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Hydrological models are widely used to characterize, understand and manage hydrosystems. Lumped parameter models are of particular interest in karst environments given the complexity and heterogeneity of these systems. There is a multitude of lumped parameter modelling approaches, which can make it difficult for a manager or researcher to choose. We therefore conducted a comparison of two lumped parameter modelling approaches: artificial neural networks (ANNs) and reservoir models. We investigate five karst systems in the Mediterranean and Alpine regions with different characteristics in terms of climatic conditions, hydrogeological properties and data availability. We compare the results of ANN and reservoir modelling approaches using several performance criteria over different hydrological periods. The results show that both ANNs and reservoir models can accurately simulate karst spring discharge but also that they have different advantages and drawbacks: (i) ANN models are very flexible regarding the format and amount of input data, (ii) reservoir models can provide good results even with a few years of relevant discharge in the calibration period and (iii) ANN models seem robust for reproducing high-flow conditions, while reservoir models are superior in reproducing low-flow conditions. However, both modelling approaches struggle to reproduce extreme events (droughts, floods), which is a known problem in hydrological modelling. For research purposes, ANN models have been shown to be useful for identifying recharge areas and delineating catchments, based on insights into the input data. Reservoir models are adapted to understand the hydrological functioning of a system by studying model structure and parameters.

Performance criteria play a key role in the calibration and evaluation of hydrological models and have been extensively developed and studied, but some of the most used criteria still have unknown pitfalls. This study set out to examine counterbalancing errors, which are inherent to the Kling–Gupta efficiency (KGE) and its variants. A total of nine performance criteria – including the KGE and its variants, as well as the Nash–Sutcliffe efficiency (NSE) and the modified index of agreement (d1) – were analysed using synthetic time series and a real case study. Results showed that, when assessing a simulation, the score of the KGE and some of its variants can be increased by concurrent overestimation and underestimation of discharge. These counterbalancing errors may favour bias and variability parameters, therefore preserving an overall high score of the performance criteria. As bias and variability parameters generally account for two-thirds of the weight in the equation of performance criteria such as the KGE, this can lead to an overall higher criterion score without being associated with an increase in model relevance. We recommend using (i) performance criteria that are not or less prone to counterbalancing errors (d1, modified KGE, non-parametric KGE, diagnostic efficiency) and/or (ii) scaling factors in the equation to reduce the influence of relative parameters.

International audience; Despite many existing approaches, modeling karst water resources remains challenging as conventional approaches usually heavily rely on distinct system knowledge. Artificial neural networks (ANNs), however, require only little prior knowledge to automatically establish an input-output relationship. For ANN modeling in karst, the temporal and spatial data availability is often an important constraint, as usually no or few climate stations are located within or near karst spring catchments. Hence, spatial coverage is often not satisfactory and can result in substantial uncertainties about the true conditions in the catchment, leading to lower model performance. To overcome these problems, we apply convolutional neural networks (CNNs) to simulate karst spring discharge and to directly learn from spatially distributed climate input data (combined 2D-1D CNNs). We investigate three karst spring catchments in the Alpine and Mediterranean region with different meteorological-hydrological characteristics and hydrodynamic system properties. We compare the proposed approach both to existing modeling studies in these regions and to our own 1D CNN models that are conventionally trained with climate station input data. Our results show that all the models are excellently suited to modeling karst spring discharge (NSE: 0.73-0.87, KGE: 0.63-0.86) and can compete with the simulation results of existing approaches in the respective areas. The 2D models show a better fit than the 1D models in two of three cases and automatically learn to focus on the relevant areas of the input domain. By performing a spatial input sensitivity analysis, we can further show their usefulness in localizing the position of karst catchments.

