A computationally practical method for stochastic groundwater modeling

Li, Shu Guang; McLaughlin, Dennis K.; Liao, Hua Sheng

doi:10.1016/j.advwatres.2003.08.003

Cited by 27 publications

(24 citation statements)

References 26 publications

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“…Note that the assumption that products of fluctuations can be neglected can only be justified when the fluctuation variances of K in aquifers are very small (Dagan, 1989;Gelhar, 1993;Zhang, 2002;Li et al, 2003). Here the perturbations (i.e.…”

Section: Mean and Perturbation Equationsmentioning

confidence: 99%

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Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Lin

et al. 2011

Hydrol. Earth Syst. Sci.

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Abstract. This study presents a numerical first-order spectral model to quantify transient flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers. Taking advantages of spectral theories in solving unmodeled small-scale variability in hydraulic conductivity (K), the presented nonstationary spectral method (NSM) can efficiently estimate flow uncertainties, including hydraulic heads and Darcy velocities in r-and z-directions in a cylindrical coordinate system. The velocity uncertainties associated with the particle backward tracking algorithm are then used to estimate stochastic remediation zones for scenarios with partially opened well screens. In this study the flow and remediation zone uncertainties obtained by NSM were first compared with those obtained by Monte Carlo simulations (MCS). A layered aquifer with different geometric mean of K and screen locations was then illustrated with the developed NSM. To compare NSM flow and remediation zone uncertainties with those of MCS, three different small-scale K variances and correlation lengths were considered for illustration purpose. The MCS remediation zones for different degrees of heterogeneity were presented with the uncertainty clouds obtained by 200 equally likely MCS realizations. Results of simulations reveal that the first-order NSM solutions agree well with those of MCS for partially opened wells. The flow uncertainties obtained by using NSM and MCS show identically for aquifers with small ln K variances and correlation lengths. Based on the test examples, the remediation zone uncertainties (bandwidths) are not sensitive to the changes of small-scale ln K correlation lengths. However, the increases of remediation zone uncertainties (i.e. the Correspondence to: C.-F. Ni (nichuenfa@geo.ncu.edu.tw) uncertainty bandwidths) are significant with the increases of small-scale ln K variances. The largest displacement uncertainties may have several meters of differences when the ln K variances increase from 0.1 to 1.0. Such conclusions are also valid for the estimations of remediation zones in layered aquifers.

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Section: Mean and Perturbation Equationsmentioning

confidence: 99%

“…Discussions regarding to the limitations of MCS have been made in many previous studies (e.g. Neuman, 1999, Kunstmann andKinzelbach, 2000;Zhang, 2002, Feyen et al, 2003aBallio and Guadagnini, 2004;Dagan, 2004;Neuman, 2004;Li et al, 2003, 2004a, b, Ni and Li, 2005.…”

Section: Introductionmentioning

confidence: 97%

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Lin

et al. 2011

Hydrol. Earth Syst. Sci.

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“…Spectral methods offer a particularly convenient way to derive groundwater velocity statistics from linearized fluctuation equations such as (1) and (2) [1,4,[13][14][15]11,12]. Invoking the spectral representation in each subregion for the locally stationary log conductivity perturbation gives…”

Section: Spectral Solution In Composite Mediamentioning

confidence: 99%

“…2c representation theorem and solves numerically the full version of the linearized perturbation equation. Without having to make the ''local stationarity'' assumption and dropping the secondary terms (in the head perturbation equation), the nonstationary spectral approach allows accommodating exactly boundary conditions, spatially variable mean gradients, and other sources of nonstationarity [13][14][15]11,12].…”

Section: Illustration Examplesmentioning

confidence: 99%

“…These include, for example, Monte Carlo methods (e.g., [28,29,20,15]) and perturbation techniques, such as the moment equation methods (e.g., [5,38,33,17,34,37]) and the so called first-order second-moment methods based on Taylor's expansions (e.g., [30,35,2]). All of these methods, however, are computationally demanding when applied to flow and transport problems of realistic size, mostly because they all require solving large numbers of partial differential equations on very fine spatial discretizations in order to predict the impact of the small-scale heterogeneous dynamics (e.g., [5,4,15,11,12]). …”

Section: Introductionmentioning

confidence: 99%

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Modeling groundwater velocity uncertainty in nonstationary composite porous media

Ni¹,

Li²

2006

Advances in Water Resources

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Prediction and uncertainty analysis of a parsimonious floodplain surface water‐groundwater interaction model

Maier

Kraft

2017

Water Resources Research

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Floodplains provide a variety of hydrological and ecological functions and are therefore of great importance. The flooding frequency, as well as the height and duration of inundations are particularly relevant for ecosystem states and are dependent on the exchange between surface water and groundwater. In this study, we developed a fully distributed model approach to simulate distributed groundwater levels in a floodplain in Hesse, Germany (14.8 km2). To overcome the problem of large computation times, we simplified the surface water equation. Thus, the water surface of flooding is at the same level everywhere and the dynamic effect of the flooding is ignored. In this way, it was possible to run the model 5000 times and investigate its parameter uncertainty using Latin hypercube sampling. Behavioral model runs were selected based on a threshold criterion of a mean root‐mean‐square error that was smaller than 0.26 m. All the simulated groundwater wells show an individual RMSE between 0.17 and 0.41 m for the calibration period. Regarding the parameterization, the model shows rather large variance in parameters that are capable of generating good simulations: a range of saturated conductivity of 2793 m/d, porosity of 0.4 m3/m3, residual wetness of soil of 0.2 m3/m3/soil and range of soil thickness of 2.9 m.

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A computationally practical method for stochastic groundwater modeling

Cited by 27 publications

References 26 publications

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Modeling groundwater velocity uncertainty in nonstationary composite porous media

Prediction and uncertainty analysis of a parsimonious floodplain surface water‐groundwater interaction model

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