Using a state-of-the-art coupled ice-ocean-circulation model, we perform a number of sensitivity experiments to examine how the central Arctic Ocean stratification responds to changes in river runoff and precipitation. The simulations yield marked changes in the cold halocline and the Arctic Atlantic layer. Increased precipitation yields a warming of the Atlantic layer, which primarily is an advective signal, propagated through the St. Anna Trough, reflecting air-sea heat flux changes over the Barents Sea. As the freshwater supply is increased, the anticyclonic Beaufort Gyre is weakened and a greater proportion of the Arctic Ocean freshwater is exported via the Fram Strait, with nearly compensating export decreases through the Canadian Arctic Archipelago. The corresponding reorganization of the freshwater pool appears to be controlled by advective processes, rather than by the local changes in the surface freshwater flux. A simple conceptual model of the Arctic Ocean, based on a geostrophically controlled discharge of the low-salinity water, is introduced and compared with the simulations. Key predictions of the conceptual model are that the halocline depth should decrease with increasing freshwater input and that the Arctic Ocean freshwater storage should increase proportionally to the square root of the freshwater input, which are in broad qualitative agreement with the sensitivity experiments. However, the model-simulated rate of increase of the freshwater storage is weaker, indicating that effects related to wind forcing and rerouting of the freshwater-transport pathways play an important role for the dynamics of the Arctic Ocean freshwater storage.