International audience; The complexity of karst groundwater flow modelling is reflected by the amount of simulation approaches. The goal of the Karst Modelling Challenge (KMC) is comparing different approaches on one single system using the same data set. Thirteen teams with different computational models for simulating discharge variations at karst springs have applied their respective models on one single data set coming from the Milandre Karst Hydrogeological System (MKHS). The approaches include neural networks, reservoir models, semi-distributed models and fully distributed groundwater models. Four and a half years of hourly or daily meteorological input and hourly discharge data were provided for model calibration. The validation comprised forecasting one year of discharge, without the observed discharge data. The model performance was evaluated using the volume conservation, Nash-Sutcliffe efficiency (NSE) and the Kling-Gupta efficiency (KGE) applied on the total discharge and individual flow components. As a result, the comparison of model performances is a challenging task due to the differences in the model architecture but also required time steps: some of the models require aggregated daily steps while others could be run using hourly data, which provided some interesting differences depending on how the data was transformed. The use of instantaneous data (e.g. value at noon) produces less bias that averaging hourly data over one day. The transformation of hourly into daily data produces a decrease of Nash and KGE of 0.05 to 0.08 (i.e. from 1 to ~0.93). The resulting simulations (forecasted values for year 2016) produced KGEs ranging between 0.83 and 0.37 (0.83 to −0.24 for NSE). Although the simulations matched the monitored flows reasonably well, most models struggled to simulate baseflow conditions accurately. In general, the models that performed the best for this exercise were the global ones (Gardenia and Varkarst), with a limited number of parameters, which can be calibrated using automatic calibration procedures. The neural network models also showed a fair potential, with one providing reasonable results despite the relatively short dataset available for warming-up (4.5 years). Semi-and fully distributed models also suggested that with some more effort they could perform well. The accuracy of model predictions does not seem to increase by using models with more than 9–12 calibration parameters. An evaluation of the relative errors between the forecasted and the observed values revealed that for most models, 50% of the forecasted values contained more than 50% of difference against the observed discharge rate, with 25% having a difference larger than 100%. A significant part of the poorly forecasted values corresponded to base-flow which was surprising given that as base-flow is generally much easier to predict than peak flow. Hence, this shows that modelling approaches and criteria for the calibration are too oriented towards peak-flow sections of the hydrographs, and that improvements could be gained by more focus on the base-flow.

Clear signs of climate stress on groundwater resources have been observed in recent years even in generally water-rich regions such as Germany. Severe droughts, resulting in decreased groundwater recharge, led to declining groundwater levels in many regions and even local drinking water shortages have occurred in past summers. We investigate how climate change will directly influence the groundwater resources in Germany until the year 2100. For this purpose, we use a machine learning groundwater level forecasting framework, based on Convolutional Neural Networks, which has already proven its suitability in modelling groundwater levels. We predict groundwater levels on more than 120 wells distributed over the entire area of Germany that showed strong reactions to meteorological signals in the past. The inputs are derived from the RCP8.5 scenario of six climate models, pre-selected and pre-processed by the German Meteorological Service, thus representing large parts of the range of the expected change in the next 80 years. Our models are based on precipitation and temperature and are carefully evaluated in the past and only wells with models reaching high forecasting skill scores are included in our study. We only consider natural climate change effects based on meteorological changes, while highly uncertain human factors, such as increased groundwater abstraction or irrigation effects, remain unconsidered due to a lack of reliable input data. We can show significant (p

Hydrograph clustering helps to identify dynamic patterns within aquifers systems, an important foundation of characterizing groundwater systems and their influences, which is necessary to effectively manage groundwater resources. We develope an unsupervised modeling approach to characterize and cluster hydrographs on regional scale according to their dynamics. We apply feature-based clustering to improve the exploitation of heterogeneous datasets, explore the usefulness of existing features and propose new features specifically useful to describe groundwater hydrographs. The clustering itself is based on a powerful combination of Self-Organizing Maps with a modified DS2L-Algorithm, which automatically derives the cluster number but also allows to influence the level of detail of the clustering. We further develop a framework that combines these methods with ensemble modeling, internal cluster validation indices, resampling and consensus voting to finally obtain a robust clustering result and remove arbitrariness from the feature selection process. Further we propose a measure to sort hydrographs within clusters, useful for both interpretability and visualization. We test the framework with weekly data from the Upper Rhine Graben System, using more than 1800 hydrographs from a period of 30 years (1986-2016). The results show that our approach is adaptively capable of identifying homogeneous groups of hydrograph dynamics. The resulting clusters show both spatially known and unknown patterns, some of which correspond clearly to external controlling factors, such as intensive groundwater management in the northern part of the test area. This framework is easily transferable to other regions and, by adapting the describing features, also to other time series-clustering applications.

