The sediment budget equations for a typical beach cell (see Fig. 41) 

 are: 



Sediment sources: Q n -1 n + ^n+1 n 



Sediment losses: Q n n _j + Q n n+ i + SL n + 0T n 



Annual volumetric beach change: 



V n = Vl.n + Qn + 1 ,n " Qn,o-l " Qn,n + 1 " s L n - 0T n (13) 



where n, n-1 , and n+1 are individual beach cells, SL n is the annual 

 sediment loss from cell n due to the rise in sea level, 0T n is the 

 annual sediment loss from cell n due to wave overtopping, and Q n n+ ± 

 is the annual longshore sediment transport from cell n into cell n+1. 



Equation (11) is used to predict the quantity Q between littoral 

 cells located on a continuous beach; however, a problem with this 

 formulation arises when a cell boundary borders an inlet, weir jetty, 

 headland, etc. In these situations, the actual quantity of sediment 

 moving in the littoral drift may be less than that predicted by 

 equation (11) and so a modification must be incorporated into the 

 sediment budget equations. The actual longshore sediment transport 

 rate, Q a , is related to the potential longshore sediment transport rate 

 by the "efficiency factor," a, such that 



Q a = a (jSPx) (14) 



Along straight and continuous beaches, the value of a must be unity; 

 however, at inlets and other sediment traps, its value is less than or 

 equal to one. In extreme cases of total sediment removal, the value of a 

 is zero. The solution of all sediment budget equations for a set of 

 littoral cells defines the values of a at each cell boundary. 



The sediment budget schematizations for Wrightsville and Carolina 

 Beaches are shown in Figure 42. The values of the northerly and 

 southerly components of the longshore energy flux at each littoral cell 

 boundary are shown in Table 18. The values of /3 used in the longshore 

 sediment transport equations were /3 =300 for Wrightsville Beach and 

 /3 =900 for Carolina Beach. The measured volumetric change within each 

 cell, the annual volumetric loss due to sea level rise, and the loss due 

 to wave overtopping are shown in Table 17. 



The sets of a values at each inlet boundary (i.e., aj j and 



a 2 1> a 4 5 and a 5 4» and a 7,8 an< * ^8,7) cannot be uniquely 

 determined (there are more unknowns than equations) and therefore, the 

 values of one efficiency factor of each pair must be assumed. For an 

 unimproved inlet (i.e., no jetties, weirs, etc.), it was assumed that 

 all sediment contained within the littoral drift system entered the 

 inlet cell. In this case, the northerly longshore transport from the 

 northern ends of Wrightsville and Carolina Beaches was assumed to enter 

 Mason and Carolina Beach Inlets, respectively. Consequently, a2 1 

 and ag 7 were set equal to one and the sediment budget equations 

 solved resulting in the values of aj 2 = 0.09 and a 7 8 = 0.31. 



79 



