There is a great deal of literature about how to best determine the DSF from a variety 

 of arrangements of measurements. Current practice is reviewed in Mansard (1997). 

 Unfortunately, all of these methods are limited in their ability to define accurately 

 the DSF. 



The time series measurements used to determine the variance spectrum commonly 

 include in excess of 1000 points in time. This much data in the time domain allows 

 a very high resolution computation of the spectrum of a stationary process in the 

 frequency domain. In the spatial domain, by contrast, there are only as many data 

 points as there are instruments in the particular measurement array. This may be 

 as few as three, and perhaps as many as a dozen, but it is too expensive to use 

 many more than that. As a result, there is little information to define the DSF. For 

 example, when data from an array of three instruments is analyzed by the standard 

 linear method, the DSF can be specified by only five independent coefficients (Dean 

 and Dalrymple 1991). While these few coefficients may serve well for determining 

 integral properties, such as the mean direction and radiation stress, it is not enough 

 information to accurately specify the complete kinematics. 



Another difficulty arises when determining the spectrum from measurements other 

 than wave staffs. Most often, subsurface pressure gauges or a combination of pressure 

 gauges and orthogonal velocity gauges are used. In this case, the measured quantity 

 must be related by a transfer function to the equivalent water surface. The transfer 

 function is most commonly determined from linear wave theory. This use of linear 

 wave theory once again contributes to errors in situations where linear theory is not 

 entirely appropriate. Bishop and Donelan (1987) discuss the difficulties in determin- 

 ing the transfer function from a subsurface pressure measurenaent to the equivalent 

 water surface. 



The commonly used methods for determining the DSF are statistical methods, 

 in that they rely on the assumption that the phases of the individual components 

 are randomly distributed. This assumption allows the DSF to be computed by dis- 

 regarding the phase information. Unfortunately, without the phase information, it is 

 impossible to reconstruct the detailed kinematics, only statistical descriptions can be 

 formulated. 



