In Equation 33, the wave and roller properties are taken at the cell
which is taken in the middle of the cell. After solving the wave action flux
conservation equation, all wave quantities are known at all grid points and the
roller mass flux mR is the only unknown. Thus, starting from the most
offshore grid point where wave breaking should be absent (mR = 0), mR can be
determined at all shoreward grid points.
The cross-shore momentum equation is also solved through an explicit
finite-difference approach following Kraus and Larson (1991). Thus, no
iteration is performed between the wave and setup/setdown calculations,
implying that the water depth for the water-level calculations are displaced
half of a grid cell from the true value. Setup/setdown calculations are
typically well behaved, so this shift has negligible influence on accuracy,
although on a steep foreshore some loss of accuracy can result.
Chapter 3 Wave Model