Transformation of a wave energy spectrum from encounter to absolute domain when observing from an advancing ship

The article presents a practical approach to transform a wave energy spectrum from encounter domain to absolute domain. This problem has its specific relevance, when shipboard sea state estimation is conducted by the wave buoy analogy; notably for some particular implementation solving for the sea state directly in the encounter domain. In this context, the encounter domain is that observed from a ship when it advances in a seaway, whereas the absolute domain is that corresponding to making observations from a fixed point in the inertial frame. Spectrum transformation can be uniquely carried out if the ship sails “against” the waves (beam to head sea) but in following sea conditions there exists no unique solution to the problem. Instead, a reasonable approach valid for practical engineering must be applied, and the article outlines one viable solution that can be used to transform a wave spectrum from encounter to absolute domain. Specifically, two pseudo algorithms are presented, and good performance is achieved with both algorithms when they are tested at different operational scenarios.