Estimating the parameters of ocean wave spectra using Bayesian methods

<p dir="ltr">Wind-generated ocean waves are a natural occurrence, transforming wind energy into waves on the sea surface. The spectral density function of these waves describes the distribution of wave energy across different frequencies. Estimating parameters such as wave height, peak frequency, and bandwidth is crucial due to the varied nature of these parameters influenced by location, time, and weather conditions. Parametric and nonparametric techniques have been utilised for estimation, with the Joint North Sea Wave Project (JONSWAP) model being widely employed as a parametric form.</p><p dir="ltr">Bayesian computational methods can be used to estimate highly non-linear and non-Gaussian wave models by employing the Markov chain Monte Carlo (MCMC) method. However, to date, there is no available Bayesian approach to fit ocean wave models that provide full uncertainty quantification. By applying Bayesian methods to estimate ocean wave spectra parameters, we can improve the accuracy and reliability of wave predictions and enable better decision-making in offshore engineering, coastal management, and maritime operations. The main contributions of this thesis are:</p><p dir="ltr"><br></p><ol><li>Efficient Bayesian inference using the Hamiltonian Monte Carlo (HMC) is proposed for estimating Pierson-Moskowitz (PM) and JONSWAP models,</li><li>A novel mixture of ocean wave spectra model is proposed to fit multi-modal ocean wave spectra,</li><li>The uncertainty for significant wave height (Hs) is taken into account.</li></ol><p dir="ltr">To validate the effectiveness and accuracy of our methods and wave models, we employ prior predictive checks and Simulation-Based Calibration (SBC). We apply our proposed method to real data from ocean wave buoys in New Zealand and Western Australia.</p>