Articles | Volume 24, issue 6
https://doi.org/10.5194/hess-24-3097-2020
© Author(s) 2020. 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-24-3097-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
16 Jun 2020
Research article |
| 16 Jun 2020
| 16 Jun 2020
Interpretation of multi-scale permeability data through an information theory perspective
Aronne Dell'Oca
CORRESPONDING AUTHOR
Department of Civil and Environmental Engineering, Politecnico di Milano, 20133, Milan, Italy
Alberto Guadagnini
Department of Civil and Environmental Engineering, Politecnico di Milano, 20133, Milan, Italy
Monica Riva
Department of Civil and Environmental Engineering, Politecnico di Milano, 20133, Milan, Italy
Related authors
David Luttenauer, Aronne Dell'Oca, Alberto Guadagnini, Sylvain Weill, and Philippe Ackerer
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-73, https://doi.org/10.5194/hess-2024-73, 2024
Preprint under review for HESS
Short summary
Short summary
Land Surface Model outputs (evaporation, transpiration, groundwater recharge) are influenced by uncertain parameters. Global sensitivity metrics provide a ranking of the importance of uncertain factors. Evaporation is directly influenced by the net radiation and by the parameters associated with the top litter layer. Transpiration appears as mainly influenced by the vegetation characteristics and by albedo. Groundwater recharge is influenced mainly by soil-related parameters.
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.
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.
Stefano Conversi, Daniela Carrion, Francesco Gioia, Alessandra Norcini, and Monica Riva
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVIII-4-W12-2024, 19–27, https://doi.org/10.5194/isprs-archives-XLVIII-4-W12-2024-19-2024, https://doi.org/10.5194/isprs-archives-XLVIII-4-W12-2024-19-2024, 2024
David Luttenauer, Aronne Dell'Oca, Alberto Guadagnini, Sylvain Weill, and Philippe Ackerer
Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2024-73, https://doi.org/10.5194/hess-2024-73, 2024
Preprint under review for HESS
Short summary
Short summary
Land Surface Model outputs (evaporation, transpiration, groundwater recharge) are influenced by uncertain parameters. Global sensitivity metrics provide a ranking of the importance of uncertain factors. Evaporation is directly influenced by the net radiation and by the parameters associated with the top litter layer. Transpiration appears as mainly influenced by the vegetation characteristics and by albedo. Groundwater recharge is influenced mainly by soil-related parameters.
S. Conversi, D. Carrion, A. Norcini, and M. Riva
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLVIII-1-W2-2023, 1363–1371, https://doi.org/10.5194/isprs-archives-XLVIII-1-W2-2023-1363-2023, https://doi.org/10.5194/isprs-archives-XLVIII-1-W2-2023-1363-2023, 2023
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
Short summary
Short summary
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.
Giulia Ceriotti, Claudio Geloni, Matilde Dalla Rosa, Alberto Guadagnini, and Giovanni Porta
Hydrol. Earth Syst. Sci., 25, 3539–3553, https://doi.org/10.5194/hess-25-3539-2021, https://doi.org/10.5194/hess-25-3539-2021, 2021
Short summary
Short summary
Understanding the natural generation of CO2 in sedimentary basins is key to optimizing exploitation of natural resources and exploring feasibility of carbon capture and storage. We present a novel modeling approach to estimate the probability of CO2 generation caused by geochemical reactions at high temperatures and pressure in realistic sedimentary basins. Our model allows estimation of the most probable CO2 source depth and generation rate as a function of the composition of the source rock.
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.
Martina Siena and Monica Riva
Hydrol. Earth Syst. Sci., 22, 2971–2985, https://doi.org/10.5194/hess-22-2971-2018, https://doi.org/10.5194/hess-22-2971-2018, 2018
Short summary
Short summary
The development of sustainable strategies for groundwater resources exploitation in coastal regions is subordinated to the characterization of seawater intrusion (SWI) phenomena. We develop a numerical model tailored to a real coastal aquifer to investigate quantitatively the joint effects of hydraulic properties heterogeneity and pumping configuration on saltwater inland penetration and saltwater–freshwater mixing. Our results allowed identifying efficient scenarios for the reduction of SWI.
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.
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.
