24 



Elevations of water surface 



I nodes are sought 



Bernoulli equation appHed 

 at known elevation, zp 



at 



Figure 3.1: Schematic of system of equations in a window 



jf and w^l^ terms in Eq. 3.2). There is also a significant nonlinearity introduced by 



the application of the boundary conditions at the unknown and varying free surface. 



Observational Equations The given form for the potential function could repre- 

 sent any periodic flow, subject to the bottom boundary condition. The FSBCs define 

 the flow as a gravity-constrained, free surface flow. The observational equations are 

 the equations in the system that force the solution to fit the given record. For a 

 subsurface pressure record, this is the Bernoulli equation, applied at the location of 

 the pressure measurement. The required number of independent equations are es- 

 tablished by applying the Bernoulli equation at a number of times throughout the 

 window considered. The error in the Bernoulli equation is the difference between the 

 measured dynamic pressure and that computed from the kinematics defined by the 

 potential function. The solution is the set of parameters in the potential function 

 and the set of water surface nodes that produces a predicted dynamic pressure that 

 matches the measured record, while simultaneously satisfying the FSBCs. 



A system of equations is specified if there are as many independent equations as 

 unknown parameters in the system. If there are more equations than unknowns, the 

 solution can be defined as that which results in the smallest squared errors in the 

 equations. This least squares formulation is also appropriate for a uniquely defined 



