A METHOD FOR ESTIMATING LONG-TERM EROSION 

 RATES FROM A LONG-TERM RISE IN WATER LEVEL 



by 

 J. Richard Weggel 



I . INTRODUCTION 



Bruun (1962) proposed a method for determining the distance a shore- 

 line will retreat if the mean sea level rises slightly. His method is 

 based on the assumption that the beach profile after the sea level rise 

 will be identical to the original profile shifted upward and landward a 

 specified amount. The landward shift of the profile represents the shore- 

 line retreat. The total volume of beach material per unit length of beach 

 involved in the profile shift can also be determined. This volume repre- 

 sents the volume of sand per unit length of beach that must be placed on 

 a beach to extend the beach seaward to its location before the rise in 

 water level. Application of Bruun' s method requires that the water depth 

 beyond which there is no significant sediment motion be determined and 

 that the distance from shore to this depth contour be known. This paper 

 proposes a reproducible procedure for establishing the shoreline retreat 

 associated with a water level rise. 



This procedure is applicable only to sandy beaches having an uninter- 

 rupted supply of sand. Any bluffs or dunes that are eroding should be of 

 material essentially the same as the material on the active profile and 

 the longshore transport should be in equilibrium; i.e., the longshore 

 transport out of the beach segment should be balanced by the longshore 

 transport into the segment. Also, since little is known about the rate 

 at which profiles respond to changes in water level, the procedure should 

 be used only for estimating long-term changes such as occur over a number 

 of years rather than seasonal changes. The procedure is not a substitute 

 for the analysis of historical shoreline and profile changes when the 

 necessary data are available; it is intended to supplement such analyses 

 or to provide an estimate of long-term erosion rates due to sea level 

 rise when little or no historical data are available. 



II. BRUUN 'S METHOD 



In estimating long-term erosion rates along Florida beaches, Bruun 

 (1962) assumed that the erosion rates were the result of a long-term rise 

 in the position of mean sea level with respect to the land. Such changes 

 of sea level can result from either an increase in water level or by sub- 

 sidence of the region adjacent to the sea. As the water level rises, the 

 profile is assumed to move without changing its shape (a decline in water 

 level will not reverse the process) . It should also be emphasized that 

 shorter term shoreline changes will occur independently of the sea level 

 rise and shoreline retreat process; these changes may be much larger in 

 magnitude than changes caused by sea level rise. The landward migration 

 of a profile for an increase in water level is graphically shown in Figure 

 1. If the water level rises by an amount, A, the quantity of material 



