98 



width), and 2) the portion of the profile now being "mined" to yield 

 compatible sediment is the difference between ocean and bay depths, h^-, — 

 h]~, (i.e., smaller). This equation simplifies to the Bruun Rule if only 

 the ocean side of the barrier system is active. Finally it is noted that 

 as the bay depth h^, approaches the active ocean depth, h^, , Eq. 7.4 

 predicts an infinite retreat rate. This may explain in part the phenomenon 

 of "overstepping" in which barrier islands, rather than migrating landward 

 retaining their identity in the process, are overwashed and left in place 

 as a linear shoal (see, for example, Sanders and Kumar, 1975). 



It is noted that Eqs . 7.3 and 7.4 both consider the portion of the 

 profile being "mined" for sand as containing 100% compatible material. If 

 a portion of the profile contains peat or fine fraction that will not 

 remain in the active system, a rather straightforward modification of the 

 equations is required. 



Kriebel and Dean (1985) have described a dynamic cross -shore transport 

 model in which the input includes the time -varying water level and wave 

 height. In addition to predicting long-term responses, this model accounts 

 for profile response to very short-term events such as hurricanes. Thus an 

 equilibrium profile is not assumed and, in addition to a sand budget 

 "volumetric equation," a "dynamic equation," is required which was 

 hypothesized as 



Qs = K(D - D*) (7.5) 



in which Qg represents the offshore sediment transport per unit length of 

 beach, K is a universal constant (K = 2.2 x 10"° m^/N in the metric system) 

 and D and D* represent the actual and equilibrium wave energy dissipation 

 per unit water voliome. Eq. 7.5 is suggested following the determination by 

 Bruun (1954) and later by Dean (1977) that most equilibrium beach profiles 

 are of the form 



h = Ax2/3 (7.6) 



