| Abstract: | Monte Carlo simulation of wave spectra was carried out to provide an assessment of JONSWAP spectral model and parameters. The simulation method is found to be satisfactory because (a) it excludes the spectral variability due to geophysical factors from the sampling errors in the spectral estimates and the statistical uncertainty in determining the model parameters; and (b) the simulated spectra can represent ideal spectral estimates where the sampling errors have been minimized by increasing the degrees of freedom of the spectra. The latter (b) allows both the magnitude of sampling errors to be evaluated and errors due to statistical uncertainty to be isolated. Thus, the stimulation study provides a useful error analysis to assess the JONSWAP spectral model and parameters. For instance, it is found from the results that the sampling errors could be as high as 20% while errors due to uncertainty in determining the model parameter could be as high as 17%. However, the overall errors may be reduced to the minimum of approx. 15% if the simulated spectra have 80 degrees of freedom and constant values of σa and σb i.e. σa = 0.07 and σb = 0.09. This implies that the maximum accuracy of 85% may be achieved in JONSWAP spectral model even though the α parameter has been underestimated by about 1.5%. The overestimated values of γ might come from the underestimated α and the biased φm estimator caused by the statistical uncertainty in the presence of a sharp spectral peak. Although the scale parameters (α and φm) exhibit smaller errors and variability than the shape parameters (ψ, σa and σb), they are more sensitive to the degrees of freedom of the spectra and their estimators are not better than the estimators of shape parameters. The simulation experiments have also shown that simulated spectra at 20–40 degrees of freedom contain a substantial amount of sampling errors. Therefore, the measured wave spectra at the same degrees of freedom (20–40) are not suitable and should not be used for evaluating the accuracy of any wave spectral model. |
