Models are regularly updated (each year); see website of publisher www.aquapublications.nl)

This model is a very advanced cross-shore profile model (Fortran code) which computes the cross-shore distribution of:

2) longshore and cross-shore flow velocity,

3) peak orbital velocities (including asymmetry effects),

4) bed load and suspended load transport (using a single-fraction or multi-fraction method),

5) morphological changes (including dune erosion).

The CROSMOR profile model is a probabilistic model (wave by wave model) which simulates the propagation, transformation (shoaling) and breaking of individual waves along a cross-shore profile, which is assumed to be uniform in longshore direction. Statistical parameters are computed from the results of the individual waves. The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay due to bottom friction and breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore and cross-shore currents are also modelled. The near-bed orbital velocities of the high-frequency waves (low-frequency effects are neglected) are described by the method of Isobe and Horikawa to account for wave asymmetry effects in the nearshore zone (forward peak orbital velocity is larger then backward peak orbital velocity). The depth-averaged return current (U

The sediment transport rate of the model is determined for each wave (or wave class), based on the computed wave height, depth-averaged cross-shore and longshore velocities, orbital velocities, friction factors and sediment parameters. The net (averaged over the wave period) total sediment transport is obtained as the sum of the net bed load (q

Special versions are available for depoistion and erosion in river reservoirs.

(three formulae are available: CERC, KAMPHUIS and VAN RIJN),

2) coastline changes (including structures such as groynes).

Coastline changes can be computed by considering the sand continuity equation for the littoral zone (surf zone) with an alongshore length of DX, a cross-shore length of DY and a vertical layer thickness (h). The sand balance reads as (see upper plot):

h [d(Ys)/dt] + d(Qs)/dx - qs=0

with: Ys=cross-shore position of shoreline, x=longshore coordinate, h=thickness of active littoral zone layer, Qs=longshore transport, qs=source, sink or cross-shore transport contribution.

This expression states that: a coastal section will erode if more sand is carried away than supplied; vice versa coastal accretion will occur if there is a net supply of sand.

The longshore sand or gravel transport depends on the angle of the wave direction at the breaker line and the shoreline angle.

Download here: Littoral.xls

Cross-shore data of hydrodynamics, sand transport and morphodynamics at Egmond beach, The Netherlands.