Articles | Volume 25, issue 3
https://doi.org/10.5194/hess-25-1671-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-25-1671-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
01 Apr 2021
Research article |
| 01 Apr 2021
| 01 Apr 2021
Groundwater level forecasting with artificial neural networks: a comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX)
Hydrogeology, Karlsruhe Institute of Technology (KIT), Institute of Applied Geosciences, Kaiserstr. 12, 76131 Karlsruhe, Germany
Tanja Liesch
Hydrogeology, Karlsruhe Institute of Technology (KIT), Institute of Applied Geosciences, Kaiserstr. 12, 76131 Karlsruhe, Germany
Stefan Broda
Federal Institute for Geosciences and Natural Resources (BGR), Wilhelmstr. 25–30, 13593 Berlin, Germany
Related authors
Andreas Wunsch, Tanja Liesch, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 28, 2167–2178, https://doi.org/10.5194/hess-28-2167-2024, https://doi.org/10.5194/hess-28-2167-2024, 2024
Short summary
Short summary
Seasons have a strong influence on groundwater levels, but relationships are complex and partly unknown. Using data from wells in Germany and an explainable machine learning approach, we showed that summer precipitation is the key factor that controls the severeness of a low-water period in fall; high summer temperatures do not per se cause stronger decreases. Preceding winters have only a minor influence on such low-water periods in general.
Raoul Alexander Collenteur, Ezra Haaf, Mark Bakker, Tanja Liesch, Andreas Wunsch, Jenny Soonthornrangsan, Jeremy White, Nick Martin, Rui Hugman, Michael Fienen, Ed de Sousa, Didier Vanden Berghe, Xinyang Fan, Tim Peterson, Janis Bikše, Antoine Di Ciacca, Xinyue Wang, Yang Zheng, Maximilian Nölscher, Julian Koch, Raphael Schneider, Nikolas Benavides Höglund, Sivarama Krishna Reddy Chidepudi, Abel Henriot, Nicolas Massei, Abderrahim Jardani, Max Gustav Rudolph, Amir Rouhani, Jaime Gómez-Hernández, Seifeddine Jomaa, Anna Pölz, Tim Franken, Morteza Behbooei, Jimmy Lin, Bryan Tolson, and Rojin Meysami
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-111, https://doi.org/10.5194/hess-2024-111, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
We present the results of the 2022 groundwater modeling challenge, where 15 teams applied data-driven models to simulate hydraulic heads. 3 groups of models were identified: lumped models, machine learning models, and deep learning models. For all wells, reasonable performance was obtained by at least 1 team from group. There was not 1 team that performed best for all wells. In conclusion, the challenge was a successful initiative to compare different models and learn from each other.
Guillaume Cinkus, Naomi Mazzilli, Hervé Jourde, Andreas Wunsch, Tanja Liesch, Nataša Ravbar, Zhao Chen, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 27, 2397–2411, https://doi.org/10.5194/hess-27-2397-2023, https://doi.org/10.5194/hess-27-2397-2023, 2023
Short summary
Short summary
The Kling–Gupta Efficiency (KGE) is a performance criterion extensively used to evaluate hydrological models. We conduct a critical study on the KGE and its variant to examine counterbalancing errors. Results show that, when assessing a simulation, concurrent over- and underestimation of discharge can lead to an overall higher criterion score without an associated increase in model relevance. We suggest that one carefully choose performance criteria and use scaling factors.
Guillaume Cinkus, Andreas Wunsch, Naomi Mazzilli, Tanja Liesch, Zhao Chen, Nataša Ravbar, Joanna Doummar, Jaime Fernández-Ortega, Juan Antonio Barberá, Bartolomé Andreo, Nico Goldscheider, and Hervé Jourde
Hydrol. Earth Syst. Sci., 27, 1961–1985, https://doi.org/10.5194/hess-27-1961-2023, https://doi.org/10.5194/hess-27-1961-2023, 2023
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Numerous modelling approaches can be used for studying karst water resources, which can make it difficult for a stakeholder or researcher to choose the appropriate method. We conduct a comparison of two widely used karst modelling approaches: artificial neural networks (ANNs) and reservoir models. Results show that ANN models are very flexible and seem great for reproducing high flows. Reservoir models can work with relatively short time series and seem to accurately reproduce low flows.
Marc Ohmer, Tanja Liesch, and Andreas Wunsch
Hydrol. Earth Syst. Sci., 26, 4033–4053, https://doi.org/10.5194/hess-26-4033-2022, https://doi.org/10.5194/hess-26-4033-2022, 2022
Short summary
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We present a data-driven approach to select optimal locations for groundwater monitoring wells. The applied approach can optimize the number of wells and their location for a network reduction (by ranking wells in order of their information content and reducing redundant) and extension (finding sites with great information gain) or both. It allows us to include a cost function to account for more/less suitable areas for new wells and can help to obtain maximum information content for a budget.
Andreas Wunsch, Tanja Liesch, Guillaume Cinkus, Nataša Ravbar, Zhao Chen, Naomi Mazzilli, Hervé Jourde, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 26, 2405–2430, https://doi.org/10.5194/hess-26-2405-2022, https://doi.org/10.5194/hess-26-2405-2022, 2022
Short summary
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Modeling complex karst water resources is difficult enough, but often there are no or too few climate stations available within or close to the catchment to deliver input data for modeling purposes. We apply image recognition algorithms to time-distributed, spatially gridded meteorological data to simulate karst spring discharge. Our models can also learn the approximate catchment location of a spring independently.
Mariana Gomez, Maximilian Nölscher, Andreas Hartmann, and Stefan Broda
Hydrol. Earth Syst. Sci., 28, 4407–4425, https://doi.org/10.5194/hess-28-4407-2024, https://doi.org/10.5194/hess-28-4407-2024, 2024
Short summary
Short summary
To understand the impact of external factors on groundwater level modelling using a 1-D convolutional neural network (CNN) model, we train, validate, and tune individual CNN models for 505 wells distributed across Lower Saxony, Germany. We then evaluate the performance of these models against available geospatial and time series features. This study provides new insights into the relationship between these factors and the accuracy of groundwater modelling.
