Modelling multivariate serially correlated sea states

This work presents a framework for simulating multivariate sea-state processes by combining marginal distribution modelling with flexible representations of serial and cross-dependence through transformation methods. The approach assumes that a multivariate stochastic process with prescribed marginal behaviour and temporal correlation structure can be constructed via Gaussian-based transformations, enabling the coherent simulation of non-Gaussian processes with complex dependence structures. The framework focuses on the consistent simulation of these features, including full observations of sea states, while acknowledging that fully extreme-value-based dependence modelling would require alternative approaches. Moreover, seasonal variability can be naturally incorporated within the framework as a pre-processing step. So, a theoretical formulation is introduced for modelling bivariate cross-correlated sea state processes, based on parametric correlation transformation functions that enable direct estimation of both auto- and cross-correlation structures in the transformed space. The methodology also allows investigation of dependence at high quantiles through extremogram-based diagnostics, providing insight into temporal dependence relevant for extreme-event analysis. Finally, statistical inference on extreme values is performed using data simulated from the proposed framework. The correlated estimates are compared with those obtained under the assumption of independence, revealing a positive bias when serial dependence is neglected, even with identical marginal distributions, which affects extreme-value results.