Karst systems are challenging to model due to their heterogeneous hydraulic properties resulting in highly variable discharge behavior. Distributed models can be applied to karst aquifers but require detailed system knowledge and extensive hydraulic parameter datasets; lumped-parameter models are less complex, but still require parametrization. In this work, we demonstrate the application of a data-driven approach to model the discharge behavior of the Aubach spring in the Gottesacker karst system in the northern Alps, a well-investigated study site for which previous models are available for comparison (Chen et al. 2018; Fandel et al. 2020). Our approach is based on convolutional neural networks (CNN), which have proved to be well suited for time series forecasting in water-related contexts like runoff modelling or groundwater level prediction (Wunsch et al.). The approach is comparably simple in terms of data requirements as we rely mainly on widely available and easy-to-measure parameters such as precipitation and temperature. By implementing Bayesian techniques (Monte-Carlo dropout) we are able to report the predictive uncertainty of the CNN based forecasts. Our results challenge existing modelling results based on lumped-parameter models in terms of common error measures such as Nash-Sutcliffe efficiency. Furthermore, we explore the important role of snow accumulation and melting by coupling our model with a snow-routine to better represent their influence on spring discharge and further improve model performance. Our results demonstrate that the presented machine-learning approach can be applied to simulate karst spring discharge and has certain advantages in comparison with conventional karst modelling approaches, which require hydraulic parameters that are often not available.Chen, Z.; Hartmann, A.; Wagener, T.; Goldscheider, N. (2018) Dynamics of water fluxes and storages in an Alpine karst catchment under current and potential future climate conditions. Hydrology and earth system sciences, 22 (7), 3807–3823.Fandel, C.; Ferré, T.; Chen, Z.; Renard, P.; Goldscheider, N. (2020) A model ensemble generator to explore structural uncertainty in karst systems with unmapped conduits. Hydrogeology journal, published online.Wunsch, A.; Liesch, T.; Broda, S. (2020) Groundwater Level Forecasting with Artificial Neural Networks: A Comparison of LSTM, CNN and NARX. Hydrology and Earth System Sciences Discussions 2020:1–23. https://doi.org/10/ghtcz3

Effective groundwater monitoring networks are important, as systematic data collected at observation wells provide a crucial understanding of the dynamics of hydrogeological systems as well as the basis for many other applications. This study investigates the influence of six groundwater level monitoring network (GLMN) sampling designs (random, grid, spatial coverage, and geostatistical) with varying densities on the accuracy of spatially interpolated groundwater surfaces. To obtain spatially continuous prediction errors (in contrast to point cross‐validation errors), we used nine potentiometric groundwater surfaces from three regional MODFLOW groundwater flow models with different resolutions as a priori references. To assess the suitability of frequently‐used cross‐validation error statistics (MAE, RMSE, RMSSE, ASE, and NSE), we compared them with the actual prediction errors (APE). Additionally, we defined upper and lower thresholds for an appropriate spatial density of monitoring wells. Below the lower threshold, the observation density appears insufficient, and additional wells lead to a significant improvement of the results. Above the upper threshold, additional wells lead to only minor and inefficient improvements. According to the APE, systematic sampling lead to the best results but is often not suited for GLMN due to its nonprogressive characteristic. Geostatistical and spatial coverage sampling are considerable alternatives, which are in contrast progressive and allow evenly spaced and, in the case of spatial coverage sampling, yet reproducible coverage with accurate results. We found that the global cross‐validation error statistics are not suitable to compare the performance of different sampling designs, although they allow rough conclusions about the quality of the GLMN.

International audience; In semi-arid regions with high seasonal variability of water availability, adaptive management strategies and technical measures are required to ensure the sustainable use of water resources. In this study, managed recharge of storm water into a karst aquifer and the water level fluctuations related to pumping in a nearby wellfield were simulated at Wadi Wala, Jordan. We used a numerical equivalent porous medium (EPM) approach with specific adaptations to account for the heterogeneity and anisotropy of the karst aquifer. The model domain was vertically projected along the wadi course, resulting in a 2-dimensional model, and subdivided into hydraulic zones representing the karst-specific flow pattern of fast flow and slow depletion. Results show satisfying agreement of measured and simulated groundwater tables from 2002 to 2012 and predict a lowering of the average groundwater table until 2022 of around 2.7m in the immediate surroundings of the reservoir and an increased depletion towards the wellfield, mainly caused by sedimentation in the reservoir and an associated decrease in infiltration. Abstraction at the wellfield changed considerably over the regarded time period and strongly influences the groundwater fluctuations, which shows the need of improved pumping management and monitoring. The results can serve as a basis for decision makers regarding an optimization of water management at the reservoir and wellfield. Furthermore, the presented numerical approach can be transferred to karst regions with similar physio-geographical conditions to assess managed aquifer recharge.