M. Riva, S. P. Neuman, and A. Guadagnini
Nonlin. Processes Geophys., 20, 549–561, https://doi.org/10.5194/npg-20-549-2013, https://doi.org/10.5194/npg-20-549-2013, 2013
Related subject area
Subject: Groundwater hydrology | Techniques and Approaches: Uncertainty analysis
Data-driven estimates for the geostatistical characterization of subsurface hydraulic properties
Hierarchical sensitivity analysis for a large-scale process-based hydrological model applied to an Amazonian watershed
Spatially distributed sensitivity of simulated global groundwater heads and flows to hydraulic conductivity, groundwater recharge, and surface water body parameterization
Multi-model approach to quantify groundwater-level prediction uncertainty using an ensemble of global climate models and multiple abstraction scenarios
Influence of input and parameter uncertainty on the prediction of catchment-scale groundwater travel time distributions
Numerical modeling and sensitivity analysis of seawater intrusion in a dual-permeability coastal karst aquifer with conduit networks
On the efficiency of the hybrid and the exact second-order sampling formulations of the EnKF: a reality-inspired 3-D test case for estimating biodegradation rates of chlorinated hydrocarbons at the port of Rotterdam
Testing alternative uses of electromagnetic data to reduce the prediction error of groundwater models
Groundwater flow processes and mixing in active volcanic systems: the case of Guadalajara (Mexico)
Analyses of uncertainties and scaling of groundwater level fluctuations
Analyzing the effects of geological and parameter uncertainty on prediction of groundwater head and travel time
Interpolation of groundwater quality parameters with some values below the detection limit
An approach to identify urban groundwater recharge
Assessment of conceptual model uncertainty for the regional aquifer Pampa del Tamarugal – North Chile
Falk Heße, Sebastian Müller, and Sabine Attinger
Hydrol. Earth Syst. Sci., 28, 357–374, https://doi.org/10.5194/hess-28-357-2024, https://doi.org/10.5194/hess-28-357-2024, 2024
Short summary
Short summary
In this study, we have presented two different advances for the field of subsurface geostatistics. First, we present data of variogram functions from a variety of different locations around the world. Second, we present a series of geostatistical analyses aimed at examining some of the statistical properties of such variogram functions and their relationship to a number of widely used variogram model functions.
Haifan Liu, Heng Dai, Jie Niu, Bill X. Hu, Dongwei Gui, Han Qiu, Ming Ye, Xingyuan Chen, Chuanhao Wu, Jin Zhang, and William Riley
Hydrol. Earth Syst. Sci., 24, 4971–4996, https://doi.org/10.5194/hess-24-4971-2020, https://doi.org/10.5194/hess-24-4971-2020, 2020
Short summary
Short summary
It is still challenging to apply the quantitative and comprehensive global sensitivity analysis method to complex large-scale process-based hydrological models because of variant uncertainty sources and high computational cost. This work developed a new tool and demonstrate its implementation to a pilot example for comprehensive global sensitivity analysis of large-scale hydrological modelling. This method is mathematically rigorous and can be applied to other large-scale hydrological models.
Robert Reinecke, Laura Foglia, Steffen Mehl, Jonathan D. Herman, Alexander Wachholz, Tim Trautmann, and Petra Döll
Hydrol. Earth Syst. Sci., 23, 4561–4582, https://doi.org/10.5194/hess-23-4561-2019, https://doi.org/10.5194/hess-23-4561-2019, 2019
Short summary
Short summary
Recently, the first global groundwater models were developed to better understand surface-water–groundwater interactions and human water use impacts. However, the reliability of model outputs is limited by a lack of data as well as model assumptions required due to the necessarily coarse spatial resolution. In this study we present the first global maps of model sensitivity according to their parameterization and build a foundation to improve datasets, model design, and model understanding.
Syed M. Touhidul Mustafa, M. Moudud Hasan, Ajoy Kumar Saha, Rahena Parvin Rannu, Els Van Uytven, Patrick Willems, and Marijke Huysmans
Hydrol. Earth Syst. Sci., 23, 2279–2303, https://doi.org/10.5194/hess-23-2279-2019, https://doi.org/10.5194/hess-23-2279-2019, 2019
Short summary
Short summary
This study evaluates the effect of conceptual hydro(geo)logical model (CHM) structure, climate change and groundwater abstraction on future groundwater-level prediction uncertainty. If the current groundwater abstraction trend continues, groundwater level is predicted to decline quickly. Groundwater abstraction in NW Bangladesh should decrease by 60 % to ensure sustainable use. Abstraction scenarios are the dominant uncertainty source, followed by CHM uncertainty and climate model uncertainty.
