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AGU: Water Resources Research

 

Keywords

  • probabilistic collocation method
  • unsaturated flow
  • stochastic modeling
  • random fields

Index Terms

  • Hydrology: Computational hydrology
  • Hydrology: Stochastic hydrology
  • Hydrology: Uncertainty assessment
  • Hydrology: Vadose zone

Abstract

WATER RESOURCES RESEARCH, VOL. 45, W08425, 13 PP., 2009
doi:10.1029/2008WR007530

Stochastic analysis of unsaturated flow with probabilistic collocation method

Weixuan Li

Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing, China

Zhiming Lu

Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

Dongxiao Zhang

Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing, China

In this study, we present an efficient approach, called the probabilistic collocation method (PCM), for uncertainty analysis of flow in unsaturated zones, in which the constitutive relationship between the pressure head and the unsaturated conductivity is assumed to follow the van Genuchten-Mualem model. Spatial variability of soil parameters leads to uncertainty in predicting flow behaviors. The aim is to quantify the uncertainty associated with flow quantities such as the pressure head and the effective saturation. In the proposed approach, input random fields, i.e., the soil parameters, are represented via the Karhunen-Loeve expansion, and the flow quantities are expressed by polynomial chaos expansions (PCEs). The coefficients in the PCEs are determined by solving the equations for a set of carefully selected collocation points in the probability space. To illustrate this approach, we use two-dimensional examples with different input variances and correlation scales and under steady state and transient conditions. We also demonstrate how to deal with multiple-input random parameters. To validate the PCM, we compare the resulting mean and variance of the flow quantities with those from Monte Carlo (MC) simulations. The comparison reveals that the PCM can accurately estimate the flow statistics with a much smaller computational effort than the MC.

Received 18 October 2008; accepted 27 May 2009; published 18 August 2009.

Citation: Li, W., Z. Lu, and D. Zhang (2009), Stochastic analysis of unsaturated flow with probabilistic collocation method, Water Resour. Res., 45, W08425, doi:10.1029/2008WR007530.

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