13.4 meters Estimated closure depth d = 2.1 h^ (from eq. 5) 

 +7.6 meters Average height of the eroding dunes above 

 Stillwater level. 



Z = 21 meters Sum of the two values obtained above. 



X = 2,414 Average distance of the 13.4-meter depth con- 



tour from shore. The vertical datum should 

 be the same reference below which the closure 

 depth was measured in the previous step. 



R = 1 All of the material eroded from the upper 



beach is expected to remain within the 

 bounds' of the responding profile. 



zX(R^Y& ^^) 0.3(2,414) 1^ 



X = = = 34 meters Evaluating equation (1) 



Z 21 



It is estimated that the higher stages shift the equilibrium shore profile 

 an average of 34 meters inland and raise it 0.3 meter above present condi- 

 tions. 

 *************** EXAMPLE PROBLEM 2*************** 



GIVEN: Assume a new regulation plan is proposed to modify the inflow to Lake 



Michigan and Lake Huron via the St. Marys River. If adopted, this plan 



would lower the long-term mean surface elevation of Lake Michigan and Lake 

 Huron by 0.3 meter. 



FIND: What effect will the lower water levels have on shore erosion at the 

 Indiana Dunes National Seashore? 



ANALYSIS: The dredged channel and navigation structures at Michigan City, 

 updrift of the Indiana Dunes National Seashore, block some of the potential 

 sediment input from the east. Westward longshore transport out of the dune 

 area thus creates a sand deficit and contributes to a long-standing erosion 

 problem in the park. As lake levels fall the shoreline withdraws and the 

 beach widens. Assuming lake currents and waves are not altered, they tend 

 to reestablish the previous profile shape at a lower and more lakeward posi- 

 tion. Longshore losses to the west continue to exceed the net supply from 

 the east. However, offshore where the bottom slope is gradual, lowering of 

 the water surface brings bottom sediments into a shallower hydraulic regime. 

 This results in offshore sediments moving landward to steepen nearshore 

 slopes, to build dunes on the widened beach, and to feed the longshore 

 currents leaving the dune area to the west. The cumulative effects of these 

 adjustments can be estimated using equation (1). See Hands (1979) for 

 documentation of shore accretion during period of declining lake level. 



EVALUATION OF TERMS: 



z = -0.3 meter Given 



hr = 5.3 meters Average from sites 28 and 29 (App. C) 



11.1 meters Depth of profile closure = 2.1 h^ (from eq. 5) 



+ 2.9 meters Estimated average height of dunes expected to 

 form on the widened beach lakeward of the 

 present foredune. 



52 