Andreas Wunsch, Tanja Liesch, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 28, 2167–2178, https://doi.org/10.5194/hess-28-2167-2024, https://doi.org/10.5194/hess-28-2167-2024, 2024
Short summary
Short summary
Seasons have a strong influence on groundwater levels, but relationships are complex and partly unknown. Using data from wells in Germany and an explainable machine learning approach, we showed that summer precipitation is the key factor that controls the severeness of a low-water period in fall; high summer temperatures do not per se cause stronger decreases. Preceding winters have only a minor influence on such low-water periods in general.
Raoul Alexander Collenteur, Ezra Haaf, Mark Bakker, Tanja Liesch, Andreas Wunsch, Jenny Soonthornrangsan, Jeremy White, Nick Martin, Rui Hugman, Michael Fienen, Ed de Sousa, Didier Vanden Berghe, Xinyang Fan, Tim Peterson, Janis Bikše, Antoine Di Ciacca, Xinyue Wang, Yang Zheng, Maximilian Nölscher, Julian Koch, Raphael Schneider, Nikolas Benavides Höglund, Sivarama Krishna Reddy Chidepudi, Abel Henriot, Nicolas Massei, Abderrahim Jardani, Max Gustav Rudolph, Amir Rouhani, Jaime Gómez-Hernández, Seifeddine Jomaa, Anna Pölz, Tim Franken, Morteza Behbooei, Jimmy Lin, Bryan Tolson, and Rojin Meysami
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-111, https://doi.org/10.5194/hess-2024-111, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
We present the results of the 2022 groundwater modeling challenge, where 15 teams applied data-driven models to simulate hydraulic heads. 3 groups of models were identified: lumped models, machine learning models, and deep learning models. For all wells, reasonable performance was obtained by at least 1 team from group. There was not 1 team that performed best for all wells. In conclusion, the challenge was a successful initiative to compare different models and learn from each other.
Benedikt Heudorfer, Tanja Liesch, and Stefan Broda
Hydrol. Earth Syst. Sci., 28, 525–543, https://doi.org/10.5194/hess-28-525-2024, https://doi.org/10.5194/hess-28-525-2024, 2024
Short summary
Short summary
We build a neural network to predict groundwater levels from monitoring wells. We predict all wells at the same time, by learning the differences between wells with static features, making it an entity-aware global model. This works, but we also test different static features and find that the model does not use them to learn exactly how the wells are different, but only to uniquely identify them. As this model class is not actually entity aware, we suggest further steps to make it so.
Guillaume Cinkus, Naomi Mazzilli, Hervé Jourde, Andreas Wunsch, Tanja Liesch, Nataša Ravbar, Zhao Chen, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 27, 2397–2411, https://doi.org/10.5194/hess-27-2397-2023, https://doi.org/10.5194/hess-27-2397-2023, 2023
Short summary
Short summary
The Kling–Gupta Efficiency (KGE) is a performance criterion extensively used to evaluate hydrological models. We conduct a critical study on the KGE and its variant to examine counterbalancing errors. Results show that, when assessing a simulation, concurrent over- and underestimation of discharge can lead to an overall higher criterion score without an associated increase in model relevance. We suggest that one carefully choose performance criteria and use scaling factors.
Guillaume Cinkus, Andreas Wunsch, Naomi Mazzilli, Tanja Liesch, Zhao Chen, Nataša Ravbar, Joanna Doummar, Jaime Fernández-Ortega, Juan Antonio Barberá, Bartolomé Andreo, Nico Goldscheider, and Hervé Jourde
Hydrol. Earth Syst. Sci., 27, 1961–1985, https://doi.org/10.5194/hess-27-1961-2023, https://doi.org/10.5194/hess-27-1961-2023, 2023
Short summary
Short summary
Numerous modelling approaches can be used for studying karst water resources, which can make it difficult for a stakeholder or researcher to choose the appropriate method. We conduct a comparison of two widely used karst modelling approaches: artificial neural networks (ANNs) and reservoir models. Results show that ANN models are very flexible and seem great for reproducing high flows. Reservoir models can work with relatively short time series and seem to accurately reproduce low flows.
Marc Ohmer, Tanja Liesch, and Andreas Wunsch
Hydrol. Earth Syst. Sci., 26, 4033–4053, https://doi.org/10.5194/hess-26-4033-2022, https://doi.org/10.5194/hess-26-4033-2022, 2022
Short summary
Short summary
We present a data-driven approach to select optimal locations for groundwater monitoring wells. The applied approach can optimize the number of wells and their location for a network reduction (by ranking wells in order of their information content and reducing redundant) and extension (finding sites with great information gain) or both. It allows us to include a cost function to account for more/less suitable areas for new wells and can help to obtain maximum information content for a budget.
Andreas Wunsch, Tanja Liesch, Guillaume Cinkus, Nataša Ravbar, Zhao Chen, Naomi Mazzilli, Hervé Jourde, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 26, 2405–2430, https://doi.org/10.5194/hess-26-2405-2022, https://doi.org/10.5194/hess-26-2405-2022, 2022
Short summary
Short summary
Modeling complex karst water resources is difficult enough, but often there are no or too few climate stations available within or close to the catchment to deliver input data for modeling purposes. We apply image recognition algorithms to time-distributed, spatially gridded meteorological data to simulate karst spring discharge. Our models can also learn the approximate catchment location of a spring independently.
