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.

Clumping index (CI) is a measure of foliage aggregation relative to a random distribution of leaves in space. The CI can help with estimating fractions of sunlit and shaded leaves for a given value of leaf area index (LAI). Both the CI and LAI can be obtained from global Earth Observing (EO) systems such as the Moderate Resolution Imaging Spectrometer (MODIS). Here, the compatibility between CI and LAI products derived from EO data is examined independently using the theory of spectral invariants, also referred to as photon recollision probability theory (i.e. ‘ $p$ -theory’), along with raw LAI-2000/2200 Plant Canopy Analyzer data from 75 sites distributed across a range of plant functional types (PFTs). The $p$ -theory describes the probability (p-value) that a photon, having intercepted an element in the canopy, will recollide with another canopy element rather than escape the canopy. Our results indicate that the integration of empirically-based CI maps with the MODIS LAI product is feasible, providing a potential means to improve the accuracy of LAI EO data products. Given the strong results for the large range of PFTs explored here, we demonstrate the capacity to obtain p-values for any location solely from EO data. This is relevant for future applications of the photon recollision probability concept for global and local monitoring of vegetation using EO data.

Abstract Clumping index (CI) is a measure of foliage aggregation relative to a random distribution of leaves in space. The CI can help with estimating fractions of sunlit and shaded leaves for a given leaf area index (LAI) value. Both the CI and LAI can be obtained from global Earth Observation data from sensors such as the Moderate Resolution Imaging Spectrometer (MODIS). Here, the synergy between a MODIS-based CI and a MODIS LAI product is examined using the theory of spectral invariants, also referred to as photon recollision probability (‘p-theory’), along with raw LAI-2000/2200 Plant Canopy Analyzer data from 75 sites distributed across a range of plant functional types. The p-theory describes the probability (p-value) that a photon, having intercepted an element in the canopy, will recollide with another canopy element rather than escape the canopy. We show that empirically-based CI maps can be integrated with the MODIS LAI product. Our results indicate that it is feasible to derive approximate p-values for any location solely from Earth Observation data. This approximation is relevant for future applications of the photon recollision probability concept for global and local monitoring of vegetation using Earth Observation data.