Maintaining global freshwater conservation in climate models is crucial for accurately simulating Earth's hydrological cycle. This property particularly deserves specific attention in the deep-time paleoclimate simulations for the different geographies that changes the river route to the ocean. Changes in the volume of runoff directly exert significant impact on the ocean circulation. Large uncertainties in paleo-topography causes the uncertainties in runoff, but the latter receives less attention in the model simulations. To investigate the effects of the uncertainties on the model simulations, climate simulations of the Pre-Industrial (PI) and the Middle Miocene Climatic Optimum (MMCO) are compared by two sets of experiments —— freshwater conservative and non-conservative experiments that with sufficient and insufficient runoff import to the ocean model, respectively. Compared to the non-conservative experiments, the conservative experiments show that more riverine freshwater flux could reduce the salinity in the North Atlantic and collapse the Atlantic Meridional Overturning Circulation (AMOC), in contrast to the high salinity distribution and much strong AMOC in the non-conservative experiments. These differences related to the AMOC also cause the discrepancies in volume transport through the oceanic seaway, as well as contribute to the temperature, sea ice and surface albedo changes in different amplitude in the North Atlantic. Moreover, more riverine freshwater flux could enhance the Atlantic Multidecadal Oscillation (AMO) in the MMCO and PI simulations. Besides, the reduced or collapsed AMOC could weaken the intensity of the South Asian monsoon. The study suggests that runoff changes have great effect on the global climate change especially the North Atlantic.

runoff;,AMOC;,ocean circulation