Related subject area
Subject: Groundwater hydrology | Techniques and Approaches: Modelling approaches
Assessing groundwater level modelling using a 1-D convolutional neural network (CNN): linking model performances to geospatial and time series features
Short high-accuracy tritium data time series for assessing groundwater mean transit times in the vadose and saturated zones of the Luxembourg Sandstone aquifer
High-resolution long-term average groundwater recharge in Africa estimated using random forest regression and residual interpolation
Towards understanding the influence of seasons on low-groundwater periods based on explainable machine learning
Data-driven modeling of hydraulic head time series: results and lessons learned from the 2022 groundwater modeling challenge
Shannon entropy of transport self-organization due to dissolution–precipitation reaction at varying Peclet numbers in initially homogeneous porous media
A high-resolution map of diffuse groundwater recharge rates for Australia
Influence of bank slope on sinuosity-driven hyporheic exchange flow and residence time distribution during a dynamic flood event
Technical note: A model of chemical transport in a wellbore–aquifer system
Disentangling coastal groundwater level dynamics in a global dataset
The impact of future climate projections and anthropogenic activities on basin-scale groundwater availability
Current and future roles of meltwater–groundwater dynamics in a proglacial Alpine outwash plain
On the challenges of global entity-aware deep learning models for groundwater level prediction
Incorporating interpretation uncertainties from deterministic 3D hydrostratigraphic models in groundwater models
Adjoint subordination to calculate backward travel time probability of pollutants in water with various velocity resolutions
On the optimal level of complexity for the representation of groundwater-dependent wetland systems in land surface models
Estimation of groundwater age distributions from hydrochemistry: comparison of two metamodelling algorithms in the Heretaunga Plains aquifer system, New Zealand
Technical note: Novel analytical solution for groundwater response to atmospheric tides
Calibration of groundwater seepage against the spatial distribution of the stream network to assess catchment-scale hydraulic properties
Climate-warming-driven changes in the cryosphere and their impact on groundwater–surface-water interactions in the Heihe River basin
Comparison of artificial neural networks and reservoir models for simulating karst spring discharge on five test sites in the Alpine and Mediterranean regions
A general model of radial dispersion with wellbore mixing and skin effects
Estimation of hydraulic conductivity functions in karst regions by particle swarm optimization with application to Lake Vrana, Croatia
The origin of hydrological responses following earthquakes in a confined aquifer: insight from water level, flow rate, and temperature observations
Advance prediction of coastal groundwater levels with temporal convolutional and long short-term memory networks
Three-dimensional hydrogeological parametrization using sparse piezometric data
Machine-learning-based downscaling of modelled climate change impacts on groundwater table depth
Frequency domain water table fluctuations reveal impacts of intense rainfall and vadose zone thickness on groundwater recharge
Characterizing groundwater heat transport in a complex lowland aquifer using paleo-temperature reconstruction, satellite data, temperature–depth profiles, and numerical models
Karst spring recession and classification: efficient, automated methods for both fast- and slow-flow components
Exploring river–aquifer interactions and hydrological system response using baseflow separation, impulse response modeling, and time series analysis in three temperate lowland catchments
Experimental study of non-Darcy flow characteristics in permeable stones
Karst spring discharge modeling based on deep learning using spatially distributed input data
HESS Opinions: Chemical transport modeling in subsurface hydrological systems – space, time, and the “holy grail” of “upscaling”
Spatiotemporal variations in water sources and mixing spots in a riparian zone
Delineation of discrete conduit networks in karst aquifers via combined analysis of tracer tests and geophysical data
Reactive transport modeling for supporting climate resilience at groundwater contamination sites
Improved understanding of regional groundwater drought development through time series modelling: the 2018–2019 drought in the Netherlands
Simulation of long-term spatiotemporal variations in regional-scale groundwater recharge: contributions of a water budget approach in cold and humid climates
Feedback mechanisms between precipitation and dissolution reactions across randomly heterogeneous conductivity fields
Taking theory to the field: streamflow generation mechanisms in an intermittent Mediterranean catchment
Coupling saturated and unsaturated flow: comparing the iterative and the non-iterative approach
Time lags of nitrate, chloride, and tritium in streams assessed by dynamic groundwater flow tracking in a lowland landscape
Using Long Short-Term Memory networks to connect water table depth anomalies to precipitation anomalies over Europe
Estimation of groundwater recharge from groundwater levels using nonlinear transfer function noise models and comparison to lysimeter data
Early hypogenic carbonic acid speleogenesis in unconfined limestone aquifers by upwelling deep-seated waters with high CO2 concentration: a modelling approach
Impacts of climate change on groundwater flooding and ecohydrology in lowland karst
How daily groundwater table drawdown affects the diel rhythm of hyporheic exchange
Groundwater and baseflow drought responses to synthetic recharge stress tests
Determination of vadose zone and saturated zone nitrate lag times using long-term groundwater monitoring data and statistical machine learning
Mariana Gomez, Maximilian Nölscher, Andreas Hartmann, and Stefan Broda
Hydrol. Earth Syst. Sci., 28, 4407–4425, https://doi.org/10.5194/hess-28-4407-2024, https://doi.org/10.5194/hess-28-4407-2024, 2024
Short summary
Short summary
To understand the impact of external factors on groundwater level modelling using a 1-D convolutional neural network (CNN) model, we train, validate, and tune individual CNN models for 505 wells distributed across Lower Saxony, Germany. We then evaluate the performance of these models against available geospatial and time series features. This study provides new insights into the relationship between these factors and the accuracy of groundwater modelling.
Laurent Gourdol, Michael K. Stewart, Uwe Morgenstern, and Laurent Pfister
Hydrol. Earth Syst. Sci., 28, 3519–3547, https://doi.org/10.5194/hess-28-3519-2024, https://doi.org/10.5194/hess-28-3519-2024, 2024
Short summary
Short summary
Determining water transit times in aquifers is key to a better understanding of groundwater resources and their sustainable management. For our research, we used high-accuracy tritium data from 35 springs draining the Luxembourg Sandstone aquifer. We assessed the mean transit times of groundwater and found that water moves on average more than 10 times more slowly vertically in the vadose zone of the aquifer (~12 m yr-1) than horizontally in its saturated zone (~170 m yr-1).
Anna Pazola, Mohammad Shamsudduha, Jon French, Alan M. MacDonald, Tamiru Abiye, Ibrahim Baba Goni, and Richard G. Taylor
Hydrol. Earth Syst. Sci., 28, 2949–2967, https://doi.org/10.5194/hess-28-2949-2024, https://doi.org/10.5194/hess-28-2949-2024, 2024
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This study advances groundwater research using a high-resolution random forest model, revealing new recharge areas and spatial variability, mainly in humid regions. Limited data in rainy zones is a constraint for the model. Our findings underscore the promise of machine learning for large-scale groundwater modelling while further emphasizing the importance of data collection for robust results.
Andreas Wunsch, Tanja Liesch, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 28, 2167–2178, https://doi.org/10.5194/hess-28-2167-2024, https://doi.org/10.5194/hess-28-2167-2024, 2024
Short summary
Short summary
Seasons have a strong influence on groundwater levels, but relationships are complex and partly unknown. Using data from wells in Germany and an explainable machine learning approach, we showed that summer precipitation is the key factor that controls the severeness of a low-water period in fall; high summer temperatures do not per se cause stronger decreases. Preceding winters have only a minor influence on such low-water periods in general.
