APPENDIX A 



A PROCEDURE FOR ADJUSTING RATES OF SHORE RETREAT 

 TO COMPENSATE FOR WATER LEVEL DIFFERENCES 



1. Problem . 



The rate at which a particular beach retreats will depend on inter- 

 actions among a large number of factors. These factors can be grouped 

 into categories, such as (a) the characteristics of littoral materials 

 that determine their mobility or resistance to erosion, (b) the intensity 

 of waves and currents, and (c) the degree to which the littoral materials 

 are in or out of adjustment with the potentially erosive forces. Some-' 

 times the activities of man can have a drastic and obvious influence on 

 retreat rates. In other instances man's impact, though substantial, is 

 difficult to assess because it cannot be isolated from the total effect 

 due to the interaction of many varying but poorly known factors. 



It is well known that a long-term increase in water levels on the 

 Great Lakes promotes rapid shore retreat . There have been a number of 

 attempts to quantify certain aspects of the relationship between lake 

 levels and erosion (Beach Erosion Board, 1946; Davis, 1976; Berg and 

 Collinson, 1976). Because water levels are always varying on the lakes, 

 it would often be helpful if the effect of water levels on erosion rates 

 could be removed from measured rates so that the impact of the other 

 factors would be clearer. The following is a description of how shore 

 retreat measurements made on eastern Lake Michigan between 1969 and 1976 

 can be used to estimate the minimum amount of shore retreat in response 

 to various lake level changes. 



2. Data . 



The data base consists of shoreline changes measured over 1- to 6- 

 year intervals at 33 stations along a 50-kilometer reach centered on 

 Little Sable Point, Lake Michigan. Station locations, survey dates, and 

 lake level elevations are described in the text. Figure A-1 gives an 

 estimate of the mean shoreline change due to the long-term net differ- 

 ences in lake levels. Figure A-1 is similar to Figure 15 except (a) 

 measurements made within 1 kilometer of Pentwater are deleted as unrep- 

 resentative of the natural processes on an unobstructed coast, and (b) 

 all measurements of shoreline retreat have been reduced by 3 meters (the 

 residual retreat presumably not due to any water level effect) so that 

 the predicted response is zero when there is no water level change. 



The amount of recession is a function of many factors. Submergence 

 explains roughly half the variance in the test data. The mean shore 

 response to submergence by a given amount will probably fall within the 

 bounds shown in Figure A-1. These bounds indicate the nominal 95-percent 

 confidence limits for the mean recession based on a least squares fit 

 (r = 0.75) to the 105 data points. The fact that most of the points fall 

 outside the confidence band illustrates the greater difficulty of 



45 



