Ocean Surface Wave Fields Research Articles

On Surface Waves Generated by Extra-Tropical Cyclones—Part II: Simulations

In the previous companion study, satellite data were used to describe peculiar characteristics of ocean surface wave fields, generated by two extra-tropical cyclones (ETCs) rapidly propagating in the North Atlantic. Based on a 2D parametric wave model, further details are now provided to analyse and interpret the spatio-temporal evolution of very intense ETC-generated waves. Significant wave height and wavelength values are shown to reach extreme values, 18 m and 500 m, respectively. Resulting energetic swell systems waves then radiate in the whole eastern part of the North Atlantic, and more particularly in the Norwegian sea region. Moving to higher latitudes, wind forcing characteristics of ETCs evolve, with the shape of the wind field changing from quasi-cyclonic to “air jets/Icelandic lows”. In this paper, the resulting swell generation and propagation, after the deformation of an individual ETC, were studied, as well. Confirmed with comparisons with multi-satellite observations, the application of the parametric-2D wave-ray model was demonstrated to provide robust and highly detailed information on wave generation under very complex wind regime changes.

WIFF1.0: a hybrid machine-learning-based parameterization of wave-induced sea ice floe fracture

Abstract. Ocean surface waves play an important role in maintaining the marginal ice zone, a heterogenous region occupied by sea ice floes with variable horizontal sizes. The location, width, and evolution of the marginal ice zone are determined by the mutual interaction of ocean waves and floes, as waves propagate into the ice, bend it, and fracture it. In previous work, we developed a one-dimensional “superparameterized” scheme to simulate the interaction between the stochastic ocean surface wave field and sea ice. As this method is computationally expensive and not bitwise reproducible, here we use a pair of neural networks to accelerate this parameterization, delivering an adaptable, computationally inexpensive, reproducible approach for simulating stochastic wave–ice interactions. Implemented in the sea ice model CICE, this accelerated code reproduces global statistics resulting from the full wave fracture code without increasing computational overheads. The combined model, Wave-Induced Floe Fracture (WIFF v1.0), is publicly available and may be incorporated into climate models that seek to represent the effect of waves fracturing sea ice.

Hilbert-Huang transform analysis of surface wavefield under tropical cyclone Hudhud

The characteristics of an evolving ocean surface wavefield under tropical cyclone Hudhud that took place in October 2014 are investigated. The Hilbert-Huang transformation (HHT) is used for the spectral analysis of the cyclone generated waves. Empirical mode decomposition (EMD) is used to decompose the wave data into different intrinsic mode function (IMF). Hilbert Marginal Spectra and the Fourier Spectra for the wavefield data and the corresponding IMF are compared. In addition to the frequency wave elevation spectrum, the wave group characteristics and their relationship with the local wave characteristics are studied.

Modeling Microseism Generation by Inhomogeneous Ocean Surface Waves in Hurricane Bonnie Using the Non-Linear Wave Equation

It has been shown that hurricanes generate seismic noise, called microseisms, through the creation and non-linear interaction of ocean surface waves. Here we model microseisms generated by the spatially inhomogeneous waves of a hurricane using the non-linear wave equation where a second-order acoustic field is created by first-order ocean surface wave motion. We treat range-dependent waveguide environments to account for microseisms that propagate from the deep ocean to a receiver on land. We compare estimates based on the ocean surface wave field measured in hurricane Bonnie in 1998 with seismic measurements made roughly 1000 km away in Florida.

Use of Proper Orthogonal Decomposition for Extraction of Ocean Surface Wave Fields from X-Band Radar Measurements of the Sea Surface

Radar remote sensing of the sea surface for the extraction of ocean surface wave fields requires separating wave and non-wave contributions to the sea surface measurement. Conventional methods of extracting wave information from radar measurements of the sea surface rely on filtering the wavenumber-frequency spectrum using the linear dispersion relationship for ocean surface waves. However, this technique has limitations, e.g., it isn’t suited for the inclusion of non-linear wave features. This study evaluates an alternative method called proper orthogonal decomposition (POD) for the extraction of ocean surface wave fields remotely sensed by marine radar. POD is an empirical and optimal linear method for representing non-linear processes. The method was applied to Doppler velocity data of the sea surface collected using two different radar systems during two different experiments that spanned a variety of environmental conditions. During both experiments, GPS mini-buoys simultaneously collected wave data. The POD method was used to generate phase-resolved wave orbital velocity maps that are statistically evaluated by comparing wave statistics computed from the buoy data to those obtained from these maps. The results show that leading POD modes contain energy associated with the peak wavelength(s) of the measured wave field, and consequently, wave contributions to the radar measurement of the sea surface can be separated based on modes. Wave statistics calculated from optimized POD reconstructions are comparable to those calculated from GPS wave buoys. The accuracy of the wave statistics generated from POD-reconstructed orbital velocity maps was not sensitive to the radar configuration or environmental conditions examined. Further research is needed to determine a rigorous method for selecting modes a priori.

