Graph-Search and Differential Equations for Time-Optimal Vessel Route Planning in Dynamic Ocean Waves

Time-optimal paths are evaluated by VISIR (\u201cdis- coVerIng Safe and effIcient Routes\u201d), a graph-search ship routing model, with respect to the solution of the fundamental differential equations governing optimal paths in a dynamic wind-wave environment. The evaluation exercise makes use of identical setups: topological constraints, dynamic wave environmental conditions, and vessel-ocean parametrizations, while advection by external currents is not considered. The emphasis is on predicting the time-optimal ship headings and Speeds Through Water constrained by dynamic ocean wave fields. VISIR upgrades regarding angular resolution, time-interpolation, and static nav- igational safety constraints are introduced. The deviations of the graph-search results relative to the solution of the exact differential equations in both the path duration and length are assessed. They are found to be of the order of the discretization errors, with VISIR\u2019s solution converging to that of the differential equation for sufficient resolution

VISIR-2: ship weather routing in Python

Ship weather routing, which involves suggesting low-emission routes, holds potential for contributing to the decarbonisation of maritime transport. However, including because of a lack of readily deployable open-source and open-language computational models, its quantitative impact has been explored only to a limited extent. As a response, the graph-search VISIR (discoVerIng Safe and effIcient Routes) model has been refactored in Python, incorporating novel features. For motor vessels, the angle of attack of waves has been considered, while for sailboats the combined effects of wind and sea currents are now accounted for. The velocity composition with currents has been refined, now encompassing leeway as well. Provided that the performance curve is available, no restrictions are imposed on the vessel type. A cartographic projection has been introduced. The graph edges are quickly screened for coast intersection via a K-dimensional tree. A least-CO2 algorithm in the presence of dynamic graph edge weights has been implemented and validated, proving a quasi-linear computational performance. The software suite's modularity has been significantly improved, alongside a thorough validation against various benchmarks. For the visualisation of the dynamic environmental fields along the route, isochrone-bounded sectors have been introduced. The resulting VISIR-2 model has been employed in numerical experiments within the Mediterranean Sea for the entirety of 2022, utilising meteo-oceanographic analysis fields. For a 125 m long ferry, the percentage saving of overall CO2 expenditure follows a bi-exponential distribution. Routes with a carbon dioxide saving of at least 2 % with respect to the least-distance route were found for prevailing beam or head seas. Two-digit savings, up to 49 %, were possible for about 10 d in a year. In the case of an 11 m sailboat, time savings increased with the extent of path elongation, particularly during upwind sailing. The sailboat's routes were made approximately 2.4 % faster due to optimisation, with the potential for an additional 0.8 % in savings by factoring in currents. VISIR-2 serves as an integrative model, uniting expertise from meteorology, oceanography, ocean engineering, and computer science, to evaluate the influence of ship routing on decarbonisation efforts within the shipping industry.</p