where Q c represents cross-shore transport, K is an empirical transport 

 rate parameter, D represents wave energy dissipation, and D eq represents 

 energy dissipation D for a beach in equilibrium according to the profile 

 described by Equation 1. Wave energy dissipation can be written as a function 

 of the gradient of the wave energy flux F per unit depth as 



If the beach is in equilibrium according to Equation 1 and all the terms in 

 Equation 3 are expressed according to linear wave theory, the equilibrium 

 dissipation term D can be expressed as a function of only the equilibrium 

 coefficient A according to the relationship: 



D eq = §5 7* 2 g 1/2 A 3 ' 2 (4) 



where 7 is the specific weight of water, g is the acceleration due to 

 gravity, and k is the breaking wave height to depth ratio (0.78). Here, the 

 assumption is made that the surf zone is dominated by a spilling type breaker 

 with a constant height to depth ratio. 



From Equations 2, 3, and 4, it can be seen that no transport occurs for a 

 beach in equilibrium (D = D eq ) , transport is in an offshore direction if the 

 profile is more reflective (steeper) than the equilibrium profile (D > D ), 

 and it is onshore when the beach is more dissipative (flatter) than the 

 equilibrium profile (D < D eq ) . The transport rate distribution is computed at 

 each time step according to Equation 2 for each grid cell from the shoreline 

 to the breaker line. A one -dimensional continuity equation, 



dx ^1 



dt " " dh (5) 



is then used to compute the offshore profile response as a function of the 

 distribution of sediment transport. In Equation 5, x represents the 

 distance offshore to a known depth contour h , and t is time. The total 



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