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Title: Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ

Abstract

Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scale $$\eta^*$$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. We demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.

Authors:
 [1]; ORCiD logo [2];  [3]; ORCiD logo [2]
  1. Computational Mathematics Group, Pacific Northwest National Laboratory, Richland WA USA
  2. Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milano Italy
  3. Hydrology Group, Pacific Northwest National Laboratory, Richland WA USA
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1430446
Report Number(s):
PNNL-SA-114624
Journal ID: ISSN 0043-1397; KJ0401000
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Water Resources Research; Journal Volume: 53; Journal Issue: 11
Country of Publication:
United States
Language:
English
Subject:
scale-depent analysis; uncertainty quantification; moment equations

Citation Formats

Tartakovsky, A. M., Panzeri, M., Tartakovsky, G. D., and Guadagnini, A. Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ. United States: N. p., 2017. Web. doi:10.1002/2017WR020905.
Tartakovsky, A. M., Panzeri, M., Tartakovsky, G. D., & Guadagnini, A. Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ. United States. doi:10.1002/2017WR020905.
Tartakovsky, A. M., Panzeri, M., Tartakovsky, G. D., and Guadagnini, A. Wed . "Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ". United States. doi:10.1002/2017WR020905.
@article{osti_1430446,
title = {Uncertainty Quantification in Scale-Dependent Models of Flow in Porous Media: SCALE-DEPENDENT UQ},
author = {Tartakovsky, A. M. and Panzeri, M. and Tartakovsky, G. D. and Guadagnini, A.},
abstractNote = {Equations governing flow and transport in heterogeneous porous media are scale-dependent. We demonstrate that it is possible to identify a support scale $\eta^*$, such that the typically employed approximate formulations of Moment Equations (ME) yield accurate (statistical) moments of a target environmental state variable. Under these circumstances, the ME approach can be used as an alternative to the Monte Carlo (MC) method for Uncertainty Quantification in diverse fields of Earth and environmental sciences. MEs are directly satisfied by the leading moments of the quantities of interest and are defined on the same support scale as the governing stochastic partial differential equations (PDEs). Computable approximations of the otherwise exact MEs can be obtained through perturbation expansion of moments of the state variables in orders of the standard deviation of the random model parameters. As such, their convergence is guaranteed only for the standard deviation smaller than one. We demonstrate our approach in the context of steady-state groundwater flow in a porous medium with a spatially random hydraulic conductivity.},
doi = {10.1002/2017WR020905},
journal = {Water Resources Research},
number = 11,
volume = 53,
place = {United States},
year = {Wed Nov 01 00:00:00 EDT 2017},
month = {Wed Nov 01 00:00:00 EDT 2017}
}