where n is the number of wave types used to represent the seasonal or 

 annual wave climate, P^ . is the longshore component of wave 

 energy flux (at breaking), p^ is the percent occurrence of that wave 

 type, Q is the long-term longshore sediment transport rate, and /3 is 

 the dimensional constant (found from correlation) relating Q to Pl h • 

 The dimensions of each term are shown in brackets. 



A sediment budget approach can be used for the correlation of Q and 

 P]_. For a beach cell, as shown below, Qf n represents all long-term 

 sources of sediment supplied into the cell-per-unit time and Q ou t 

 all long-term losses from the cell-per-unit time. The difference, 

 Qout~Qin> represents the long-term change in beach volume for 

 that cell. 



The longshore components of wave energy flux, as calculated in 

 Section V,3, are Pj, and P]~ and their respective beach coordinates are 

 Xi and X 2 . 



X| x 2 



Qin > I beach celT] > Q out 



Pi! Pl 2 



From equation (11), Q ou t"Qin = £ [ P ll7 P l?]' Let q/h be the long 

 -term erosion or accretion rate per unit length of beach, then 



Q -Q. 



q out in 



L= V x i 



and hence, 



q L = /3 



P^-Pl! 



V 



V x i 



q L= fi 



A P i 



In the limit, as A X 



dP i 

 L p dX 



(12) 



At any point along the beach, /3 can be determined from the ratio of the 

 long-term erosion-accretion rate to the spatial gradient of the 

 longshore component of wave energy flux. 



75 



