| Summary: | We propose linear response functions to separately estimate the sea-level contributions of thermal expansion and solid ice discharge from Greenland and Antarctica. The response function formalism introduces a time-dependence which allows for future rates of sea-level rise to be influenced by past climate variations. We find that this time-dependence is of the same functional type, R(t) ∼ t α, for each of the three subsystems considered here. The validity of the approach is assessed by comparing the sea-level estimates obtained via the response functions to projections from comprehensive models. The pure vertical diffusion case in one dimension, corresponding to α=-0.5, is a valid approximation for thermal expansion within the ocean up to the middle of the twenty first century for all Representative Concentration Pathways. The approximation is significantly improved for α = - 0.7. For the solid ice discharge from Greenland we find an optimal value of α = -0.7. Different from earlier studies we conclude that solid ice discharge from Greenland due to dynamic thinning is bounded by 0.42 m sea-level equivalent. Ice discharge induced by surface warming on Antarctica is best captured by a positive value of α = 0.1 which reflects the fact that ice loss increases with the cumulative amount of heat available for softening the ice in our model. © 2012 Springer-Verlag.
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