Ocean Wave Data Research Articles

An investigation on the performance of the Hilbert-Huang Transform on the analysis of ocean waves time series

This work discusses the performance of the Hilbert-Huang method applied to the time-frequency analysis of ocean wave data. Brief conceptual and practical reviews are presented for both Fourier and Hilbert-Huang approaches to the analysis of ocean wave data. Then, both methods are applied to the analysis of real wave time series. The time series subject to analyses were obtained by a directional wave meter installed on the southern Brazil continental shelf (32 10′S, 51 58′W). The water depth at the location is 15 meters and the data were obtained during three years. The Hilbert-Huang results for spectra are compared with those of the Fourier analysis. The application of the time-frequency method leads to significant improvements regarding the representation of both nonlinear and non-stationary ocean wave processes.

The Earth’s ‘hum’ is driven by ocean waves over the continental shelves

Observations show that the seismic normal modes of the Earth at frequencies near 10 mHz are excited at a nearly constant level in the absence of large earthquakes. This background level of excitation has been called the 'hum' of the Earth, and is equivalent to the maximum excitation from a magnitude 5.75 earthquake. Its origin is debated, with most studies attributing the forcing to atmospheric turbulence, analogous to the forcing of solar oscillations by solar turbulence. Some reports also predicted that turbulence might excite the planetary modes of Mars to detectable levels. Recent observations on Earth, however, suggest that the predominant excitation source lies under the oceans. Here I show that turbulence is a very weak source, and instead it is interacting ocean waves over the shallow continental shelves that drive the hum of the Earth. Ocean waves couple into seismic waves through the quadratic nonlinearity of the surface boundary condition, which couples pairs of slowly propagating ocean waves of similar frequency to a high phase velocity component at approximately double the frequency. This is the process by which ocean waves generate the well known 'microseism peak' that dominates the seismic spectrum near 140 mHz (refs 11, 12), but at hum frequencies, the mechanism differs significantly in frequency and depth dependence. A calculation of the coupling between ocean waves and seismic modes reproduces the seismic spectrum observed. Measurements of the temporal correlation between ocean wave data and seismic data have confirmed that ocean waves, rather than atmospheric turbulence, are driving the modes of the Earth.

The effect of wave period filtering on wave power extraction and device tuning

The variations in the quantity of wave power available to a wave energy converter by filtering out short-period waves have been examined in this paper. Ocean wave data recorded at three different locations and water depths around northern Europe are used for this purpose along with numerically synthesized wave time series. A wave power ratio, defined as the ratio between the wave power for the filtered and unfiltered data, is calculated for each data set, and the variation of this quantity with the degree of filtering is investigated. Two new parameters namely, R and S are defined to quantify the effect of this filtering on the variation of wave-to-wave period and height. It is shown that removing the shorter period waves has little effect upon the power available for extraction but may significantly reduce the rate at which the wave energy converter must retune to achieve optimum power conversion.

Data quality check procedures of an operational coastal ocean monitoring network

Field oceanographic and meteorological data are required for ocean engineering. In response to the requirement of field data, an operational coastal ocean monitoring network was established around Taiwan coast, including nine deep-water data buoys, one shallow-water pile station, 10 coastal weather stations and 10 tide stations. Data quality check procedures are necessary to ensure the accuracy of measurements. This paper presents the data quality check procedures on ocean wave data which includes automatic and manual check procedures. The checking criteria are derived using statistical theory in this paper. In addition, a sea-state-dependent algorithm is presented in this study in order to derive checking criteria of time-continuity check. It is showed to have better performance of picking up suspicious data than using fixed threshold process. This data quality check program is now used on the operational monitoring network.

Statistical distribution of nonlinear random water wave surface elevation

This study deals with the development of statistical modeling for water wave surface elevation by using a method that combines a dynamic solution with random process statistics. Ocean wave data taken from four NOAA (National Oceanic and Atmospheric Administration) buoys moored in the northeast Pacific were used to validate the model. The results indicated that the nonlinear probability density distribution of ocean wave surface elevation derived from the model described the measurements much better than Gaussian distribution and Longuet-Higgins distribution.

