Parameterization Solutions for Basal Melting at the Grounding Line in Ice Flow Models

Recent studies have indicated that the migration of grounding line is extremely sensitive to basal melt in the grounding zone. Different representations of melting at the grounding line introduce significant uncertainties in predictions of ice mass loss and global sea level rise. However, there remains an absence of targeted, systematic studies grounded in real-domain, and robustly representing melt in partially floating cells of ice sheet models remains a pressing technical challenge. This study delves into four distinct melt schemes at the grounding line within the Wilkes Subglacial Basin (WSB) model, focusing on their impact on ice loss predictions. Specifically, we analyse the No Melt Parameterization (NMP), Full Melt Parameterization (FMP), and two variants of the Sub-Element Melt parameterization (SEM1, SEM3) as applied to partially floating elements at the grounding line. We found that both the SEM and NMP schemes outperform FMP in terms of convergence with finer mesh resolution, with each exhibiting varying advantages over the other.  Notably, the discrepancies in results attributed to various melt schemes are significantly amplified when high melt rates are applied near the grounding line. Our results consistently suggest that the FMP should be avoided under all circumstances due to its poor convergence and substantial overestimation of ice mass loss. We recommend that future ice sheet models carefully evaluate the choice between NMP and SEM in their specific model contexts.