PIXAL: a physics-inspired explainable machine learning architecture for Greenland ice albedo modeling

Abstract. The Greenland ice sheet (GrIS) is a major contributor to global sea level rise. A significant portion of the GrIS' contribution can be attributed to increased ice surface melting, which is strongly controlled by ice albedo, a property that regulates the amount of absorbed solar radiation that leads to surface melting. Yet, we lack a comprehensive understanding of the complex and nonlinear relationships ice albedo has with its environment and is, therefore, often simplified or crudely parameterized in climate models. However, an accurate representation of future ice albedo evolution is essential for reducing uncertainties in sea level rise projections. This study presents PIXAL, a physics-inspired explainable machine learning architecture that significantly outperforms the Modèle Atmosphérique Régional (MAR), a state-of-the-art regional climate model, in modeling ice albedo on the southwestern GrIS. PIXAL is based on an Extreme Gradient Boosting (XGBoost) model and is trained on a suite of modeled topographic, atmospheric, radiative, and glaciologic variables from MAR to capture the complex and nonlinear relationships with ice albedo observations obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS). Performance metrics show that PIXAL achieves an R2 of 0.563, a structural similarity index measure (SSIM) of 0.620, a mean squared error (MSE) of 0.005, and a mean absolute percentage error (MAPE) of 14.699 %, compared to MAR's R2 of 0.062, SSIM of 0.112, MSE of 0.032, and MAPE of 46.202 %. Explainable artificial intelligence analysis reveals that topographic features, specifically ice sheet surface height and slope, are important drivers of ice albedo variability due to their relationships with ice exposure duration and the effectiveness in accumulating meltwater and light-absorbing constituents (LACs) on flat ice surfaces. Near-surface air temperature and runoff further significantly impact ice albedo variability by affecting the ice metamorphic state and accumulation of meltwater and LACs. These findings highlight that understanding the complex physical processes underlying ice albedo variability is essential for accurate climate modeling and sea level rise predictions. PIXAL represents a crucial advancement in ice albedo modeling and paves the way for improved representation of ice sheets in Earth system models.