Miao Jing, Falk Heße, Rohini Kumar, Olaf Kolditz, Thomas Kalbacher, and Sabine Attinger
Hydrol. Earth Syst. Sci., 23, 171–190, https://doi.org/10.5194/hess-23-171-2019, https://doi.org/10.5194/hess-23-171-2019, 2019
Short summary
Short summary
We evaluated the uncertainty propagation from the inputs (forcings) and parameters to the predictions of groundwater travel time distributions (TTDs) using a fully distributed numerical model (mHM-OGS) and the StorAge Selection (SAS) function. Through detailed numerical and analytical investigations, we emphasize the key role of recharge estimation in the reliable predictions of TTDs and the good interpretability of the SAS function.
Zexuan Xu, Bill X. Hu, and Ming Ye
Hydrol. Earth Syst. Sci., 22, 221–239, https://doi.org/10.5194/hess-22-221-2018, https://doi.org/10.5194/hess-22-221-2018, 2018
Short summary
Short summary
This study helps hydrologists better understand the parameters in modeling seawater intrusion in a coastal karst aquifer. Local and global sensitivity studies are conducted to evaluate a density-dependent numerical model of seawater intrusion. The sensitivity analysis indicates that karst features are critical for seawater intrusion modeling, and the evaluation of hydraulic conductivity is biased in continuum SEAWAT model. Dispervisity is no longer important in the advection-dominated aquifer.
Mohamad E. Gharamti, Johan Valstar, Gijs Janssen, Annemieke Marsman, and Ibrahim Hoteit
Hydrol. Earth Syst. Sci., 20, 4561–4583, https://doi.org/10.5194/hess-20-4561-2016, https://doi.org/10.5194/hess-20-4561-2016, 2016
Short summary
Short summary
The paper addresses the issue of sampling errors when using the ensemble Kalman filter, in particular its hybrid and second-order formulations. The presented work is aimed at estimating concentration and biodegradation rates of subsurface contaminants at the port of Rotterdam in the Netherlands. Overall, we found that accounting for both forecast and observation sampling errors in the joint data assimilation system helps recover more accurate state and parameter estimates.
Nikolaj Kruse Christensen, Steen Christensen, and Ty Paul A. Ferre
Hydrol. Earth Syst. Sci., 20, 1925–1946, https://doi.org/10.5194/hess-20-1925-2016, https://doi.org/10.5194/hess-20-1925-2016, 2016
Short summary
Short summary
Our primary objective in this study is to provide a virtual environment that allows users to determine the value of geophysical data and, furthermore, to investigate how best to use those data to develop groundwater models and to reduce their prediction errors. When this has been carried through for alternative data sampling, parameterization and inversion approaches, the best alternative can be chosen by comparison of prediction results between the alternatives.
A. Hernández-Antonio, J. Mahlknecht, C. Tamez-Meléndez, J. Ramos-Leal, A. Ramírez-Orozco, R. Parra, N. Ornelas-Soto, and C. J. Eastoe
Hydrol. Earth Syst. Sci., 19, 3937–3950, https://doi.org/10.5194/hess-19-3937-2015, https://doi.org/10.5194/hess-19-3937-2015, 2015
Short summary
Short summary
A conceptual model of groundwater flow processes and mixing was developed using a combination of hydrogeochemistry, isotopes and multivariate analysis. The implementation to the case of Guadalajara showed that groundwater was classified into four groups: cold groundwater, hydrothermal water, polluted groundwater and mixed groundwater. A multivariate mixing model was used to calculate the proportion of different fluids in sampled well water. The result helps authorities in decision making.
X. Y. Liang and Y.-K. Zhang
Hydrol. Earth Syst. Sci., 19, 2971–2979, https://doi.org/10.5194/hess-19-2971-2015, https://doi.org/10.5194/hess-19-2971-2015, 2015
Short summary
Short summary
The error or uncertainty in head, obtained with an analytical or numerical solution, at an early time is mainly caused by the random initial condition. The error reduces with time, later reaching a constant error. The constant error at a later time is mainly due to the effects of the uncertain source/sink. The error caused by the uncertain boundary is limited to a narrow zone. Temporal scaling of head exists in most parts of a low permeable aquifer, mainly caused by recharge fluctuation.
