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Left: First page of Hilbert’s “Mathematical problems” (Hilbert 1900). Right: David Hilbert around 1900. English translation8 see Hilbert (1902).
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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, p...
Citations
... In the hydrology context, unlike the reasons expressed in the general AI/ML/DL community, the main reasons stated by researchers for the incorporation of XAI/iML are related to their contribution to greater understanding of the hydrological process, coinciding with the epistemic value of understanding in the progress of the discipline [18][19][20][21]. In the opinion of the authors of this paper, however, the incorporation of XAI/iML into the discipline should involve at least two main reasons based on the factors that have historically shaped the progress of the discipline: technological development and the needs of society [88]. ...
... Hydrology, a discipline that throughout its history has known how to adapt to the context of technological development and social needs in which it is immersed [88], due to its own evolution, is inextricably linked to human affairs. And while an understanding of the processes and the progress of hydrological knowledge continue to be the main value of the discipline [19][20][21], the contribution of hydrology to solving the problems of society will require consideration of the ethical issues behind the solutions it provides [18,100]. This idea is reinforced when the discipline itself has explicitly recognized the increasingly substantial role of human-water interactions, and where communication of scientific knowledge and the acquisition of feedback from stakeholders are key factors in the progress of the discipline and its mission to be a "science for solutions" [101]. ...
In recent years, a new discipline known as Explainable Artificial Intelligence (XAI) has emerged, which has followed the growing trend experienced by Artificial Intelligence over the last decades. There are, however, important gaps in the adoption of XAI in hydrology research, in terms of application studies in the southern hemisphere, or in studies associated with snowmelt-driven streamflow prediction in arid regions, to mention a few. This paper seeks to contribute to filling these knowledge gaps through the application of XAI techniques in snowmelt-driven streamflow prediction in a basin located in the arid region of north-central Chile in South America. For this, two prediction models were built using the Random Forest algorithm, for one and four months in advance. The models show good prediction performance in the training set for one (RMSE:1.33, R2: 0.94, MAE:0.55) and four (RMSE: 5.67, R2:0.94, MAE: 1.51) months in advance. The selected interpretation techniques (importance of the variable, partial dependence plot, accumulated local effects plot, Shapley values and local interpretable model-agnostic explanations) show that hydrometeorological variables in the vicinity of the basin are more important than climate variables and this occurs both for the dataset level and for the months with the lowest streamflow records. The importance of the XAI approach adopted in this study is discussed in terms of its contribution to the understanding of hydrological processes, as well as its role in high-stakes decision-making.
... and future climate projections (Blöschl et al., 2019;Meixner et al., 2016;Musselman et al., 2021;Segura, 2021;Siirila-Woodburn et al., 2021;Zapata-Rios et al., 2016). As a result, hydrologists are still working to predict how headwater streamflow quantity and quality will respond to a changing climate. ...
The western U.S. is experiencing increasing rain to snow ratios due to climate change, and scientists are uncertain how changing recharge patterns will affect future groundwater‐surface water connection. We examined how watershed topography and streambed hydraulic conductivity impact groundwater age and stream discharge at eight sites along a headwater stream within the Manitou Experimental Forest, CO USA. To do so, we measured: (a) continuous stream and groundwater discharge/level and specific conductivity from April to November 2021; (b) biweekly stream and groundwater chemistry; (c) groundwater chlorofluorocarbons and tritium in spring and fall; (d) streambed hydraulic conductivity; and (e) local slope. We used the chemistry data to calculate fluorite saturation states that were used to inform end‐member mixing analysis of streamflow source. We then combined chlorofluorocarbon and tritium data to estimate the age composition of riparian groundwater. Our data suggest that future stream drying is more probable where local slope is steep and streambed hydraulic conductivity is high. In these areas, groundwater source shifted seasonally, as indicated by age increases, and we observed a high fraction of groundwater in streamflow, primarily interflow from adjacent hillslopes. In contrast, where local slope is flat and streambed hydraulic conductivity is low, streamflow is more likely to persist as groundwater age was seasonally constant and buffered by storage in alluvial sediments. Groundwater age and streamflow paired with characterization of watershed topography and subsurface characteristics enabled identification of likely controls on future stream drying patterns.
