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Abstract Global water models are increasingly used to understand past, present and future water cycles, but disagreements between simulated variables make model-based inferences uncertain. Although there is empirical evidence of different large-scale relationships in hydrology, these relationships are rarely considered in model evaluation. Here we evaluate global water models using functional relationships that capture the spatial co-variability of forcing variables (precipitation, net radiation) and key response variables (actual evapotranspiration, groundwater recharge, total runoff). Results show strong disagreement in both shape and strength of model-based functional relationships, especially for groundwater recharge. Empirical and theory-derived functional relationships show varying agreements with models, indicating that our process understanding is particularly uncertain for energy balance processes, groundwater recharge processes and in dry and/or cold regions. Functional relationships offer great potential for model evaluation and an opportunity for fundamental advances in global hydrology and Earth system research in general.