Relationship between global mean sea-level and global mean temperature in a climate simulation of the past millennium

The possibility of using global mean near-surface temperature, its rate of change or the global mean ocean heat-flux as predictors to statistically estimate the change of global mean sea-level is explored in the context of a long climate simulation of the past millennium with the climate model ECHO-G. Such relationships have recently been proposed to by-pass the difficulty of estimating future sea-level changes based on simulations with coarse-resolution climate models. It is found that, in this simulation, a simple linear relationship between mean temperature and the rate of change of sea level does not exist. A regression parameter linking both variables, and estimated in sliding 120-year windows, varies widely along the simulation and, in some periods, even attains negative values. The ocean heat-flux and the rate-of-change of mean temperature seem to better capture the rate-of-change of sea level due to thermal expansion.