Dependence of Shape Parameter of Weibull Distribution on Wave Spectral Width and Nonlinearity

In practice, the wave height distribution associated with an irregular wave train is always mathematically modeled as a Rayleigh distribution. However, the realistic ocean wave height distribution might deviate from a Rayleigh distribution. The present study demonstrates that a better mathematical model for wave height distribution under realistic ocean environment is a Weibull distribution. In comparison with a Rayleigh distribution, a Weibull distribution has the flexibility on choosing its “shape parameter”. According to the nonlinear Monte Carlo simulations, this study investigates the nonlinearity and spectral width effects on the shape parameter for the Weibull wave height distribution. A new empirical formula for calculating the shape parameter is proposed, which can be used easily in application.