Articles | Volume 20, issue 1
https://doi.org/10.5194/hess-20-55-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/hess-20-55-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
15 Jan 2016
Research article |
| 15 Jan 2016
Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer
C.-S. Huang
Institute of Environmental Engineering, National Chiao Tung
University, Hsinchu, Taiwan
J.-J. Chen
Institute of Environmental Engineering, National Chiao Tung
University, Hsinchu, Taiwan
H.-D. Yeh
CORRESPONDING AUTHOR
Institute of Environmental Engineering, National Chiao Tung
University, Hsinchu, Taiwan
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Chia-Hao Chang, Ching-Sheng Huang, and Hund-Der Yeh
Hydrol. Earth Syst. Sci., 20, 1225–1239, https://doi.org/10.5194/hess-20-1225-2016, https://doi.org/10.5194/hess-20-1225-2016, 2016
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Most previous solutions for groundwater flow due to localized recharge assumed either aquifer incompressibility or 2-D flow without vertical flow. This paper develops a 3-D flow model for hydraulic head change induced by the recharge with random transient rates in a compressible unconfined aquifer. The analytical solution of the model for the head is derived. The quantitative criteria for the validity of those two assumptions are presented by the developed solution.
C.-S. Huang, S.-Y. Yang, and H.-D. Yeh
Hydrol. Earth Syst. Sci., 19, 2639–2647, https://doi.org/10.5194/hess-19-2639-2015, https://doi.org/10.5194/hess-19-2639-2015, 2015
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Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem. The solution is in terms of a simple series expanded by integers and thus very convenient for those who are not familiar with numerical methods. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is provided.
Ching-Sheng Huang, Ya-Hsin Tsai, Hund-Der Yeh, and Tao Yang
Hydrol. Earth Syst. Sci., 23, 1323–1337, https://doi.org/10.5194/hess-23-1323-2019, https://doi.org/10.5194/hess-23-1323-2019, 2019
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The study develops a new model describing head fluctuation induced by oscillatory pumping test (OPT) in an unconfined aquifer with effects of delayed gravity drainage (DGD) and initial condition regarding the hydraulic head prior to OPT. The DGD reduces to instantaneous gravity drainage when a dimensionless parameter exceeds 500. A pseudo-steady-state model excluding initial condition causes a time-shift from the actual transient model in predicting simple harmonic motion of head fluctuation.
Chia-Hao Chang, Ching-Sheng Huang, and Hund-Der Yeh
Hydrol. Earth Syst. Sci., 22, 3951–3963, https://doi.org/10.5194/hess-22-3951-2018, https://doi.org/10.5194/hess-22-3951-2018, 2018
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Existing analytical solutions associated with groundwater recharge are only applicable to the studies of saturated flow in aquifers. This paper develops an analytical solution for 3-D unsaturated–saturated flow due to localized recharge into an unconfined aquifer. The effects of unsaturated flow on the recharge process are analyzed. The present solution agrees well with a finite-difference solution. The solution’s predictions also match well with observed data obtained by a field experiment.
Ching-Sheng Huang, Ya-Hsin Tsai, Hund-Der Yeh, and Tao Yang
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2018-199, https://doi.org/10.5194/hess-2018-199, 2018
Manuscript not accepted for further review
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A number of analytical models are presented for the analyses of oscillatory pumping test (OPT). The effects of wellbore storage and initial condition regarding the hydraulic head prior to OPT are commonly neglected in existing models. This study aims to develop a new model describing head fluctuation induced by OPT in unconfined aquifers. The effects are analyzed using the analytical solution of the model. Solution prediction agrees well to head fluctuation data observed at a field experiment.
Chao-Chih Lin, Ya-Chi Chang, and Hund-Der Yeh
Hydrol. Earth Syst. Sci., 22, 2359–2375, https://doi.org/10.5194/hess-22-2359-2018, https://doi.org/10.5194/hess-22-2359-2018, 2018
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An semanalytical model is developed for estimating the groundwater flow and stream depletion rates (SDR) from two streams in an L-shaped fluvial aquifer located at Gyeonggi-do, Korea. The predicted spatial and temporal hydraulic heads agree well with those of simulations and measurements. The model can be applied to evaluate the contribution of extracted water from storage and nearby streams.
