Digital Data Analysis and Summarization 



The data were collected, analyzed, and then archived on optical disk using 

 the FRF's VAX computer. Data sets were normally collected every 3 hr. For 

 each gauge, a data set consisted of five contiguous records of 4,096 points 

 recorded at 0.5 Hz (approximately 34-min long), for a total of 2 hr and 

 50 minutes, resulting in only a 10-min gap between data sets. Analysis was 

 performed on individual 34-min records. 



The analysis program computes the first moment (mean) and the second 

 moment about the mean (variance) and then edits the data by checking for 

 "jumps," "spikes," and points exceeding the voltage limit of the gauge. A jump is 

 defined as a data value greater than five standard deviations firom the previous 

 data value, whereas a spike is a data value more than five standard deviations 

 from the mean. If less than five consecutive jumps or spikes are found, the 

 program linearly interpolates between acceptable data and replaces the erroneous 

 data values. The editing stops if the program finds more than five consecutive 

 jumps or spikes, or more than a total of 100 bad points, or the variance of the volt- 

 age is below 1x10'^ squared volts. The statistics and diagnostics from the 

 analysis are saved. 



Sea surface energy spectra are computed from the edited time series. 

 Spectral estimates are computed from smaller data segments obtained by 

 dividing the 4,096-point record into several 5 12-point segments. The estimates are 

 then ensemble-averaged to produce a more acciu-ate spectrum. These data 

 segments are overlapped by 50 percent (known as the Welch (1967) method) 

 which has been shown to produce better statistical properties than nonoverlapped 

 segments. The mean and linear trends are removed from each segment prior to 

 spectral analysis. To reduce side-lobe leakage in the spectral 

 estimates, a data window was applied. The first and last 10 percent of data points 

 were mvdtiplied by a cosine bell (Bingham, Godfrey, and Tukey 1967). Spectra 

 were computed from each segment with a discrete Fast Fourier 

 Transform and then ensemble-averaged. Sea siurface spectra from subsurface 

 pressure gauges were obtained by applying the linear wave theory fransfer 

 fiuiction. 



Unless otherwise stated, wave height in this report refers to the energy- 

 based parameter H^ defmed as four tunes the zeroth moment wave height of 

 the estimated sea surface spectrum (i.e., four times die square root of the 

 variance) computed from the spectrum passband. Energy computations from 

 the spectta are limited to a passband between 0.05 and 0.50 Hz for surface 

 gauges and between 0.05 Hz and a high-frequency cutoff for subsurface 

 gauges. This high-frequency limit is imposed to eliminate aliased energy and 

 noise measurements from biasing tiie computation of H^ and is defined as the 

 frequency where the linear theory fransfer function is less than 0.1 

 (spectial values are multiplied by 100 or more). Smoother and more 

 statistically significant spectral estunates are obtained by band-averaging 

 contiguous spectral components (three components are averaged per band. 



Chapter 3 Waves 



21 



