27 



of the gradients from a measured record is very sensitive to error in the record, and 

 thus Sobey found it necessary to smooth field and laboratory measurements with a 

 simple moving average filter. 



There are no pressure gradient terms in the Bernoulli equation, so the application 

 of the LFI method to a measured pressure trace should be less sensitive to noise. 

 Nevertheless, measurement error remains a problem in applying the LFI method to a 

 pressure record. When there is obvious noise in the record, an alternative to smooth- 

 ing is to substantially overspecify the system of equations. By taking many samples 

 on the pressure record in each window, the least squares optimization may accommo- 

 date the errors in the measurements. This is preferable to smoothing, as no smoothing 

 algorithm can reproduce lost data, but will rather impose some apriori assumption 

 about the nature of the record on the results. Accommodating the measurement error 

 with many samples on the pressure record allows the least squares optimization to 

 find the best fit without imposing any further assumptions on the results. This was 

 the approach taken with the presented laboratory data (Section 3.5). Records gener- 

 ated analytically by Fourier wave theory contained no error, and therefore required 

 no special accommodation. 



The Mean Water Level 



The mean water depth, h, is included in the potential function (Eq. 3.1). This 

 is an unknown value when the only data available is a pressure record. While an 

 approximate depth of water is likely to be known at a given deployment site, the 

 water level fluctuates due to astronomical and storm tides. These processes happen 

 over a much larger time scale than the periods of wind generated waves. An estimate 

 for the local mean water level (MWL) can be determined by averaging the measured 

 pressure (after subtracting out the atmospheric pressure) over a period of time that 

 must be larger than a typical wave period, but smaller than the period of tidal 

 fluctuations, to accommodate changes in the mean water level. This mean pressure 

 is the local hydrostatic pressure, which is used to compute the mean water level, and 

 is subtracted from the pressure record to define the dynamic pressure. While this is 



