Question of the pitch-roll buoy response to ocean waves as a simple harmonic oscillator?

The assumption that the East and North deck slopes of a pitch–roll buoy respond to East and North sea slopes as simple harmonic oscillators is routinely made by the National Data Buoy Center (NDBC) and others producing directional wave data. Although directional wave data derived with this assumption usually appear to be of good quality, the validity of the assumption has not previously been more directly demonstrated. In this paper, a method is proposed to judge the validity of the assumption for any set of time series records of buoy angular motion. The proposed method is applied to 200 record sets taken by an NDBC buoy located at ocean station 46024, and to five record sets taken by another NDBC buoy at 46051. For the 46024 data, it was demonstrated that the simple harmonic oscillator assumption was near perfectly valid. For the smaller 46051 data set, the simple harmonic oscillator assumption was shown to be slightly less valid.