Articles | Volume 16, issue 3
https://doi.org/10.5194/hess-16-641-2012
© Author(s) 2012. 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-16-641-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Technical note
| 
01 Mar 2012
Technical note |
| 01 Mar 2012
Stochastic analysis of field-scale heat advection in heterogeneous aquifers
C.-M. Chang
Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan
H.-D. Yeh
Institute of Environmental Engineering, National Chiao Tung University, Hsinchu, Taiwan
Related subject area
Subject: Groundwater hydrology | Techniques and Approaches: Stochastic approaches
A comprehensive framework for stochastic calibration and sensitivity analysis of large-scale groundwater models
An ensemble-based approach for pumping optimization in an island aquifer considering parameter, observation and climate uncertainty
Improving understanding of groundwater flow in an alpine karst system by reconstructing its geologic history using conduit network model ensembles
The effects of rain and evapotranspiration statistics on groundwater recharge estimations for semi-arid environments
Characterization of the highly fractured zone at the Grimsel Test Site based on hydraulic tomography
Influence of low-frequency variability on high and low groundwater levels: example of aquifers in the Paris Basin
Technical note: Using long short-term memory models to fill data gaps in hydrological monitoring networks
Technical note: Discharge response of a confined aquifer with variable thickness to temporal, nonstationary, random recharge processes
Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations
A field evidence model: how to predict transport in heterogeneous aquifers at low investigation level
3D multiple-point statistics simulations of the Roussillon Continental Pliocene aquifer using DeeSse
Technical Note: Improved sampling of behavioral subsurface flow model parameters using active subspaces
Efficient screening of groundwater head monitoring data for anthropogenic effects and measurement errors
Regionalization with hierarchical hydrologic similarity and ex situ data in the context of groundwater recharge estimation at ungauged watersheds
Long-term groundwater recharge rates across India by in situ measurements
Stochastic hydrogeology's biggest hurdles analyzed and its big blind spot
Contributions to uncertainty related to hydrostratigraphic modeling using multiple-point statistics
Recent trends of groundwater temperatures in Austria
Moment-based metrics for global sensitivity analysis of hydrological systems
Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies
Characterizing the spatiotemporal variability of groundwater levels of alluvial aquifers in different settings using drought indices
Testing the use of standardised indices and GRACE satellite data to estimate the European 2015 groundwater drought in near-real time
Modeling 3-D permeability distribution in alluvial fans using facies architecture and geophysical acquisitions
A Bayesian consistent dual ensemble Kalman filter for state-parameter estimation in subsurface hydrology
Technical note: Application of artificial neural networks in groundwater table forecasting – a case study in a Singapore swamp forest
Regional analysis of groundwater droughts using hydrograph classification
Scalable statistics of correlated random variables and extremes applied to deep borehole porosities
Observed groundwater temperature response to recent climate change
The effect of training image and secondary data integration with multiple-point geostatistics in groundwater modelling
Is high-resolution inverse characterization of heterogeneous river bed hydraulic conductivities needed and possible?
Investigation of solute transport in nonstationary unsaturated flow fields
Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks
Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter
Extended power-law scaling of air permeabilities measured on a block of tuff
Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers
Bayesian approach for three-dimensional aquifer characterization at the Hanford 300 Area
Spectral approach to seawater intrusion in heterogeneous coastal aquifers
Andrea Manzoni, Giovanni Michele Porta, Laura Guadagnini, Alberto Guadagnini, and Monica Riva
Hydrol. Earth Syst. Sci., 28, 2661–2682, https://doi.org/10.5194/hess-28-2661-2024, https://doi.org/10.5194/hess-28-2661-2024, 2024
Short summary
Short summary
We introduce a comprehensive methodology that combines multi-objective optimization, global sensitivity analysis (GSA) and 3D groundwater modeling to analyze subsurface flow dynamics across large-scale domains. In this way, we effectively consider the inherent uncertainty associated with subsurface system characterizations and their interactions with surface waterbodies. We demonstrate the effectiveness of our proposed approach by applying it to the largest groundwater system in Italy.
