Manly Hydraulics Laboratory

NSW Public Works

Manly Hydraulics Laboratory

Analysis of Ocean Wave Data

Wave data is transmitted from the Waverider buoy or Zwarts pole to a shore station where it is processed to produce wave data statistics. The recorded bursts of wave data (normally 34 minutes long starting on the hour) are digitised at 0.5 second intervals and the data conditioned to remove any erroneous data points. The data is then analysed by two procedures; the zero crossing analysis and spectral analysis.

Zero Crossing Analysis

A widely accepted method to extract representative statistics from the wave traces is the zero crossing method. For this method, a wave is defined as the portion of record between two successive zero upcrossings. The waves are ranked (with their corresponding periods), and the following statistics computed:

Hsig: Significant wave height = average height of the waves which comprise the top 33% of wave heights.
H10: Average height of the waves which comprise the top 10%.
Hmax: Maximum wave height in a record.
Hrms: Root mean square wave height.
Hmean: Mean wave height.
Tz: Zero crossing period = mean period of all the waves in the record.
Tsig: Significant period = average period of the waves used to define Hsig.
Tc: Crest period = average time between successive crests (this involves a different definition of wave)

Spectral Analysis

One of the limitations of the zero crossing method is the poor definition of wave period. For example, a swell with a dominant period of 10 seconds will suffer a reduction in Tz with a superimposed locally generated sea. Both cases may however have a similar effect on a coastal structure. Further, the response of a structure, harbour or beach may be strongly dependant on period. In these cases an analysis which accounts for all components of wave period should be used.

The sea's motion at a point can be thought of as being composed of the sum of an infinite number of sine waves, each with its own amplitude, frequency and phase. Spectral analysis using the Fast Fourier Transform technique provides estimates of the components. Rather than plotting the amplitudes, it is conventional to plot the energy density (ie energy for each increment in frequency).

For convenience and because users are often interested in the shape of spectra the values are scaled to give unity area.

The following statistics are computed from the spectrum:

TP1 Period of highest peak.
TP2 Period of 2nd highest peak.
Yrms Root mean square surface vertical displacement.
M0, M1, M2, M3 Spectral moments. These provide parameters describing the shape of the spectrum. Spectral moments can also be related statistically to the zero crossing parameters:

Hrms approx. =  2*sqrt(2*M0)  =   2*sqrt(2)*Yrms  where M0 = Yrms²

Hsig approx. =  4*sqrt(M0)    =   4*Yrms   =    sqrt(2)*Hrms

H10  approx. =  5.1*sqrt(M0)  =   5.1*yrms

H1   approx. =  6.68*sqrt(M0) =   6.68*Yrms

Hmean approx.=  2.5sqrt(M0)   =   2.5*Yrms =   0.886*Hrms

Use of Analysed Wave Statistics

The analysed wave statistics define the wave conditions at the instrument location. The height and direction of waves propogating from the instrument location to the shoreline is altered due to refraction, diffraction, shoaling, attenuation due to seabed friction losses and wave breaking. Wave statistics therefore can only provide an indication of wave conditions at locations other than the instrument location.

Often users of wave data are interested in the ocean swell height and period. The wave statistics which best define the swell are Hsig and TP1. It is important to note that Hsig represents an average of many wave heights recorded during a sampling period. The individual Hmax recorded during the same sampling period may be up to twice the calculated Hsig.