The main equation in coastline evolution modelling is the continuity equation for sediment volumes expressed by:
where yc(x) is the distance from the baseline to the coastline, t is the time,
hact(x) is the height of the active cross-shore profile, Q(x) is the longshore transport of sediment expressed in volumes, Qsou(x) is the source/sink term expressed in volume/Dx, x is the longshore position and Dx is the longshore discretisation step.
As sketched in Figure 5.24 the active profile height, hact(x), is composed of two components and it is calculated by the sum of the beach height, hbeach, and the local active depth, Dactive(x).
(5.4) 
where hbeach is the height of the ‘front beach’ and Dactive(x) is the local active depth.
Figure 5.24 Definition of active profile height and initial movement of coastline