The oceanic excitation hypothesis for the continuous oscillations of the Earth

Continuous oscillations of the Earth are observed for frequencies between 2 and 7 mHz at almost every seismically quiet site in the world. These oscillations ride on a broad noise peak which spans the frequency band from 3 to 15 mHz and reaches its maximum at 7-9 mHz. We propose an oceanic excitation hypothesis which explains both the modal oscillations and the broad noise peak, specifically the action of oceanic infragravity waves on the solid Earth. Using the estimated amplitudes of oceanic infragravity waves from observation, although they are limited in number at the moment, we show that there is sufficient energy in these waves to excite observed seismic signals; for a given time window, the contribution from a small area (which may be as small as 100 km x 100 km) is all that is required to explain the seismic observations. The advantage of this oceanic mechanism over the previously proposed atmospheric mechanism is in the simultaneous explanation of the above two features in seismograms, whereas the atmospheric hypothesis has only explained the modal oscillations. The oceanic mechanism naturally explains the predominant 6-month periodicity as a result of semi-hemispheric ocean-wave activities in the Northern and Southern hemispheres, showing a good match between seismic data and satellite ocean-wave data both in the amplitude and phase of seasonal variation. Our Earth seems to be filled with ubiquitous propagating Rayleigh waves, generated directly by oceanic infragravity waves, for the frequency band 3-15 mHz.

On the generation of secondary microseisms observed in northern and central Europe

Microseism recordings from four European broadband stations and from three seismic arrays in Scotland, Norway, and Germany are compared with model wave data of the oceanic wave field in the North Atlantic and local ocean wave data from the Norwegian coast at 60°N, both measured during February–March 2000. Two approaches have been tested to locate generation areas of microseismic energy: a new amplitude correlation technique and beam backprojection from the three seismic arrays. Both techniques reveal that the main generation areas are located in specific regions off the coast of Southwest Norway and North Scotland. Seismic stations distant from these generation areas record a superposition of seismic energy from different source regions. Those close to a specific source region also show a high correlation with it. Both techniques give upper limits for the extent of the generation area of the strongest storm on 6/7 March at the southwest Norwegian coast of about 500 km. By using marine X‐band radar measurements of the two‐dimensional wave height spectrum, we estimate that the relative change of the extension of the generation area off the coast of southwest Norway during several storms is less than a factor of 3. This indicates that the size of the generation area is controlled by static features as coastline or bathymetry, and not by the extent of the storms. Microseism energy appears to be mainly controlled by the wave height in distinct and identifiable generation regions, so that the wave climate in these regions can be studied using historical records of microseisms.

A note on analyzing nonlinear and nonstationary ocean wave data

The Huang–Hilbert transformation (HHT, composed of empirical mode decomposition and Hilbert transformation) can be applied to calculate the spectrum of nonlinear and nonstationary signals. The superior temporal and frequency resolutions of the HHT spectrum are illustrated by several examples in this article. The HHT analysis interprets wave nonlinearity in terms of frequency modulation instead of harmonic generation. The resulting spectrum contains much higher spectral energy at low frequency and sharper drop off at high frequency in comparison with the spectra derived from Fourier-based analysis methods (e.g. FFT and wavelet techniques). For wind generated waves, the spectral level of the Fourier spectrum is about two orders of magnitude smaller than that of the HHT spectrum at the first subharmonic of the peak frequency. The resulting average frequency as defined by the normalized first momentum of the spectrum is about 1.2 times higher in the Fourier-based spectra than that of the HHT spectrum.

A linear functional relationship model for circular data with an application to the assessment of ocean wave measurements

This article suggests a linear functional relationship model for comparing two sets of circular data subject to unobservable errors. Unlike the corresponding and relatively well-studied model for linear data, maximum likelihood estimation for this model is very complicated and no explicit solutions are possible. Using a numerical approximation, we are able to solve the likelihood equations approximately, and to obtain good approximations to the likelihood estimates of the parameters. The quality of our estimates and the feasibility of the estimation method are illustrated via simulation. By establishing a parallel with the model for linear data, we are able to explain the various problems occurring in the process of estimation and to substantiate our numerical results. The interest in the model arose in connection with the study of ocean wave data; an application to such data is also given.