X. He, T. O. Sonnenborg, F. Jørgensen, A.-S. Høyer, R. R. Møller, and K. H. Jensen
Hydrol. Earth Syst. Sci., 17, 3245–3260, https://doi.org/10.5194/hess-17-3245-2013, https://doi.org/10.5194/hess-17-3245-2013, 2013
A. Bárdossy
Hydrol. Earth Syst. Sci., 15, 2763–2775, https://doi.org/10.5194/hess-15-2763-2011, https://doi.org/10.5194/hess-15-2763-2011, 2011
E. Vázquez-Suñé, J. Carrera, I. Tubau, X. Sánchez-Vila, and A. Soler
Hydrol. Earth Syst. Sci., 14, 2085–2097, https://doi.org/10.5194/hess-14-2085-2010, https://doi.org/10.5194/hess-14-2085-2010, 2010
R. Rojas, O. Batelaan, L. Feyen, and A. Dassargues
Hydrol. Earth Syst. Sci., 14, 171–192, https://doi.org/10.5194/hess-14-171-2010, https://doi.org/10.5194/hess-14-171-2010, 2010
Cited articles
Andersson, J. E., Ekman, L., Gustafsson, E., Nordqvist, R., and Tiren, S.:
Hydraulic interference tests and tracer tests within the Brändöan area, Finnsjon study site, the fracture zone project-Phase 3, Technical Report 89-12, Sweden Nuclear Fuel and Waste Management Company, Stockholm, 1988.
Attinger, S.: Generalized coarse graining procedures for flow in porous
media, Comput. Geosci., 7, 253–273, https://doi.org/10.1023/B:COMG.0000005243.73381.e3, 2003.
Barahona-Palomo, M., Riva, M., Sanchez-Vila, X., Vazquez-Sune, E., and
Guadagnini, A.: Quantitative comparison of impeller flowmeter and particle-size distribution techniques for the characterization of hydraulic
conductivity variability, Hydrogeol. J., 19, 603–612,
https://doi.org/10.1007/s10040-011-0706-5, 2011.
Beckie, R.: A comparison of methods to determine measurement support
volumes, Water Resour. Res., 37, 925–936, https://doi.org/10.1029/2000WR900366, 2001.
Bertschinger, N., Rauh, J., Olbrich, E., Jost, J., and Ay, N.: Quantifying
unique information, Entropy, 16, 2161–2183, https://doi.org/10.3390/e16042161, 2014.
Bianchi, M. and Pedretti, D.: Geological entropy and solute transport in
heterogeneous porous media, Water Resour. Res., 53, 4691–4708,
https://doi.org/10.1002/2016WR020195, 2017.
Bianchi, M. and Pedretti, D.: An entrogram-based approach to describe spatial heterogeneity with applications to solute transport in porous media, Water Resour. Res., 54, 4432–4448, https://doi.org/10.1029/2018WR022827, 2018.
Boso, F. and Tartakovsky, D. M.: Information-theoretic approach to bidirectional scaling, Water Resour. Res., 54, 4916–4928,
https://doi.org/10.1029/2017WR021993, 2018.
Brace, W. F.: Permeability of crystalline rocks: New in situ measurements, J. Geophys. Res., 89, 4327–4330, https://doi.org/10.1029/JB089iB06p04327, 1984.
Butera, I., Vallivero, L., and Rodolfi, L.: Mutual information analysis to
approach nonlinearity in groundwater stochastic fields, Stoch. Environ. Res.
Risk Assess., 32, 2933–2942, https://doi.org/10.1007/s00477-018-1591-4, 2018.
Cintoli, S., Neuman, S. P., and Di Federico, V.: Generating and scaling
fractional Brownian motion on finite domains, Geophys. Res. Lett., 32, 925–936, https://doi.org/10.1029/2005GL022608, 2005
Clauser, C.: Permeability of crystalline rocks, Eos Trans. AGU, 73, 233–238, 1992.
Cover, T. M. and Thomas, J. A.: Elements of Information Theory, John Wiley,
Hoboken, NJ, 2006.
Dausse, A., Leonardi, V., and Jourde, H.: Hydraulic characterization and
identification of flow-bearing structures based on multiscale investigations
applied to the Lez karst aquifer, J. Hydrol.: Reg. Stud., 26, 100627,
https://doi.org/10.1016/j.ejrh.2019.100627, 2019.