Cécile Coulon, Jeremy T. White, Alexandre Pryet, Laura Gatel, and Jean-Michel Lemieux
Hydrol. Earth Syst. Sci., 28, 303–319, https://doi.org/10.5194/hess-28-303-2024, https://doi.org/10.5194/hess-28-303-2024, 2024
Short summary
Short summary
In coastal areas, groundwater managers require information on the risk of well salinization associated with various pumping scenarios. We developed a modeling approach to identify the optimal tradeoff between groundwater pumping and probability of salinization, considering model parameter and historical observation uncertainty as well as uncertainty in sea level and recharge projections. The workflow can be implemented in a wide range of coastal settings.
Chloé Fandel, Ty Ferré, François Miville, Philippe Renard, and Nico Goldscheider
Hydrol. Earth Syst. Sci., 27, 4205–4215, https://doi.org/10.5194/hess-27-4205-2023, https://doi.org/10.5194/hess-27-4205-2023, 2023
Short summary
Short summary
From the surface, it is hard to tell where underground cave systems are located. We developed a computer model to create maps of the probable cave network in an area, based on the geologic setting. We then applied our approach in reverse: in a region where an old cave network was mapped, we used modeling to test what the geologic setting might have been like when the caves formed. This is useful because understanding past cave formation can help us predict where unmapped caves are located today.
Tuvia Turkeltaub and Golan Bel
Hydrol. Earth Syst. Sci., 27, 289–302, https://doi.org/10.5194/hess-27-289-2023, https://doi.org/10.5194/hess-27-289-2023, 2023
Short summary
Short summary
Groundwater is an essential resource affected by climate conditions and anthropogenic activities. Estimations of groundwater recharge under current and future climate conditions require long-term climate records that are scarce. Different methods to synthesize climate data, based on observations, are used to estimate groundwater recharge. In terms of groundwater recharge estimation, the best synthesis method is based on the daily statistics corrected to match the observed monthly statistics.
Lisa Maria Ringel, Mohammadreza Jalali, and Peter Bayer
Hydrol. Earth Syst. Sci., 26, 6443–6455, https://doi.org/10.5194/hess-26-6443-2022, https://doi.org/10.5194/hess-26-6443-2022, 2022
Short summary
Short summary
Fractured rocks host a class of aquifers that serve as major freshwater resources worldwide. This work is dedicated to resolving the three-dimensional hydraulic and structural properties of fractured rock. For this purpose, hydraulic tomography experiments at the Grimsel Test Site in Switzerland are utilized, and the discrete fracture network is inverted. The comparison of the inversion results with independent findings from other studies demonstrates the validity of the approach.
Lisa Baulon, Nicolas Massei, Delphine Allier, Matthieu Fournier, and Hélène Bessiere
Hydrol. Earth Syst. Sci., 26, 2829–2854, https://doi.org/10.5194/hess-26-2829-2022, https://doi.org/10.5194/hess-26-2829-2022, 2022
Short summary
Short summary
Aquifers often act as low-pass filters, dampening high-frequency (intra-annual) and amplifying low-frequency (LFV, multi-annual to multidecadal) variabilities originating from climate variability. By processing groundwater level signals, we show the key role of LFV in the occurrence of groundwater extremes (GWEs). Results highlight how changes in LFV may impact future GWEs as well as the importance of correct representation of LFV in general circulation model outputs for GWE projection.
Huiying Ren, Erol Cromwell, Ben Kravitz, and Xingyuan Chen
Hydrol. Earth Syst. Sci., 26, 1727–1743, https://doi.org/10.5194/hess-26-1727-2022, https://doi.org/10.5194/hess-26-1727-2022, 2022
Short summary
Short summary
We used a deep learning method called long short-term memory (LSTM) to fill gaps in data collected by hydrologic monitoring networks. LSTM accounted for correlations in space and time and nonlinear trends in data. Compared to a traditional regression-based time-series method, LSTM performed comparably when filling gaps in data with smooth patterns, while it better captured highly dynamic patterns in data. Capturing such dynamics is critical for understanding dynamic complex system behaviors.
Ching-Min Chang, Chuen-Fa Ni, We-Ci Li, Chi-Ping Lin, and I-Hsien Lee
Hydrol. Earth Syst. Sci., 25, 2387–2397, https://doi.org/10.5194/hess-25-2387-2021, https://doi.org/10.5194/hess-25-2387-2021, 2021
Short summary
Short summary
A transfer function to describe the variation in the integrated specific discharge in response to the temporal variation in the rainfall event in the frequency domain is developed. It can be used to quantify the variability in the integrated discharge field induced by the variation in rainfall field or to simulate the discharge response of the system to any varying rainfall input, at any time resolution, using the convolution model.