Horizontal asymmetry and steepness distributions for wind-driven ocean waves from severe storms

Results on horizontal asymmetry and steepness distributions from analyses of ocean wave data collected during 10 severe storms in the northern North Sea are presented. The data have been collected at a sampling rate of 5 Hz using laser altimeters mounted on a fixed platform permitting the shapes of individual waves to be quite closely defined. This has allowed the steepness of the fronts and backs of wave crests and troughs to be examined. It is found that, on an average, as the non-dimensionalised wave height increases, the horizontal asymmetry becomes more pronounced. That is, the fronts of large wave crests tend to be steeper than their backs. Regression has been used to establish relationships between individual non-dimensionalised wave heights and steepness measures. The generalised Pareto distribution has then been used to establish a simple model for predicting the probability of extreme wave steepness conditional on the non-dimensionalised wave height.

Validation of ocean wind and wave data using triple collocation

Significant wave height and wind speed fields from ERA‐40 are validated against buoy, ERS‐1, and Topex altimeter measurements. To do so, we propose and apply a triple collocation statistical model. The model takes into account the random errors in observations and model results and allows the estimation of the variances of the errors. We first examine the case where the random errors of the different systems are independent, but situations where independence is not strictly observed are also considered. The results show that the ERA‐40 predictions underestimate high values of significant wave height and, contrary to what would be obtained by less sophisticated statistical methods, wind speed, that the variance of the errors associated with the ERA‐40 system is much higher than that of the errors of the measurements, and that the former shows a dependence on the value of the observations not present in the latter. The altimeter measurements of significant wave height are very precise, in contrast to the large uncertainty associated with the altimeter retrieved wind speeds.

Satellite wave measurements for coastal engineering applications

Measurements from the GEOSAT, ERS-1 and 2 and Topex/Poseidon satellites have now accumulated to over 15 years of global ocean wave and wind data. Extraction of wave height, wind speed and wave period from the satellite altimeters and directional wave spectra from the synthetic aperture radars are reviewed along with recent validation and calibration efforts. Applications of the data to a variety of problems illustrate the potential of satellite wave measurements.

Methods for intercomparison of wave measurements

The paper reviews methods for quality assessment and intercomparison of ocean wave data. The sampling variability for conventional time series recordings is summarized and compared to less common area measuring measurements. The sampling variability affects the scatter seen in simultaneous observations, and variability in excess of the sampling variability signifies real differences between the instruments. Various means of intercomparing wave parameters and spectra are discussed and two somewhat unconventional ways of deriving regression and calibration relationships are also shown. The methods are illustrated using data from SCAWVEX, focusing mainly on wave data from the HF radars and Directional Waveriders.

Microseisms and ocean wave measurements

Measurements of microseisms in Auckland, New Zealand, are compared with ocean wave data taken on the west coast of New Zealand, about 150 km southwest of Auckland. There is strong correlation at most times. Exceptions are when the Auckland area is subject to strong winds from the easterly quarter. Microseism activity in Auckland in the 0.05-1-Hz band appears to be entirely due to ocean waves.

Probability Density Distribution of Mean Added Wave Resistance

The long term characteristics of mean added wave resistance (AWR) is very important from the view point of long term ship operation and ship design. Today, the short term prediction of AWR can be made through theoretical calculation. So, by using the long-term ocean wave data, we can carry out long term prediction of AWR. Here we carried out long term prediction, and found that the mean AWR follows the so called log-normal distribution. Furthermore, we investigated into the effect of wave data and ship form on that distribution. As wave data, we adopted the database of North Pacific Ocean by SRI and by BMT (GWS). As ship type, we adopted the bulk carrier with large B/d ratio.