... The 100 questions approach is a process of identifying emerging issues or questions that, if answered, have the potential to impact decision-making in the respective sector [35][36][37][38]. Over the last 20 years, this approach has been successfully conducted in many fields, including landscape restoration [39], forestry [40], agriculture [41], urban stream ecology [42], microbial ecology [43], hydrology [44], conservation physiology [45], fish migration [46], recreational fisheries [47], and smart (energy) consumption [48,49]. This integrative approach seeks to incorporate and dialogue with various stakeholders, including practitioners, legislators, and researchers, to refine and distill a set of questions until 100 high-priority questions emerge [35][36][37]. ...
... Although we intended to reach an audience as broad as possible, we acknowledge that the input received from participants had certain limitations in terms of geography, background, and domains of interestan issue also inherent to other exercises of the type [43,44,47]. Despite making the global questionnaire available in six widely-spoken languages [38] and widely distributing it through various channels (resulting in ca. ...
As the share of renewable energy grows worldwide, flexible energy production from peak-operating hydropower and the phenomenon of hydropeaking have received increasing attention. In this study, we collected open research questions from 220 experts in river science, practice, and policy across the globe using an online survey available in six languages related to hydropeaking. We used a systematic method of determining expert consensus (Delphi method) to identify 100 high-priority questions related to the following thematic fields: (a) hydrology, (b) physico-chemical properties of water, (c) river morphology and sediment dynamics, (d) ecology and biology, (e) socioeconomic topics, (f) energy markets, (g) policy and regulation, and (h) management and mitigation measures. The consensus list of high-priority questions shall inform and guide researchers in focusing their efforts to foster a better science-policy interface, thereby improving the sustainability of peak-operating hydropower in a variety of settings. We find that there is already a strong understanding of the ecological impact of hydropeaking and efficient mitigation techniques to support sustainable hydropower. Yet, a disconnect remains in its policy and management implementation.
... As such, the airGRteaching tool is not intended to be used to realize extended hydrological research studies, and therefore it does not aim to be used to contribute to the actual solving of any of the 23 UPHs (unsolved problems in hydrology; Blöschl et al., 2019). However, as it is a tool to teach hydrology, to understand hydrological processes, and to master hydrological modeling, we believe that airGRteaching could be used as a preliminary step in the solving of some UPHs. ...
Hydrological modeling is at the core of most studies related to water, especially for anticipating disasters, managing water resources, and planning adaptation strategies. Consequently, teaching hydrological modeling is an important, but difficult, matter. Teaching hydrological modeling requires appropriate software and teaching material (exercises, projects); however, although many hydrological modeling tools exist today, only a few are adapted to teaching purposes. In this article, we present the airGRteaching package, which is an open-source R package. The hydrological models that can be used in airGRteaching are the GR rainfall-runoff models, i.e., lumped processed-based models, allowing streamflows to be simulated, including the GR4J model. In this package, thanks to a graphical user interface and a limited number of functions, numerous hydrological modeling exercises representing a wide range of hydrological applications are proposed. To ease its use by students and teachers, the package contains several vignettes describing complete projects that can be proposed to investigate various topics such as streamflow reconstruction, hydrological forecasting, and assessment of climate change impact.
... Besides inconsistencies and methodological biases supported in Gleeson et al. (2014), the compiled permeabilities above the regional scale (> 5 km) are not suitable at the catchment scale. Therefore, estimating subsurface hydraulic properties that correctly represent observed catchment-scale processes remains a major challenge for the hydrological community (Blöschl et al., 2019). New opportunities have been identified through the increasing availabilities of surface observations (Beven et al., 2020;Gleeson et al., 2021), specifically with an application for ungauged basins. ...
