The Silala is a small river, originating in the Andean Altiplano, which flows from Bolivia into Chile. Prior to a legal dispute between Chile and Bolivia over the status and use of the waters of the Silala, few hydrological studies had been performed in the basin. Further insights were required to better understand the surface-water and groundwater discharges from Bolivia to Chile, and the effects of historical channelization of the Bolivian wetlands on these flows. A semi-distributed hydrological model was therefore developed to estimate the discharges from the basin and provide recharge inputs to a groundwater model used to investigate the effects of channelization. Long-term temperature and precipitation data were available for 1969–1992, while more detailed data were available for 2018–2019. 1969–1992 was selected as a suitable length of record for long-term groundwater recharge estimation, and the recent data were reserved for model validation, reported in a companion paper. Prior model parameter ranges were identified based on field observations and scientific literature, and sampling of both input and parameter uncertainty allowed determination of representative, lower and upper groundwater recharge scenarios. Results show strong inter-annual and seasonal variability, the largest groundwater recharge being observed during the Austral summer. A representative groundwater recharge rate of 39.5 mm/year was obtained for the basin to the international border, with feasible lower and upper bounds of 34.9 and 50.2 mm/year, respectively. This lies within the range of 21–51 mm/year estimated by Bolivia for 1969–2017, albeit higher than their best estimate (24 mm/year). This article is categorized under: Science of Water > Hydrological Processes.