Sebastian Gnann , Robert Reinecke , Lina Stein , Yoshihide Wada, Wim Thiery, Hannes Müller Schmied, Yusuke Satoh, Yadu Pokhrel, Sebastian Ostberg, Aristeidis Koutroulis, Naota Hanasaki, Manolis Grillakis, Simon Gosling, Peter Burek, Marc Bierkens, Thorsten Wagener 

Global water models are increasingly used to understand the past, present, and future water cycle, but disagreements between models make model-based inferences uncertain. While there is empirical evidence of a number of large-scale hydrologic relationships, these relationships are rarely used for model evaluation. Here we evaluate global water models using functional relationships that capture the spatial co-variability of forcing (precipitation, net radiation) and response variables (actual evapotranspiration, groundwater recharge, total runoff). We find strong disagreement in the shape and strength of model-based forcing-response 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 the potential for fundamental advances in global hydrology and should be a revived focus of hydrological research, with great potential for model evaluation.