26 



(d) Define a continuous record from the discrete observations by cubic spline 

 interpolation. 



(e) Specify spacing of output locations. 



(f) Compute mean zero crossing frequency. 



(g) Non-dimensionalize record and all parameters. 



2. Primary values of numerical solution parameters are chosen. 



(a) Window width (tq) 



(b) Order of solution (J) 



(c) Number of sample locations on record within each window (/) 



(d) Number of water surface nodes within each window (N) 



3. For each selected output location, a window in the record is defined, and an 

 LFI solution is computed. 



(a) Initial guess for the optimization is computed. 



(b) Full nonlinear optimization for all unknown components of the potential 

 function is computed. 



(c) Results are checked for spurious solution. 



i. If no solution, or a spurious solution, is found the solution parameters 



are adjusted, and the optimization repeated, 

 ii. If a good solution is found, progress to the next window. 



3.3.1 Pre-Processing of Record 



Accommodating Measurement Error 



Measurement error can be a major source of diflficulty, as the method relies on 

 the details of a small segment of the record. In Sobey's work (1992), the primitive 

 kinematic free surface boundary condition (Eq. 2.4) was applied at the measured water 

 surface, requiring an estimate for the time gradient of the surface. The estimation 



