Abstract We examine a 1000-yr-long forced historical run of the Max Planck Institute Earth System Model (henceforth, past1000) with respect to freshwater-induced sea surface height (SSH) variability in the Arctic Ocean, with a focus on time scales up to and longer than centuries. As a test of the degree to which sea surface height and freshwater content covariability is due to internal climate variability in the model, and how much is due to external forcing, the past1000 results are compared to a control run using the same model, (henceforth, Ctl-P). We find that the freshwater transport associated with circulation changes, the freshwater input at the surface from the atmosphere and runoff, and ice export out of the Arctic jointly contribute to the centennial-scale freshwater variability in the Arctic. Low-frequency winds generate freshwater variability mostly through ocean circulation changes, but appear to be less important compared with earlier studies. The ice transport varies most clearly with Arctic air temperatures, and it appears that ice thickness variability is at least as important as the wind and ocean current transport variability. The largest difference in freshwater forcing in the forced run, compared to Ctl-P, is enhanced precipitation variability driven by the volcanic forcing only present in the forced, past1000 run.