Distribution of sea-surface elevations in intermediate and shallow water depths

Waveforms described by the second-order Stokes-type approximations are prone to display anomalous troughs with spurious negative crests. The systemic occurrence of such physically unrealistic features restricts the range of relative validity of second-order models and causes serious errors in modeling the statistics of sea-surface elevations, especially in intermediate and shallow water depths. As a case of practical importance in this regard, this study focuses on and elaborates the nature of the second-order finite-depth narrowband model. A critical review of the conventional formulation of this model reveals that its range of applicability as a statistically viable model of irregular waves is severely limited at relatively shallow water depths. However, a subsequent analysis allows the same model to be modified and reduced to a simpler stochastic form with an attendant first-order probability structure free of anomalies from deep to shallow water depths. Comparisons with laboratory and field data representative of highly nonlinear waves in the shoaling and surf zones indicate that given the skewness coefficient, the modified model provides predictions in general agreement with the distributions of observed surface elevations. It also offers relative simplicity and a wider range of applicability than some other models previously proposed elsewhere. •Finite-depth narrowband model of nonlinear waves is critically reviewed.•A modified model and attendant first-order probability distribution are developed.•Results are verified with lab and field data representative of the shoaling and surf zones.