Dell'Oca, A.: Berea Permeabilities, available at: https://data.mendeley.com/datasets/ygcgv32nw5/1, last access:
26 August 2019.
Deutsch, C. V. and Journel, A. G.: Integrating well test derived effective
absolute conductivities in geostatistical reservoir modeling, in: Stochastic
Modeling and Geostatistics: Principles, Methods and Case Studies, AAPG Computer Applications in Geology, No. 3, edited by: Yarus, J. and Chambers, R., Amer. Assoc. of Petrol. Geol., Tulsa, 131–142, 1994.
Dykaar, B. B. and Kitanidis, P. K.: Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 1. Methods, Water Resour. Res., 28, 1155–1166, https://doi.org/10.1029/91WR03084, 1992a.
Dykaar, B. B. and Kitanidis, P. K.: Determination of the effective hydraulic conductivity for heterogeneous porous media using a numerical spectral approach, 2. Results, Water Resour. Res., 28, 1167–1178, https://doi.org/10.1029/91WR03083, 1992b.
Galvão, P., Halihan, T., and Hirata, R.: The karst permeability scale
effect of Sete Lagos, MG, Brazil, J. Hydrol., 532, 149–162, https://doi.org/10.1016/j.jhydrol.2015.11.026, 2016.
Goggin, D. J., Thrasher, R. L., and Lake, L. W.: A theoretical and experimental analysis of minipermeameter response including gas slippage and
high velocity flow effects, In Situ, 12, 79–116, 1988.
Gong, W., Gupta, H. V., Yang, D., Sricharan, K., and Hero III, A. O.:
Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach, Water Resour. Res., 49, 2253–2273,
https://doi.org/10.1002/wrcr.20161, 2013.
Gong, W., Yang, D., Gupta, H. V., and Nearing, G.: Estimating information
entropy for hydrological data: One-dimensional case, Water Resour. Res., 50, 5003–5018, https://doi.org/10.1002/2014WR015874, 2014.
Goodwell, A. E. and Kumar, P.: Temporal information partitioning: Characterizing synergy, uniqueness, and redundancy in interacting environmental variables, Water Resour. Res., 53, 5920–5942, https://doi.org/10.1002/2016WR020216, 2017.
Gotovac, H., Cvetkovic, V., and Andrievic, R.: Significance of higher moments for complete characterization of the travel time probability density function in heterogeneous porous media using the maximum entropy principle, Water Resour. Res., 46, W05502, https://doi.org/10.1029/2009WR008220, 2010.
Griffith, V. and Ho, T.: Quantifying redundant information in predicting a
target random variable, Entropy, 17, 4644–4653, https://doi.org/10.3390/e17074644, 2015.
Griffith, V. and Koch, C.: Quantifying synergistic mutual information,
Guided Self-Organization: Inception, edited by: Prokopenko, Springer-Verlag, Berlin, Germany, 159–190, 2014.
Guadagnini, A., Neuman, S. P., Schaap, M. G., and Riva, M.: Anisotropic
statistical scaling of vadose zone hydraulic property estimates near Maricopa, Arizona, Water Resour. Res., 49, 1–17, https://doi.org/10.1002/2013WR014286,
2013.
Guadagnini, A., Riva, M., and Neuman, S. P.: Recent advances in scalable
non-Gaussian geostatistics: the generalized sub-Gaussian model, J. Hydrol.,
562, 685–691, https://doi.org/10.1016/j.jhydrol.2018.05.001, 2018.
Guzman, A., Neuman, S. P., Lohrstorfer, C., and Bassett, R. L.: Validation studies for assessing flow and transport through unsaturated fractured rocks, in: Rep. NUREG/CR-6203, chap. 4, edited by: Bassett, R. L., Neuman, S. P., Rasmussen, T. C., Guzman, A., Davidson, G. R., and Lohrstorfer, C. E., US Nuclear Regulatory Commission, Washington, D.C., 1994.
Guzman, A. G., Geddis, A. M., Henrich, M. J., Lohrstorfer, C. F., and Neuman, S. P.: Summary of air permeability data from single-hole injection tests in unsaturated fractured tuffs at the Apache Leap research site: Results of steady state test interpretation, Rep. NUREG/CR-6360, US Nuclear Regulatory Commission, Washington, D.C., 1996.
Harder, M., Salge, C., and Polani, D.: Bivariate measure of redundant
information, Phys. Rev. E, 87, 012130, https://doi.org/10.1103/PhysRevE.87.012130, 2013.
