## 1 Introduction  
Ocean-going ship weather routing is a navigation service designed to optimize voyage planning by leveraging forecasted sea conditions along the route or within a specific navigation area, in conjunction with the vessel's performance characteristics. Its primary objective is to determine an optimal route that avoids adverse wind and wave zones, thereby minimizing voyage distance and duration, reducing fuel consumption, and enhancing operational efficiency and safety. The modern concept of ship weather routing originated in the early 1950s when the United States Navy first introduced it as a navigational strategy. The U.S. Navy, along with several private commercial navigation organizations, began utilizing surface and upper-air weather forecasts to assist transatlantic vessels in avoiding hazardous weather conditions. This approach not only improved navigational safety but also enhanced the economic efficiency of voyages [1, 2]. Subsequently, countries such as the United Kingdom, the Netherlands, the former Soviet Union, Norway, and Japan established their own weather routing institutions, further advancing the field. In 1983, the International Maritime Organization (IMO) adopted Resolution A.528(13) on the Recommendation on Weather Routing, which encourages vessels to utilize weather routing services to determine the optimal route, thereby avoiding severe weather conditions and enhancing navigational safety. The resolution also recommends that governments advise ships flying their flags about the availability of weather routing information, particularly those services recognized by the World Meteorological Organization (WMO) [3]. With the expansion of global trade, emissions from the shipping industry have been increasing annually. Statistics indicate that shipping accounts for approximately 3% of global carbon emissions [4]. Therefore, reducing carbon dioxide (CO\({}_{2}\)) emissions in the shipping industry is essential for achieving global climate targets. In recent years, the International Maritime Organization (IMO) has introduced a series of policies and technological measures to drive the green transition of the shipping industry. Annex VI of the International Convention for the Prevention of Pollution from Ships (MARPOL) establishes specific targets and pathways for reducing ship carbon emissions through mechanisms such as the Energy Efficiency Design Index (EEDI), the Ship Energy Efficiency Management Plan (SEEMP), and Carbon Intensity Indicators (CII) [5]. To support emission reduction, the IMO has recommended various measures focusing on technology, operations, and ship design. Among these, weather routing services play a crucial role by optimizing ship speed and routes. Route optimization alone can potentially reduce carbon emissions by up to 10%, while optimized speed management, often integrated within weather routing, can contribute significantly more, with combined strategies potentially achieving emission reductions in the range of 5-20% or higher depending on the voyage and vessel specifics [6; 7; 8]. Marine meteorological observation and forecasting capabilities are fundamental to ocean-going ship weather routing services. In recent years, advancements in China's meteorological satellite technology (e.g., the Fengyun series) and the continuous development of numerical weather prediction (NWP) systems [9], particularly with the implementation of the National Marine Meteorological Support Project [10], have significantly enhanced the country's marine meteorological observation, forecasting, and service capabilities. This progress has accelerated development and strengthened the competitiveness of China's national ship weather routing services. Additionally, leading international numerical forecasting agencies have progressively adopted open data policies [11].