time between observations is extended. 



A problem frequently faced by engineers is to choose a sampling in- 

 terval adequate to determine a mean recession rate for a given beach. 

 The precision of the estimated mean recession will depend on the inherent 

 longshore variability of recession which can be large (see Fig, 11); e.g., 

 4 meters of advance and 34 meters of retreat were measured over the same 

 7.4-year period at two stations less than 2 kilometers apart. It is well 

 known that for a fixed level of longshore variability, the precision of 

 the estimated regional mean can be improved by increasing the number of 

 survey stations. Less well recognized is that inherent variability 

 usually does not increase greatly with time. Thus, the probable error 

 of mean rates and the percent error in mean recession tend to decrease 

 with time. The variance of these estimates would also tend to decrease 

 (thus, the precision increase) in direct proportion to the number of years 

 between surveys. 



The claim that longshore variability in recession does not increase 

 with time nearly so fast as does recession itself, is supported by ob- 

 serving the spread among individual recession measurements from a fixed 

 set of stations over 2-, 4-, and 6-year intervals (1969-71; 1971-75; 

 1969-75). UTiile the mean recession grew from 5 to 12 to 17 meters, the 

 standard deviations of the measurements only increased from 6.2 to 7.1 to 

 7.6 meters. Nearly constant variability may be partially related to sand- 

 wave migration, etc., which tends with time to merely distribute the same 

 variability uniformly along the shore. 



The clear improvement with time in the precision of the estimated 

 mean rate is shown by the histograms of retreat rate measurements in 

 Figure 14. Note at the top of the figure that the variability in retreat 

 rates based on net change over a 5-month period is relatively large. An 

 estimate of the true rate of recession would require a relatively large 

 number of measurements, even if the need is only to typify the mean re- 

 cession for this short period. As the length of time between observations 

 increases, the individual measurements more closely cluster about their 

 mean, and thus an estimate from a fixed number of measurements tends to 

 better represent the true mean rate for that section of beach. 



Variability need not always decrease with time, nor with number of 

 observations, if the character of the processes themselves changes. This 

 is where the engineer's judgment must be applied in selecting appropriate 

 historic data to fit the specific case at hand. Various aspects of how 

 lake level changes affect the process of shore erosion are discussed later 

 in this report. 



3. Effects of the Recent Lake Levels on Shore Retreat Rates. 



The annual cycle of high lake levels in summer and low lake levels in 

 winter was superimposed on a fairly steady rise in mean level that began 

 several years before the first profiles were taken and ended at a record 

 high annual mean elevation for this century in 1973 (see Fig. 15). The 



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