Statistically parameterizing and evaluating a positive degree-day model to estimate surface melt in Antarctica from 1979 to 2022

Abstract

Surface melting is one of the primary drivers of ice shelf collapse in Antarctica and is expected to increase in the future as the global climate continues to warm because there is a statistically significant positive relationship between air temperature and melting. Enhanced surface melt will impact the mass balance of the Antarctic Ice Sheet (AIS) and, through dynamic feedbacks, induce changes in global mean sea level (GMSL). However, the current understanding of surface melt in Antarctica remains limited in terms of the uncertainties in quantifying surface melt and understanding the driving processes of surface melt in past, present and future contexts. Here, we construct a novel grid-cell-level spatially distributed positive degree-day (PDD) model, forced with 2 m air temperature reanalysis data and spatially parameterized by minimizing the error with respect to satellite estimates and surface energy balance (SEB) model outputs on each computing cell over the period 1979 to 2022. We evaluate the PDD model by performing a goodness-of-fit test and cross-validation. We assess the accuracy of our parameterization method, based on the performance of the PDD model when considering all computing cells as a whole, independently of the time window chosen for parameterization. We conduct a sensitivity experiment by adding ±10 % to the training data (satellite estimates and SEB model outputs) used for PDD parameterization and a sensitivity experiment by adding constant temperature perturbations (+1, +2, +3, +4 and +5 ∘C) to the 2 m air temperature field to force the PDD model. We find that the PDD melt extent and amounts change analogously to the variations in the training data with steady statistically significant correlations and that the PDD melt amounts increase nonlinearly with the temperature perturbations, demonstrating the consistency of our parameterization and the applicability of the PDD model to warmer climate scenarios. Within the limitations discussed, we suggest that an appropriately parameterized PDD model can be a valuable tool for exploring Antarctic surface melt beyond the satellite era.