Ching-Min Chang and Hund-Der Yeh
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-19, https://doi.org/10.5194/hess-2017-19, 2017
Revised manuscript not accepted
Chia-Hao Chang, Ching-Sheng Huang, and Hund-Der Yeh
Hydrol. Earth Syst. Sci., 20, 1225–1239, https://doi.org/10.5194/hess-20-1225-2016, https://doi.org/10.5194/hess-20-1225-2016, 2016
Short summary
Short summary
Most previous solutions for groundwater flow due to localized recharge assumed either aquifer incompressibility or 2-D flow without vertical flow. This paper develops a 3-D flow model for hydraulic head change induced by the recharge with random transient rates in a compressible unconfined aquifer. The analytical solution of the model for the head is derived. The quantitative criteria for the validity of those two assumptions are presented by the developed solution.
C.-S. Huang, S.-Y. Yang, and H.-D. Yeh
Hydrol. Earth Syst. Sci., 19, 2639–2647, https://doi.org/10.5194/hess-19-2639-2015, https://doi.org/10.5194/hess-19-2639-2015, 2015
Short summary
Short summary
Existing solutions for the problem of constant-flux pumping (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem. The solution is in terms of a simple series expanded by integers and thus very convenient for those who are not familiar with numerical methods. A quantitative criterion for the validity of neglecting the vertical flow component due to a partially penetrating well is provided.
C.-M. Chang and H.-D. Yeh
Hydrol. Earth Syst. Sci., 19, 2505–2511, https://doi.org/10.5194/hess-19-2505-2015, https://doi.org/10.5194/hess-19-2505-2015, 2015
Related subject area
Subject: Groundwater hydrology | Techniques and Approaches: Theory development
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Revised manuscript accepted for HESS
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Hydrol. Earth Syst. Sci., 26, 5035–5049, https://doi.org/10.5194/hess-26-5035-2022, https://doi.org/10.5194/hess-26-5035-2022, 2022
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Gabriel C. Rau, Timothy C. McMillan, Martin S. Andersen, and Wendy A. Timms
Hydrol. Earth Syst. Sci., 26, 4301–4321, https://doi.org/10.5194/hess-26-4301-2022, https://doi.org/10.5194/hess-26-4301-2022, 2022
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Georg J. Houben and Okke Batelaan
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Unbeknown to most hydrologists, many methods used in groundwater hydrology today go back to work by Adolf and Günther Thiem. Their work goes beyond the Dupuit–Thiem analytical model for pump tests mentioned in many textbooks. It includes, e.g., the development and improvement of isopotential maps, tracer tests, and vertical well constructions. Extensive literature and archive research has been conducted to identify how and where the Thiems developed their methods and how they spread.
Zhaoyang Luo, Jun Kong, Chengji Shen, Pei Xin, Chunhui Lu, Ling Li, and David Andrew Barry
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Analytical solutions are derived for steady-state seawater intrusion in annulus segment aquifers. These analytical solutions are validated by comparing their predictions with experimental data. We find seawater intrusion is the most extensive in divergent aquifers, and the opposite is the case for convergent aquifers. The analytical solutions facilitate engineers and hydrologists in evaluating seawater intrusion more efficiently in annulus segment aquifers with a complex geometry.
Dylan J. Irvine, Cameron Wood, Ian Cartwright, and Tanya Oliver
Hydrol. Earth Syst. Sci., 25, 5415–5424, https://doi.org/10.5194/hess-25-5415-2021, https://doi.org/10.5194/hess-25-5415-2021, 2021
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It is widely assumed that 14C is in contact with the atmosphere until recharging water reaches the water table. Unsaturated zone (UZ) studies have shown that 14C decreases with depth below the land surface. We produce a relationship between UZ 14C and depth to the water table to estimate input 14C activities for groundwater age estimation. Application of the new relationship shows that it is important for UZ processes to be considered in groundwater mean residence time estimation.
