transform and cosine bell function were used to obtain a spectral 

 analysis of each record (Harris, 1974). A record length of 512 points 

 was used in these analyses to obtain detailed spectral line resolution. 

 Spectral analysis indicated the period and amplitude of long waves of 

 interest (Q.5 to 5 hours) in the record. This analysis is necessary 

 because several long waves are generally simultaneously present and the 

 superposition of the waves gives the impression of a confused record. 

 Examples of spectra for Pentwater bay water levels recorded during 5 to 

 14 May 1975 are shown in Figure 12. 



If water level records were of good quality, levels measured in the 

 bay were then used to predict inlet water velocities using the finite- 

 difference continuity equation (6) . 



The resolution of the continuity equation should be checked to judge 

 the usefulness of the predicted velocities; e.g., at Pentwater, the level 

 recorder has a vertical resolution of 3 millimeters , the sampling interval 

 is 5 minutes (300 seconds), and the ratio ^hay^^o ~ ^^^ > ^° ^^^ velocity 

 prediction resolution, Vj,, based on equation (6), is: 



Vj, = 10^ ( ■' ) = 0.33 foot or 10.1 centimeters per second . (10) 



Thus, the velocity will be expressed as multiples of 10.1 centimeters 

 (0.33 foot) per second which may be adequate for many purposes. For 

 example, if A^^^/A^ was 10^, then with the given vertical resolution, 

 velocities could only be expressed as multiples of 100 centimeters 

 (3 feet) per second, which is inadequate for most purposes. 



At Pentwater, the measured velocities in the inlet were digitized at 

 a sampling rate of 5 minutes so that a direct comparison could be made 

 of measured and predicted (eq. 6) velocities. Cumulative frequency 

 distributions of measured and predicted (eq. 6) inlet velocities are 

 shown in Figure 13. The 2 months of record in 1974 show that velocities 

 predicted by continuity are slightly higher than measured velocities, 

 but adequate for many design purposes. 



IV. RESULTS 

 1. Seiching of the Great Lakes . 



Free modes of oscillation of the Great Lakes have been identified by 

 spectral analysis of water level records in this study and others 

 (Mortimer, 1965; Mortimer and Fee, 1974; Hamblin, 1975; Rao and Schwab, 

 1974), and have been predicted using numerical techniques (Rockwell, 

 1966; Mortimer, 1965; Birchfield and Murty, 1974; Rao and Schwab, 1974). 

 Table 3 summarizes the known modes of oscillation of Lakes Michigan, 

 Superior, Erie, and Ontario. 



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