Chuan-An Xia, Xiaodong Luo, Bill X. Hu, Monica Riva, and Alberto Guadagnini
Hydrol. Earth Syst. Sci., 25, 1689–1709, https://doi.org/10.5194/hess-25-1689-2021, https://doi.org/10.5194/hess-25-1689-2021, 2021
Short summary
Short summary
Our study shows that (i) monitoring wells installed with packers provide the (overall) best conductivity estimates; (ii) conductivity estimates anchored on information from partially and fully screened wells are of similar quality; (iii) inflation of the measurement-error covariance matrix can improve conductivity estimates when a simplified flow model is adopted; and (iv) when compared to the MC-based EnKF, the MEs-based EnKF can efficiently and accurately estimate conductivity and head fields.
Alraune Zech, Peter Dietrich, Sabine Attinger, and Georg Teutsch
Hydrol. Earth Syst. Sci., 25, 1–15, https://doi.org/10.5194/hess-25-1-2021, https://doi.org/10.5194/hess-25-1-2021, 2021
Valentin Dall'Alba, Philippe Renard, Julien Straubhaar, Benoit Issautier, Cédric Duvail, and Yvan Caballero
Hydrol. Earth Syst. Sci., 24, 4997–5013, https://doi.org/10.5194/hess-24-4997-2020, https://doi.org/10.5194/hess-24-4997-2020, 2020
Short summary
Short summary
Due to climate and population evolution, increased pressure is put on the groundwater resource, which calls for better understanding and models. In this paper, we describe a novel workflow to model the geological heterogeneity of coastal aquifers and apply it to the Roussillon plain (southern France). The main strength of the workflow is its capability to model aquifer heterogeneity when only sparse data are available while honoring the local geological trends and quantifying uncertainty.
Daniel Erdal and Olaf A. Cirpka
Hydrol. Earth Syst. Sci., 24, 4567–4574, https://doi.org/10.5194/hess-24-4567-2020, https://doi.org/10.5194/hess-24-4567-2020, 2020
Short summary
Short summary
Assessing model sensitivities with ensemble-based methods can be prohibitively expensive when large parts of the plausible parameter space result in model simulations with nonrealistic results. In a previous work, we used the method of active subspaces to create a proxy model with the purpose of filtering out such unrealistic runs at low cost. This work details a notable improvement in the efficiency of the original sampling scheme, without loss of accuracy.
Christian Lehr and Gunnar Lischeid
Hydrol. Earth Syst. Sci., 24, 501–513, https://doi.org/10.5194/hess-24-501-2020, https://doi.org/10.5194/hess-24-501-2020, 2020
Short summary
Short summary
A screening method for the fast identification of well-specific peculiarities in hydrographs of groundwater head monitoring networks is suggested and tested. The only information required is a set of time series of groundwater head readings all measured at the same instants of time. The results were used to check the data for measurement errors and to identify wells with possible anthropogenic influence.
Ching-Fu Chang and Yoram Rubin
Hydrol. Earth Syst. Sci., 23, 2417–2438, https://doi.org/10.5194/hess-23-2417-2019, https://doi.org/10.5194/hess-23-2417-2019, 2019
Short summary
Short summary
Estimates of hydrologic responses at ungauged watersheds can be conditioned on information transferred from other gauged watersheds. This paper presents an approach to consider the variable controls on information transfer among watersheds under different conditions while at the same time featuring uncertainty representation in both the model structure and the model parameters.
Soumendra N. Bhanja, Abhijit Mukherjee, R. Rangarajan, Bridget R. Scanlon, Pragnaditya Malakar, and Shubha Verma
Hydrol. Earth Syst. Sci., 23, 711–722, https://doi.org/10.5194/hess-23-711-2019, https://doi.org/10.5194/hess-23-711-2019, 2019
Short summary
Short summary
Groundwater depletion in India has been a much-debated issue in recent years. Here we investigate long-term, spatiotemporal variation in prevailing groundwater recharge rates across India. Groundwater recharge rates have been estimated based on field-scale groundwater-level measurements and the tracer injection approach; recharge rates from the two estimates compared favorably. The role of precipitation in controlling groundwater recharge is studied.
