81 



in Chapter 3: the mass density of water (/>), acceleration of gravity (5), and the mean 

 zero crossing frequency of the measured record (cj,). 



Length scale = g/uil 

 Time scale = l/uj (5 7) 



Mass scale = — — 



5.3.2 Optimization Procedure 



The nonlinear optimization in the LFI method for the analysis of arrays of water 

 surface measurements is very similar to that used for the analysis of a subsurface 

 pressure trace. In the single wave approach, the solution is somewhat easier. The 

 potential function used by the single wave approach is almost the same as that used 

 with a point measurement (both Chapter 3 and Sobey (1992)), with the addition 

 of a directional component to the wave number. This results in a single additional 

 unknown, but the array of measurements provides at least three times as much data, 

 with gauges at at least three spatial locations to specify uniquely the directional 

 structure of the sea. The optimization tends to converge more rapidly and robustly 

 than with a single point measurement. 



When applying the method with the two wave potential function, there are many 

 more unknowns, and the optimization once again becomes somewhat tenuous. As 

 with the previous chapter, in is essential to identify a good initial estimate to reduce 

 the chances that the optimization will converge to a spurious minimum. 



Global Solution 



The strength of local methods is that they seek a single solution for only a short 

 segment of a record at a time. The downside is that a single short segment often 

 may not contain sufficient information to identify the directional nature of the wave 

 field. In the method presented in the previous chapter the initial estimate could be 

 computed from the data in the current window. In contrast, when working with 

 spatial arrays, it is necessary to examine a larger segment of the record, for example 