Raoul Alexander Collenteur, Ezra Haaf, Mark Bakker, Tanja Liesch, Andreas Wunsch, Jenny Soonthornrangsan, Jeremy White, Nick Martin, Rui Hugman, Michael Fienen, Ed de Sousa, Didier Vanden Berghe, Xinyang Fan, Tim Peterson, Janis Bikše, Antoine Di Ciacca, Xinyue Wang, Yang Zheng, Maximilian Nölscher, Julian Koch, Raphael Schneider, Nikolas Benavides Höglund, Sivarama Krishna Reddy Chidepudi, Abel Henriot, Nicolas Massei, Abderrahim Jardani, Max Gustav Rudolph, Amir Rouhani, Jaime Gómez-Hernández, Seifeddine Jomaa, Anna Pölz, Tim Franken, Morteza Behbooei, Jimmy Lin, Bryan Tolson, and Rojin Meysami
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-111, https://doi.org/10.5194/hess-2024-111, 2024
Revised manuscript accepted for HESS
Short summary
Short summary
We present the results of the 2022 groundwater modeling challenge, where 15 teams applied data-driven models to simulate hydraulic heads. 3 groups of models were identified: lumped models, machine learning models, and deep learning models. For all wells, reasonable performance was obtained by at least 1 team from group. There was not 1 team that performed best for all wells. In conclusion, the challenge was a successful initiative to compare different models and learn from each other.
Evgeny Shavelzon and Yaniv Edery
Hydrol. Earth Syst. Sci., 28, 1803–1826, https://doi.org/10.5194/hess-28-1803-2024, https://doi.org/10.5194/hess-28-1803-2024, 2024
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We investigate the interaction of transport with dissolution–precipitation reactions in porous media using the concepts of entropy and work to quantify the emergence of preferential flow paths. We show that the preferential-flow-path phenomenon and the hydraulic power required to maintain the driving pressure drop intensify over time along with the heterogeneity due to the interaction between the transport and the reactive processes. This is more pronounced in diffusion-dominated flows.
Stephen Lee, Dylan J. Irvine, Clément Duvert, Gabriel C. Rau, and Ian Cartwright
Hydrol. Earth Syst. Sci., 28, 1771–1790, https://doi.org/10.5194/hess-28-1771-2024, https://doi.org/10.5194/hess-28-1771-2024, 2024
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Global groundwater recharge studies collate recharge values estimated using different methods that apply to different timescales. We develop a recharge prediction model, based solely on chloride, to produce a recharge map for Australia. We reveal that climate and vegetation have the most significant influence on recharge variability in Australia. Our recharge rates were lower than other models due to the long timescale of chloride in groundwater. Our method can similarly be applied globally.
Yiming Li, Uwe Schneidewind, Zhang Wen, Stefan Krause, and Hui Liu
Hydrol. Earth Syst. Sci., 28, 1751–1769, https://doi.org/10.5194/hess-28-1751-2024, https://doi.org/10.5194/hess-28-1751-2024, 2024
Short summary
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Meandering rivers are an integral part of many landscapes around the world. Here we used a new modeling approach to look at how the slope of riverbanks influences water flow and solute transport from a meandering river channel through its bank and into/out of the connected groundwater compartment (aquifer). We found that the bank slope can be a significant factor to be considered, especially when bank slope angles are small, and riverbank and aquifer conditions only allow for slow water flow.
Yiqun Gan and Quanrong Wang
Hydrol. Earth Syst. Sci., 28, 1317–1323, https://doi.org/10.5194/hess-28-1317-2024, https://doi.org/10.5194/hess-28-1317-2024, 2024
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1. A revised 3D model of solute transport is developed in the well–aquifer system. 2. The accuracy of the new model is tested against benchmark analytical solutions. 3. Previous models overestimate the concentration of solute in both aquifers and wellbores in the injection well test case. 4. Previous models underestimate the concentration in the extraction well test case.
Annika Nolte, Ezra Haaf, Benedikt Heudorfer, Steffen Bender, and Jens Hartmann
Hydrol. Earth Syst. Sci., 28, 1215–1249, https://doi.org/10.5194/hess-28-1215-2024, https://doi.org/10.5194/hess-28-1215-2024, 2024
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This study examines about 8000 groundwater level (GWL) time series from five continents to explore similarities in groundwater systems at different scales. Statistical metrics and machine learning techniques are applied to identify common GWL dynamics patterns and analyze their controlling factors. The study also highlights the potential and limitations of this data-driven approach to improve our understanding of groundwater recharge and discharge processes.
Steven Reinaldo Rusli, Victor F. Bense, Syed M. T. Mustafa, and Albrecht H. Weerts
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-26, https://doi.org/10.5194/hess-2024-26, 2024
Revised manuscript accepted for HESS
Short summary
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In this paper, we investigate the impact of climatic and anthropogenic factors on future groundwater availability. The changes are simulated using hydrological and groundwater flow models. We found out that the future groundwater status is influenced more so by anthropogenic factors compared to climatic factors. The results are beneficial to inform the responsible parties in operational water management to achieve future (ground)water governance.
Tom Müller, Matteo Roncoroni, Davide Mancini, Stuart N. Lane, and Bettina Schaefli
Hydrol. Earth Syst. Sci., 28, 735–759, https://doi.org/10.5194/hess-28-735-2024, https://doi.org/10.5194/hess-28-735-2024, 2024
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We investigate the role of a newly formed floodplain in an alpine glaciated catchment to store and release water. Based on field measurements, we built a numerical model to simulate the water fluxes and show that recharge occurs mainly due to the ice-melt-fed river. We identify three future floodplains, which could emerge from glacier retreat, and show that their combined storage leads to some additional groundwater storage but contributes little additional baseflow for the downstream river.
