Most of the world’s watersheds lack streamflow measurements, making it hard to choose and set up hydrologic models. We developed a machine-learning approach that uses rainfall and landscape data to tell whether an ungauged catchment behaves simply (deterministic, linear, and time-invariant response), or is intermediate, or complex (threshold-driven, nonlinear, and nonstationary response). By training on over 4,000 gauged basins across six continents and then applying our model to more than 76,000 ungauged catchments—covering 132 million km²—we can map each basin’s “functional class” for both dormant and growing seasons. Knowing this class in advance lets water managers pick models that match real behavior: where simple basins may need only basic, low-parameter models, while complex basins require richer, adaptive approaches. This targeted strategy improves model realism and potentially helps to guide and prioritize where to install gauges in data-poor regions.