... These approaches are especially relevant as rapid advances in remote sensing are improving the description of global river networks (Schneider et al., 2017;Lehner and Grill, 2013), wetlands (Tootchi et al., 2019;Rapinel et al., 2023) and soil moisture (Vergopolan et al., 2021). Lidar and high-resolution satellite imagery offer new opportunities to determine the surface characteristics of landscapes (Levizzani and Cattani, 2019;Blöschl et al., 2019) and, by extension, the hydrological parameters of local to continental ungauged catchments (Barclay et al., 2020;Dembélé et al., 2020). In this work, we propose a new methodology to quantify effective hydraulic properties of unconfined aquifers from topographical and stream network observations now available at high resolution. ...
The assessment of effective hydraulic properties at the catchment scale,
i.e., hydraulic conductivity (K) and transmissivity (T), is particularly
challenging due to the sparse availability of hydrological monitoring
systems through stream gauges and boreholes. To overcome this challenge, we
propose a calibration methodology which only considers information from a digital elevation model (DEM) and the spatial distribution of the stream
network. The methodology is built on the assumption that the groundwater
system is the main driver controlling the stream density and extension,
where the perennial stream network reflects the intersection of the
groundwater table with the topography. Indeed, the groundwater seepage at
the surface is primarily controlled by the topography, the aquifer
thickness and the dimensionless parameter K/R, where R is the average
recharge rate. Here, we use a process-based and parsimonious 3D groundwater
flow model to calibrate K/R by minimizing the relative distances between
the observed and the simulated stream network generated from groundwater
seepage zones. By deploying the methodology in 24 selected headwater
catchments located in northwestern France, we demonstrate that the method
successfully predicts the stream network extent for 80 % of the cases.
Results show a high sensitivity of K/R to the extension of the low-order
streams and limited impacts of the DEM resolution as long the DEM remains
consistent with the stream network observations. By assuming an average
recharge rate, we found that effective K values vary between 1.0×10-5 and 1.1×10-4 m s−1, in agreement with local estimates derived from hydraulic tests and independent calibrated groundwater model. With the emergence of global remote-sensing databases compiling information on high-resolution DEM and stream networks, this approach provides new opportunities to assess hydraulic properties of unconfined aquifers in ungauged basins.
... Rainfall extreme values are required in many hydrological applications, e.g. for dimensioning purposes in engineering hydrology, soil erosion estimation (Pidoto et al., 2022), flood risk management (Viglione et al., 2010, Tarasova et al., 2019 and in urban hydrology (Ochoa-Rodriguez et al., 2015). Knowledge about future changes of temporal high-resolution rainfall extreme values directly relates to one of the twenty-three unsolved problems in hydrology described by Blöschl et al. (2019), i.e. question 9: 'How do flood-rich and drought-rich periods arise, are they changing, and if so why?'). In this context 35 we expect that the introduction of temperature dependency in rainfall disaggregation improves the representations of sub-daily rainfall extreme values in climate change projections. ...
Rainfall time series with high temporal resolution play a crucial role in various hydrological fields, such as urban hydrology, flood risk management, and soil erosion. Understanding the future changes in rainfall extreme values is essential for these applications. Since climate scenarios typically offer daily resolution only, statistical downscaling in time seems a promising and computational effective solution. The micro-canonical cascade model conserves the daily rainfall amounts exactly and with all model parameters expressed as physical interpretable probabilities avoids assumptions about future rainfall changes. Taking into account that rainfall extreme values are linked to high temperatures, the micro-canonical cascade model is further developed in this study. As the introduction of the temperature-dependency increases the number of cascade model parameters, several modifications for parameter reduction are tested beforehand. For this study 45 locations across Germany are selected. To ensure spatial coherence with the climate model data (~∆l=5 km*5 km), a composite product of radar and rain gauges with the same resolution was used for the estimation of the cascade model parameters. For the climate change analysis the core ensemble of the German Weather Service, which comprises six combinations of global and regional climate models is applied for both, RCP 4.5 and RCP 8.5 scenarios. For parameter reduction two approaches were analysed: i) the reduction via position-dependent probabilities and ii) parameter reduction via scale-independency. A combination of both approaches led to a reduction in the number of model parameters (48 parameters instead of 144 in the reference model) with only a minor worsening of the disaggregation results. The introduction of the temperature dependency improves the disaggregation results, particularly regarding rainfall extreme values and is therefore important to consider for future rainfall extreme value studies. For the disaggregated rainfall time series of climate scenarios, an increase of the rainfall extreme values is observed. Analyses of rainfall extreme values for different return periods for a rainfall duration of 5 min and 1 h indicate an increase of 5–10 % in the near-term future (2021–2050) and 15–25 % in the long-term future (2071–2100) compared to the control period (1971–2000).