Benedikt Heudorfer, Tanja Liesch, and Stefan Broda
Hydrol. Earth Syst. Sci., 28, 525–543, https://doi.org/10.5194/hess-28-525-2024, https://doi.org/10.5194/hess-28-525-2024, 2024
Short summary
Short summary
We build a neural network to predict groundwater levels from monitoring wells. We predict all wells at the same time, by learning the differences between wells with static features, making it an entity-aware global model. This works, but we also test different static features and find that the model does not use them to learn exactly how the wells are different, but only to uniquely identify them. As this model class is not actually entity aware, we suggest further steps to make it so.
Trine Enemark, Rasmus Bødker Madsen, Torben O. Sonnenborg, Lærke Therese Andersen, Peter B. E. Sandersen, Jacob Kidmose, Ingelise Møller, Thomas Mejer Hansen, Karsten Høgh Jensen, and Anne-Sophie Høyer
Hydrol. Earth Syst. Sci., 28, 505–523, https://doi.org/10.5194/hess-28-505-2024, https://doi.org/10.5194/hess-28-505-2024, 2024
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In this study, we demonstrate an approach to evaluate the interpretation uncertainty within a manually interpreted geological model in a groundwater model. Using qualitative estimates of uncertainties, several geological realizations are developed and implemented in groundwater models. We confirm existing evidence that if the conceptual model is well defined, interpretation uncertainties within the conceptual model have limited impact on groundwater model predictions.
Yong Zhang, Graham E. Fogg, HongGuang Sun, Donald M. Reeves, Roseanna M. Neupauer, and Wei Wei
Hydrol. Earth Syst. Sci., 28, 179–203, https://doi.org/10.5194/hess-28-179-2024, https://doi.org/10.5194/hess-28-179-2024, 2024
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Pollutant release history and source identification are helpful for managing water resources, but it remains a challenge to reliably identify such information for real-world, complex transport processes in rivers and aquifers. In this study, we filled this knowledge gap by deriving a general backward governing equation and developing the efficient solver. Field applications showed that this model and solver are applicable for a broad range of flow systems, dimensions, and spatiotemporal scales.
Mennatullah T. Elrashidy, Andrew M. Ireson, and Saman Razavi
Hydrol. Earth Syst. Sci., 27, 4595–4608, https://doi.org/10.5194/hess-27-4595-2023, https://doi.org/10.5194/hess-27-4595-2023, 2023
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Wetlands are important ecosystems that store carbon and play a vital role in the water cycle. However, hydrological computer models do not always represent wetlands and their interaction with groundwater accurately. We tested different possible ways to include groundwater–wetland interactions in these models. We found that the optimal method to include wetlands and groundwater in the models is reliant on the intended use of the models and the characteristics of the land and soil being studied.
Conny Tschritter, Christopher J. Daughney, Sapthala Karalliyadda, Brioch Hemmings, Uwe Morgenstern, and Catherine Moore
Hydrol. Earth Syst. Sci., 27, 4295–4316, https://doi.org/10.5194/hess-27-4295-2023, https://doi.org/10.5194/hess-27-4295-2023, 2023
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Understanding groundwater travel time (groundwater age) is crucial for tracking flow and contaminants. While groundwater age is usually inferred from age tracers, this study utilised two machine learning techniques with common groundwater chemistry data. The results of both methods correspond to traditional approaches. They are useful where hydrochemistry data exist but age tracer data are limited. These methods could help enhance our knowledge, aiding in sustainable freshwater management.
Jose M. Bastias Espejo, Chris Turnadge, Russell S. Crosbie, Philipp Blum, and Gabriel C. Rau
Hydrol. Earth Syst. Sci., 27, 3447–3462, https://doi.org/10.5194/hess-27-3447-2023, https://doi.org/10.5194/hess-27-3447-2023, 2023
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Analytical models estimate subsurface properties from subsurface–tidal load interactions. However, they have limited accuracy in representing subsurface physics and parameter estimation. We derived a new analytical solution which models flow to wells due to atmospheric tides. We applied it to field data and compared our findings with subsurface knowledge. Our results enhance understanding of subsurface systems, providing valuable information on their behavior.
Ronan Abhervé, Clément Roques, Alexandre Gauvain, Laurent Longuevergne, Stéphane Louaisil, Luc Aquilina, and Jean-Raynald de Dreuzy
Hydrol. Earth Syst. Sci., 27, 3221–3239, https://doi.org/10.5194/hess-27-3221-2023, https://doi.org/10.5194/hess-27-3221-2023, 2023
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We propose a model calibration method constraining groundwater seepage in the hydrographic network. The method assesses the hydraulic properties of aquifers in regions where perennial streams are directly fed by groundwater. The estimated hydraulic conductivity appear to be highly sensitive to the spatial extent and density of streams. Such an approach improving subsurface characterization from surface information is particularly interesting for ungauged basins.
Amanda Triplett and Laura E. Condon
Hydrol. Earth Syst. Sci., 27, 2763–2785, https://doi.org/10.5194/hess-27-2763-2023, https://doi.org/10.5194/hess-27-2763-2023, 2023
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Accelerated melting in mountains is a global phenomenon. The Heihe River basin depends on upstream mountains for its water supply. We built a hydrologic model to examine how shifts in streamflow and warming will impact ground and surface water interactions. The results indicate that degrading permafrost has a larger effect than melting glaciers. Additionally, warming temperatures tend to have more impact than changes to streamflow. These results can inform other mountain–valley system studies.
Guillaume Cinkus, Andreas Wunsch, Naomi Mazzilli, Tanja Liesch, Zhao Chen, Nataša Ravbar, Joanna Doummar, Jaime Fernández-Ortega, Juan Antonio Barberá, Bartolomé Andreo, Nico Goldscheider, and Hervé Jourde
Hydrol. Earth Syst. Sci., 27, 1961–1985, https://doi.org/10.5194/hess-27-1961-2023, https://doi.org/10.5194/hess-27-1961-2023, 2023
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Numerous modelling approaches can be used for studying karst water resources, which can make it difficult for a stakeholder or researcher to choose the appropriate method. We conduct a comparison of two widely used karst modelling approaches: artificial neural networks (ANNs) and reservoir models. Results show that ANN models are very flexible and seem great for reproducing high flows. Reservoir models can work with relatively short time series and seem to accurately reproduce low flows.
