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 on-line 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 focussed on 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.

Large Arctic river basins experience substantial variability in climatic, landscape, and permafrost conditions. However, the processes behind the observed changes at the scale of these basins are relatively poorly understood. While most studies have been focused on the “Big 6” Arctic rivers – the Ob', Yenisey, Lena, Mackenzie, Yukon, and Kolyma – few or no assessments exist for small and medium-sized river basins, such as the Yana and Indigirka River basins. Here, we provide a detailed analysis of streamflow data from 22 hydrological gauges in the Yana and Indigirka River basins with a period of observation ranging from 35 to 79 years up to 2015. These river basins are fully located in the zone of continuous permafrost. Our analysis reveals statistically significant (p<0.05) positive trends in the monthly streamflow time series during the autumn–winter period for most of the gauges. The streamflow increases in a stepwise pattern (post-1981) for 17 out of 22 gauges in September (average trend value for the period of record is 58 % or 9.8 mm) and 15 out of 22 gauges in October (61 % or 2.0 mm). The positive trends are seen in 9 out of 19 rivers that do not freeze in November (54 %, 0.4 mm) and 6 out of 17 rivers that do not freeze in December (95 %, 0.15 mm). Precipitation is shown to decrease in late winter by up to 15 mm over the observational period. Additionally, about 10 mm of precipitation that used to fall as snow at the beginning of winter now falls as rain. Despite the decrease in winter precipitation, no decrease in streamflow has been observed during the spring freshet in May and June in the last 50 years (from 1966); moreover, five gauges show an increase of 86 % or 12.2 mm in spring floods via an abrupt change in 1987–1993. The changes in spring freshet start date are identified for 10 gauges; the earlier onset in May varies from 4 to 10 d over the observational period. We conclude that warmer temperatures due to climate change are impacting the hydrological regime of these rivers via changes in precipitation type (rain replacing snow). Other factors, such as the melting of permafrost, glaciers, and aufeis or changes in groundwater conditions, are likely to contribute as well; however, no direct observations of these changes are available. The changes in streamflow can have a significant impact on the ecology of the zone of continuous permafrost, while the increasing freshwater fluxes to the Arctic Ocean can impact the Arctic thermohaline circulation.

A detailed spatial geodatabase of aufeis (or naled in Russian) within the Indigirka River watershed (305 000 km²), Russia, was compiled from historical Russian publications (year 1958), topographic maps (years 1970–1980s) and Landsat images (year 2013–2017). Identification of aufeis by late spring Landsat images was performed with a semi-automated approach according to Normalized Difference Snow Index (NDSI) and additional data. After this, a cross-reference index was set for each aufeis field to link and compare historical and satellite-based aufeis datasets. The aufeis coverage varies from 0.26 % to 1.15 % in different sub-basins within the Indigirka River watershed. The digitized historical archive (Cadastre, 1958) contains the coordinates and characteristics of 896 aufeis fields with a total area of 2064 km². The Landsat-based dataset included 1213 aufeis fields with a total area of 1287 km². Accordingly, the satellite-derived total aufeis area is 1.6 times less than the Cadastre (1958) dataset. However, more than 600 aufeis fields identified from Landsat images are missing in the Cadastre (1958) archive. It is therefore possible that the conditions for aufeis formation may have changed from the mid-20th century to the present. Most present and historical aufeis fields are located in the elevation band of 1000–1200 m. About 60 % of the total aufeis area is represented by just 10 % of the largest aufeis fields. Interannual variability of aufeis area for the period of 2001–2016 was assessed for the Bolshaya Momskaya aufeis and for a group of large aufeis fields (11 aufeis fields with areas from 5 to 70 km²) in the basin of the Syuryuktyakh River. The results of this analysis indicate a tendency towards an area decrease in the Bolshaya Momskaya aufeis in recent years, while no reduction in Syuryuktyakh River aufeis area was observed. The combined digital database of the aufeis is available at https://doi.org/10.1594/PANGAEA.891036.

Based on the analysis of Landsat satellite images over the period of 2013–2019, the number (6683) and total area (4529 km²) of giant aufeis fields (area ≥ 0.1 km²) were estimated for the territory of North-Eastern Eurasia. The contribution of aufeis runoff to river streamflow in different seasons was calculated for 58 hydrological gauges (area 523–526,000 km²). The contribution of aufeis and glaciers to water balance is compared. The aufeis resources vary from 0.4 to 4.25 km³ (or 3.7–11 mm) for individual basins of large rivers. They are at least 10.6 km³ in total or 5 mm of water depth on average for the study area. Aufeis annual runoff varies from 0.3 to 29 mm (0.1–22%, average 3.8%), with the share in winter runoff amount about 6–712% (average 112%) and the spring freshet 0.2–43% (average 7.1%). In general, the aufeis runoff exceeds the glacial runoff. The dynamics of aufeis formation are directly related to winter runoff, whose changes are observed in different parts of the cryosphere. The presented results are relevant for studying the impact of climate change on the hydrological cycle and its components in the permafrost regions of the Northern Hemisphere.