New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion.The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves.The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves,which is done by introducing a representative wave amplitude for the carrier waves.The computation time is greatly saved by the introduction of the representative wave amplitude.The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone.The model is validated for random waves propagate over a shoal and in surf zone against measurements.
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