33 



of the record. In order to improve them, the estimates are refined by optimizing for 

 the best least squares fit in the window. 



/ 

 minimizeO(X) = } [Pdi — a cos {kx — toti)) 



^ tr ' (3.13) 



X = (a, kx,uj) 



Where Pd,i is the measured dynamic pressure at time i,-. The result of this optimiza- 

 tion is a linear estimate for the pressure record that fits the measured record most 

 closely in the window. 



Wave Number and Fourier Amplitudes Once the optimum initial frequency, 

 phase and amplitude are found, the wave number is computed with the linear disper- 

 sion relation (Eq. 3.9), and the first estimates for Fourier amplitudes are computed 

 as follows: 



a cosh kh 



^= T-JT, 7 ('^•14) 



pLU cosh k[n + Zp) 



Aj = oMi (3.15) 



The value of a is not critical and o = 0.1 was found to be satisfactory. 



Water Surface The location of the water surface at the A'^ nodes throughout 

 the window is estimated from the linear pressure response function with stretching 

 (Nielsen 1989): 



Pd(t„) cosh {k {h + Pd{tn)lpg)) i^.r.. 



pg cosh k[n -\- Zp) 



where Zp is the vertical location of the pressure gauge, and rjn is the elevation of the 

 water surface node at f„. pd{t) is computed from Eq. 3.8. 