Harvey, C. F.: Interpreting parameter estimates obtained from slug tests in
heterogeneous aquifers, MS thesis, Appl. Earth Science Department, Stanford University, Stanford, 1992.
Hyun, Y., Neuman, S. P., Vesselinov, V. V., Illman, W. A., Tartakovsky, D. M., and Di Federico, V.: Theoretical interpretation of a pronounced permeability scale effect in unsaturated fractured tuff, Water Resour. Res.,
38, 1092, https://doi.org/10.1029/2001WR000658, 2002.
Illman, W. A.: Analysis of permeability scaling within single boreholes, Geophys. Res. Lett., 31, L06503, https://doi.org/10.1029/2003GL019303, 2004.
Kaiser, A. and Schreiber, T.: Information transfer in continuous processes, Physica D, 166, 43–62, https://doi.org/10.1016/S0167-2789(02)00432-3, 2002.
Kitanidis, P. K.: The concept of the dilution index, Water Resour. Res., 30, 2011–2016, https://doi.org/10.1029/94WR00762, 1994.
Loritz, R., Gupta, H., Jackisch, C., Westhoff, M., Kleidon, A., Ehret, U., and Zehe, E.: On the dynamic nature of hydrological similarity, Hydrol. Earth Syst. Sci., 22, 3663–3684, https://doi.org/10.5194/hess-22-3663-2018, 2018.
Lowry, T. S. and Tidwell, V. C.: Investigation of permeability upscaling
experiments using deterministic modeling and monte carlo analysis, in: World Water and Environmental Resources Congress 2005, 15–19 May 2005, Anchorage,
Alaska, USA, https://doi.org/10.1061/40792(173)372, 2005.
Mälicke, M., Hassler, S. K., Blume, T., Weiler, M., and Zehe, E.: Soil moisture: variable in space but redundant in time, Hydrol. Earth Syst. Sci., 24, 2633–2653, https://doi.org/10.5194/hess-24-2633-2020, 2020.
Maréchal, J. C., Dewandel, B., and Subrahmanyam, K.: Use of hydraulic
tests at different scales to characterize fracture network properties in the
weathered-fractured layer of a hard rock aquifer, Water Resour. Res., 40,
W11508, https://doi.org/10.1029/2004WR003137, 2004.
Medici, G., West, L. J., and Mountney, N. P.: Characterization of a fluvial
aquifer at a range of depths and scales: the Triassic St. Bees sandstone
formation, Cumbria, UK, Hydrogelog. J., 26, 565–591, https://doi.org/10.1007/s10040-017-1676-z, 2018.
Menafoglio, A., Guadagnini, A., and Secchi, P.: A Class-Kriging predictor for functional compositions with application to particle-size curves in
heterogeneous aquifers, Math. Geosci., 48, 463–485, https://doi.org/10.1007/s11004-015-9625-7, 2016.
Mishra, S., Deeds, N., and Ruskauff, G.: Global sensitivity analysis techniques for probabilistic ground water modeling, Ground Water, 47, 730–747, https://doi.org/10.1111/j.1745-6584.2009.00604.x, 2009.
Molz, F., Dinwiddie, C. L., and Wilson, J. L.: A physical basis for calculating instrument spatial weighting functions in homogeneous systems,
Water Resour. Res., 39, 1096, https://doi.org/10.1029/2001WR001220, 2003.
Nearing, G. S., Ruddell, B. J., Clark, P. M., Nijssen, B., and Peters-Lidard, C. D.: Benchmarking and process diagnostic of land models, J. Hydrometeorol., 19, 1835–1852, https://doi.org/10.1175/JHM-D-17-0209.1, 2018.
Neuman, S. P.: Generalized scaling of permeabilities: Validation and effect of support scale, Geophys. Res. Lett., 21, 349–352, https://doi.org/10.1029/94GL00308, 1994.
Neuman, S. P. and Di Federico, V.: Multifaceted nature of hydrogeologic scaling and its interpretation, Rev. Geophys., 41, 1014, https://doi.org/10.1029/2003RG000130, 2003.
Neuman, S. P., Riva, M., and Guadagnini, A.: On the geostatistical characterization of hierarchical media, Water Resour. Res., 44, W02403,
https://doi.org/10.1029/2007WR006228, 2008.
Nowak, W. and Guthke, A.: Entropy-based experimental design for optimal model discrimination in the geosciences, Entropy, 18, 409, https://doi.org/10.3390/e18110409, 2016.
