The value of functional relationships for large scale hydrology

We increasingly rely on complex models to understand the functioning and fate of our planet. But what hydrological theory underlies these models and thus the conclusions we draw from them? How do old and rapidly increasing new observations help to advance both theory and models? In this contribution, we discuss the importance of functional relationships for (large-scale) hydrology. We define functional relationships as relationships between two or more variables that characterize the functioning of hydrological systems, such as relationships between forcing and response variables (e.g. precipitation and runoff). Functional relationships are not only a central part of hydrological theory, but they also inform how we contextualize and make measurements, and they help us to build, constrain, and evaluate models. To illustrate their value, we first provide an overview of some relationships in large-scale hydrology. We then show how such relationships can be used to evaluate global water models. We conclude by discussing what our current state of knowledge can tell us about what we should explore next, in particular the need for mechanistic explanations of empirical relationships and the potential of linking multiple hydrological fluxes within a unified framework.