Fig. 1. Overview of a coastal setting to which the Cascade model can be applied
for simulating longshore sediment transport and coastal evolution.
The longshore sediment transport rate Q at the local scale is described by,
Q = Qo sin 2(αo )
where Qo = transport rate amplitude (a function of the wave properties at breaking and the
sediment characteristics), and αo is the angle between the breaking waves and the local
shoreline orientation expressed as,
αo = αb - arctan(∂y / ∂x)
where αb = wave angle at breaking, y = shoreline position, and x = alongshore coordinate.
If the regional transport obeys a similar relationship, then,
Qr = Qor sin 2(αor )
αor = αbr - arctan(∂yr / ∂x)
in the same notation as above with subscript r for the regional scale. The shoreline position
yr describes trends in the shoreline at the regional scale, being a function of the transport
gradients at this scale.
Larson, Kraus, and Hanson