Joint calibration of multi-scale hydrological data sets using probabilistic water balance data fusion: methodology and application to the irrigated Hindon River Basin, India

Abstract. 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 of 21 mm month^-1 for storage, 7 mm month^-1 for precipitation, 10 mm month^-1 for evaporation, 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 them. 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. Future opportunities exist to further constrain the generated water balance variables and their associated errors within process-based models.