Yoram Rubin, Ching-Fu Chang, Jiancong Chen, Karina Cucchi, Bradley Harken, Falk Heße, and Heather Savoy
Hydrol. Earth Syst. Sci., 22, 5675–5695, https://doi.org/10.5194/hess-22-5675-2018, https://doi.org/10.5194/hess-22-5675-2018, 2018
Short summary
Short summary
This paper addresses questions related to the adoption of stochastic methods in hydrogeology, looking at factors such as environmental regulations, financial incentives, higher education, and the collective feedback loop involving these factors. We show that stochastic hydrogeology's blind spot is in focusing on risk while ignoring uncertainty, to the detriment of its potential clients. The imbalance between the treatments of risk and uncertainty is shown to be common to multiple disciplines.
Adrian A. S. Barfod, Troels N. Vilhelmsen, Flemming Jørgensen, Anders V. Christiansen, Anne-Sophie Høyer, Julien Straubhaar, and Ingelise Møller
Hydrol. Earth Syst. Sci., 22, 5485–5508, https://doi.org/10.5194/hess-22-5485-2018, https://doi.org/10.5194/hess-22-5485-2018, 2018
Short summary
Short summary
The focus of this study is on the uncertainty related to using multiple-point statistics (MPS) for stochastic modeling of the upper 200 m of the subsurface. The main research goal is to showcase how MPS methods can be used on real-world hydrogeophysical data and show how the uncertainty related to changing the underlying MPS setup propagates into the finalized 3-D subsurface models.
Susanne A. Benz, Peter Bayer, Gerfried Winkler, and Philipp Blum
Hydrol. Earth Syst. Sci., 22, 3143–3154, https://doi.org/10.5194/hess-22-3143-2018, https://doi.org/10.5194/hess-22-3143-2018, 2018
Short summary
Short summary
Climate change is one of the most pressing challenges modern society faces. Increasing temperatures are observed both above ground and, as discussed here, in the groundwater – the source of most drinking water. Within Austria average temperature increased by 0.7 °C over the past 20 years, with an increase of more than 3 °C in some wells and temperature decrease in others. However, these extreme changes can be linked to local events such as the construction of a new drinking water supply.
Aronne Dell'Oca, Monica Riva, and Alberto Guadagnini
Hydrol. Earth Syst. Sci., 21, 6219–6234, https://doi.org/10.5194/hess-21-6219-2017, https://doi.org/10.5194/hess-21-6219-2017, 2017
Short summary
Short summary
We propose new metrics to assist global sensitivity analysis of Earth systems. Our approach allows assessing the impact of model parameters on the first four statistical moments of a target model output, allowing us to ascertain which parameters can affect some moments of the model output pdf while being uninfluential to others. Our approach is fully compatible with analysis in the context of model complexity reduction, design of experiment, uncertainty quantification and risk assessment.
Anne-Sophie Høyer, Giulio Vignoli, Thomas Mejer Hansen, Le Thanh Vu, Donald A. Keefer, and Flemming Jørgensen
Hydrol. Earth Syst. Sci., 21, 6069–6089, https://doi.org/10.5194/hess-21-6069-2017, https://doi.org/10.5194/hess-21-6069-2017, 2017
Short summary
Short summary
We present a novel approach for 3-D geostatistical simulations. It includes practical strategies for the development of realistic 3-D training images and for incorporating the diverse geological and geophysical inputs together with their uncertainty levels (due to measurement inaccuracies and scale mismatch). Inputs consist of well logs, seismics, and an existing 3-D geomodel. The simulation domain (45 million voxels) coincides with the Miocene unit over 2810 km2 across the Danish–German border.
Johannes Christoph Haas and Steffen Birk
Hydrol. Earth Syst. Sci., 21, 2421–2448, https://doi.org/10.5194/hess-21-2421-2017, https://doi.org/10.5194/hess-21-2421-2017, 2017
Short summary
Short summary
We show that the variability of groundwater levels within an Alpine river valley is more strongly affected by human impacts on rivers than by extreme events in precipitation. The influence of precipitation is found to be more pronounced in the shallow wells of the Alpine foreland. Groundwater levels, river stages and precipitation behave more similar under drought than under flood conditions and generally exhibit a tendency towards more similar behavior in the most recent decade.