Erwin Zehe, Ralf Loritz, Yaniv Edery, and Brian Berkowitz
Hydrol. Earth Syst. Sci., 25, 5337–5353, https://doi.org/10.5194/hess-25-5337-2021, https://doi.org/10.5194/hess-25-5337-2021, 2021
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This study uses the concepts of entropy and work to quantify and explain the emergence of preferential flow and transport in heterogeneous saturated porous media. We found that the downstream concentration of solutes in preferential pathways implies a downstream declining entropy in the transverse distribution of solute transport pathways. Preferential flow patterns with lower entropies emerged within media of higher heterogeneity – a stronger self-organization despite a higher randomness.
Jiancong Chen, Bhavna Arora, Alberto Bellin, and Yoram Rubin
Hydrol. Earth Syst. Sci., 25, 4127–4146, https://doi.org/10.5194/hess-25-4127-2021, https://doi.org/10.5194/hess-25-4127-2021, 2021
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We developed a stochastic framework with indicator random variables to characterize the spatiotemporal distribution of environmental hot spots and hot moments (HSHMs) that represent rare locations and events exerting a disproportionate influence over the environment. HSHMs are characterized by static and dynamic indicators. This framework is advantageous as it allows us to calculate the uncertainty associated with HSHMs based on uncertainty associated with its contributors.
Gabriel C. Rau, Mark O. Cuthbert, R. Ian Acworth, and Philipp Blum
Hydrol. Earth Syst. Sci., 24, 6033–6046, https://doi.org/10.5194/hess-24-6033-2020, https://doi.org/10.5194/hess-24-6033-2020, 2020
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This work provides an important generalisation of a previously developed method that quantifies subsurface barometric efficiency using the groundwater level response to Earth and atmospheric tides. The new approach additionally allows the quantification of hydraulic conductivity and specific storage. This enables improved and rapid assessment of subsurface processes and properties using standard pressure measurements.
Xiao-Wei Jiang, John Cherry, and Li Wan
Hydrol. Earth Syst. Sci., 24, 6001–6019, https://doi.org/10.5194/hess-24-6001-2020, https://doi.org/10.5194/hess-24-6001-2020, 2020
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The gushing of water from flowing wells is a natural phenomenon of interest to the public. This review demonstrates that this spectacular phenomenon also instigated the science of groundwater and can be considered a root of groundwater hydrology. Observations of flowing wells not only led to the foundation of many principles of traditional groundwater hydrology but also played a vital role in the paradigm shift from aquitard-bound flow to cross-formational flow driven by topography.
Doris E. Wendt, Anne F. Van Loon, John P. Bloomfield, and David M. Hannah
Hydrol. Earth Syst. Sci., 24, 4853–4868, https://doi.org/10.5194/hess-24-4853-2020, https://doi.org/10.5194/hess-24-4853-2020, 2020
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Groundwater use changes the availability of groundwater, especially during droughts. This study investigates the impact of groundwater use on groundwater droughts. A methodological framework is presented that was developed and applied to the UK. We identified an asymmetric impact of groundwater use on droughts, which highlights the relation between short-term and long-term strategies for sustainable groundwater use.
Quanrong Wang, Junxia Wang, Hongbin Zhan, and Wenguang Shi
Hydrol. Earth Syst. Sci., 24, 3983–4000, https://doi.org/10.5194/hess-24-3983-2020, https://doi.org/10.5194/hess-24-3983-2020, 2020
Franklin W. Schwartz, Ganming Liu, and Zhongbo Yu
Hydrol. Earth Syst. Sci., 24, 489–500, https://doi.org/10.5194/hess-24-489-2020, https://doi.org/10.5194/hess-24-489-2020, 2020
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We are concerned about the sad state of affairs around groundwater in the developing countries of Asia and the obvious implications for sustainability. Groundwater production for irrigated agriculture has led to water-level declines that continue to worsen. Yet in the most populous countries, China, India, Pakistan, and Iran, there are only token efforts towards evidence-based sustainable management. It is unrealistic to expect evidence-based groundwater sustainability to develop any time soon.
