Wavelet And Local Directional Analysis of Ocean Waves

While local and wavelet-based methods have mostly been applied to single time records of wave data, Donelan et al. (1996) derived and applied the Wavelet Directional Method (WDM) to small arrays of wave elevation recorders. After a short review of the Morlet wavelet transform applied to random signals, the WDM is revisited and compared to a Local Triplet Analysis (LTA) where the wavelet transform replaces the discrete Fourier transform in the directional analysis. The sampling statistics of the WDM and LTA are summarized, assuming that the wave records are weakly stationary stochastic processes. All methods show consistent results when applied to real data. Time-averaged local estimates of common wave parameters closely fit the estimates from the standard analysis. Frequency-averaged local wave directions show considerable variation and, in addition, the local directional spread tends to take a significant drop during the passage of large wave groups. The methods are illustrated using offshore directional wave data from the Ekofisk field in the North Sea.