where the value of h = 23.0 feet was obtained from the Table since 



h = 78.0 - d = 78.0 - 55.0 = 23.0 feet (7.0 meters). However, there is 



a great deal of variability in the distance of the 55 -foot contour from 



the shoreline at Ocean Beach, ranging from 34,600 feet (10,546 meters) 



to a low of 12,600 feet (3,840 meters) along about a 5-mile (8 kilometers) 



stretch of coast. This would result in erosion rates ranging from 2.3 



to 0.87 foot (0.73 to 0.27 meter) per year. 



An alternative method of computing the erosion rate can be obtained 

 by making use of the assumption of an exponential profile. The value of 

 B can be determined from equation 3 by finding the value of x when 

 y - y = A. When y-y =A, x=B; therefore, 



A = de" aB (6) 



or taking logarithms of both sides and rearranging, 



B=-i&^. (7) 



d 



Substituting into equation 2, 



Ax = in - . (8) 



a(h + d) d 



For the example problem 



Ax = 1^0054 ^ -0-0054 = 1U £eet ^^ meter) per year _ 



0.000564(78.0) 55 



This estimate is within the bounds computed from equation 2 although it 

 is significantly less than the value computed for B = 32,600 feet. It 

 is based on consistent assumptions regarding the geometry of the profiles 



V. SUMMARY AND CONCLUSIONS 



A method for estimating the long-term average retreat rate of a 

 sandy shoreline resulting from a long-term change in mean sea level was 

 developed. The method is approximate and is intended to supplement con- 

 ventional analyses of historical profile and shoreline changes rather 

 than to supplant such analyses. In cases where little or no data are 

 available, a rough estimate of the shoreline retreat rate can be made 

 from recent profiles and sea level change data available in Hicks (1973) . 



Offshore profiles can, in many cases, be described by an exponential 

 curve and long-term erosion rates calculated from the equation, 



-A „ A 



Ax = in - , 



a(h + d) d 



where - (1/a) in (A/d) = B = the distance from shore of the d, depth 

 contour. 



12 



