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. Since Hurst [1951] detected the presence of long-term persistence in hydrologic data, new estimation methods and long-memory models have been developed. The lack of flexibility in representing the combined effect of short and long memory has been the major limitation of stochastic models used to analyze hydrologic time series. In the present paper a fractionally differenced autoregressive integrated moving average (FARIMA) model is considered. In contrast to using traditional ARIMA models, this approach allows the modeling of both short-and long-term persistence in a time series. A framework for identification and estimation is presented. The data do not have to be Gaussian. The resulting model, which replicates the sample probability density of the data, can be used for the generation of long synthetic series. An application to the monthly and daily inflows of Lake Maggiore, Italy, is presented. Once a suitable model is chosen, this method gives a more accurate estimate of H. In this paper, the fractionally differenced autoregressive integrated moving average models (FARIMA, see section 3) are considered because they account for both the short-and long-memory components that are present in many hydrologic long-memory processes. An identification procedure consisting of several steps is introduced in order to determine the most suitable model. This method is then applied to daily flows to Lake Maggiore, Italy. For purposes of comparison we also apply it to monthly flows to Lake Maggiore and to monthly rainfall in Genoa, Italy. A stochastic simulation of the non-Gaussian observations is also performed.In the next section the determination of the Hurst exponent from observed hydrologic time series is discussed. Although heuristic graphical methods can detect the presence of long memory, they are not capable of estimating its intensity with a sufficient degree of accuracy. Therefore, in section 3 a stochastic modeling framework is introduced in order to combine long-memory effects with the traditional identification and estimation approach of autoregressive integrated moving average (ARIMA) models. The application of the model to daily (and monthly) flows is discussed in the section 4. An application to monthly rainfall is also presented in order to assess the flexibility of the proposed approach when modeling data not affected by persistence. Detecting Long Memory in Hydrologic Time SeriesThe relative simplicity of the heuristic estimation methods for H has made them popular as diagnostic tools. Their purpose is only to detect long memory and to provide a rough estimate of the value of the H exponent; they are not able to supply any additional information concerning the spectral density function of the data. Among the methods found in the literature, the best known is the R/S statistic, which was introduced by Hurst [1951]. Other methods have been proposed. 1035

The problem of selecting the appropriate design flood is a constant concern to dam engineering and, in general, in the hydrological practice. Overtopping represents more than 40% of dam failures in the world. The determination of the design flood is based in some cases on the T-year quantile of flood peak, and in other cases considering also the T-year quantile of flood volume. However, flood peak and flood volume have a positive (strong or weak) dependence. To model properly this aspect a bivariate probability distribution is considered using the concept of 2-Copulas, and a bivariate extreme value distribution with generalized extreme value marginals is proposed. The peak-volume pair can then be transformed into the correspondent flood hydrograph, representing the river basin response, through a simple linear model. The hydrological safety of dams is considered checking adequacy of dam spillway. The reservoir behavior is tested using a long synthetic series of flood hydrographs. An application to an existing dam is given.

The Nash model of the instantaneous unit hydrograph (IUH) is parameterized in terms of Horton order ratios of a catchment on the basis of a geomorphologic model of catchment response. The shape parameter of the Nash model is found to depend on Horton's numbers RA, RB, and RL of a catchment; thus catchment geomorphology can provide a synthesis of the shape of the hydrologic response. The scale parameter of the Nash model results to be a time‐varying character depending on both geomorphology and average streamflow velocity along the stream network; thus the time scale of the IUH could account for the variability of the hydrologic response for different storms and throughout a storm.