Paul C. Liu

Wavelet Spectrum Analysis and Ocean Wind Waves

Abstract Wavelet spectrum analysis is applied to a set of measured ocean wind waves data collected during the 1990 SWADE (Surface Wave Dynamics Experiment) program. The results reveal significantly new and previously unexplored insights on wave grouping parameterizations, phase relations during wind wave growth, and detecting wave breaking characteristics. These insights are due to the nature of the wavelet transform that would not be immediately evident using a traditional Fourier transform approach.

Analysis of freak wave measurements in the Sea of Japan

Abstract This paper presents an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity to catch a glimpse of the statistics of freak waves in the ocean. The results show that a well-defined freak wave may occur in the developed wind–wave condition: S ( f )∝ f −4 , with single-peak directional spectra. The crest and trough amplitude distributions of the observed sea waves including freak waves are different from the Rayleigh distribution, although the wave height distribution tends to agree with the Rayleigh distribution. Freak waves can be readily identified from the wavelet spectrum where a strong energy density occurs in the spectrum, and is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs.

Is the wind wave frequency spectrum outdated

This paper presents a detailed examination of the practice of using the frequency spectrum to characterize wind waves. In particular, the issue of stationarity and Gaussian random process in connection with wind wave studies is addressed. We describe a test for nonstationarity based on the wavelet spectrum. When this test is applied to wind wave time series, the results significantly diverge from those expected for a Gaussian random process, thus casting critical doubts on the conventional concept of the wind wave frequency spectrum.

Has wind–wave modeling reached its limit?

This article uses a comparison of four different numerical wave prediction models for hindcast wave conditions in Lake Michigan during a 10-day episode in October 1988 to illustrate that typical wave prediction models based on the concept of a wave energy spectrum may have reached a limit in the accuracy with which they can simulate realistic wave generation and growth conditions. In the hindcast study we compared the model results to observed wave height and period measurements from two deep water NOAA/NDBC weather buoys and from a nearshore Waverider buoy. Hourly wind fields interpolated from a large number of coastal and overlake observations were used to drive the models. The same numerical grid was used for all the models. The results show that while the individual model predictions deviate from the measurements by various amounts, they all tend to reflect the general trend and patterns of the wave measurements. The differences between the model results are often similar in magnitude to differences between model results and observations. Although the four models tested represent a wide range of sophistication in their treatment of wave growth dynamics, they are all based on the assumption that the sea state can be represented by a wave energy spectrum. Because there are more similarities among the model results than significant differences, we believe that this assumption may be the limiting factor for substantial improvements in wave modeling.

Comparison of a Two-Dimensional Wave Prediction Model with Synoptic Measurements in Lake Michigan

Abstract We compare results from a simple parametric, dynamical, deep-water wave prediction model with two sets of measured wave height maps of Lake Michigan. The measurements were made with an airborne laser altimeter under two distinctly different wind fields during November 1977. The results show that the model predicted almost all of the synoptic features. Both the magnitude and the general pattern of the predicted wave-height contours compared well with the measurements. The model also predicts the direction for wave propagation in conjunction with the wave height map, which is useful for practical ship routing and can be significantly different form the prevailing wind direction.

Wave grouping characteristics in nearshore Great Lakes II

The recently advanced approach of wavelet transform is applied to the analysis of wave data measured in the nearshore areas of the Great Lakes. The conventional spectrum analysis of wave time series in the frequency domain can be readily generalized to the frequency and time domain using the wavelet transform. The traditional Fourier transform approach has not been able to directly assess the time localized nature of wave groups. With the application of wavelet transformation, the relatively unexplored wave grouping characteristics come to light as the predominant feature of wave processes.

Intraseasonal oscillations in sea surface temperature, wind stress, and sea level off the central California coast

Abstract The wavelet transform is used to conduct spectral and cross-spectral analysis of daily time series of sea surface temperature (SST), surface wind stress, and sea level off the central California coast for an 18-year period from 1974 through 1991. The spectral band of primary interest is given by intraseasonal time scales ranging from 30 to 70 days. Using the wavelet transform, we examine the evolutionary behavior of the frequently observed 40–50 day oscillation originally discovered in the tropics by Madden and Julian, and explore the relative importance of atmospheric vs oceanic forcing for a range of periods where both could be important. Wavelet power spectra of each variable reveal the event-like, nonstationary nature of the intraseasonal band. Peaks in wavelet power typically last for 3–4 months and occur, on average, approximately once every 18 months. Thus, their occurrence and/or duration off central California is somewhat reduced in comparison to their presence in the tropics. Although peaks in wind stress often coincide with peaks in SST and/or sea level, no consistent relationships between the variables was initially apparent. The spectra suggest, however, that relationships between the variables, if and where they do exist, are event-dependent and thus have time scales of the same order. Cross-wavelet spectra between wind stress and SST indicate that periods of high coherence (>0.90) occur on at least six occasions over the 18-year period of record. Phase differences tend to be positive, consistent with wind forcing. For wind stress vs sea level, the cross-wavelet spectra indicate that periods of high coherence, which tend to correlate with lags close to zero, also occur, but are less frequent. As with SST, the periods of high coherence usually coincide with events in the wavelet power spectra. The somewhat weaker relationship between wind stress and sea level may be due to an independent contribution to sea level through remote forcing by the ocean originating in the tropics. Finally, simple dynamical arguments regarding the lag relationships between the variables appear to be consistent with the cross-wavelet results.

Representing frequency spectra for shallow water waves

Abstract Wind waves recorded in water from 1.4 to 3.8 m deep near the southeastern shore of Lake Erie during 1981 were used to compare two methods for representing wave spectra in shallow water. The results show that the semi-theoretical Wallops model, which requires total energy, peak energy frequency, and depth as parameters, provides fair agreement with observed spectra at the deeper stations but only marginal agreement in very shallow water. The general empirical model, which requires average frequency and energy density at the spectral peak as additional parameters, provides closer agreement with observed wave spectra for all depths.

Wavelet Spectrum of Freak Waves in the Ocean

This paper presents a wavelet transform analysis of continuous wave recordings in the Sea of Japan during 1986 1990. The analysis is carried out to study the incidents of freak waves. The results show that a well-defined freak wave can be readily identified from the wavelet spect rum where strong energy density in the spectrum is instantly surged and seemingly carried over to the high frequency components at the ins tant the freak wave occurs. Thus for a given freak wave, there appears a clear corresponding signature shown in the time-frequency wavelet spectrum. Since freak waves are primarily transient events occurring unexpectedly, wavelet transform analysis on continuous, long duration wave measurements clearly represents the most ideal approach to discern the localized characteristics of freak waves for further exploration. 1 I n t r o d u c t i o n Coasta l and open oceans are known to have occasionally observed waves of unusually large size, generally known as the freak waves, which can be hazardous to mariners . As the occurrence of freak waves has been mostly during unknown and unexpec ted conditions, available measurement and analysis are extremely rare. Because of i ts rareness and lack of measurement , nei ther the cause of the occurrence nor a specific definition of freak waves have been sufficiently

Assessing wind wave spectrum representations in a shallow lake

Abstract This paper presents an objective assessment of three published wave spectrum formulas for the shallow sea. It compares wave spectra estimated by these formulas with those calculated from actual field measurements made in Lake Erie during 1981 in depths ranging from 1.4 to 14.0 m. The results show that the models each have various degrees of effectiveness and applicability. The choice of which model to use may depend upon the availability of input parameters, and is still basically subjective. The models specifically developed for the shallow depth are found to be less effective. The form of spectral representation may remain similar at all depths, with depth affecting only the wave parameters that characterize the spectrum form.