Anne F. Van Loon, Rohini Kumar, and Vimal Mishra
Hydrol. Earth Syst. Sci., 21, 1947–1971, https://doi.org/10.5194/hess-21-1947-2017, https://doi.org/10.5194/hess-21-1947-2017, 2017
Short summary
Short summary
Summer 2015 was extremely dry in Europe, hampering groundwater supply to irrigation and drinking water. For effective management, the groundwater situation should be monitored in real time, but data are not available. We tested two methods to estimate groundwater in near-real time, based on satellite data and using the relationship between rainfall and historic groundwater levels. The second method gave a good spatially variable representation of the 2015 groundwater drought in Europe.
Lin Zhu, Huili Gong, Zhenxue Dai, Gaoxuan Guo, and Pietro Teatini
Hydrol. Earth Syst. Sci., 21, 721–733, https://doi.org/10.5194/hess-21-721-2017, https://doi.org/10.5194/hess-21-721-2017, 2017
Short summary
Short summary
We developed a method to characterize the distribution and variance of the hydraulic conductivity k in a multiple-zone alluvial fan by fusing multiple-source data. Consistently with the scales of the sedimentary transport energy, the k variance of the various facies decreases from the upper to the lower portion along the flow direction. The 3-D distribution of k is consistent with that of the facies. The potentialities of the proposed approach are tested on the Chaobai River megafan, China.
Boujemaa Ait-El-Fquih, Mohamad El Gharamti, and Ibrahim Hoteit
Hydrol. Earth Syst. Sci., 20, 3289–3307, https://doi.org/10.5194/hess-20-3289-2016, https://doi.org/10.5194/hess-20-3289-2016, 2016
Short summary
Short summary
We derive a new dual ensemble Kalman filter (EnKF) for state-parameter estimation. The derivation is based on the one-step-ahead smoothing formulation, and unlike the standard dual EnKF, it is consistent with the Bayesian formulation of the state-parameter estimation problem and uses the observations in both state smoothing and forecast. This is shown to enhance the performance and robustness of the dual EnKF in experiments conducted with a two-dimensional synthetic groundwater aquifer model.
Yabin Sun, Dadiyorto Wendi, Dong Eon Kim, and Shie-Yui Liong
Hydrol. Earth Syst. Sci., 20, 1405–1412, https://doi.org/10.5194/hess-20-1405-2016, https://doi.org/10.5194/hess-20-1405-2016, 2016
Short summary
Short summary
This study applies artificial neural networks (ANN) to predict the groundwater table variations in a tropical wetland in Singapore. Surrounding reservoir levels and rainfall are selected as ANN inputs. The limited number of inputs eliminates the data-demanding restrictions inherent in the physical-based numerical models. The forecast is made at 4 locations with 3 leading times up to 7 days. The ANN forecast shows promising accuracy with decreasing performance when leading time progresses.
J. P. Bloomfield, B. P. Marchant, S. H. Bricker, and R. B. Morgan
Hydrol. Earth Syst. Sci., 19, 4327–4344, https://doi.org/10.5194/hess-19-4327-2015, https://doi.org/10.5194/hess-19-4327-2015, 2015
Short summary
Short summary
To improve the design of drought monitoring networks and water resource management during episodes of drought, there is a need for a better understanding of spatial variations in the response of aquifers to major meteorological droughts. This paper is the first to describe a suite of methods to quantify such variations. Using an analysis of groundwater level data for a case study from the UK, the influence of catchment characteristics on the varied response of groundwater to droughts is explored
A. Guadagnini, S. P. Neuman, T. Nan, M. Riva, and C. L. Winter
Hydrol. Earth Syst. Sci., 19, 729–745, https://doi.org/10.5194/hess-19-729-2015, https://doi.org/10.5194/hess-19-729-2015, 2015
Short summary
Short summary
Previously we have shown that many earth-system and other variables can be viewed as samples from scale mixtures of truncated fractional Brownian motion or fractional Gaussian noise. Here we study statistical scaling of extreme absolute increments associated with such samples. As a real example we analyze neutron porosities from deep boreholes in diverse depositional units. Phenomena we uncover are relevant to the analysis of fluid flow and solute transport in complex hydrogeologic environments.
