This study documents the development of a semi-distributed hydrological model aimed at reflecting the dominant controls on observed streamflow spatial variability. The process is presented through the case study of the Thur catchment (Switzerland, 1702 km²), an alpine and pre-alpine catchment where streamflow (measured at 10 subcatchments) has different spatial characteristics in terms of amounts, seasonal patterns, and dominance of baseflow. In order to appraise the dominant controls on streamflow spatial variability and build a model that reflects them, we follow a two-stage approach. In a first stage, we identify the main climatic or landscape properties that control the spatial variability of streamflow signatures. This stage is based on correlation analysis, complemented by expert judgement to identify the most plausible cause–effect relationships. In a second stage, the results of the previous analysis are used to develop a set of model experiments aimed at determining an appropriate model representation of the Thur catchment. These experiments confirm that only a hydrological model that accounts for the heterogeneity of precipitation, snow-related processes, and landscape features such as geology produces hydrographs that have signatures similar to the observed ones. This model provides consistent results in space–time validation, which is promising for predictions in ungauged basins. The presented methodology for model building can be transferred to other case studies, since the data used in this work (meteorological variables, streamflow, morphology, and geology maps) are available in numerous regions around the globe.