What is the role of hydrological science in the age of machine learning?

Recent experiments applying deep learning to rainfall-runoff simulation indicate that there is significantly more information in large-scale hydrological data sets than hydrologists have been able to translate into theory or models. We argue that these results challenge certain `sacred cows' in the surface hydrology community, and may be a bellwether for the discipline as a whole. While there is growing interest in machine learning in the hydrological sciences community, in many ways our community still holds deeply subjective and non-evidence-based preferences for process understanding that has historically not translated into accurate theory, models, or predictions. We suggest that, due to the perennial failure in the surface hydrology community to develop scale-relevant theories, one possible future is a discipline based primarily in machine learning and other AI methods, with a more limited role for what we currently recognize as hydrological science. We do not want this to happen and suggest a `grand challenge' for the community to work toward demonstrating where and when hydrological theory provides information in a world dominated by big data.