Journal of Applied Mathematics
Volume 2004 (2004), Issue 5, Pages 379-394

A discrete wavelet analysis of freak waves in the ocean

En-Bing Lin1 and Paul C. Liu2

1Department of Mathematics, University of Toledo, Toledo 43606, OH, USA
2Great Lakes Environmental Research Laboratory, National Oceanic and Atmospheric Administration (NOAA), Ann Arbor 48105-2945, MT, USA

Received 25 June 2003; Revised 7 June 2004

Copyright © 2004 En-Bing Lin and Paul C. Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A freak wave is a wave of very considerable height, ahead of which there is a deep trough. A case study examines some basic properties developed by performing wavelet analysis on a freak wave. We demonstrate several applications of wavelets and discrete and continuous wavelet transforms on the study of a freak wave. A modeling setting for freak waves will also be mentioned.