### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy(all)

### Cite this

*Journal of Computational Physics*,

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

**Multivariate sensitivity analysis of saturated flow through simulated highly heterogeneous groundwater aquifers.** / Winter, C Larrabee; Guadagnini, A.; Nychka, D.; Tartakovsky, D. M.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 217, no. 1, pp. 166-175. https://doi.org/10.1016/j.jcp.2006.01.047

}

TY - JOUR

T1 - Multivariate sensitivity analysis of saturated flow through simulated highly heterogeneous groundwater aquifers

AU - Winter, C Larrabee

AU - Guadagnini, A.

AU - Nychka, D.

AU - Tartakovsky, D. M.

PY - 2006/9/1

Y1 - 2006/9/1

N2 - 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.

AB - 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.

KW - Groundwater flow

KW - Parametric uncertainty

KW - Sensitivity analysis

KW - Stochastic partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=33746325151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746325151&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2006.01.047

DO - 10.1016/j.jcp.2006.01.047

M3 - Article

AN - SCOPUS:33746325151

VL - 217

SP - 166

EP - 175

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -