As stated on the Governing Equations page, the governing equation of GenCade is

${\displaystyle {\frac {\partial y}{\partial t}}+{\frac {1}{(D_{B}+D_{C})}}({\frac {\partial Q}{\partial x}}-q)=0}$

This equation is solved with the inputs of boundary conditions and values for Q, q, DB and DC given.

The sand transport rates, Q, is taken from the 'CERC' equation for calculating longshore sediment transport. As formulated in Komar (1969):

${\displaystyle Q=\left(H^{2}C_{g}\right)_{b}a_{1}\sin 2a_{b}}$

where H is the wave height (meters), ${\displaystyle C_{g}}$ is the group wave celerity (meters/second), ${\displaystyle a_{b}}$ is the angle of the breaking waves to the shoreline, with the subscript b indicating the wave breaker position. Lastly, ${\displaystyle a_{1}}$ is a non-dimensional parameter:

${\displaystyle a_{1}={\frac {K_{1}}{16\left({\frac {\rho _{s}}{\rho -1}}\right)(1-p)1.416^{5/2}}}}$

where K1 is an empirical coefficient with a nominal value of 0.77, ps and p are the density of sand and water, respectively, and p is the porosity of sand. In the GENESIS model (Hanson 1987) used an extended version of this relation (Kraus and Harikai 1983):

${\displaystyle Q=\left(H^{2}C_{g}\right)_{b}\left(a_{1}\sin 2a_{b}-a_{2}\cos a_{b}{\frac {\partial H_{b}}{\partial x}}\right)}$

where ${\displaystyle a_{2}}$ is a non dimensional parameter given by:

${\displaystyle a_{2}={\frac {K_{2}}{8\left({\frac {\rho _{s}}{\rho -1}}\right)(1-p)\tan \beta 1.416^{5/2}}}}$

where ${\displaystyle \tan \beta }$ is the average bottom slope from the shoreline to the "maximum depth of longshore transport" (See Empirical Parameters). The nominal value of ${\displaystyle K_{1}}$ is 0.39 if waves are specified in terms of RMS wave heights (Komar 1976) and 0.77 when using significant wave heights. As a rule of thumb, based on modeling experience, Hanson and Kraus (1989) recommend ${\displaystyle 0.5K_{1}.

In the calibration and verification process, ${\displaystyle K_{1}}$ and ${\displaystyle K_{2}}$ values are determined by reproducing changes in shoreline position measured over a certain time interval. Adjusting the ${\displaystyle K_{1}}$ coefficient will effect the entire modeling domain while ${\displaystyle K_{2}}$ will only affect the evolution in areas influenced by wave diffraction near structures. In the calibration process, it is recommended that the ${\displaystyle K_{1}}$ value is adjusted first to get a reasonable agreement with respect to annual transport rates and overall shoreline evolution. Then, the ${\displaystyle K_{2}}$ value may be altered to improve predicted shoreline response near structures.

Using the immersed weight transport rate to update the volumetric transport rate results in:

${\displaystyle Q=\left(H^{2}C_{g}\right)_{b}\left(a_{1}\sin 2a_{b}+(a_{3}{\frac {\bar {v_{t}}}{u_{m}}}-a_{2}{\frac {\partial H_{b}}{\partial x}})\cos a_{b}\right)}$

where ${\displaystyle a_{3}}$ is a non-dimensional parameter given by:

${\displaystyle a_{3}={\frac {K_{3}}{8({\frac {\rho _{s}}{\rho }}-1)(1-p)1.415^{5/2}}}}$

In GenCade, the calculated breaking wave condition at each grid point is converted to a wave-driven longshore current velocity from which the associated longshore sediment transport rate is calculated. A tidal or wind driven current (or both) are read from files and linearly added to the wave generated current before calculating the transport rate. GenCade at present does not calculate the current produced from the tide or the wind. These currents should be represented by an average through the surf zone and must be obtained from an external source, such as from a model or measurements. For further guidance on modeling wind-driven surf zone currents, see Kraus and Larson (1991) and Long and Hubertz (1988). Values of the external current are stored in a file that provides tide and wind currents at each calculation cell wall. These currents then serve as input for continued transport calculations.