... Hydrological models, such as process-based modelsencompassing physical and conceptual modelsand data-driven models like deep learning (DL) models, play a crucial role in addressing issues related to flood mitigation and water supplies (Blöschl et al., 2019;Cui et al., 2023). Process-based hydrological models are based on established hydrological knowledge (Knoben et al., 2020;Li et al., 2021a) but may use empirical formulas to represent certain hydrological processes that are not fully understood or are difficult to represent due to limited computational resources, such as the degree-day factor for snowmelt and the temperature threshold for precipitation partition (He et al., 2014;Hock, 2003). ...
... Process-based hydrological models are based on established hydrological knowledge (Knoben et al., 2020;Li et al., 2021a) but may use empirical formulas to represent certain hydrological processes that are not fully understood or are difficult to represent due to limited computational resources, such as the degree-day factor for snowmelt and the temperature threshold for precipitation partition (He et al., 2014;Hock, 2003). Due to the inadequate nature of these empirical relationships in incorporating comprehensive physics, the process-based models may exhibit lower performance in hydrological modeling (Blöschl et al., 2019;Nearing et al., 2021). DL hydrological models, particularly long-short memory (LSTM) networks (Hochreiter and Schmidhuber, 1997), have demonstrated superior performance in hydrological modeling compared to traditional process-based hydrological models in various scenarios. ...
Deep learning (DL) models have demonstrated exceptional performance in hydrological modeling; however, they are limited by their inability to output untrained hydrological variables and lack of interpretability compared to process-based hydrological models. We propose a hybrid approach that combines the conceptual EXP-Hydro model with embedded neural networks (ENNs), replacing its internal modules while maintaining adherence to hydrological knowledge. The resulting hybrid model can predict untrained hydrological variables without requiring post-processing or pre-training procedures. We tested 15 hybrid models that replace different internal modules across 569 basins in the contiguous United States using the CAMELS dataset. Additional experiments were conducted to generalize hydrological relationships within ENNs and further use them to improve the EXP-Hydro model's performance. Results show that all hybrid scenarios outperform the ordinary EXP-Hydro model, with an optimal median Nash-Sutcliffe efficiency (NSE) of 0.701 in the evaluation period– comparable to state-of-the-art LSTM and conceptual hydrological model featuring an error-correcting post-processor. Reasonable patterns of runoff and snow-related processes are captured by ENNs in respective hybrid models. We further used the runoff (snow-related) pattern to improve the ordinary EXP-Hydro model with median NSE increasing from 0.496 to 0.567 (raising median NSE from 0.601 to 0.677 in snow-influenced region). . Our study highlights the potential for using ENNs in enhancing process-based hydrological models' performance while maintaining interpretability within a novel hybrid framework.
... While these provide a useful first guess, storylines could be used to provide explainable and hence actionable information from deterministic physically-based hydrological models, driven with meaningful hydrometeorological events selected from counterfactual analysis, possibly based on patterns identified via conceptual and data-based models. We argue that storylines can provide a framework to adapt and prepare for extreme hydrological events, by supporting the understanding of risk causality (explanatory power) including local conditions, and contextualising (into actionable information) the plausible risks triggered by extreme events not well captured by probabilistic representations [11]. Moreover, storylines incorporating physically-based simulation can enrich the local impact assessment of rare extreme events by assimilating events which have occurred elsewhere, but for which the conditions are plausible in the place of interest due to changing climate [12]. ...
