Uncertainties in the monthly mean estimates of precipitation are the largest over oceanic regions with the heaviest rainfall. Using the adjoint sensitivity analysis and 4d variational assimilation of sea surface salinity (SSS) into an ocean model, we show that rainfall estimation errors in the regions of heavy precipitation could be reduced by taking SSS observations into account. Inverse analysis of SSS in the Bay of Bengal also indicates that the monthly mean rainfall of the Global Precipitation Climatology Project (GPCP) is more consistent with SSS and river runoff data than other precipitation climatologies.