This study explores the decomposition of predictive uncertainty in hydrological modeling into its contributing sources. This is pursued by developing data-based probability models describing uncertainties in rainfall and runoff data, and incorporating them into the Bayesian Total Error Analysis methodology (BATEA). A case study based on the Yzeron catchment (France) and the conceptual rainfall-runoff model GR4J is presented. It exploits a calibration period where dense raingauge data is available to characterize the uncertainty in the catchment-average rainfall using geostatistical conditional simulation. The inclusion of information about rainfall and runoff data uncertainties overcomes ill-posedness problems and enables simultaneous estimation of forcing and structural errors as part of the Bayesian inference. This yields more reliable predictions than approaches that ignore or lump different sources of uncertainty in a simplistic way (e.g., standard least squares). It is shown that independently-derived data quality estimates are needed to decompose the total uncertainty in the runoff predictions into the individual contributions of rainfall, runoff and structural errors. In this case study, the total predictive uncertainty appears dominated by structural errors. Although further research is needed to interpret and verify this decomposition, it can provide strategic guidance for investments in environmental data collection and/or modeling improvement. More generally, this study demonstrates the power of the Bayesian paradigm to improve the reliability of environmental modeling using independent estimates of sampling and instrumental data uncertainties.