For both autospectra and cross spectra, smooth estimates are formed by averag- 

 ing raw estimates over all 15 segments, and averaging results over 10 adjacent 

 frequency bands. Final resolution frequency bandwidth is df = 0.00977 Hz, and 

 the pass band of frequencies ranges from 0.044 to 0.162 Hz, which corresponds to 

 (N =) 13 discrete frequency bands. Degrees of freedom for spectral estimates 

 range from 160 to about 200, depending on the extent to which the second halves 

 of time series segments are correlated with the first halves (Welch 1967). 



Autospectral intercomparisons 



One part of error checking is a graphic intercomparison of signal means and 

 autospectra, an example of which is shown in the lower left graph of Figure 3. 

 Frequency autospectral estimates of data from all six pressure gauges are plotted 

 on the same set of axes from the first resolvable frequency band out to the tempo- 

 ral Nyquist frequency. If a pressure gauge is malfunctioning, its autospectrum 

 will deviate obviously from the main group of curves. 



The small inset graph in the lower left graph of Figure 3 is an analysis of sig- 

 nal means. The closely packed group of symbols of nearly constant value repre- 

 sents the deviations of the segment means from the median of the set of segment 

 means for each of the 15 segments. If a gauge develops signal drift problems, it 

 will be obvious as a symbol that deviates from the main group of symbols. Trian- 

 gle symbols in the small inset graph show the deviation of the indicated water sur- 

 face from mean sea level (gauge height off the bottom plus median of gauge mean 

 depths for each segment minus the total long-term mean ocean depth of 202 m), 

 and is therefore an indication of tide stage at Harvest Platform for each of the 15 

 segments in a collection. 



Coherence and phase comparisons 



The next step in error checking is computation of a dimensionless cross spec- 

 trum M r (f n ), defined by 



C(f) -iQif) 



Equation 1 is used in error checking in the form of coherence and phase estimates. 

 Coherence of signals from gauges i and j at discrete frequency f n is 



lt</„) = I M tj {f n ) | 2 (2) 



Signal phase difference of gauge i relative to gauge j at frequency f n is 



\ 



*<,(/■„> = tan_1 



Im[Jl/ /y (/■„)] 



[**{M v (f m )l) 



(3) 



Chapter 3 Primary Data Analysis 



