Modeling Heterogeneity across Varying Spatial Extents: Discovering Linkages between Sea Ice Retreat and Ice Shelve Melt in the Antarctic

Spatial phenomena often exhibit heterogeneity across spatial extents and in proximity, making them complex to model-especially in dynamic regions like ice shelves and sea ice. In this study, we address this challenge by exploring the linkages between sea ice retreat and Antarctic ice shelf (AIS) melt. Although atmospheric forcing and basal melting have been widely studied, the direct impact of sea ice retreat on AIS mass loss remains underexplored. Traditional models treat sea ice and AIS as separate systems. It limits their ability to capture localized linkages and cascading feedback. To overcome this, we propose Spatial-Link, a novel graph-based framework that quantifies spatial heterogeneity to capture linkages between sea ice retreat and AIS melt. Our method constructs a spatial graph using Delaunay triangulation of satellite-derived ice change matrices, where nodes represent regions of significant change and edges encode proximity and directional consistency. We extract and statistically validate linkage paths using breadth-first search and Monte Carlo simulations. Results reveal non-local, spatially heterogeneous coupling patterns, suggesting sea ice loss can initiate or amplify downstream AIS melt. Our analysis shows how sea ice retreat evolves over an oceanic grid and progresses toward ice shelves-establishing a direct linkage. To our knowledge, this is the first proposed methodology linking sea ice retreat to AIS melt. Spatial-Link offers a scalable, data-driven tool to improve sea-level rise projections and inform climate adaptation strategies.