Z = 14 meters Sum of tiie two values obtained above. 



X = 3,030 meters Average distance of the 11.1-meter contour 

 from shore, based on field surveys. 



R. = 1 Offshore sands are expected to move onshore, 



and the wind is not expected to carry sand 

 inland past the present foredune. 



zX(R^)^8 ^'^ -0.3(3,030) l'^ 



X = = = -65 meters Evaluating equation (I). 



Z 14 



It is thus estimated that lowering the lake level 0.3 meter effectively 

 shifts the eqwiUhvium position 65 meters lakeward. As discussed, there will 

 still be a net loss of sand due to net transport to the west; therefore, the 

 actual shoreline is not expected to advance 65 meters lakeward. A reasonable 

 interpretation is that there will be a long-term gain of 65 meters of beach 

 that otherwise would have been lost by erosion at the previous water levels. 

 Dividing 65 meters by the appropriate recession rate provides an estimate of 

 when the avoided erosion would otherwise have occurred. 



If 15 percent of the offshore sediments are in the clay- or silt-size 

 range and are thouglit to be too fine to remain in the active shore zone, 

 the width of shore saved should be reduced to (1 - 0.15) x 65 meters = 55 

 meters. Note that a liberal estimate of future dune heights, D, would also 

 make the predicted savings more conservative. 



**************************************** 



VI. SUMMARY 



Adjustments of the beach and the nearshore zone to long-term changes in 

 lake level were monitored between 1967 and 197b along a 50-kiloraeter stretch of 

 shore centered on Little Sable Point, Michigan. The bathymetry of this region 

 is marked by a sequence of four to five longshore bars which are persistent 

 from year to year. The bars are continuous over tens of kilometers, though the 

 pattern is disrupted in an area opposite Little Sable Point. In the cross sec- 

 tion the bars are much less regular and smooth in an area 4 to 5 kilometers 

 around this broad protrusion of the shoreline. The bars soutli of the point are 

 deeper than to the north. Grain sizes throughout the study area, both on the 

 beach and along the bar crests, decrease toward the point. The longshore 

 transport converges toward the point. The tendency of profiles to be irregular 

 in areas with an overabundance of sand has been noted elsewhere by Bruun 

 (1962). The similarity and symmetry of the other patterns suggest a common 

 dependence of all the discussed variables on long-term directional wave 

 characteristics. 



The longshore drift which converges on Little Sable Point is primarily from 

 areas encompassed by the study. So the fact that the longshore transport rates 

 within the study area are not well known does not hinder the calculation of a 

 net sediment balance for the overall region. The volume of material eroded 

 from the upper beach over 4 years averaged 41 cubic meters per meter-length of 



53 