Floris Loys Naus, Paul Schot, Koos Groen, Kazi Matin Ahmed, and Jasper Griffioen
Hydrol. Earth Syst. Sci., 23, 1431–1451, https://doi.org/10.5194/hess-23-1431-2019, https://doi.org/10.5194/hess-23-1431-2019, 2019
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In this paper, we postulate a possible evolution of the groundwater salinity around a village in southwestern Bangladesh, based on high-density fieldwork. We identified that the thickness of the surface clay layer, the surface elevation and the present-day land use determine whether fresh or saline groundwater has formed. The outcomes show how the large groundwater salinity variation in southwestern Bangladesh can be understood, which is valuable for the water management in the region.
John P. Bloomfield, Benjamin P. Marchant, and Andrew A. McKenzie
Hydrol. Earth Syst. Sci., 23, 1393–1408, https://doi.org/10.5194/hess-23-1393-2019, https://doi.org/10.5194/hess-23-1393-2019, 2019
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Groundwater is susceptible to drought due to natural variations in climate; however, to date there is no evidence of a relationship between climate change and groundwater drought. Using two long groundwater level records from the UK, we document increases in frequency, magnitude and intensity and changes in duration of groundwater drought associated with climate warming and infer that, given the extent of shallow groundwater globally, warming may widely effect changes to groundwater droughts.
Bin Ma, Menggui Jin, Xing Liang, and Jing Li
Hydrol. Earth Syst. Sci., 23, 427–446, https://doi.org/10.5194/hess-23-427-2019, https://doi.org/10.5194/hess-23-427-2019, 2019
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Groundwater supplies the most freshwater for industrial and agricultural production and domestic use in the arid northwest of China. This research uses environmental tracers to enhance one's understanding of groundwater, including aquifer recharge sources and groundwater mean residence times in the alluvium aquifers. The results provide valuable implications for groundwater resources regulation and sustainable development and have practical significance for other arid areas.
Hubert H. G. Savenije
Hydrol. Earth Syst. Sci., 22, 1911–1916, https://doi.org/10.5194/hess-22-1911-2018, https://doi.org/10.5194/hess-22-1911-2018, 2018
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This paper provides the connection between two simple equations describing groundwater flow at different scales: the Darcy equation describes groundwater flow at pore scale, the linear reservoir equation at catchment scale. The connection between the two appears to be very simple. The two parameters of the equations are proportional, depending on the porosity of the subsoil and the resistance for the groundwater to enter the surface drainage network.
Ming Wu, Jianfeng Wu, Jichun Wu, and Bill X. Hu
Hydrol. Earth Syst. Sci., 22, 1001–1015, https://doi.org/10.5194/hess-22-1001-2018, https://doi.org/10.5194/hess-22-1001-2018, 2018
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Fractal models of regular triangle arrangement (RTA) and square pitch arrangement (SPA) are developed in this study. Results suggest RTA can cause more groundwater contamination and make remediation more difficult. In contrast, the cleanup of contaminants in aquifers with SPA is easier. This study demonstrates how microscale arrangements control contaminant migration and remediation, which is helpful in designing successful remediation schemes for subsurface contamination.
Rui Ma, Ziyong Sun, Yalu Hu, Qixin Chang, Shuo Wang, Wenle Xing, and Mengyan Ge
Hydrol. Earth Syst. Sci., 21, 4803–4823, https://doi.org/10.5194/hess-21-4803-2017, https://doi.org/10.5194/hess-21-4803-2017, 2017
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The roles of groundwater flow in the hydrological cycle within the alpine area characterized by permafrost or seasonal frost are poorly known. We investigated the role of permafrost in controlling groundwater flow and hydrological connections between glaciers and river. The recharge, flow path and discharge of permafrost groundwater at the study site were explored. Two mechanisms were proposed to explain the significantly seasonal variation in interaction between groundwater and surface water.
Bing Zhang, Jing Zhang, and Takafumi Yoshida
Hydrol. Earth Syst. Sci., 21, 3417–3425, https://doi.org/10.5194/hess-21-3417-2017, https://doi.org/10.5194/hess-21-3417-2017, 2017
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Since groundwater is the linkage between climate changes and fresh submarine groundwater discharge, the variations of and relationships among monthly groundwater table, rainfall, snowfall, and climate change events from 1985 to 2015 were analyzed by wavelet coherence to discuss the implications for climate changes. The results show the increase in precipitation and the groundwater table, indicating that fresh submarine groundwater discharge flux may increase under climate change.