Olbrich, E., Bertschinger, N., and Rauh, J.: Information decomposition and
synergy, Entropy, 11, 3501–3517, https://doi.org/10.3390/e17053501, 2015.
Oliver, D. S.: The averaging process in permeability estimation from well-test data, SPE Form Eval., 5, 319–324, https://doi.org/10.2118/19845-PA, 1990.
Paillet, P. L.: Analysis of geophysical well logs and flowmeter measurements
in borehole penetrating subhorizontal fracture zones, Lac du Bonnet Batholith, Manitoba, Canada, Water-Resources investigation report 89, US Geological Survey, Lakewood, Colorado, 30 pp., 1989.
Pavelic, P., Dillon, P., and Simmons, C. T.: Multiscale characterization of
a heterogeneous aquifer using an ASR operation, Ground Water, 44, 155–164, https://doi.org/10.1111/j.1745-6584.2005.00135.x, 2006.
Quinn, P., Cherry, J. A., and Parker, B. L.: Hydraulic testing using a versatile straddle packer system for improved transmissivity estimation in
fractured-rock boreholes, Hydrogeol. J., 20, 1529–1547, 2012.
Riva, M., Neuman, S. P., Guadagnini, A., and Siena, S.: Anisotropic scaling of Berea sandstone log air permeability statistics, Vadose Zone J., 12, 1–15, https://doi.org/10.2136/vzj2012.0153, 2013.
Rovey, C. W. and Cherkauer, D. S.: Scale dependency of hydraulic conductivity measurements, Ground Water, 33, 769–780, https://doi.org/10.1111/j.1745-6584.1995.tb00023.x, 1995.
Ruddell, B. L. and Kumar, P.: Ecohydrologic process networks: 1. Identification, Water Resour. Res., 45, W03419, https://doi.org/10.1029/2008WR007279, 2009.
Sanchez-Vila, X., Carrera, J., and Girardi, J. P.: Scale effects in
transmissivity, J. Hydrol., 183, 1–22, https://doi.org/10.1016/S0022-1694(96)80031-X, 1996.
Schad, H. and Teutsch, G.: Effects of the investigation scale on pumping test results in heterogeneous porous aquifers, J. Hydrol., 159, 61–77,
https://doi.org/10.1016/0022-1694(94)90249-6, 1994.
Schulze-Makuch, D. and Cherkauer, D. S.: Variations in hydraulic conductivity with scale of measurements during aquifer tests in heterogenous, porous carbonate rock, Hydrogeol. J., 6, 204–215, https://doi.org/10.1007/s100400050145, 1998.
Schulze-Makuch, D., Carlson, D. A., Cherkauer, D. S., and Malik, P.: Scale
dependency of hydraulic conductivity in heterogeneous media, Ground Water,
37, 904–919, https://doi.org/10.1111/j.1745-6584.1999.tb01190.x, 1999.
Shannon, C.: A mathematical theory of communication, Bell Syst. Tech. J.,
27, 379–423, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x, 1948.
Shapiro, A. M., Ladderud, J. A., and Yager, R. M.: Interpretation of hydraulic conductivity in a fractured-rock aquifer over increasingly larger
length dimensions, Hydrogeol. J., 23, 1319–1339, https://doi.org/10.1007/s10040-015-1285-7, 2015.
Siena, M., Guadagnini, A., Riva, M., and Neuman, S. P.: Extended power-law
scaling of air permeabilities measured on a block of tuff, Hydrol. Earth Syst. Sci., 16, 29–42, https://doi.org/10.5194/hess-16-29-2012, 2012.
Stone, J. V.: Information Theory: A Tutorial Introduction, Sebtel Press,
preprint: arXiv:1802.05968, 2015.
Tartakovsky, D. M., Moulton, J. D., and Zlotnik, V. A.: Kinematic structure of minipermeameter flow, Water Resour. Res., 36, 2433–2442,
https://doi.org/10.1029/2000WR900178, 2000.
Tidwell, V. C. and Wilson, J. L.: Laboratory method for investigating
permeability upscaling, Water Resour. Res., 33, 1607–1616,
https://doi.org/10.1029/97WR00804, 1997.
Tidwell, V. C. and Wilson, J. L.: Permeability upscaling measured on a block of Berea Sandstone: Results and interpretation, Math. Geol., 31, 749–769, https://doi.org/10.1023/A:1007568632217, 1999a.
