Voronoi-Induced Artifacts from Grid-to-Mesh Coupling and Bathymetry-Aware Meshes in Graph Neural Networks for Sea Surface Temperature Forecasting

Abstract

Accurate sea surface temperature (SST) forecasting in coastal upwelling systems requires predictive models capable of representing complex oceanic geometries. This work revisits grid-to-mesh coupling strategies in Graph Neural Networks (GNNs) and analyzes how mesh topology and connectivity influence prediction accuracy and artifact formation. This standard coupling process is a significant source of discretization errors and spurious numerical artifacts that compromise the final forecast’s accuracy. Using daily Copernicus SST and 10 m wind reanalysis data from 2000 to 2020 over the Canary Islands and the Northwest African region, we evaluate four mesh configurations under varying grid-to-mesh connection densities. We analyze two structured meshes and propose two new unstructured meshes for which their nodes are distributed according to the bathymetry of the ocean region. The results show that forecast errors exhibit geometric patterns equivalent to order-k Voronoi tessellations generated by the k-nearest neighbor association rule. Bathymetry-aware meshes with 𝑘=3 and 𝑘=4 grid-to-mesh connections significantly reduce polygonal artifacts and improve long-term coherence, achieving up to 30% lower RMSE relative to structured baselines. These findings reveal that the underlying geometry, rather than node count alone, governs error propagation in autoregressive GNNs. The proposed analysis framework provides a clear understanding of the implications of grid-to-mesh connections and establishes a foundation for artifact-aware, geometry-adaptive learning in operational oceanography.