This paper presents a novel deep learning framework for estimating multivariate joint extremes of metocean variables, based on the Semi-Parametric Angular-Radial (SPAR) model. When considered in polar coordinates, the problem of modelling multivariate extremes is transformed to one of modelling an angular density, and the tail of a univariate radial variable conditioned on angle. In the SPAR approach, the tail of the radial variable is modelled using a generalised Pareto (GP) distribution, providing a natural extension of univariate extreme value theory to the multivariate setting. In this work, we show how the method can be applied in higher dimensions, using a case study for five metocean variables: wind speed, wind direction, wave height, wave period and wave direction. The angular variable is modelled empirically, while the parameters of the GP model are approximated using fully-connected deep neural networks. Our data-driven approach provides great flexibility in the dependence structures that can be represented, together with computationally efficient routines for training the model. Furthermore, the application of the method requires fewer assumptions about the underlying distribution(s) compared to existing approaches, and an asymptotically justified means for extrapolating outside the range of observations. Using various diagnostic plots, we show that the fitted models provide a good description of the joint extremes of the metocean variables considered.

Unmanned Surface Vehicles (USVs) have become critical tools for marine exploration, environmental monitoring, and autonomous navigation. Accurate estimation of wave direction is essential for improving USV navigation and ensuring operational safety, but traditional methods often suffer from high costs and limited spatial resolution. This paper proposes a machine learning-based approach leveraging LSTM (Long Short-Term Memory) networks to predict wave direction using sensor data collected from USVs. Experimental results show the capability of the LSTM model to learn temporal dependencies and provide accurate predictions, outperforming simpler baselines.

Operational guidance is provided in the form of selection of speeds and headings, and is generally based on accessing ship motions response predictions from a pre-computed database or lookup table for a given condition. Operational guidance is an important consideration in the survival of a ship and has been the focus of many International Maritime Organization (IMO) publications, IMO (1995), IMO (2007), IMO (2020). Recommendations for ship-specific operational guidance has been developed and discussed in the interim guidelines of the Second Generation Intact Stability by IMO, IMO (2020). While these guidelines are certainly useful in design and at sea, they are not comprehensive. The ocean environment is random and complex.