25 



system, with an expected error of zero in all the equations. In order to specify the 

 solution to the LFI formulation, the boundary conditions (/^ and f^ ) are applied at 

 each of the water surface nodes, yielding "2A^ equations, and the Bernoulli equation 

 ifP) is applied at / nodes on the pressure record within the local window (Fig. 3.1). 

 There are a total of 3 + J + A' unknowns (/c, kx, a;, Ai . . . Aj, and rji . . . rjf^'). The 

 system is uniquely specified for / + A'^ = 3 + J and overspecified for / + A' > 3 + J, 

 resulting in the following least squares optimization: 



N 



minimizeO(X) = J] /f (X; r?„, i^' + /f (X; Vn^Uf 



n=l 



+ J]/f(X;P,.„.p,i.f (3.6) 



X = (/c, kx, u.Ai... Aj, 7/1 .. . 777v) 



where i„ are the locations in time where the water surface nodes, r/m are sought. 

 ti are the times within the window where the Bernoulli equation is applied, P^,! 

 are the measured dynamic pressures at ti, and Zp is the elevation of the pressure 

 gauge. Overspecification, particularly with additional nodes on the pressure record, 

 is advantageous for an actual record as a way to minimize the effect of any noise in 

 the measurements. Additional nodes on the pressure record also serve to emphasize 

 the measured data, which directly define the local kinematics. The details of the 

 solution to this system of equations is given in the following section. 



3.3 Computation Methods 



The LFI method can be broken down into the following sequence of steps: 

 1. Pre-processing of record. 



(a) Determine estimate for level of noise in the record. 



(b) Determine MWL and subtract hydrostatic pressure from record. 



(c) Determine estimate for magnitude and direction of Eulerian current. 



