Hydrological data sets have vast potential for water resource management applications; however, they are subject to uncertainties. In this paper, we develop and apply a monthly probabilistic water balance data fusion approach for automatic bias correction and noise filtering of multi-scale hydrological data. The approach first calibrates the independent data sets by linking them through the water balance, resulting in hydrologically consistent estimates of precipitation (P), evaporation (E), storage (S), irrigation canal water imports (C), and river discharge (Q) that jointly close the basin-scale water balance. Next, the basin-scale results are downscaled to the pixel-scale, to generate calibrated ensembles of gridded Precipitation (P) and Evaporation (E) that reflect the basin-wide water balance closure constraints. An application to the irrigated Hindon River basin in India illustrates that the approach generates physically reasonable estimates of all basin-scale variables, with average standard errors decreasing in the following order: 21 mm month−1 for storage, 10 mm month−1 for evaporation, 7 mm month−1 for precipitation, 4 mm month−1 for irrigation canal water imports, and 2 mm month−1 for river discharge. Results show that updating the original independent data with water balance constraint information reduces uncertainties by inducing cross-correlations between all independent variables linked through the water balance. In addition, the introduced approach yields (i) hydrologically consistent gridded P and E estimates that fuse information from prior (original) data across different land use elements and (ii) statistically consistent random errors that reflect the model's confidence about P and E estimates at each grid cell. The analysis also shows a long-term decreasing trend in groundwater, which is better captured by the more severe decline from GRACE JPL mascon than GRACE Spherical Harmonic data. This finding points towards the possible sustainability issues for irrigation in the basin and requires further validation using piezometer groundwater-level measurements. Future opportunities exist to further constrain the generated water balance variables and their associated errors within process-based models and with additional data.

Study region: Hindon River Basin, North India. Study focus: Accurate estimation of water balance components is crucial for water management applications yet challenging due to errors in monthly gridded water balance data products. Error and uncertainty quantification is especially important in the absence of extensive in-situ data. This paper presents a prior uncertainty analysis for such situations consisting of two components: (i) quantification of prior uncertainties using metrics that quantify errors in individual products and variability and consistency between products, and (ii) reduction of prior uncertainties by eliminating unrealistic water balance estimates. New hydrological insights for the region: Grid-scale inter-product uncertainty or variability, computed as the coefficient of variation (CV, %) at various temporal scales, reveals discrepancies between water balance products due to a combination of factors, including methodological differences, inherent spatial variability, data sources, and resolution disparities. At the mean annual scale, P fluxes display a lower grid-scale inter-product uncertainty (5–9 %) than ET (20–55 %), while the ∆TWS from GRACE solutions show a moderate mean annual grid-scale inter-product uncertainty (15–19 %). Grid-scale inter-product uncertainties of ∆SMS for July – representing the onset of the monsoon season – are high (CV = 54–122 %), indicating that the uncertainty in estimates of this component may have a large impact on water balance analyses. P fluxes exhibited fewer spatio-temporal uncertainties (R² above 0.8) than ET fluxes (R² less than 0.75). The exclusion of the unreliable data sets resulted in (a) reducing uncertainties in input water balance components with triple collocation range shifting from 15–38 to 17–23 mm/month for ET and from 16–52 to 11–23 mm/month for P, (b) obtaining updated prior estimates of seasonal water balance. The updated priors of water balance variables per season suggest a net basin outflow (from −318 to −57 mm/season) during the monsoon (rainy) season and net basin inflow (from −38 to 330 mm/season) during the non-monsoon (dry) season, the latter related to surface-water imports from outside the basin. All GRACE data sets exhibit a regional long-term decreasing trend in total water storage (ranging from −31 to −61 mm/year), qualitatively confirming previously documented unsustainable groundwater depletion in the basin. Prior ranges and uncertainties for all water balance variables reported here can be used as input into a posterior analysis that uses in-situ data for locally calibrating (bias-correcting, noise-filtering) and further updating the prior estimates.