Tidwell, V. C. and Wilson, J. L.: Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution, Water Resour. Res., 35, 3375–3387, https://doi.org/10.1029/1999WR900161, 1999b.
Tidwell, V. C. and Wilson, J. L.: Heterogeneity, permeability patterns, and
permeability upscaling: Physical characterization of a block of Massillon
Sandstone exhibiting nested scales of heterogeneity, SPE Reser. Eval. Eng., 3, 283–291, https://doi.org/10.2118/65282-PA, 2000.
Tidwell, V. C. and Wilson, J. L.: Visual attributes of a rock and their
relationship to permeability: A comparison of digital image and minipermeameter data, Water Resour. Res., 38, 1261, https://doi.org/10.1029/2001WR000932, 2002.
Vesselinov, V. V., Neuman, S. P., and Illman, W. A.: Three-dimensional numerical inversion of pneumatic cross-hole tests in unsaturated fractured
tuff: 1. Methodology and borehole effects, Water Resour. Res., 37, 3001–3018, https://doi.org/10.1029/2000WR000133, 2001a.
Vesselinov, V. V., Neuman, S. P., and Illman, W. A.: Three-dimensional numerical inversion of pneumatic cross-hole tests in unsaturated fractured
tuff: 2. Equivalent parameters, high-resolution stochastic imaging and scale
effects, Water Resour. Res., 37, 3019–3042, https://doi.org/10.1029/2000WR000135, 2001b.
Wellman, F. J. and Regenaur-Lieb, K.: Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models, Tectonophysics, 526–529, 207–216, https://doi.org/10.1016/j.tecto.2011.05.001, 2012.
Wellman, F. J.: Information theory for correlation analysis and estimation of uncertainty reduction in maps and models, Entropy, 15, 1464–1485,
https://doi.org/10.3390/e15041464, 2013.
Williams, P. L. and Beer, R. D.: Nonnegative decomposition of multivariate
information, CoRR, available at: http://arxiv.org/abs/1004.2515, last access: 14 April 2010.
Winter, C. L. and Tartakovsky, D. M.: Theoretical foundation for conductivity scaling, Geophys. Res. Lett., 28, 4367–4369, https://doi.org/10.1029/2001GL013680, 2001.
Woodbury, A. D. and Ulrych, T. J.: Minimum relative entropy: forward probabilistic modeling, Water Resour. Res., 29, 2847–2860, https://doi.org/10.1029/93WR00923, 1993.
Woodbury, A. D. and Ulrych, T. J.: Minimum relative entropy inversion: theory and application to recovering the release history of a groundwater contaminant, Water Resour. Res. 32, 2671–2681, https://doi.org/10.1029/95WR03818, 1996.
Woodbury, A. D. and Ulrych, T. J.: A full-Bayesian approach to the groundwater inverse problem for steady state flow, Water Resour. Res., 36,
2081–2093, https://doi.org/10.1029/2000WR900086, 2000.
Zeng, X. K., Wan, D., and Wu, J. C.: Sensitivity analysis of the probability
distribution of groundwater level series based on information entropy, Stoch. Environ. Res. Risk. Assess., 26, 345–356, https://doi.org/10.1007/s00477-012-0556-2, 2012.
Zhang, D. and Winter, C. L.: Theory, modeling and field investigation in Hydrogeology: A special volume in honor of Shlomo P. Neuman's 60th birthday, Special paper, Geological Society of America, Boulder, Colorado, 2000.
Zlotnik, V. A., Zurbuchen, B. R., Ptak, T., and Teutsch, G.: Support volume
and scale effect in hydraulic conductivity: experimental aspects, in: Theory, Modeling, and Field Investigation in Hydrogeology: A Special Volume in Honor of Shlomo P. Neuman's 60th Birthday, Geological Society of America Special Paper 348, edited by: Zhang, D. and Winter, C. L., Geological Society of America, Boulder, CO, 191–213, 2000.
Short summary
Permeability of natural systems exhibits heterogeneous spatial variations linked with the size of the measurement support scale. As the latter becomes coarser, the system appearance is less heterogeneous. As such, sets of permeability data associated with differing support scales provide diverse amounts of information. In this contribution, we leverage information theory to quantify the information content of gas permeability datasets collected with four diverse measurement support scales.
Permeability of natural systems exhibits heterogeneous spatial variations linked with the size...
