We analyze the surface sigma O-18 - salinity relationships of the Bay of Bengal and the Arabian Sea, in the northern Indian Ocean, known for their contrasting hydrological conditions. New measurements of these tracers show a very low sigma O-18 - salinity slope associated with the strong dilution in the Bay of Bengal, but a slope more typical of this latitude in the Arabian Sea. Although this region is marked by a complex monsoonal regime, numerical modeling using a box model and a general circulation model is able to capture the sigma O-18 - salinity slope and its geographical variation. Both models clearly show that the low sigma O-18 - salinity slope is due to the evaporation-minus-precipitation balance, with an important contribution of the continental runoff in the Bay of Bengal. Although the low value of these slopes (similar to 0.25) makes past salinity reconstructions uncertain, insight into the Last Glacial Maximum conditions shows a probable stability of these slopes and limited error on paleosalinity.