











station No. 





29 27 



24 



21 



19 



16 



13 12 8 



6 4 2 



"0 ' ' 



1 



1 



1 



, 1 



1 1 1 



1 r 1 





1 1 

 28 26 





1 1 

 23 20 





1 

 17 



1 1 1 

 14 iO 9 



II II 

 7 5 3 1 



10 



- 













• 















• 





JJ§.9.StiOLeJJ[Le 





• 











• • 



10 



- • 

 • 











• • 



• • 



20 



« 







• 





• 



• 



• 



30 



- • 











• 



. 



40 



1 



1 



1 



j^ 





-•—Silver Lake Dunes 

 -J HH~. 1 \ i W/_l 



^ -ZQ « 



40 30 20 10 5 I I 5 10 



Distance Measured Alongshore in o Norttierly Direction 



from ttie Pentwater Ctiannel (km) 



Figure 19. Longshore variation in net shore retreat from 

 1969 to 1976. 



significant scarp in 1969, the average dune height for the period of 

 adjustment was approximately one-half the average scarp height in 1976. 

 Average dune height added to the average pinch-out depth taken from Figure 11 

 established the vertical dimension of the adjusting profile (the Z in eq. 1 

 and Fig. 13). The resulting average value of Z was 13.6 meters. Under the 

 discussed assumption of regional sediment balance, the ratio X/Z times the 

 measured water level change (z = 0.20 meter) equals the ultimate shore retreat 

 (-13.6 meters). The retreat actually measured between 1969 and 1976 also 

 averaged -13.6 meters. Considering the measurement and sampling errors in- 

 volved in determining each independent variable a predictive capability of 

 less than a tenth of a meter certainly is not claimed, but the results clearly 

 confirm the appropriateness of the equilibrium-sediment balance approach when 

 applied in the proper setting. 



As noted previously, pinch-out depths are deeper south of Little Sable 

 Point than to the north. The eroding dunes are also higher there, which even 

 further enlarges the vertical dimension of profile adjustment south of Little 

 Sable Point. Consequently, the equilibrium prediction might be applied sepa- 

 rately to the two regions. Likewise, because additional surveys were con- 

 ducted in 1971 and 1975, separate predictions could be applied to these 

 shorter time intervals (1969 to 1971 and 1969 to 1975) as well. Thus, par- 

 titioning the original data provides nine individual, though not independent 

 tests (Table 2) . The greater pinch-out depth south of Little Sable Point 

 increases both the width, X, and height, Z, estimates in a compensating 

 fashion so that there is little effect on the predicted outcomes. The values 

 predicted for north of Little Sable Point are essentially the same as pre- 

 dicted for south of Little Sable Point for each of the three time periods 

 (Fig. 20). Considering prediction versus measurement, the predicted retreat 

 from 1969 to 1971 was too high for all three areas (117 percent high for the 

 area as a whole). The prediction for 1969 to 1975 was also high, but not as 

 far off as before (45 percent high for the whole area). These overestimations 



37 



