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This study evaluates the ability of different gridded rainfall datasets to plausibly represent the spatio-temporal patterns of multiple hydrological processes (i.e. streamflow, actual evaporation, soil moisture and terrestrial water storage) for large-scale hydrological modelling in the predominantly semi-arid Volta River basin (VRB) in West Africa. Seventeen precipitation products based essentially on gauge-corrected satellite data (TAMSAT, CHIRPS, ARC, RFE, MSWEP, GSMaP, PERSIANN-CDR, CMORPH-CRT, TRMM 3B42 and TRMM 3B42RT) and on reanalysis (ERA5, PGF, EWEMBI, WFDEI-GPCC, WFDEI-CRU, MERRA-2 and JRA-55) are compared as input for the fully distributed mesoscale Hydrologic Model (mHM). To assess the model sensitivity to meteorological forcing during rainfall partitioning into evaporation and runoff, six different temperature reanalysis datasets are used in combination with the precipitation datasets, which results in evaluating 102 combinations of rainfall-temperature input data. The model is recalibrated for each of the 102 input combinations, and the model responses are evaluated by using in situ streamflow data and satellite remote-sensing datasets from GLEAM evaporation, ESA CCI soil moisture and GRACE terrestrial water storage. A bias-insensitive metric is used to assess the impact of meteorological forcing on the simulation of the spatial patterns of hydrological processes. The results of the process-based evaluation show that the rainfall datasets have contrasting performances across the four climatic zones present in the VRB. The top three best-performing rainfall datasets are TAMSAT, CHIRPS and PERSIANN-CDR for streamflow; ARC, RFE and CMORPH-CRT for terrestrial water storage; MERRA-2, EWEMBI/WFDEI-GPCC and PGF for the temporal dynamics of soil moisture; MSWEP, TAMSAT and ARC for the spatial patterns of soil moisture; ARC, RFE and GSMaP-std for the temporal dynamics of actual evaporation; and MSWEP, TAMSAT and MERRA-2 for the spatial patterns of actual evaporation. No single rainfall or temperature dataset consistently ranks first in reproducing the spatio-temporal variability of all hydrological processes. A dataset that is best in reproducing the temporal dynamics is not necessarily the best for the spatial patterns. In addition, the results suggest that there is more uncertainty in representing the spatial patterns of hydrological processes than their temporal dynamics. Finally, some region-tailored datasets outperform the global datasets, thereby stressing the necessity and importance of regional evaluation studies for satellite and reanalysis meteorological datasets, which are increasingly becoming an alternative to in situ measurements in data-scarce regions.