Extreme Wave-Induced Oscillation in Paradip Port Under the Resonance Conditions

A mathematical model is constructed to analyze the long wave-induced oscillation in Paradip Port, Odisha, India under the resonance conditions to avert any extreme wave hazards. Boundary element method (BEM) with corner contribution is utilized to solve the Helmholtz equation under the partial reflection boundary conditions. Furthermore, convergence analysis is also performed for the boundary element scheme with uniform and non-uniform discretization of the boundary. The numerical scheme is also validated with analytic approximation and existing studies based on harbor resonance. Then, the amplification factor is estimated at six key record stations in the Paradip Port with multidirectional incident waves and resonance modes are also estimated at the boundary of the port. Ocean surface wave field is predicted in the interior of Paradip Port for the different directional incident wave at various resonance modes. Moreover, the safe locations in the port have been identified for loading and unloading of moored ship with different resonance modes and directional incident waves.

Observations of Surface Wave–Current Interaction

AbstractWave–current interaction can result in significant inhomogeneities of the ocean surface wave field, including modulation of the spectrum, wave breaking rates, and wave statistics. This study presents novel airborne observations from two experiments: 1) the High-Resolution Air–Sea Interaction (HiRes) experiment, with measurements across an upwelling jet off the coast of Northern California, and 2) an experiment in the Gulf of Mexico with measurements of waves interacting with the Loop Current and associated eddies. The significant wave height and slope varies by up to 30% because of these interactions at both sites, whereas whitecap coverage varies by more than an order of magnitude. Whitecap coverage is well correlated with spectral moments, negatively correlated with the directional spreading, and positively correlated with the saturation. Surface wave statistics measured in the Gulf of Mexico, including wave crest heights and lengths of crests per unit surface area, show good agreement with second-order nonlinear approximations, except over a focal area. Similarly, distributions of wave heights are generally bounded by the generalized Boccotti distribution, except at focal regions where the wave height distribution reaches the Rayleigh distribution with a maximum wave height of 2.55 times the significant wave height, which is much larger than the standard classification for extreme waves. However, theoretical distributions of spatial statistics that account for second-order nonlinearities approximately bound the observed statistics of extreme wave elevations. The results are discussed in the context of improved models of breaking and related air–sea fluxes.

Polar Fourier Transform Processing of Marine Radar Signals

AbstractThis paper describes a method of processing marine radar signals for the purpose of generating phase-resolved surface elevation maps as well as statistical measures of ocean surface wave fields. The method is well suited to the processing of data collected by marine radars because it allows for the incorporation of effects dependent on the radar look direction relative to the propagation direction of ocean waves. Applications to Doppler radar and backscattered power measurements are described, and example results are presented using simulated radar data.

Synergistic measurements of ocean winds and waves from SAR

AbstractIn this study we present a synergistic method to retrieve both ocean surface wave and wind fields from spaceborne quad‐polarization (QP) synthetic aperture radar (SAR) imaging mode data. This algorithm integrates QP‐SAR wind vector retrieval model and the wave retrieval model, with consideration to the nonlinear mapping relationship between ocean wave spectra and SAR image spectra, in order to synergistically retrieve wind fields and wave directional spectra. The method does not require a priori information on the sea state. It combines the observed VV‐polarized SAR image spectra with the retrieved wind vectors from the VH‐polarized SAR image, to estimate the wind‐generated wave directional spectra. The differences between the observed SAR spectra and optimal SAR image spectra associated with the wind waves are interpreted as the contributions from the swell waves. The retrieved ocean wave spectra are used to estimate the integrated spectral wave parameters such as significant wave heights, wavelengths, wave directions and wave periods. The wind and wave parameters retrieved by QP‐SAR are validated against those measured by the National Data Buoy Center (NDBC) directional wave buoys under different sea states. The validation results show that the QP‐SAR SAR has potential to simultaneously measure the ocean surface waves and wind fields from space.