Wenguang Shi, Quanrong Wang, Hongbin Zhan, Renjie Zhou, and Haitao Yan
Hydrol. Earth Syst. Sci., 27, 1891–1908, https://doi.org/10.5194/hess-27-1891-2023, https://doi.org/10.5194/hess-27-1891-2023, 2023
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The mechanism of radial dispersion is important for understanding reactive transport in the subsurface and for estimating aquifer parameters required in the optimization design of remediation strategies. A general model and associated analytical solutions are developed in this study. The new model represents the most recent advancement on radial dispersion studies and incorporates a host of important processes that are not taken into consideration in previous investigations.
Vanja Travaš, Luka Zaharija, Davor Stipanić, and Siniša Družeta
Hydrol. Earth Syst. Sci., 27, 1343–1359, https://doi.org/10.5194/hess-27-1343-2023, https://doi.org/10.5194/hess-27-1343-2023, 2023
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In order to model groundwater flow in karst aquifers, it is necessary to approximate the influence of the unknown and irregular structure of the karst conduits. For this purpose, a procedure based on inverse modeling is adopted. Moreover, in order to reconstruct the functional dependencies related to groundwater flow, the particle swarm method was used, through which the optimal solution of unknown functions is found by imitating the movement of ants in search of food.
Shouchuan Zhang, Zheming Shi, Guangcai Wang, Zuochen Zhang, and Huaming Guo
Hydrol. Earth Syst. Sci., 27, 401–415, https://doi.org/10.5194/hess-27-401-2023, https://doi.org/10.5194/hess-27-401-2023, 2023
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We documented the step-like increases of water level, flow rate, and water temperatures in a confined aquifer following multiple earthquakes. By employing tidal analysis and a coupled temperature and flow rate model, we find that post-seismic vertical permeability changes and recharge model could explain the co-seismic response. And co-seismic temperature changes are caused by mixing of different volumes of water, with the mixing ratio varying according to each earthquake.
Xiaoying Zhang, Fan Dong, Guangquan Chen, and Zhenxue Dai
Hydrol. Earth Syst. Sci., 27, 83–96, https://doi.org/10.5194/hess-27-83-2023, https://doi.org/10.5194/hess-27-83-2023, 2023
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In a data-driven framework, groundwater levels can generally only be calculated 1 time step ahead. We discuss the advance prediction with longer forecast periods rather than single time steps by constructing a model based on a temporal convolutional network. Model accuracy and efficiency were further compared with an LSTM-based model. The two models derived in this study can help people cope with the uncertainty of what might occur in hydrological scenarios under the threat of climate change.
Dimitri Rambourg, Raphaël Di Chiara, and Philippe Ackerer
Hydrol. Earth Syst. Sci., 26, 6147–6162, https://doi.org/10.5194/hess-26-6147-2022, https://doi.org/10.5194/hess-26-6147-2022, 2022
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The reproduction of flows and contaminations underground requires a good estimation of the parameters of the geological environment (mainly permeability and porosity), in three dimensions. While most researchers rely on geophysical methods, which are costly and difficult to implement in the field, this study proposes an alternative using data that are already widely available: piezometric records (monitoring of the water table) and the lithological description of the piezometric wells.
Raphael Schneider, Julian Koch, Lars Troldborg, Hans Jørgen Henriksen, and Simon Stisen
Hydrol. Earth Syst. Sci., 26, 5859–5877, https://doi.org/10.5194/hess-26-5859-2022, https://doi.org/10.5194/hess-26-5859-2022, 2022
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Hydrological models at high spatial resolution are computationally expensive. However, outputs from such models, such as the depth of the groundwater table, are often desired in high resolution. We developed a downscaling algorithm based on machine learning that allows us to increase spatial resolution of hydrological model outputs, alleviating computational burden. We successfully applied the downscaling algorithm to the climate-change-induced impacts on the groundwater table across Denmark.
Luca Guillaumot, Laurent Longuevergne, Jean Marçais, Nicolas Lavenant, and Olivier Bour
Hydrol. Earth Syst. Sci., 26, 5697–5720, https://doi.org/10.5194/hess-26-5697-2022, https://doi.org/10.5194/hess-26-5697-2022, 2022
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Recharge, defining the renewal rate of groundwater resources, is difficult to estimate at basin scale. Here, recharge variations are inferred from water table variations recorded in boreholes. First, results show that aquifer-scale properties controlling these variations can be inferred from boreholes. Second, groundwater is recharged by both intense and seasonal rainfall. Third, the short-term contribution appears overestimated in recharge models and depends on the unsaturated zone thickness.
Alberto Casillas-Trasvina, Bart Rogiers, Koen Beerten, Laurent Wouters, and Kristine Walraevens
Hydrol. Earth Syst. Sci., 26, 5577–5604, https://doi.org/10.5194/hess-26-5577-2022, https://doi.org/10.5194/hess-26-5577-2022, 2022
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Heat in the subsurface can be used to characterize aquifer flow behaviour. The temperature data obtained can be useful for understanding the groundwater flow, which is of particular importance in waste disposal studies. Satellite images of surface temperature and a temperature–time curve were implemented in a heat transport model. Results indicate that conduction plays a major role in the aquifer and support the usefulness of temperature measurements.
Tunde Olarinoye, Tom Gleeson, and Andreas Hartmann
Hydrol. Earth Syst. Sci., 26, 5431–5447, https://doi.org/10.5194/hess-26-5431-2022, https://doi.org/10.5194/hess-26-5431-2022, 2022
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Analysis of karst spring recession is essential for management of groundwater. In karst, recession is dominated by slow and fast components; separating these components is by manual and subjective approaches. In our study, we tested the applicability of automated streamflow recession extraction procedures for a karst spring. Results showed that, by simple modification, streamflow extraction methods can identify slow and fast components: derived recession parameters are within reasonable ranges.
Min Lu, Bart Rogiers, Koen Beerten, Matej Gedeon, and Marijke Huysmans
Hydrol. Earth Syst. Sci., 26, 3629–3649, https://doi.org/10.5194/hess-26-3629-2022, https://doi.org/10.5194/hess-26-3629-2022, 2022
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Lowland rivers and shallow aquifers are closely coupled. We study their interactions here using a combination of impulse response modeling and hydrological data analysis. The results show that the lowland catchments are groundwater dominated and that the hydrological system from precipitation impulse to groundwater inflow response is a very fast response regime. This study also provides an alternative method to estimate groundwater inflow to rivers from the perspective of groundwater level.
