14 



the instrument center using four differential pressure gauges, 

 (Figure II-5) . The differential gauges directly infer water surface 

 slope, and since there are two such measurements along two axes 

 through the instrument center, it is possible to arithmetically 

 develop the water surface curvature along each axis. It will be 

 demonstrated in Chapter IV that these measurements permit the 

 estimation of the first seven Fourier coefficients of the directional 

 wave spectrum. Conventional analysis from submerged pressure sensor 

 arrays arithmetically develops one measurement of the water siirface 

 slope along each of two axes. Typical surface riding buoys similarly 

 measure the slope along each of the two axes. This data, along with 

 the water surface displacement record, permits the generation from 

 these systems of the first five directional Fourier coefficients. 

 The cloverleaf buoy, a cluster of three surface riding buoys, is 

 capable of estimating the first nine Fourier coefficients, 

 (Mitsuyasu,1973; Cartwright and Smith, 1964). 



It can be shown that it is possible to generate up to the 

 first M(M-1)+1 directional Fourier coefficients for an array with M 

 number of gauges (Borgman, 1969) • Using this technique, pressure 

 sensor arrays such as the Scripps Sxy gauge (Seymour , 1978) could 

 generate the first nine directional Fourier coefficients. The DPG, 

 in the configuration described, could develop the first eleven 

 coefficients. The DPG could potentially develop the first twenty-one 

 coefficients with the same number of transducers in a different 