Koen Gerardus Zuurbier and Pieter Jan Stuyfzand
Hydrol. Earth Syst. Sci., 21, 1173–1188, https://doi.org/10.5194/hess-21-1173-2017, https://doi.org/10.5194/hess-21-1173-2017, 2017
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The subsurface is increasingly perforated for exploitation of water and energy. This has increased the risk of leakage between originally separated aquifers. It is shown how this leakage can have a very negative impact on the recovery of freshwater during aquifer storage and recovery (ASR) in brackish-saline aquifers. Deep interception of intruding brackish-saline water can mitigate the negative effects and buoyancy of freshwater to some extent, but not completely.
Ulrike Unterbruner, Sylke Hilberg, and Iris Schiffl
Hydrol. Earth Syst. Sci., 20, 2251–2266, https://doi.org/10.5194/hess-20-2251-2016, https://doi.org/10.5194/hess-20-2251-2016, 2016
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Studies show that young people have difficulties with correctly understanding groundwater. We designed a multimedia learning program about groundwater and tested its learning efficacy with pupils and teacher-training students. A novelty is the theory-guided designing of the program on the basis of hydrogeology and science education. The pupils and students greatly benefited from working through the multimedia learning program.
Kosta Urumović and Kosta Urumović Sr.
Hydrol. Earth Syst. Sci., 20, 1669–1680, https://doi.org/10.5194/hess-20-1669-2016, https://doi.org/10.5194/hess-20-1669-2016, 2016
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Calculation of hydraulic conductivity of porous materials is crucial for further use in hydrogeological modeling. The Kozeny–Carman model is theoretically impeccable but has not been properly used in recent scientific and expert literature. In this paper, proper use of the Kozeny-Carman formula is given through presentation of geometric mean grain size in the drilled-core sample as the referential mean grain size. Also, procedures for identification of real effective porosity of porous media are presented.
R. A. Crane, M. O. Cuthbert, and W. Timms
Hydrol. Earth Syst. Sci., 19, 3991–4000, https://doi.org/10.5194/hess-19-3991-2015, https://doi.org/10.5194/hess-19-3991-2015, 2015
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We present an interrupted-flow centrifugation technique to characterise the vertical hydraulic properties of dual porosity, low permeability media. Use of large core samples (100mm diameter) enables hydraulic-conductivity-scale issues in dual porosity media to be overcome. Elevated centrifugal force also enables simulating in situ total stress conditions. The methodology is an important tool to assess the ability of dual porosity aquitards to protect underlying aquifer systems.
B. L. Kurylyk, K. T. B. MacQuarrie, D. Caissie, and J. M. McKenzie
Hydrol. Earth Syst. Sci., 19, 2469–2489, https://doi.org/10.5194/hess-19-2469-2015, https://doi.org/10.5194/hess-19-2469-2015, 2015
Short summary
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Changes in climate and land cover are known to warm streams by altering surface heat fluxes. However, the influence of these disturbances on shallow groundwater temperature are not as well understood. In small streams, groundwater discharge may also exert a control on stream temperature, and thus groundwater warming may eventually produce additional stream warming not considered in most existing models. This study investigates these processes and suggests stream temperature model improvements.
S. Luoma, J. Okkonen, K. Korkka-Niemi, N. Hendriksson, and B. Backman
Hydrol. Earth Syst. Sci., 19, 1353–1370, https://doi.org/10.5194/hess-19-1353-2015, https://doi.org/10.5194/hess-19-1353-2015, 2015
N. P. Unland, I. Cartwright, D. I. Cendón, and R. Chisari
Hydrol. Earth Syst. Sci., 18, 5109–5124, https://doi.org/10.5194/hess-18-5109-2014, https://doi.org/10.5194/hess-18-5109-2014, 2014
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Periodic flooding of rivers should result in increased groundwater recharge near rivers and thus - younger and fresher groundwater near rivers. This study found the age and salinity of shallow groundwater to increase with proximity to the Tambo River in South East Australia. This appears to be due to the upwelling of older, regional groundwater closer the river. Other chemical parameters are consistent with this. This is a process that may be occurring in other similar river systems.
