### Abstract

A multivariate Analysis of Variance (ANOVA) is used to measure the relative sensitivity of groundwater flow to two factors that indicate different dimensions of aquifer heterogeneity. An aquifer is modeled as the union of disjoint volumes, or blocks, composed of different materials with different hydraulic conductivities. The factors are correlation between the hydraulic conductivities of the different materials and the contrast between mean conductivities in the different materials. The precise values of aquifer properties are usually uncertain because they are only sparsely sampled, yet are highly heterogeneous. Hence, the spatial distribution of blocks and the distribution of materials in blocks are uncertain and are modeled as stochastic processes. The ANOVA is performed on a large sample of Monte Carlo simulations of a simple model flow system composed of two materials distributed within three disjoint blocks. Our key finding is that simulated flow is much more sensitive to the contrast between mean conductivities of the blocks than it is to the intensity of correlation, although both factors are statistically significant. The methodology of the experiment - ANOVA performed on Monte Carlo simulations of a multi-material flow system - constitutes the basis of additional studies of more complicated interactions between factors that define flow and transport in aquifers with uncertain properties.

Original language | English (US) |
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Pages (from-to) | 166-175 |

Number of pages | 10 |

Journal | Journal of Computational Physics |

Volume | 217 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2006 |

Externally published | Yes |

### Keywords

- Groundwater flow
- Parametric uncertainty
- Sensitivity analysis
- Stochastic partial differential equations

### ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computational Physics*,

*217*(1), 166-175. https://doi.org/10.1016/j.jcp.2006.01.047