K. Menberg, P. Blum, B. L. Kurylyk, and P. Bayer
Hydrol. Earth Syst. Sci., 18, 4453–4466, https://doi.org/10.5194/hess-18-4453-2014, https://doi.org/10.5194/hess-18-4453-2014, 2014
X. L. He, T. O. Sonnenborg, F. Jørgensen, and K. H. Jensen
Hydrol. Earth Syst. Sci., 18, 2943–2954, https://doi.org/10.5194/hess-18-2943-2014, https://doi.org/10.5194/hess-18-2943-2014, 2014
W. Kurtz, H.-J. Hendricks Franssen, P. Brunner, and H. Vereecken
Hydrol. Earth Syst. Sci., 17, 3795–3813, https://doi.org/10.5194/hess-17-3795-2013, https://doi.org/10.5194/hess-17-3795-2013, 2013
C.-M. Chang and H.-D. Yeh
Hydrol. Earth Syst. Sci., 16, 4049–4055, https://doi.org/10.5194/hess-16-4049-2012, https://doi.org/10.5194/hess-16-4049-2012, 2012
A. Guadagnini, M. Riva, and S. P. Neuman
Hydrol. Earth Syst. Sci., 16, 3249–3260, https://doi.org/10.5194/hess-16-3249-2012, https://doi.org/10.5194/hess-16-3249-2012, 2012
L. Li, H. Zhou, H. J. Hendricks Franssen, and J. J. Gómez-Hernández
Hydrol. Earth Syst. Sci., 16, 573–590, https://doi.org/10.5194/hess-16-573-2012, https://doi.org/10.5194/hess-16-573-2012, 2012
M. Siena, A. Guadagnini, M. Riva, and S. P. Neuman
Hydrol. Earth Syst. Sci., 16, 29–42, https://doi.org/10.5194/hess-16-29-2012, https://doi.org/10.5194/hess-16-29-2012, 2012
C.-F. Ni, C.-P. Lin, S.-G. Li, and J.-S. Chen
Hydrol. Earth Syst. Sci., 15, 2291–2301, https://doi.org/10.5194/hess-15-2291-2011, https://doi.org/10.5194/hess-15-2291-2011, 2011
H. Murakami, X. Chen, M. S. Hahn, Y. Liu, M. L. Rockhold, V. R. Vermeul, J. M. Zachara, and Y. Rubin
Hydrol. Earth Syst. Sci., 14, 1989–2001, https://doi.org/10.5194/hess-14-1989-2010, https://doi.org/10.5194/hess-14-1989-2010, 2010
C.-M. Chang and H.-D. Yeh
Hydrol. Earth Syst. Sci., 14, 719–727, https://doi.org/10.5194/hess-14-719-2010, https://doi.org/10.5194/hess-14-719-2010, 2010
Cited articles
Ababou, R., Gelhar, L. W., and McLaughlin, D.: (1988), Three-dimensional flow in random porous media, Parsons Lab. Rep. 318, Mass. Inst. of Technol., Cambridge, 1988.
Anderson, M. P.: Heat as a ground water tracer, Ground Water, 43, 951–968, 2005.
Andričević, R.: Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers, Water Resour. Res., 34, 1115–1129, 1998.
Attinger, S., Dentz, M., and Kinzelbach, W.: Exact transverse macrodispersion coefficients for transport in heterogeneous porous media, Stochastic Environ. Res. Risk Assess., 18, 9–15, 2004.
Bear, J.: Dynamics of Fluids in Porous Media. New York: American Elsevier Publishing Company Inc., 1972.
Bellin, A. and Tonina, D.: Probability density function of nonreactive solute concentration in heterogeneous porous formations, J. Contam. Hydrol., 94, 109–125, https://doi.org/10.1016/j.jconhyd.2007.05.005, 2007.
Bonilla, F. A. and Cushman, J. H.: Role of boundary conditions in convergence and nonlocality of solutions to stochastic flow problems in bounded domains. Water Resour. Res., 36, 981–997, 2000.
