Wavelet Spectrum Analysis and Ocean Wind Waves

Liu, Paul C.

doi:10.1016/b978-0-08-052087-2.50012-8

Cited by 186 publications

(136 citation statements)

References 18 publications

Supporting

Mentioning

131

Contrasting

Unclassified

Order By: Relevance

“…Meyers et al (1993) examined ocean wave dispersion, and others have used the method to analyze wave growth (e.g. Liu, 1994). Tokmakian and McClean (2003) used wavelets to examine the realism of SSH in high resolution ocean models as compared to satellite data.…”

Section: R Tokmakian: Multiple Time Scales Of Variability In the Pacmentioning

confidence: 99%

On the multiple time scales of variability in the Northeast Pacific Ocean

Tokmakian

2009

Ocean Sci.

View full text Add to dashboard Cite

Abstract. The spatial and temporal sea surface height energy distribution of the Northeast Pacific Ocean is described and discussed. Using an altimetric data set covering 15 years (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007), the energy within the 3-9 month band is primarily located within 10 • of the coast. In the Gulf of Alaska, this energy signal is on the shelf, while further south, west of the California/Oregon coast, the significant energy in this band is west of the shelf break. In both cases, it is primarily forced by the local wind. Within the 2-3 year band, the signal reflects energy generated by local changes to the wind stress from large atmospheric shifts indicated by the Pacific North American Index and by advective or propagating processes related to El Niño-Southern Oscillation. Over the two 4-6 year periods within this data set, the change is primarily due to the large scale shift in atmospheric systems north of about 30 • N which also affect changes in current strengths. Based on the distribution of the energy signal and its variability, a set of three winter-time indices are suggested to characterize the distinct differences in the SSH anomalies in these areas.

show abstract

Section: R Tokmakian: Multiple Time Scales Of Variability In the Pacmentioning

confidence: 99%

On the multiple time scales of variability in the Northeast Pacific Ocean

Tokmakian

2009

Ocean Sci.

View full text Add to dashboard Cite

show abstract

“…Many aspects of the random process theory that are used here have been developed in the classical texts by Jenkins & Watts (1968), Yevjevich (1972), Oppenheim & Schafer (1975), Box & Jenkins (1976), Liu (1995), Chui & Montefusco (1994), and others. These texts develop several aspects of the identification and simulation of joint random processes based on the concepts of cross-correlation (in the time domain), cross-spectrum (in the frequency domain), and cross-wavelet spectrum (in both time and scale/frequency domains).…”

Section: Theorymentioning

confidence: 99%

Characterization of a cavern conduit system in Vietnam by time series correlation, cross-spectrum and wavelet analyses / Caractérisation du système du conduit d’une grotte au Vietnam par des analyses corrélatoires, spectrales-croisées et en ondelettes de séries temporelles

Tam

Smedt

Batelaan

et al. 2004

Hydrological Sciences Journal

View full text Add to dashboard Cite

Time series analyses are applied to characterize the transient flow regimes of the Nam La cavern conduit, northwest Vietnam. The conduit transforms the input signal to an output signal, and the degree of transformation provides information on the nature of the flow system. The input for the analysis is net precipitation and the flow hydrograph at the cave entrance, while the output series is the flow hydrograph at the resurgence. Cross-correlation and cross-spectrum analysis are used to investigate the stationarity and linearity of the input-output transformation of the system, resulting in hydrodynamic properties such as system memory, response time, and mean delay between input and output. It is shown that during high flow periods, the flow in the conduit is pressurized. Consequently, the linear input-output assumption holds only for low flows. To highlight the hydrodynamics of the cavern conduit for the high flow periods, wavelet spectrum and wavelet cross-spectrum analyses are applied.Key words karst; carbonate rocks; cross-correlation; wavelet analysis; Vietnam Caractérisation du système du conduit d'une grotte au Vietnam par des analyses corrélatoires, spectrales-croisées et en ondelettes de séries temporellesRésumé Des analyses de séries temporelles sont réalisées pour caractériser les écoulements en régime transitoire dans le conduit de la grotte Nam La, au Vietnam. Le conduit transforme le signal d'entrée en un signal de sortie. Le degré de cette transformation fournit des informations sur la nature du système d'écoulement. Les données d'entrée sont la pluviométrie nette et l'hydrogramme à l'entrée de la grotte, alors que le signal de sortie est l'hydrogramme au niveau de la résurgence. L'analyse de corrélation croisée et l'analyse spectrale croisée sont employées pour étudier la stationnarité et la linéarité de la transformation entrée-sortie du système, en renseignant sur certaines propriétés hydrodynamiques comme la mémoire du système, le temps de réponse, et le délai moyen entre entrée et sortie. Il apparaît que, pendant les périodes de hautes eaux, l'écoulement dans le conduit est sous pression. En conséquence, l'hypothèse de linéarité entrée-sortie n'est valable que pour les basses eaux. Afin de mettre en évidence l'hydrodynamique du conduit pour les périodes de hautes eaux, des analyses spectrales et spectrales croisées en ondelettes sont réalisées.

