Abstract. The theory that forms the basis of TOPMODEL (a topography-based hydrological model) was first outlined by Mike Kirkby some 45 years ago. This paper recalls some of the early developments, the rejection of the first journal paper, the early days of digital terrain analysis, model calibration and validation, the various criticisms of the simplifying assumptions, and the relaxation of those assumptions in the dynamic forms of TOPMODEL. A final section addresses the question of what might be done now in seeking a simple, parametrically parsimonious model of hillslope and small catchment processes if we were starting again.

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come.

Hydrology is still, and for good reasons, an inexact science, even if evolving hydrological understanding has provided a basis for improved water management for at least the last three millennia. The limitations of that understanding have, however, become much more apparent and important in the last century as the pressures of increasing populations, and the anthropogenic impacts on catchment forcing and responses, have intensified. At the same time, the sophistication of hydrological analyses and models has been developing rapidly, often driven more by the availability of computational power and geographical data sets than any real increases in understanding of hydrological processes. This sophistication has created an illusion of real progress but a case can be made that we are still rather muddling along, limited by the significant uncertainties in hydrological observations, knowledge of catchment characteristics and related gaps in conceptual understanding, particularly of the sub-surface. These knowledge gaps are illustrated by the fact that for many catchments we cannot close the water balance without significant uncertainty, uncertainty that is often neglected in evaluating models for practical applications.