Modelling dependence between the ice-sheet components of sea-level rise

Sea-level projections are sensitive to statistical dependence between the East Antarctic, West Antarctic, and Greenland ice-sheet components.  The dependence is produced by climate uncertainty and ice-sheet process uncertainty.  To investigate this dependence, we model the dependence using copulas.  We use a vine copula to couple the ice-sheet components of projected sea level in 2100 under the SSP5-8.5 scenario.  Assumptions about rank correlation and copula family influence both the centre and the tails of the total ice-sheet contribution.  For example, rank correlation can influence the 95^th percentile by approximately 50%.  We explore three alternative approaches for specifying the dependence: shared dependence on global-mean surface temperature, dependence derived from ice-sheet model ensembles, and dependence derived from expert judgement.  Shared dependence on global-mean surface temperature produces little dependence between the ice-sheet components.  In contrast, ice-sheet model ensembles suggest that the dependence between the East and West Antarctic ice-sheet components may be strong, amplifying the uncertainty in future sea-level rise.