Analysis of the Spatial Structure of Properties of Selected Aquifers

Hoeksema, Robert J.; Kitanidis, Peter K.

doi:10.1029/wr021i004p00563

Cited by 399 publications

(216 citation statements)

References 24 publications

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“…However, recent analyses of hydraulic conductivity data (Bakr, 1976;Byers and Stephens, 1983;and Hoeksema and Kitanidis, 1985) showed that although the hydraulic conductivity values vary significantly in space, the variation is not entirely random, but correlated in space. Such a correlated nature implies that the parameter values are not statistically independent in space and they must be treated as a stochastic process, instead of a single random variable.…”

Section: Statistical Representation Of Heterogeneitymentioning

confidence: 99%

“…For instance, Law (1944) and Bennion and Griffiths (1966) reported that the distribution of porosity data in an aquifer is normal. Hoeksema and Kitanidis (1985) suggested that the spatial distribution of storage coefficient may be log-normal. Hydraulic conductivity distributions (Figure 2) are usually reported to be log-normal (Law, 1944;Bulness, 1946;Warren et al, 1961;Bakr, 1976;Freeze, 1975;and Sudicky, 1986) or other (Jensen et al, 1987).…”

Section: Statistical Representation Of Heterogeneitymentioning

confidence: 99%

“…The approach was based on the inverse method developed by Kitanidis and Vomvoris (1983) and Hoeksema and Kitanidis (1985) which involves estimating the average, yet spatially variable, hydraulic conductivity field using both hydraulic conductivity and head measurements. Then, conditional realizations with the same degree of variability as the observed hydraulic conductivity fields are generated and used as input to a solute transport model to obtain solute distributions.…”

Section: Conditional Simulationmentioning

confidence: 99%

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Stochastic modelling of groundwater flow and solute transport in aquifers

Yeh

1992

Hydrological Processes

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Section: Statistical Representation Of Heterogeneitymentioning

confidence: 99%

Section: Statistical Representation Of Heterogeneitymentioning

confidence: 99%

Section: Conditional Simulationmentioning

confidence: 99%

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Stochastic modelling of groundwater flow and solute transport in aquifers

Yeh

1992

Hydrological Processes

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“…Farthing et al [22] presented results for di↵erent porous media scenarios by using di↵erent types of sands. It has been shown [11,29,48] that although the permeability values can exhibit large spatial variations, these variations are not entirely random but spatially correlated. Previously, such fields have been modelled using a log-normal distribution assumption [39].…”

Section: Letmentioning

confidence: 99%

“…For modelling the correlation of Z, i.e., expression (21), we use the following exponential covariance function [29,54,14,13]:…”

Section: Generation Of Random Permeability Fieldsmentioning

confidence: 99%

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Crevillén-García

Wilkinson

Shah

et al. 2017

Advances in Water Resources

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(2017) Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media. Advances in Water Resources, 99 . pp. 1-14. Permanent WRAP URL:http://wrap.warwick.ac.uk/85680 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractNumerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.

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Optimal designs for variogram estimation

Müller

Zimmerman

1999

Environmetrics

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SUMMARYThe variogram plays a central role in the analysis of geostatistical data. A valid variogram model is selected and the parameters of that model are estimated before kriging (spatial prediction) is performed. These inference procedures are generally based upon examination of the empirical variogram, which consists of average squared dierences of data taken at sites lagged the same distance apart in the same direction. The ability of the analyst to estimate variogram parameters eciently is aected signi®cantly by the sampling design, i.e. the spatial con®guration of sites where measurements are taken. In this paper, we propose design criteria that, in contrast to some previously proposed criteria oriented towards kriging with a known variogram, emphasize the accurate estimation of the variogram. These criteria are modi®cations of design criteria that are popular in the context of (nonlinear) regression models. The two main distinguishing features of the present context are that the addition of a single site to the design produces as many new lags as there are existing sites and hence also produces many new squared dierences from which the variogram is estimated. Secondly, those squared dierences are generally correlated, which inhibits the use of many standard design methods that rest upon the assumption of uncorrelated errors. Several approaches to design construction which account for these features are described and illustrated with two examples. We compare their eciency to simple random sampling and regular and space-®lling designs and ®nd considerable improvements.

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Analysis of the Spatial Structure of Properties of Selected Aquifers

Cited by 399 publications

References 24 publications

Stochastic modelling of groundwater flow and solute transport in aquifers

Stochastic modelling of groundwater flow and solute transport in aquifers

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Optimal designs for variogram estimation

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