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

Swings from snow drought to extreme winter rainfall make managing reservoirs, like the Oroville Dam, incredibly difficult. But what exactly is "snow drought"?

Abstract. Lateral carbon flux through river networks is an important and poorly understood component of the global carbon budget. This work investigates how temperature and hydrology control the production and export of dissolved organic carbon (DOC) in the Susquehanna Shale Hills Critical Zone Observatory in Pennsylvania, USA. Using field measurements of daily stream discharge, evapotranspiration, and stream DOC concentration, we calibrated the catchment-scale biogeochemical reactive transport model BioRT-Flux-PIHM (Biogeochemical Reactive Transport–Flux–Penn State Integrated Hydrologic Model, BFP), which met the satisfactory standard of a Nash–Sutcliffe efficiency (NSE) value greater than 0.5. We used the calibrated model to estimate and compare the daily DOC production rates (Rp; the sum of the local DOC production rates in individual grid cells) and export rate (Re; the product of the concentration and discharge at the stream outlet, or load). Results showed that daily Rp varied by less than an order of magnitude, primarily depending on seasonal temperature. In contrast, daily Re varied by more than 3 orders of magnitude and was strongly associated with variation in discharge and hydrological connectivity. In summer, high temperature and evapotranspiration dried and disconnected hillslopes from the stream, driving Rp to its maximum but Re to its minimum. During this period, the stream only exported DOC from the organic-poor groundwater and from organic-rich soil water in the swales bordering the stream. The DOC produced accumulated in hillslopes and was later flushed out during the wet and cold period (winter and spring) when Re peaked as the stream reconnected with uphill and Rp reached its minimum. The model reproduced the observed concentration–discharge (C–Q) relationship characterized by an unusual flushing–dilution pattern with maximum concentrations at intermediate discharge, indicating three end-members of source waters. A sensitivity analysis indicated that this nonlinearity was caused by shifts in the relative contribution of different source waters to the stream under different flow conditions. At low discharge, stream water reflected the chemistry of organic-poor groundwater; at intermediate discharge, stream water was dominated by the organic-rich soil water from swales; at high discharge, the stream reflected uphill soil water with an intermediate DOC concentration. This pattern persisted regardless of the DOC production rate as long as the contribution of deeper groundwater flow remained low (<18 % of the streamflow). When groundwater flow increased above 18 %, comparable amounts of groundwater and swale soil water mixed in the stream and masked the high DOC concentration from swales. In that case, the C–Q patterns switched to a flushing-only pattern with increasing DOC concentration at high discharge. These results depict a conceptual model that the catchment serves as a producer and storage reservoir for DOC under hot and dry conditions and transitions into a DOC exporter under wet and cold conditions. This study also illustrates how different controls on DOC production and export – temperature and hydrological flow paths, respectively – can create temporal asynchrony at the catchment scale. Future warming and increasing hydrological extremes could accentuate this asynchrony, with DOC production occurring primarily during dry periods and lateral export of DOC dominating in major storm events.

Dissolved oxygen (DO) reflects river metabolic pulses and is an essential water quality measure. Our capabilities of forecasting DO however remain elusive. Water quality data, specifically DO data here, often have large gaps and sparse areal and temporal coverage. Earth surface and hydrometeorology data, on the other hand, have become largely available. Here we ask: can a Long Short-Term Memory (LSTM) model learn about river DO dynamics from sparse DO and intensive (daily) hydrometeorology data? We used CAMELS-chem, a new data set with DO concentrations from 236 minimally disturbed watersheds across the U.S. The model generally learns the theory of DO solubility and captures its decreasing trend with increasing water temperature. It exhibits the potential of predicting DO in “chemically ungauged basins”, defined as basins without any measurements of DO and broadly water quality in general. The model however misses some DO peaks and troughs when in-stream biogeochemical processes become important. Surprisingly, the model does not perform better where more data are available. Instead, it performs better in basins with low variations of streamflow and DO, high runoff-ratio (>0.45), and winter precipitation peaks. Results here suggest that more data collections at DO peaks and troughs and in sparsely monitored areas are essential to overcome the issue of data scarcity, an outstanding challenge in the water quality community.