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. ARTICLE HISTORY

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Abstract. Distributed energy and water balance models require time-series surfaces of the climatological variables involved in hydrological processes. Among them, solar radiation constitutes a key variable to the circulation of water in the atmosphere. Most of the hydrological GIS-based models apply simple interpolation techniques to data measured at few weather stations disregarding topographic effects. Here, a topographic solar radiation algorithm has been included for the generation of detailed time-series solar radiation surfaces using limited data and simple methods in a mountainous watershed in southern Spain. The results show the major role of topography in local values and differences between the topographic approximation and the direct interpolation to measured data (IDW) of up to +42% and −1800% in the estimated daily values. Also, the comparison of the predicted values with experimental data proves the usefulness of the algorithm for the estimation of spatiallydistributed radiation values in a complex terrain, with a good fit for daily values (R 2 = 0.93) and the best fits under cloudless skies at hourly time steps. Finally, evapotranspiration fields estimated through the ASCE-Penman-Monteith equation using both corrected and non-corrected radiation values address the hydrologic importance of using topographicallycorrected solar radiation fields as inputs to the equation over uniform values with mean differences in the watershed of 61 mm/year and 142 mm/year of standard deviation. High speed computations in a 1300 km 2 watershed in the south of Spain with up to a one-hour time scale in 30 × 30 m 2 cells can be easily carried out on a desktop PC.

Abstract. Longwave radiation is an important component of the energy balance of the Earth's surface. The downward component, emitted by the clouds and aerosols in the atmosphere, is rarely measured, and is still not well understood. In mountainous areas, direct observations are even scarcer and the fitting of existing models is often subjected to local parameterization in order to surplus the particular physics of the atmospheric profiles. The influence of clouds makes it even harder to estimate for all sky conditions. This work presents a long-time continuous dataset of high-resolution longwave radiation measured in a weather station at a height of 2500 m a.s.l. in Sierra Nevada, Spain, together with the parameterization of the apparent atmospheric emissivity for clear and cloudy skies resulting from three different schemes. We evaluate the schemes of Brutsaert, and Crawford and Duchon with locally adjusted coefficients and compare them with a completely parametric expression adjusted for these data that takes into account three possible significant atmospheric states related to the cloud cover: clear, completely covered, and partly covered skies. All the parametric expressions are related to the screen-level values of temperature, relative humidity and solar radiation, which can be frequently found in standard weather stations. Unobserved cloudiness measurements needed for Brutsaert scheme for cloudy sky are also parameterized from screen-level measurements. The calibration performed for a 6-yr period at the study site resulted in satisfactory estimations of emissivity for all the analyzed schemes thanks to the local fitting of the parameterizations, with the best achievement found for the completely parametric expression. Further validation of the expressions in two alternative sites showed that the greater accuracy of the latter can also be found in very close sites, while a better performance of the Brutsaert scheme, with a more physical background and the successful parameterization of the clouds effect, is found in nearby sites outside the initial mountain range. The results show the feasibility for the local calibration of expressions to estimate instantaneous atmospheric emissivity for all sky conditions only using surface data, either with a completely parametric scheme if longwave data are available, or through obtaining of locally fitted coefficients for Brutsaert and derived schemes. Nevertheless, the best performance of the first approach would be at the expense of a reduced local applicability.