Stochastic modeling of complex nonstationary groundwater systems

Li, Shu Guang; Liao, Hua Sheng; Ni, Chuen-Fa

doi:10.1016/j.advwatres.2004.08.002

Cited by 20 publications

(13 citation statements)

References 34 publications

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“…The distribution of the head variance exhibited high variation at the inlet boundary and the head variance gradually decreased to a small value at the outlet boundary (Figures 12a and b). This was an interesting result because the behavior was different from cases in heterogeneous porous media, which showed similar head variations near inlet and outlet boundaries (Li et al, 2004;Li, 2005, 2006). We believed that the extremely high head variations near DFN inlet boundary could be induced by the generated DFN realizations.…”

Section: Transport Model Verificationmentioning

confidence: 89%

Stochastic modeling of flow and conservative transport in threedimensional discrete fracture networks

Lee¹,

Ni²,

Lin³

et al. 2018

Preprint

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Section: Transport Model Verificationmentioning

confidence: 89%

Stochastic modeling of flow and conservative transport in threedimensional discrete fracture networks

Lee¹,

Ni²,

Lin³

et al. 2018

Preprint

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“…The variations in the head calculated by the general perturbation method are the same as those calculated using the method proposed in this study. In the meantime, the corresponding values of ψ all must be positive in Equation (22), because only in this case, the general perturbation method calculated results will be the same with the computational result of Equation (25), which suggests that the general perturbation method has a close relationship with the proposed method. …”

Section: Scenario Onementioning

confidence: 97%

“…The Taylor expansion or perturbation expansion method often involves the inversion of a large coefficient matrix, which could be computationally expensive. In addition, several investigators have studied the random theory using other methods [23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Groundwater Flow Determination Using an Interval Parameter Perturbation Method

Dong

Tian

Zhan

et al. 2017

Water

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Abstract:Groundwater flow simulation often inevitably involves uncertainty, which has been quantified by a host of methods including stochastic methods and statistical methods. Stochastic methods and statistical methods face great difficulties in applications. One of such difficulties is that the statistical characteristics of random variables (such as mean, variance, covariance, etc.) must be firstly obtained before the stochastic methods can be applied. The dilemma is that one is often unclear about such statistical characteristics, given the limited available data.To overcome the problems met by stochastic methods, this study provides an innovative approach in which the hydrogeological parameters and sources and sinks of groundwater flow are represented by bounded but uncertain intervals of variables called interval of uncertainty variables (IUVs) and this approach is namely the interval uncertain method (IUM). IUM requires only the maximum and minimum values of the variable. By utilizing the natural interval expansion, an interval-based parametric groundwater flow equation is established, and the solution of that equation can be found. Using a hypothetical steady-state flow case as an example, one can see that when the rate of change is less than 0.2, the relative error of this method is generally limited to less than 5%; when the rate of change is less than 0.3, the relative error of this method can be kept within 10%. This research shows that the proposed method has smaller relative errors and higher computational efficiency than the Monte Carlo methods. It is possible to use this method to analyze the uncertainties of groundwater flow when it is difficult to obtain the statistical characteristics of the hydrogeological systems. The proposed method is applicable in linear groundwater flow system. Its validity in nonlinear flow systems such as variably saturated flow or unconfined flow with considerable variation of water table will be checked in the future.

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“…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%

Modeling groundwater velocity uncertainty in nonstationary composite porous media

Ni¹,

Li²

2006

Advances in Water Resources

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Stochastic modeling of complex nonstationary groundwater systems

Cited by 20 publications

References 34 publications

Stochastic modeling of flow and conservative transport in threedimensional discrete fracture networks

Stochastic modeling of flow and conservative transport in threedimensional discrete fracture networks

Groundwater Flow Determination Using an Interval Parameter Perturbation Method

Modeling groundwater velocity uncertainty in nonstationary composite porous media

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