... The study of temporal and spatial aspects of the various hydroclimatic phenomena (e.g. the ones linked to temperature, precipitation or streamflow variables) holds a prominent position in Earth system science and engineering (see, for example, the detailed lists of research topics compiled by Montanari et al. 2013 andBlöschl et al. 2019), with a large variety of hydroclimatic features being investigated with increasing frequency. Such investigations, as well as their underlying methodologies, are indeed necessary either when referring to high-impact case studies (i.e. ...
... 3,4,5,6,7,8,9) could lead to a larger reduction of the modelling uncertainties than the respective global summaries (Fig. 2), and especially of those uncertainties that accompany the stochastic modelling and simulation of precipitation and river flow (but possibly of temperature as well) in areas with short or without earth-observed time series records. Reducing modelling uncertainties is traditionally among the most important targets in hydrology and hydroclimatology (Montanari et al. 2013;Blöschl et al. 2019). We also deem that the exploitation of our findings in this regard could be straightforward, given the direct utility of the computed statistics. ...
Detailed investigations of time series features across climates, continents and variable types can progress our understanding and modelling ability of the Earth’s hydroclimate and its dynamics. They can also improve our comprehension of the climate classification systems appearing in their core. Still, such investigations for seasonal hydroclimatic temporal dependence, variability and change are currently missing from the literature. Herein, we propose and apply at the global scale a methodological framework for filling this specific gap. We analyse over 13,000 earth-observed quarterly temperature, precipitation and river flow time series. We adopt the Köppen–Geiger climate classification system and define continental-scale geographical regions for conducting upon them seasonal hydroclimatic feature summaries. The analyses rely on three sample autocorrelation features, a temporal variation feature, a spectral entropy feature, a Hurst feature, a trend strength feature and a seasonality strength feature. We find notable differences to characterize the magnitudes of these features across the various Köppen–Geiger climate classes, as well as between continental-scale geographical regions. We, therefore, deem that the consideration of the comparative summaries could be beneficial in water resources engineering contexts. Lastly, we apply explainable machine learning to compare the investigated features with respect to how informative they are in distinguishing either the main Köppen–Geiger climates or the continental-scale regions. In this regard, the sample autocorrelation, temporal variation and seasonality strength features are found to be more informative than the spectral entropy, Hurst and trend strength features at the seasonal time scale.
... The study of Shannon entropy trends of extreme precipitation and temperature values is an important tool in the study of climate variability, which has important implications for hydrology and water resources [15,28,30,33,92]. Analysis of historical observations makes it possible to accurately assess the variability of precipitation and temperature according to the observed period and allows us to determine the form of the directions of these ongoing changes. ...
In this article, the Shannon entropy measure was used to evaluate the change in precipitation and temperature conditions. Due to the short, low-volume sequences of analyzed precipitation and temperature data, a bootstrap method was used in the procedure for calculating Shannon entropy. The analysis used minimum and maximum values of monthly precipitation totals and average monthly temperatures for 377 catchments distributed across the globe. 110-year data sequences from 1901 to 2010 were analyzed. Entropy values for the estimated parameters of the generalized extreme value distribution (GEV) were calculated for the accepted data. Entropy value calculations were performed for the left-hand constraint, based on minimum values, and for the right-hand constraint, based on maximum values. Based on the analysis of precipitation and temperature sequences, trend forms were identified for the left and right Shannon entropy values. This made it possible to obtain information on the directions of changes occurring in the area of minimum and maximum values in the field of monthly precipitation and average temperatures in the analyzed catchments. The study showed the existence of Shannon entropy trends. Evaluation of entropy trends for precipitation and temperature sequences was performed using non-parametric tests. Mann -Kendall tests at the 5% significance level were used in the trend analyses. The Pettitt test was performed to determine the point of change in trend for precipitation and temperature data. The analysis performed was supported by graphical presentations.