Caroni, E. and Fiorotto, V.: Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59, 19–45, 2005.
Chang, C.-M. and Yeh, H.-D.: Large-time behavior of macrodispersion in heterogeneous trending aquifers, Water Resour. Res., 43, W11501, https://doi.org/10.1029/2007WR006017, 2007.
Cirpka, O. A. and Attinger, S.: Effective dispersion in heterogeneous media under random transient flow conditions, Water Resour. Res., 39, 1257, https://doi.org/10.1029/2002WR001931, 2003.
Cvetkovic, V., Cheng, H., and Wen, X.-H.: Analysis of nonlinear effects on tracer migration in heterogeneous aquifers using Lagrangian travel time statistics, Water Resour. Res., 32, 1671–1680, 1996.
Dagan, G.: Solute transport in heterogeneous porous formations, J. Fluid Mech., 145, 151–177, 1984.
Dagan, G.: Theory of solute transport by groundwater, Ann. Rev. Fluid Mech., 19, 183–215, 1987.
Dagan, G.: Flow and Transport in Porous Formations, Springer, New York, 1989.
Dagan, G.: Transport by two-dimensional random velocity fields: effective dispersion coefficients of a finite plume, in: Stochastic and Statistic Methods in Hydrology and Environmental Engineering vol. 2, edited by: Keith W. Hipel, 113–126, Kluwer Acad., Norwell, Mass., 1994.
Dagan, G. and Fiori, A.: The influence of pore-scale dispersion on concentration statistical moments in transport through heterogeneous aquifers, Water Resour. Res. 33, 1595–1606, 1997.
Dagan, G., Cvetkovic, V., and Shapiro, A.: A solute flux approach to transport in heterogeneous formations: 1. The general framework, Water Resour. Res., 28, 1369–1376, 1992.
de Marsily, G.: Quantitative Hydrogeology. San Diego, California: Academic Press, 1986.
Destouni, G., Simic, E., and Graham, W.: On the applicability of analytical methods for estimating solute travel time statistics in nonuniform groundwater flow, Water Resour. Res., 37, 2303–2308, 2001.
Fiori, A. and Dagan, G.: Concentration fluctuations in transport by groundwater: comparison between theory and field experiments, Water Resour. Res. 35, 105–112, 1999.
Fiorotto, V. and Caroni, E.: Solute concentration statistics in heterogeneous aquifers for finite Peclet values, Transport Porous Media, 48,331–351, 2002.
Geiger, S. and Emmanuel, S.: Non-Fourier thermal transport in fractured geological media, Water Resour. Res., 46, W07504, https://doi.org/10.1029/2009WR008671, 2010.
Gelhar, L. W. and Axness, C. L.: Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res., 19, 161–180, 1983.
Graham, W. and McLaughlin, D.: Stochastic analysis of nonstationary subsurface solute transport: 1. Unconditional moments, Water Resour. Res., 25, 215–232, 1989.
Guadagnini, A. and Neuman, S. P.: Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 1. Theory and computational approach, Water Resour. Res., 35, 2999–3018, 1999a.
Guadagnini, A. and Neuman, S. P.: Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly nonuniform domains: 2. Computational examples, Water Resour. Res., 35, 3019–3039, 1999b.
Guadagnini, A., Sánchez-Vila, X., Riva, M., and De Simoni, M.: Mean travel time of conservative solutes in randomly heterogeneous unbounded domains under mean uniform flow, Water Resour. Res., 39, 1050, https://doi.org/10.1029/2002WR001811, 2003.
Gutjahr, A. L. and Gelhar, L. W.: Stochastic models of subsurface flow: infinite versus finite domains and stationarity, Water Resour. Res., 17, 337–350, 1981.
Hopmans, J. W., Simunek, J., and Bristow, K. L.: Indirect estimation of soil thermal properties and water flux using heat pulse probe measurements: Geometry and dispersion effects, Water Resour. Res., 38, 7-1–7-13, 1006, https://doi.org/10.1029/2000WR000071, 2002.
Indelman, P. and Rubin, Y.: Solute transport in nonstationary velocity fields, Water Resour. Res., 32, 1259–1267, 1996.