Zhongxia Li, Junwei Wan, Tao Xiong, Hongbin Zhan, Linqing He, and Kun Huang
Hydrol. Earth Syst. Sci., 26, 3359–3375, https://doi.org/10.5194/hess-26-3359-2022, https://doi.org/10.5194/hess-26-3359-2022, 2022
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Four permeable rocks with different pore sizes were considered to provide experimental evidence of Forchheimer flow and the transition between different flow regimes. The mercury injection technique was used to measure the pore size distribution, which is an essential factor for determining the flow regime, for four permeable stones. Finally, the influences of porosity and particle size on the Forchheimer coefficients were discussed.
Andreas Wunsch, Tanja Liesch, Guillaume Cinkus, Nataša Ravbar, Zhao Chen, Naomi Mazzilli, Hervé Jourde, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 26, 2405–2430, https://doi.org/10.5194/hess-26-2405-2022, https://doi.org/10.5194/hess-26-2405-2022, 2022
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Modeling complex karst water resources is difficult enough, but often there are no or too few climate stations available within or close to the catchment to deliver input data for modeling purposes. We apply image recognition algorithms to time-distributed, spatially gridded meteorological data to simulate karst spring discharge. Our models can also learn the approximate catchment location of a spring independently.
Brian Berkowitz
Hydrol. Earth Syst. Sci., 26, 2161–2180, https://doi.org/10.5194/hess-26-2161-2022, https://doi.org/10.5194/hess-26-2161-2022, 2022
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Extensive efforts have focused on quantifying conservative chemical transport in geological formations. We assert that an explicit accounting of temporal information, under uncertainty, in addition to spatial information, is fundamental to an effective modeling formulation. We further assert that efforts to apply chemical transport equations at large length scales, based on measurements and model parameter values relevant to significantly smaller length scales, are an unattainable
holy grail.
Guilherme E. H. Nogueira, Christian Schmidt, Daniel Partington, Philip Brunner, and Jan H. Fleckenstein
Hydrol. Earth Syst. Sci., 26, 1883–1905, https://doi.org/10.5194/hess-26-1883-2022, https://doi.org/10.5194/hess-26-1883-2022, 2022
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In near-stream aquifers, mixing between stream water and ambient groundwater can lead to dilution and the removal of substances that can be harmful to the water ecosystem at high concentrations. We used a numerical model to track the spatiotemporal evolution of different water sources and their mixing around a stream, which are rather difficult in the field. Results show that mixing mainly develops as narrow spots, varying In time and space, and is affected by magnitudes of discharge events.
Jacques Bodin, Gilles Porel, Benoît Nauleau, and Denis Paquet
Hydrol. Earth Syst. Sci., 26, 1713–1726, https://doi.org/10.5194/hess-26-1713-2022, https://doi.org/10.5194/hess-26-1713-2022, 2022
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Assessment of the karst network geometry is an important challenge in the accurate modeling of karst aquifers. In this study, we propose an approach for the identification of effective three-dimensional discrete karst conduit networks conditioned on tracer tests and geophysical data. The applicability of the proposed approach is illustrated through a case study at the Hydrogeological Experimental Site in Poitiers, France.
Zexuan Xu, Rebecca Serata, Haruko Wainwright, Miles Denham, Sergi Molins, Hansell Gonzalez-Raymat, Konstantin Lipnikov, J. David Moulton, and Carol Eddy-Dilek
Hydrol. Earth Syst. Sci., 26, 755–773, https://doi.org/10.5194/hess-26-755-2022, https://doi.org/10.5194/hess-26-755-2022, 2022
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Climate change could change the groundwater system and threaten water supply. To quantitatively evaluate its impact on water quality, numerical simulations with chemical and reaction processes are required. With the climate projection dataset, we used the newly developed hydrological and chemical model to investigate the movement of contaminants and assist the management of contamination sites.
Esther Brakkee, Marjolein H. J. van Huijgevoort, and Ruud P. Bartholomeus
Hydrol. Earth Syst. Sci., 26, 551–569, https://doi.org/10.5194/hess-26-551-2022, https://doi.org/10.5194/hess-26-551-2022, 2022
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Periods of drought often lead to groundwater shortages in large regions, which cause damage to nature and the economy. To take measures, we need a good understanding of where and when groundwater shortage occurs. In this study, we have tested a method that can combine large amounts of groundwater measurements in an automated way and provide detailed maps of how groundwater shortages develop during a drought period. This information can help water managers to limit future groundwater shortages.
Emmanuel Dubois, Marie Larocque, Sylvain Gagné, and Guillaume Meyzonnat
Hydrol. Earth Syst. Sci., 25, 6567–6589, https://doi.org/10.5194/hess-25-6567-2021, https://doi.org/10.5194/hess-25-6567-2021, 2021
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This work demonstrates the relevance of using a water budget model to understand long-term transient and regional-scale groundwater recharge (GWR) in cold and humid climates where groundwater observations are scarce. Monthly GWR is simulated for 57 years on 500 m x 500 m cells in Canada (36 000 km2 area) with limited uncertainty due to a robust automatic calibration method. The increases in precipitation and temperature since the 1960s have not yet produced significant changes in annual GWR.
Yaniv Edery, Martin Stolar, Giovanni Porta, and Alberto Guadagnini
Hydrol. Earth Syst. Sci., 25, 5905–5915, https://doi.org/10.5194/hess-25-5905-2021, https://doi.org/10.5194/hess-25-5905-2021, 2021
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The interplay between dissolution, precipitation and transport is widely encountered in porous media, from CO2 storage to cave formation in carbonate rocks. We show that dissolution occurs along preferential flow paths with high hydraulic conductivity, while precipitation occurs at locations close to yet separated from these flow paths, thus further funneling the flow and changing the probability density function of the transport, as measured on the altered conductivity field at various times.
Karina Y. Gutierrez-Jurado, Daniel Partington, and Margaret Shanafield
Hydrol. Earth Syst. Sci., 25, 4299–4317, https://doi.org/10.5194/hess-25-4299-2021, https://doi.org/10.5194/hess-25-4299-2021, 2021
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Understanding the hydrologic cycle in semi-arid landscapes includes knowing the physical processes that govern where and why rivers flow and dry within a given catchment. To gain this understanding, we put together a conceptual model of what processes we think are important and then tested that model with numerical analysis. The results broadly confirmed our hypothesis that there are three distinct regions in our study catchment that contribute to streamflow generation in quite different ways.