Wave field analysis in a harbor with irregular geometry through boundary integral of Helmholtz equation with corner contributions

A mathematical model has been designed to analyze the wave characteristics in a harbor, averting any possible situation of occasional extreme wave hazards due to the seasonal weather conditions. Helmholtz equation has been considered with appropriate boundary conditions on the basis of small amplitude hypothesis. Further, a solution of the Helmholtz equation is given by Green’s identity formula and then it is utilized to predict the ocean surface wave fields due to refraction and diffraction of various directional incident waves in the context of the shallow water waves. The corner angle coefficient is firstly determined at each corner segment on the boundary of the harbor and then corner contribution on the boundary is imposed by multiplying the corner angle coefficient to the boundary wave field. Further, the Chebyshev point discretization is implemented on the boundary of harbor to improve the numerical accuracy at the sharp corners. This numerical model is validated through the quantitative comparison with existing studies in literature. Further the logarithmic convergence rate is achieved for the proposed numerical scheme as well. We have implemented this numerical model practically on the Pohang New Harbor (PNH), Pohang, South Korea to compute the resonance modes for various directional incident waves. Furthermore, the wave elevation is obtained in the whole interior domain of the harbor at various modes of resonance with specific incident waves. In conclusion, this numerical scheme is a competent tool to foster the prediction of the ocean surface wave field on the boundary and interior of the harbors with complex geometries.

The low-frequency variance of the ocean surface wave field in the area of the Antarctic Circumpolar Current

The low-frequency variance of the surface wave in the area of the Antarctic Circumpolar Current (ACC) and its correlation with the antarctic circumpolar wave (ACW) are focused on. The analysis of the series of 44 a significant wave height (SWH) interannual anomalies reveals that the SWH anomalies have a strong periodicity of about 4–5 a and this signal propagates eastward obviously from 1985 to 1995, which needs about 8 a to complete a mimacircle around the earth. The method of empirical orthogonal function (EOF) is used to analyze the filtered monthly SWH anomalies to study the spatio-temporal distributions and the propagation characteristics of the low-frequency signals in the wave field. Both the dominant wavenumber-2 pattern in space and the propagation feature in the south Pacific, the south Atlantic and the south Indian ocean show strong consistency with the ACW. So it is reasonable to conclude that the ACW signal also exists in the wave field. The ACW is important for the climate in the Southern Ocean, so it is worth to pay more attention to the large-scale effect of the surface wave, which may also be important for climate studies.

Infrasound from hurricanes: Dependence on the ambient ocean surface wave field

Infrasound signals in the microbarom band (about 0.2 Hz) generated by hurricanes often do not appear to originate near the eye where the winds are strongest. This paper suggests that conditions conducive to microbarom (and microseism) generation can occur along the trailing periphery of the storm through the interaction of the storm‐generated wavefield with the ambient swell field, resulting in detection bearings that vary from the center of the storm by up to 20 degrees. Infrasound data from Typhoon Usagi (2007) is presented that supports this theory.

Changes in ocean infrasonic energy density and vector intensity with changes in wind and ocean surface wave conditions as measured by a freely drifting vector sensor

During an experiment in 1.3-km-deep water in the Southern California Bight, the wind speed decreased from about 7 to 1 m/s over a 10-h period, and then increased to 9 m/s over the next 8-h period. Measurements made by a neutrally buoyant, freely drifting vector sensor at 920-m depth show that the corresponding changes in the potential and kinetic energy density levels of the infrasonic sound field have a frequency-dependent delay. The levels in a 0.1-Hz-wide bin at 3 Hz respond to wind-speed changes with approximately a 2-h delay, and the delay in response increases with decreasing frequency at a rate of about 1 h per hertz down to 1 Hz. The corresponding evolution in directionality of the active and reactive acoustic intensity vectors in these same frequency bins and their relationship to the surrounding bathymetry will be presented. The directional spectra of the ocean surface wave field during the experiment were reconstructed using back-refraction modeling with wave data from shore stations and offshore platforms archived by the Coastal Data Information Program to obtain estimates of the temporal variability of the nonlinear wave-wave interactions generating the ocean infrasound. [Work supported by ONR.]

Wirewalker: An Autonomous Wave-Powered Vertical Profiler

An inexpensive vertically profiling float that draws its energy from the ocean surface wavefield is described. Termed the “Wirewalker,” it is a generalized platform capable of supporting a variety of self-contained instruments. The motion of the waves drives the positively buoyant profiler downward. It then free floats upward, decoupled from the surface motion field. The design focuses on mechanical simplicity and low cost. In moderate sea states, a prototype Wirewalker has completed profiles to depths of 60 m every 15 min. Profiles from the surface to 50–100 m can be obtained rapidly enough that diel and higher-frequency variability can be resolved.

