return-period wave height for the area. In the absence of direct profile 



change measurements, the pinch-out depth for other regions is thus estimated 

 as: 



d ~ 2.1 h5 (5) 



where he is the 5-year return-period height given in Appendix C. 



The accuracy of this approach is not known. For an idea of how sensitive 

 the prediction of profile response is to errors in estimated closure, assume 

 that this study is restricted to the area north of Little Sable Point (sta- 

 tions 1 to 15, Fig. 9). North of the point, the pinch-out depth (from direct 

 measurements) averages 10 meters. With no repetitive profiles south of the 

 point the estimate would be that pinch-out occurs at 1.96 h^. The 1.96 would 

 be a less reliable estimate of the coefficient in equation (5). The average 

 h5 south of Little Sable Point was 5.39 meters (Michigan stations 15 and 16, 

 see App. C), so the estimated closure depth would have been 10.56 meters which 

 is 1.43 meters or 12 percent too small (Table 3). Adding this value to the 

 mean dune height, D, south of Little Sable Point produces a new estimate 

 of Z; the distance of the 10.56-meter contour from shore produces a new 

 estimate of X (Table 3). Using these new values, the estimated response to 

 a 0.2-meter increase in lake level would be 13.9 meters which is only 1 

 percent over the value obtained from actual measurements south of the point. 

 This exercise illustrates the self-compensating tendency which errors in the 

 pinch-out depth have on equation (1). The depth estimate was 12 percent too 

 small when the procedure was applied to data different from those used to 

 estimate the coefficient k in d = kh^. The effect, however, was to 

 introduce less than 1 percent error in the predicted shore retreat. 



Table 3. Cross-validation indicates the effect of estimating pinch-out depth from wave climate 

 data. Calculated estimates (hatted) are compared to measured values (nonhatted). 





•^5 



k 



d 



d - 1.96 h5 



Z 



Z - d + D 



X X - f(d) 



zX 

 X -2- 



zX 



Whole area 



5.3 



2.1 



11 























(stations 1 to 29) 





















Northern section 



5.1 



1.96 



10 























(stations 1 to 15) 





















Southern section 



5.4 







12 



10.56 



1A.8 



13.36 



1,020 928 



13.78 



13.89 



(stations 16 to 29)^ 





















Error 











~ 



12% 







10% 



9% 







<1% 



Used for an independent determination of k. 



Used for error check by comparison with estimates based on data from the northern section only. 



To be realistically applied, the model should have input from many 

 profiles spaced along a section of coast; as a consequence, there is little 

 point in partitioning the present data set any further. The cross validation 

 shown above does not reflect all the drawbacks of estimating the pinch-out 

 depth from wave climate because, using adjacent sections of coast, it does not 

 introduce the full range of bathymetric variability nor the range of wave 

 environments within the lakes. How well wave climate estimates from widely 

 different environments will perform remains uncertain. However, the prospects 

 seem good and alternatives nonexistent. The model - should be applied cau- 

 tiously, and wherever there is any indication of how well or poorly it worked, 

 the results should be reported. 



40 



