Investigating the Multifractal Properties of Significant Wave Height Time Series Using a Wavelet-Based Approach

Abstract

Singularities play a significant role in the characterization of time series. The temporal characteristics of fluctuating significant wave height time series are investigated in this study. The hourly time series from 24 stations located off the west coast of the United States are used for the analysis. The multifractal nature of these time series is unveiled by employing a wavelet-based method. The wavelet transform modulus maxima method is applied to obtain the multifractal spectra (singularity spectrum) of the significant wave height series. The multifractal spectra and their parameters such as peak, min and max Hölder exponents, skewness coefficients, and support lengths are calculated. The peak Hölder exponent ranged from 0.30 to 0.46 throughout the study area. Hölder exponents that are less than 0.5 indicate that the time series exhibits an antipersistent random walk. The spatial variation of parameters is depicted through kriging maps. Different spatial variation patterns can be seen from the maps. It is clear that deep offshore stations have relatively higher Hölder exponents than coastal areas. This change can be related to the wave generation mechanism, by way of physical interpretations. Since the stations located in the deep offshore can receive more swell waves than coastal zones and are open to large-scale storms, they may tend to be more persistent and have greater Hölder exponents. Also, the type of the singularities occurring in deep offshore and in the coastal zones is assessed by considering the wave generating mechanisms.