Modelling the dependence between recent changes in polar ice sheets: Implications for global sea-level projections

Changes to the mass of the polar ice sheets are of scientific and socio-economic importance due to their effect on the wider Earth system and the potential to dominate future sea-level rise. Uncertainty remains around the joint behaviour of these ice sheets, leading sea-level modellers to make assumptions about their interdependence when making projections. We use a multi-cointegration vector autoregression model to assess the statistical relationships between time series of Greenland, West, and East Antarctic ice mass change (1992-2010). Since the ice sheet response to climate forcing integrates over time, we explore three alternative model specifications. We compare I(2) models of cumulative changes in ice mass (levels) with an I(1) model of changes in ice mass (rates), explore their model dynamics, and evaluate the out-of-sample forecasts (2011-2023) against observations. Our results support the use of an I(2) model, which identifies a significant relationship between Greenland and West Antarctica, and a persistent trend in both ice sheets that is correlated with global ocean heat content. Extensions of these forecasts to 2100 show Greenland and Antarctica contributions to global sea level that agree with projections from physical-process models and structured expert judgment compatible with high-emission scenarios.