PREDICTING ADJUSTMENTS IN SHORE 

 AND OFFSHORE SAND PROFILES ON THE GREAT LAKES 



hy 

 Edward B. Hands 



I. INTRODUCTION 



This report briefly describes a method for predicting long-term changes in 

 shoreline position and offshore bathymetry on the Great Lakes. Beach profiles 

 fluctuate in response to storms and water level changes. On the Great Lakes 

 both storms and water levels undergo prominent seasonal fluctuations. Super- 

 imposed on the seasonal fluctuations is a longer term variation in annual mean 

 water level elevations. When measured over a number of years the net long- 

 term change in water levels exceeds the range of seasonal fluctuations. The 

 method described here for predicting long-term profile adjustments to changing 

 lake levels is based on a conceptually sound, empirically verified model which 

 includes allowances for regional variations in storm exposure, coastal geomor- 

 phology, and sediment texture. 



II. THE IDEALIZED MODEL 



As described by Bruun (1962), a rise in the mean elevation of the water 

 surface tends to shift the equilibrium sand profile landward. As water levels 

 rise, erosion prevails on the upper beach, and the shoreline retreats. Con- 

 ceptually, the erosion supplies material to build the outer part of the 

 responding profile upward. Eventually, the initial profile shape is reestab- 

 lished farther inland and, at a distance above its initial position, equal to 

 the change in water level, z, as depicted in Figure 1. If there are no 

 longshore losses the ultimate retreat of the profile x can be calculated 

 given the dimensions of the responding profiles, X and Z, and a measure of 

 the stability of the shore-eroded material, R^. 



zX(R^)^8 ^ 



where sg z = 1 if z > 0, and sg z = -1 if z < 0. Hands (1980) provides a more 

 detailed description of the sequence of profile changes leading back to equi- 

 librium and the derivation of the equation as a direct consequence of the 

 conservation of sediment volumes. Also provided is an extended equation to 

 cover the case of longshore imbalances in sediment transport. Though the 

 concept behind the equation is straightforward, its evaluation in the field is 

 problematic because the required dimensions of the responding profile (X and 

 Z) will usually be unknown and depend on the local wave climate. Monitoring 

 of beach and offshore changes in Lake Michigan has both verified the per- 

 tinence of the equation and simplified its evaluation for sandy shores 

 throughout the Great Lakes. 



III. EVALUATION OF TERMS IN THE EQUATION 



1. Change in Water Level, z . 



This is the given or independent variable; it refers to the change in mean 

 elevation of the water surface which disturbed the equilibrium of the beach. 