A. P. Atkinson, I. Cartwright, B. S. Gilfedder, D. I. Cendón, N. P. Unland, and H. Hofmann
Hydrol. Earth Syst. Sci., 18, 4951–4964, https://doi.org/10.5194/hess-18-4951-2014, https://doi.org/10.5194/hess-18-4951-2014, 2014
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This research article uses of radiogenic isotopes, stable isotopes and groundwater geochemistry to study groundwater age and recharge processes in the Gellibrand Valley, a relatively unstudied catchment and potential groundwater resource. The valley is found to contain both "old", regionally recharged groundwater (300-10,000 years) in the near-river environment, and modern groundwater (0-100 years old) further back on the floodplain. There is no recharge of the groundwater by high river flows.
U. Lauber, P. Kotyla, D. Morche, and N. Goldscheider
Hydrol. Earth Syst. Sci., 18, 4437–4452, https://doi.org/10.5194/hess-18-4437-2014, https://doi.org/10.5194/hess-18-4437-2014, 2014
M. Huebsch, O. Fenton, B. Horan, D. Hennessy, K. G. Richards, P. Jordan, N. Goldscheider, C. Butscher, and P. Blum
Hydrol. Earth Syst. Sci., 18, 4423–4435, https://doi.org/10.5194/hess-18-4423-2014, https://doi.org/10.5194/hess-18-4423-2014, 2014
S. Hergarten, G. Winkler, and S. Birk
Hydrol. Earth Syst. Sci., 18, 4277–4288, https://doi.org/10.5194/hess-18-4277-2014, https://doi.org/10.5194/hess-18-4277-2014, 2014
M. Attwa and T. Günther
Hydrol. Earth Syst. Sci., 17, 4079–4094, https://doi.org/10.5194/hess-17-4079-2013, https://doi.org/10.5194/hess-17-4079-2013, 2013
C. Schmidt, A. Musolff, N. Trauth, M. Vieweg, and J. H. Fleckenstein
Hydrol. Earth Syst. Sci., 16, 3689–3697, https://doi.org/10.5194/hess-16-3689-2012, https://doi.org/10.5194/hess-16-3689-2012, 2012
T. Gleeson, D. M. Allen, and G. Ferguson
Hydrol. Earth Syst. Sci., 16, 2159–2168, https://doi.org/10.5194/hess-16-2159-2012, https://doi.org/10.5194/hess-16-2159-2012, 2012
G. H. de Rooij
Hydrol. Earth Syst. Sci., 16, 649–669, https://doi.org/10.5194/hess-16-649-2012, https://doi.org/10.5194/hess-16-649-2012, 2012
B. Hubinger and S. Birk
Hydrol. Earth Syst. Sci., 15, 3715–3729, https://doi.org/10.5194/hess-15-3715-2011, https://doi.org/10.5194/hess-15-3715-2011, 2011
E. Joigneaux, P. Albéric, H. Pauwels, C. Pagé, L. Terray, and A. Bruand
Hydrol. Earth Syst. Sci., 15, 2459–2470, https://doi.org/10.5194/hess-15-2459-2011, https://doi.org/10.5194/hess-15-2459-2011, 2011
P.-R. Tsou, Z.-Y. Feng, H.-D. Yeh, and C.-S. Huang
Hydrol. Earth Syst. Sci., 14, 1477–1485, https://doi.org/10.5194/hess-14-1477-2010, https://doi.org/10.5194/hess-14-1477-2010, 2010
Y.-C. Chang, D.-S. Jeng, and H.-D. Yeh
Hydrol. Earth Syst. Sci., 14, 1341–1351, https://doi.org/10.5194/hess-14-1341-2010, https://doi.org/10.5194/hess-14-1341-2010, 2010
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Short summary
Existing solutions for the problem of pumping at a radial collector well (RCW) in unconfined aquifers either require laborious calculation or predict divergent results at a middle period of pumping. This study relaxes the above two limitations to develop a new analytical solution for the problem. The application of the solution is convenient for those who are not familiar with numerical methods. New findings regarding the responses of flow to pumping at RCW are addressed.
Existing solutions for the problem of pumping at a radial collector well (RCW) in unconfined...