Natascha Brandhorst, Daniel Erdal, and Insa Neuweiler
Hydrol. Earth Syst. Sci., 25, 4041–4059, https://doi.org/10.5194/hess-25-4041-2021, https://doi.org/10.5194/hess-25-4041-2021, 2021
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We compare two approaches for coupling a 2D groundwater model with multiple 1D models for the unsaturated zone. One is non-iterative and very fast. The other one is iterative and involves a new way of treating the specific yield, which is crucial for obtaining a consistent solution in both model compartments. Tested on different scenarios, this new method turns out to be slower than the non-iterative approach but more accurate and still very efficient compared to fully integrated 3D model runs.
Vince P. Kaandorp, Hans Peter Broers, Ype van der Velde, Joachim Rozemeijer, and Perry G. B. de Louw
Hydrol. Earth Syst. Sci., 25, 3691–3711, https://doi.org/10.5194/hess-25-3691-2021, https://doi.org/10.5194/hess-25-3691-2021, 2021
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We reconstructed historical and present-day tritium, chloride, and nitrate concentrations in stream water of a catchment using
land-use-based input curves and calculated travel times of groundwater. Parameters such as the unsaturated zone thickness, mean travel time, and input patterns determine time lags between inputs and in-stream concentrations. The timescale of the breakthrough of pollutants in streams is dependent on the location of pollution in a catchment.
Yueling Ma, Carsten Montzka, Bagher Bayat, and Stefan Kollet
Hydrol. Earth Syst. Sci., 25, 3555–3575, https://doi.org/10.5194/hess-25-3555-2021, https://doi.org/10.5194/hess-25-3555-2021, 2021
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This study utilized spatiotemporally continuous precipitation anomaly (pra) and water table depth anomaly (wtda) data from integrated hydrologic simulation results over Europe in combination with Long Short-Term Memory (LSTM) networks to capture the time-varying and time-lagged relationship between pra and wtda in order to obtain reliable models to estimate wtda at the individual pixel level.
Raoul A. Collenteur, Mark Bakker, Gernot Klammler, and Steffen Birk
Hydrol. Earth Syst. Sci., 25, 2931–2949, https://doi.org/10.5194/hess-25-2931-2021, https://doi.org/10.5194/hess-25-2931-2021, 2021
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This study explores the use of nonlinear transfer function noise (TFN) models to simulate groundwater levels and estimate groundwater recharge from observed groundwater levels. A nonlinear recharge model is implemented in a TFN model to compute the recharge. The estimated recharge rates are shown to be in good agreement with the recharge observed with a lysimeter present at the case study site in Austria. The method can be used to obtain groundwater recharge rates at
sub-yearly timescales.
Franci Gabrovšek and Wolfgang Dreybrodt
Hydrol. Earth Syst. Sci., 25, 2895–2913, https://doi.org/10.5194/hess-25-2895-2021, https://doi.org/10.5194/hess-25-2895-2021, 2021
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The evolution of karst aquifers is often governed by solutions gaining their aggressiveness in depth. Although the principles of
hypogene speleogenesisare known, modelling studies based on reactive flow in fracture networks are missing. We present a model where dissolution at depth is triggered by the mixing of waters of different origin and chemistry. We show how the initial position of the mixing zone and flow instabilities therein determine the position and shape of the final conduits.
Patrick Morrissey, Paul Nolan, Ted McCormack, Paul Johnston, Owen Naughton, Saheba Bhatnagar, and Laurence Gill
Hydrol. Earth Syst. Sci., 25, 1923–1941, https://doi.org/10.5194/hess-25-1923-2021, https://doi.org/10.5194/hess-25-1923-2021, 2021
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Lowland karst aquifers provide important wetland habitat resulting from seasonal flooding on the land surface. This flooding is controlled by surcharging of the karst system, which is very sensitive to changes in rainfall. This study investigates the predicted impacts of climate change on a lowland karst catchment in Ireland and highlights the relative vulnerability to future changing climate conditions of karst systems and any associated wetland habitats.
Liwen Wu, Jesus D. Gomez-Velez, Stefan Krause, Anders Wörman, Tanu Singh, Gunnar Nützmann, and Jörg Lewandowski
Hydrol. Earth Syst. Sci., 25, 1905–1921, https://doi.org/10.5194/hess-25-1905-2021, https://doi.org/10.5194/hess-25-1905-2021, 2021
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With a physically based model that couples flow and heat transport in hyporheic zones, the present study provides the first insights into the dynamics of hyporheic responses to the impacts of daily groundwater withdrawal and river temperature fluctuations, allowing for a better understanding of transient hyporheic exchange processes and hence an improved pumping operational scheme.
Jost Hellwig, Michael Stoelzle, and Kerstin Stahl
Hydrol. Earth Syst. Sci., 25, 1053–1068, https://doi.org/10.5194/hess-25-1053-2021, https://doi.org/10.5194/hess-25-1053-2021, 2021
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Potential future groundwater and baseflow drought hazards depend on systems' sensitivity to altered recharge conditions. With three generic scenarios, we found different sensitivities across Germany driven by hydrogeology. While changes in drought hazard due to seasonal recharge shifts will be rather low, a lengthening of dry spells could cause stronger responses in regions with slow groundwater response to precipitation, urging local water management to prepare for more severe droughts.
Martin J. Wells, Troy E. Gilmore, Natalie Nelson, Aaron Mittelstet, and John K. Böhlke
Hydrol. Earth Syst. Sci., 25, 811–829, https://doi.org/10.5194/hess-25-811-2021, https://doi.org/10.5194/hess-25-811-2021, 2021
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Groundwater in many agricultural areas contains high levels of nitrate, which is a concern for drinking water supplies. The rate at which nitrate moves through the subsurface is a critical piece of information for predicting how quickly groundwater nitrate levels may improve after agricultural producers change their approach to managing crop water and fertilizers. In this study, we explored a new statistical modeling approach to determine rates at which nitrate moves into and through an aquifer.
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