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 from 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 voltage is below 1 x 10 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 divid- 

 ing the 4,096-point record into several 512-point segments. The estimates are 

 then ensemble-averaged to produce a more accurate 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 nonoverlap- 

 ped 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 multiplied 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 surface spectra from subsurface 

 pressure gauges were obtained by applying the linear wave theory transfer 

 function. 



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

 based parameter U mo defined as four times the zeroth moment wave height 

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

 variance) computed from the spectrum passband. Energy computations from 

 the spectra 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 the computation of H mo and is defined as 

 the frequency where the linear theory transfer function is less than 0. 1 

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

 statistically significant spectral estimates are obtained by band-averaging 

 contiguous spectral components (three components are averaged per band, 

 producing a frequency band width of 0.0117 Hz). 



Chapter 3 Waves 



21 



