158 



where 



also 



T = wave period in seconds; 



L = g T^ - 5.12 T^ for d/L) 0.5 

 2 n 

 Suitable graphs and tables (Wiegel, 1947) have been prepared for the solution of 

 these equations. 



Every observer who has simultaneously measured the surface waves and 

 the sub-surface pressure fluctuations has found the surface waves calculated, 

 using the theoretical response factor determined from the above equation, to be 

 too small. Ten random measurements made at the Waterways Experiment Sta- 

 tion indicated an average correction of 1.07 should be applied to the calculated 

 wave height. Seventeen laboratory measurements at Berkeley indicated an aver- 

 age correction of 1.10 (Folsom, 1949). Field data reported by the Woods Hole 

 Oceanographic Institute (Seiwell, 1949) indicated a correction in excess of 1.20, 

 while the three sets of field data obtained by the University of California (Fol" 

 som, 1946), indicated values of 1.06, 1.08 and 1.18. Recent experiments at 

 Elwood, California, indicated that errors as great as 100 per cent occured when 

 average K factors of a well-defined wave group were used to determine the 

 height of individual waves (Morrison, 1952). 



Three sources of error that may cause the discrepancy between theory 

 and experiment are as follows: 



a. Loss of information: Due to the hydrodynamic attenuation of the pres- 

 sure variations, higher frequency components are not present in the 

 pressure records. Observed wave height therefore tends to be 

 greater than wave heights calculated from pressure records. 



b. Approximation of wave period: The heights of the surface wave usual- 

 ly are calculated from K factors determined by the characteristic 

 wave period for the record; in sonae cases the surface waves are 

 calculated from a K factor determined from individual waves, or 

 perhaps each half wave (Putz, 1950). However, all of these methods 

 assume a sinusoidal wave shape and neglect higher frequency com- 

 ponents present in the wave form. Thus, even though information is 

 presented in the pressure record, the information is neglected when 

 calculating the surface waves. If a Fourier analysis is made of the 

 pressure record, more information is obtained and a more accurate 

 determination of the surface can be made (Morison, 1952), Greater 

 information is obtained by reading the record at relatively short time 

 intervals. Another technique of computing the surface wave from 

 discreet points employs the application of a "raising kernal" based 

 on a Fourier integral (Fuchs, 1952). 



As a further attempt to obtain more information from the pressure 

 record and to compute a more accurate surface wave record, the 

 design of an analog computer is being studied by the University of 

 California. The computer consists primarily of an amplifier with a 

 frequency response characteristic which is the reciprocal of the hy- 

 drodynamic attenuation of the water. The desired amplifier would 

 apply a dynamic correction factor equal to 1 /K = cosh2nd/L for wave 

 periods assumed to be present in the pressure record. 



c. Approximations used in basic wave theory: As stated above, the 



equations for K factors (relating the sub-surface pressure variations 

 to the surface wave heights) have been derived using two-dimensional 

 theory of waves of infinitesimal height in water of constant depth. 

 The errors introduced by applying these equations to waves of finite 



