailed information for the components of wind sea and swell was obtained. We found that the highest seasonal mean energy of swell and wind sea are distributed in the respective winter hemispheres. In most seas, swell carries a large part of the wave energy withWsbeing higher than 50%. Compared to swell, the global distribution of wind sea energy is highly affected by the seasons. We also established a link between inverse wave age and the ratio of swell energy to total wave energy. This study aims to improve our understanding of surface wave energy composition and thus the parameterization of global-scale wind-wave interaction and air-sea momentum flux.