Measurement of wave coherence properties using spaceborne synthetic aperture radar

There has been considerable recent interest in assessing the feasibility of constructing very large offshore structures with linear dimensions of over a kilometer. The climatology of very long ocean surface wave fields which might resonate with such structures fall outside the experience of conventional maritime design. Of particular importance are properties of wave coherence, i.e. wave groupiness and wave crest length. Spaceborne synthetic aperture radars produce high-resolution wave images over swaths 100 km wide or larger. In this paper, we review the theory of wave imaging by synthetic aperture radar, describe techniques to objectively measure the properties of wave groupiness and crest length, and apply these techniques to synthetic aperture radar images in the vicinity of hurricanes. We show that wave groupiness and wave long-crestedness are more prevalent than one might expect purely on the basis of the associated ocean wave spectrum.

Limit Distributions of Directionally Reinforced Random Walks

As a mathematical model for time and space correlations in ocean surface wave fields, Mauldin, Monticino, and von Weizsäcker (1996,Adv. in Math.117, 239–252), introduced directionally reinforced random walks and analyzed their recurrence properties. This paper develops limiting properties for these random walks inRd. In particular, it is shown that the limit distribution is a Brownian motion if the time between changes of directions has a finite second moment, and is a stable process if the time between changes of directions is in a domain of attraction of a stable law. The latter gives an affirmative answer to an open question posed by Mauldinet al.. The strong law of large numbers and strong approximations are also discussed.

Coupling between the Atmospheric Circulation and the Ocean Wave Field: An Idealized Case

This work studies the two-way coupling between the atmospheric circulation and the ocean surface wave field, as it is described by the recent observations and theories on the dependence of the sea surface roughness on the ocean wave spectrum. The effect of the coupling on the atmospheric variables and the ocean wave field is analyzed by implementing both the atmospheric and the ocean wave models in a periodic channel and simulating a wide range of different situations. In a strong atmospheric cyclone, in comparison to the one-way coupling, the two-way coupling attenuates the depth of the pressure minimum and significantly reduces the wave height and surface wind speed while it increases the momentum flux. The heat and moisture fluxes are increased if they are computed using the same wave-dependent roughness that is used for the momentum flux, while they are decreased if they are computed using the Charnock relation. The effects are proportionally larger for extreme storms because the time required for the deepening of the low pressure is much shorter than the time required by the windsea to reach a well-developed state.

Infrared remote sensing of breaking waves

ENERGY dissipation due to deep-water wave breaking plays a critical role in the development and evolution of the ocean surface wave field. Furthermore, the energy lost by the wave field via the breaking process is a source for turbulent mixing and air entrainment, which enhance air–sea heat and gas transfer1–3. But the current lack of reliable methods for measuring energy dissipation associated with wave breaking inhibits the quantitative study of processes occurring at ocean surfaces, and represents a major impediment to the improvement of global wave-prediction models4. Here we present a method for remotely quantifying wave-breaking dynamics which uses an infrared imager to measure the temperature changes associated with the disruption and recovery of the surface thermal boundary layer (skin layer). Although our present results focus on quantifying energy dissipation—in particular, we show that the recovery rate of the skin layer in the wakes of breaking waves is correlated with the energy dissipation rate—future applications of this technique should help to elucidate the nature of important small-scale surface processes contributing to air–sea heat5 and gas6 flux, and lead to a fuller understanding of general ocean–atmosphere interactions.

Directionally Reinforced Random Walks

This paper introduces and analyzes a class of directionally reinforced random walks. The work is motivated by an elementary model for time and space correlations in ocean surface wave fields. We develop some basic properties of these walks. For instance, we investigate recurrence properties and give conditions under which the limiting continuous versions of the walks are Gaussian diffusion processes.

Correlations between Ambient Noise and the Ocean Surface Wave Field

Abstract Measurements of the ambient noise spectrum level N with simultaneous, coincident wind and wave measurements were made from RP FLIP in fall 1991. The measurements were designed to investigate the correlation between the ambient noise and relevant surface wave parameters. The results suggest that wave parameters related to the incidence of wave breaking correlated well with the ambient noise level. The correlation between N and the rms wave amplitude a was found to he poor but that between N and the rms amplitude of the local wind sea aw was comparable to that between wind speed U and N. Similar good correlations were found between the rms wave slope s and N, and the higher frequency surface wave spectral levels and N. Correlations between the surface wave dissipation estimates D based on the Hasselmann and Phillips models and the ambient noise were comparable to those between the wind speed and the ambient noise. The mean square acoustic pressure was found to be proportional to Dn with n in the ra...