show abstract

“…3820 Z. Ge: Tests for the wavelet cross spectrum and wavelet linear coherence Perhaps the first one in geophysics, Liu (1994) defined the wavelet cross spectrum (WCS) between two time series x(t) and y(t) as C xy (a, b) = X * (a, b)Y (a, b),…”

Section: Introductionmentioning

confidence: 99%

“…In the definitions in Liu (1994) and TC98, the complex conjugate of Y (a, b), instead of that of X(a, b), was used. This inconsistency in definition will not affect any discussions below.…”

Section: Introductionmentioning

confidence: 99%

“…θ y (a, b)−θ x (a, b), reflects the phase difference by which y(t) leads x(t) at the given scale and time. To present the information in phase Liu (1994) suggested that both the real and imaginary parts of the WCS be shown. Alternatively, another common practice is to show both the absolute value and the phase angle of C xy in the time-scale domain.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Significance tests for the wavelet cross spectrum and wavelet linear coherence

2008

Ann. Geophys.

View full text Add to dashboard Cite

Abstract. This work attempts to develop significance tests for the wavelet cross spectrum and the wavelet linear coherence as a follow-up study on Ge (2007). Conventional approaches that are used by Torrence and Compo (1998) based on stationary background noise time series were used here in estimating the sampling distributions of the wavelet cross spectrum and the wavelet linear coherence. The sampling distributions are then used for establishing significance levels for these two wavelet-based quantities. In addition to these two wavelet quantities, properties of the phase angle of the wavelet cross spectrum of, or the phase difference between, two Gaussian white noise series are discussed. It is found that the tangent of the principal part of the phase angle approximately has a standard Cauchy distribution and the phase angle is uniformly distributed, which makes it impossible to establish significance levels for the phase angle. The simulated signals clearly show that, when there is no linear relation between the two analysed signals, the phase angle disperses into the entire range of [−π, π] with fairly high probabilities for values close to ±π to occur. Conversely, when linear relations are present, the phase angle of the wavelet cross spectrum settles around an associated value with considerably reduced fluctuations. When two signals are linearly coupled, their wavelet linear coherence will attain values close to one. The significance test of the wavelet linear coherence can therefore be used to complement the inspection of the phase angle of the wavelet cross spectrum.The developed significance tests are also applied to actual data sets, simultaneously recorded wind speed and wave elevation series measured from a NOAA buoy on Lake Michigan. Significance levels of the wavelet cross spectrum and the wavelet linear coherence between the winds and the waves reasonably separated meaningful peaks from those generated by randomness in the data set. As with simuCorrespondence to: Z. Ge (gezhfu@yahoo.com) lated signals, nearly constant phase angles of the wavelet cross spectrum are found to coincide with large values in the wavelet linear coherence between the winds and the waves. Not limited to geophysics, the significance tests developed in the present work can also be applied to many other quantitative studies using the continuous wavelet transform.

show abstract

Wavelet Spectrum Analysis and Ocean Wind Waves

Cited by 186 publications

References 18 publications

On the multiple time scales of variability in the Northeast Pacific Ocean

On the multiple time scales of variability in the Northeast Pacific Ocean

Characterization of a cavern conduit system in Vietnam by time series correlation, cross-spectrum and wavelet analyses / Caractérisation du système du conduit d’une grotte au Vietnam par des analyses corrélatoires, spectrales-croisées et en ondelettes de séries temporelles

Significance tests for the wavelet cross spectrum and wavelet linear coherence

Contact Info

Product

Resources

About