The Effective Bandwidth of a Multitaper Spectral Estimator

The bandwidth of a spectral estimator is a measure of the minimum separation in frequency between approximately uncorrelated spectral estimates. We determine an effective bandwidth measure for multitaper spectral estimators, a relatively new and very powerful class of spectral estimators proving to be very valuable whenever the spectrum of interest is detailed and/ or varies rapidly with a large dynamic range. The multitaper spectral estimator is the average of several direct spectral estimators, each of which uses one of a set of orthogonal tapers. We show that the equivalent width of the autocorrelation of the overall spectral window is a suitable measure of the effective bandwidth of a multi-taper spectral estimator and illustrate its use in the case of both Slepian and sinusoidal orthogonal tapers. This measure allows a unified treatment of bandwidth for the class of quadratic spectral estimators. Hence, for example, it is now possible properly to compare multitaper spectral estimators with traditional lag window spectral estimators, by assigning a fixed and equal effective bandwidth to both methods. An application is given to the spectral analysis of ocean wave data.

The effective bandwidth of a multitaper spectral estimator

SUMMARY The bandwidth of a spectral estimator is a measure of the minimum separation in frequency between approximately uncorrelated spectral estimates. We determine an effective bandwidth measure for multitaper spectral estimators, a relatively new and very powerful class of spectral estimators proving to be very valuable whenever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range. The multitaper spectral estimator is the average of several direct spectral estimators, each of which uses one of a set of orthogonal tapers. We show that the equivalent width of the autocorrelation of the overall spectral window is a suitable measure of the effective bandwidth of a multitaper spectral estimator and illustrate its use in the case of both Slepian and sinusoidal orthogonal tapers. This measure allows a unified treatment of bandwidth for the class of quadratic spectral estimators. Hence, for example, it is now possible properly to compare multitaper spectral estimators with traditional lag window spectral estimators, by assigning a fixed and equal effective bandwidth to both methods. An application is given to the spectral analysis of ocean wave data.

Observational evidence of the interaction of ocean wind-sea with swell

More than 10 000 spectra of ocean wave data were acquired from a series of buoys moored in the Southern Ocean off the west coast of Tasmania for a period of seven years. Spectra were grouped according to the wind speed and whether the wind direction was onshore or offshore and the mean spectrum found for each group. The frequencies of the low frequency cut-offs and of the spectral peaks of the resulting mean spectra were found to be independent of the wind speed in contrast to self-similar standard spectra such as JONSWAP. This property is attributed to the presence of a swell background which controls the evolution of wind-seas in the open ocean. During offshore winds, the spectral variance between 0.04 Hz and 0.16 Hz was found to be negatively correlated with wind speed indicating that swell is in turn shaped either by the wind-sea or by the wind itself. Relationships between various spectral and time domain parameters and the wind speed were investigated empirically. The slope/acceleration measures such as m4, the spectral fourth moment, were found to be highly correlated with wind speed.

Real-Time Quality Control of Wave Observations in the North Sea

Abstract The use of ocean wave data in new data assimilation techniques prompted the development of a real-time quality control system for wave height and wave period observations. Over the North Sea, a relatively large number of wave observations, as well as a reliable wave model, are available. Therefore, a variety of tests can be made, allowing for a quite sophisticated wave-data quality control system. The system uses some of the ideas of Gandin's comprehensive quality control. In particular, an ensemble of single-variate tests is used instead of one large multivariate test, and data are not rejected and thrown away in successive tests but can be rehabilitated until the very end. Three months of data have been used to test the system. The decisions of the system are found to agree with manual analyses. The statistical properties of the accepted and rejected data are checked. After quality control, the residuals of the quality control tests have almost Gaussian distributions.

Wave direction measurements using pitch-roll buoys

This paper describes the 3-m diameter discus buoys that the National Data Buoy Center for the U.S. National Oceanic and Atmospheric Administration now uses routinely to measure ocean directional wave data. Large quantities of these data, from which estimates of directional wave spectra can be calculated, are now in the national archives. An overview of all aspects of the buoy design is provided, with particular emphasis on data processing methods. A description of a new method for determining the total sensor-hull response phase angle, which needs to be applied each hour to calculate best estimates of directional wave spectra, is included. Examples of measured response functions and directional wave data are presented.