Abstract: A new joint distribution model based on a conditional probability approach accurately predicts the joint distribution of wave heights and periods for short-term sea states. In this model, the wave height distribution follows a two-parameter Weibull distribution, and the conditional period distribution is modeled using a log-normal distribution. To account for the effects of wave spectral shape, the Wallops spectrum with a broad spectral width is used, and the model parameters are derived. Simulations using both the Wallops spectrum and measured wave spectra as target spectra are conducted to obtain the joint distribution of wave heights and periods. Simulated data serve as the benchmark, and the proposed model is compared with five commonly used joint distribution models. The results show that the new model closely matches the simulated data for both Wallops and measured spectra, while the other models only align well with simulated data in specific cases. Additionally, wave height and period distributions are analyzed, and the sources of prediction errors are discussed. The new model includes an explicit closed-form expression, making it suitable for non-Gaussian wave conditions.

Key words: wave spectrum, joint distribution of wave height and periods, short term sea states, spectral width parameter, distribution of wave heights, distribution of wave periods