11 



in its attempt to capture an entire segment of an unsteady wave field with a single 

 expression. This complication would become at least an order of magnitude greater 

 if the method were extended to include the second horizontal dimension. 



1.2.2 Local Methods 



Nielsen (1986, 1989) introduced a method that uses a local frequency and linear 

 wave theory to find the location of the water surface from a pressure record. In this 

 method, the wave in the region of each measured point is considered to be a small 

 segment of a linear wave, so that the pressure record is locally represented by a sine 

 function. 



p = An sin (a;„i„ - «„) (1.9) 



so that: 



'pW 



Estimating the curvature by finite diff'erences, the local frequency becomes: 



-p„_l + 2pn - Pn+1 



(1.10) 



(1.11) 



Pn^t^ 



where At is the time spacing between points. Alternatively, u can be computed from 

 trigonometric identities, 



1 _i fPn-l + Pn+l 



Ur, = — cos 



(1.12) 



8 V 2p„ 



which is exact for a sinusoid. 



Once the frequency has been determined, the wave number is computed from the 

 linear dispersion relation, Eq. 1.3. The water surface elevation can then be computed 

 with the linear pressure response function: 



Vn = Tj-j r (1-13) 



pg cosh.(knZp) 



where Zp is the elevation of the pressure measurement above the bed, and h is the 

 mean water depth (As the method is a local method for the interpretation of a point 



