Teaching time-series analysis. II. Wave height and water surface elevation probability distributions

Abstract

This paper describes the second of a two-part series of pedagogical exercises to introduce students to methods of time-series analysis. While these exercises are focused on the analysis of wind generated surface gravity waves, they are cross-disciplinary in nature and can be applied to other fields dealing with random signal analysis. Two computer laboratory exercises are presented which enable students to understand many of the facets of random signal analysis with less difficulty and more understanding than standard classroom instruction alone. The first pedagogical exercise, described in the previous article, uses mathematical software on which the students execute the manual arithmetic operations of a finite Fourier analysis on a complex wave record. The results are then compared to those obtained by a fast Fourier transform. This article, the second of this two-part pedagogical series, addresses analysis of a complex sea using observed and theoretical wave height and water surface elevation probability distributions and wave spectra. These results are compared to a fast Fourier transform analysis, thus providing a link back to the first exercise.