On the conversion of wave-gauge pressure data to the spectrum of surface waves

The idea of measuring surface wind waves with a submerged pressure transduc er is well known. However. the methods for conversion of the pressure fluct uations time series to the frequency surface waves spectra use a linear alg ebraic relationship between the pressure fluctuations and surface displacem ent, which is only valid for monochromatic waves and not valid for random w ave fields. In the present study, we show that an algebraic relationship ex ists between the space-time spectra of these random processes rather than b etween the realizations of random pressure and surface displacement. The fr equency spectrum of surface displacement is determined by integrating the r elationship obtained over the entire wave number domain. Examples of calcul ations are also presented.