Kabala, Z. J. and Sposito, G.: Statistical moments of reactive solute concentration in a heterogeneous aquifer, Water Resour. Res., 30, 759–768, 1994.
Kapoor, V. and Gelhar, L. W.: Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations, Water Resour. Res., 30, 1775–1788, 1994.
Kapoor, V. and Kitanidis, P. K.: Advection-diffusion in spatially random flows: Formulation of concentration covariance, Stochastic Hydrol. Hydraul. 11, 397–422, 1997.
Lo Russo, S. and Taddia, G.: Advective heat transport in an unconfined aquifer induced by the field injection of an open-loop groundwater heat pump, American Journal of Environmental Sciences, 6, 253–259, 2010
Morales-Casique, E., Neuman, S. P., and Guadagnini, A.: Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: Theoretical framework, Adv. Water Resour., 29, 1399–1418, 2006.
Naff, R. L. and Vecchia, A. V.: Stochastic analysis of three-dimensional flow in a bounded domain, Water Resour. Res., 22, 695–70, 1986.
Neuman, S. P.: Eulerian-langrangian theory of transport in spacetime nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation, Water Resour. Res., 29, 633–645, 1993.
Neuman, S. P. and Zhang, Y.-K.: A quasi-linear theory of non-Fickian and Fickian subsurface dispersion: 1. Theoretical analysis with application to isotropic media, Water Resour. Res., 26, 887–902, 1990.
Neuman, S. P., Winter, C. L., and Newman, C. M.: Stochastic theory of field-scale Fickian dispersion in anisotropic porous media, Water Resour. Res., 23, 453–466, 1987.
Neuweiler, I., Attinger, S., and Kinzelbach, W.: Macrodispersion in a Radially Diverging Flow Field with finite Peclet Numbers I: Perturbation Theory Approach, Water Resour. Res., 37, 481–494, 2001.
Rajaram, H. and Gelhar, L. W.: Plume-scale dependent dispersion in aquifers with a wide range of scales of heterogeneity, Water Resour. Res., 31, 2469–2482, 1995.
Rehfeldt, K. R. and Gelhar, L. W.: Stochastic analysis of dispersion in unsteady flow in heterogeneous aquifers, Water Resour. Res., 28, 2085–2099, 1992.
Riva, M., Guadagnini, A., Neuman, S. P., and Franzetti, S.: Radial flow in a bounded randomly heterogeneous aquifer, Transp. Porous Media, 45, 139–193, 2001
Rubin, Y.: Applied Stochastic Hydrogeology, New York, Oxford University Press, 2003.
Rubin, Y. and Dagan, G.: Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers. 1. Constant head boundary, Water Resour. Res., 24, 1689–1697, 1988.
Rubin, Y. and Dagan, G.: Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers. 2. Impervious boundary, Water Resour. Res., 25, 707–712, 1989.
Rubin, Y. and Seong, K.: Investigation of flow and transport in certain cases of nonstationary conductivity fields, Water Resour. Res., 30, 2901–2911, 1994.
Saar, M. O.: Review: Geothermal heat as a tracer of large-scale groundwater ?ow and as a means to determine permeability fields, Hydrogeol. J., 19, 31–52, 2010.
Schwede, R. L., Olaf, A., Nowak, W., and Neuweiler, I.: Impact of sampling volume on the probability density function of steady state concentration, Water Resour. Res., 44, W12433, https://doi.org/10.1029/2007WR006668, 2008.
Stopa, J. and Wojnarowski, P.: Analytical model of cold water front movement in a geothermal reservoir, Geothermics, 35, 59–69, 2006.
Taylor, G. I.: Diffusion by continuous movements, Proc. London Math. Soc., 20, 196–212, 1921.
Vomvoris, E. G. and Gelhar, L. W.: Stochastic analysis of the concentration variability in a three-dimensional heterogeneous aquifer, Water Resour. Res., 26, 2591–2602, 1990.
Zhang, D. and Winter, C. L.: Moment equation approach to single phase fluid flow in heterogeneous reservoirs, Soc. Petrol Eng. J., 4, 118–127, 1999.
Zhang, Y.-K. and Di Federico, V.: Solute transport in three-dimensional heterogeneous media with a Gaussian covariance of log hydraulic conductivity, Water Resour. Res., 34, 1929–1934, 1998.
