## Estimation of Groundwater Flow Parameters Using Least Squares (1996)

Venue: | North Carolina State University, Center for |

Citations: | 2 - 0 self |

### BibTeX

@TECHREPORT{Bailey96estimationof,

author = {K. R. Bailey and B. G. Fitzpatrick},

title = {Estimation of Groundwater Flow Parameters Using Least Squares},

institution = {North Carolina State University, Center for},

year = {1996}

}

### OpenURL

### Abstract

In this paper, we present several variations on the least squares approach of estimating steady state flow parameters in a groundwater model. We test the approach on numerically generated data, and also apply it to field data from the MADE (MAcro Dispersion Experiment) data set obtained at Columbus AFB, Mississippi. Our results are based on a least squares cost functional with a finite difference scheme used to solve the steady state flow equation (Darcy's Law). An implicit filtering optimization algorithm is implemented in parallel using PVM. 1 Introduction The successful modeling of groundwater flow in an aquifer has numerous applications. It is a crucial first step in any quantitative analysis of groundwater contaminant transport, and would provide an invaluable tool for the field of water resource management. Given such a tool, site characterization, monitoring, and clean up could be conducted more efficiently. The most difficult aspect of getting quantitative information about th...

### Citations

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Dynamics of Fluids in Porous Media
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(Show Context)
Citation Context ...on Darcy's emperical law for fluid flow through a porous media. This states that ~v = \GammaK ~ rh; (2) which, when combined with incompressibility and conservation of mass yields (1). The references =-=[4, 1]-=- provide a detailed discussion of the Darcy model. To compute the velocity using (2), we need to know K and g in order to solve (1) for h. The coefficient, K, and the boundary values, g, must be estim... |

146 |
GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems
- Saad, Schultz
- 1986
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Citation Context ...alues, i and j ranging from 1 to nx \Gamma 1 and 1 to ny \Gamma 1 respectively. The vector ~g depends on the boundary values. To solve this problem, we apply a matrix free GMRES iterative solver (see =-=[10]-=-). Once we have a solution at the mesh points in hand, we use bilinear interpolation within mesh points to evaluate the function h at the data points, x h i . This allows computation of the cost funct... |

114 | Partial differential equations - Wloka - 1987 |

53 | An implicit filtering algorithm for optimization of functions with many local minima
- Gilmore, Kelley
- 1995
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Citation Context ...a_2) L curve for Beta_2 beta2 = 0.8 beta2 = 2.0 beta2 = 1.3 beta2 = 0.5 beta2 = 0.3 beta2 = 0.05 Figure 2: Lcurve for fi 2 The optimization routine IFFCO was used to minimize the cost functional (see =-=[6, 7]-=-). The code was modified to compute the gradient, rJ , in parallel. We used PVM (Parallel Virtual Machine) for message passing primitives on a cluster of six IBM 390's (see [5]). IFFCO uses centered d... |

39 |
Field study of dispersion in a heterogeneous aquifer. 3: Geostatistical analysis of hydraulic conductivity
- Rehfeldt, Boggs, et al.
- 1992
(Show Context)
Citation Context ...istributed fashion about the domain of interest. The second is a measurement of average hydraulic conductivity within "small" regions. These are based on the borehole flowmeter measurment de=-=vice (see [8, 9]). We say -=-"small" here since the size of these regions may be similar to the size of a coffee can while our model region is on the order of 100; 000 ft 3 . Since the measurement regions are small comp... |

10 |
IFFCO (Implicit Filtering For Constrained Optimization); software available at http://www4.ncsu.edu/˜ctk/iffco.html
- Gilmore, Choi, et al.
(Show Context)
Citation Context ...a_2) L curve for Beta_2 beta2 = 0.8 beta2 = 2.0 beta2 = 1.3 beta2 = 0.5 beta2 = 0.3 beta2 = 0.05 Figure 2: Lcurve for fi 2 The optimization routine IFFCO was used to minimize the cost functional (see =-=[6, 7]-=-). The code was modified to compute the gradient, rJ , in parallel. We used PVM (Parallel Virtual Machine) for message passing primitives on a cluster of six IBM 390's (see [5]). IFFCO uses centered d... |

9 |
Well Posedness and Convergence of Some Regularisation Methods for Non-linear
- Seidman, Vogel
- 1989
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Citation Context ... constraints directly in the minimization, we addd penalty terms to the least squares cost. These penalty terms for both K and g impose an implicit compactness constraint and avoid ill-posedness (see =-=[11]-=-). For example, since the data for hydraulic conductivity is unevenly distributed, the subdomains with no data point would not contribute to the cost functional and there would be no way to determine ... |

7 |
Database for the second macrodispersion experiment
- Boggs, Beard, et al.
- 1993
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Citation Context ...ic head was measured in both "shallow" and "deep" ranges (not precisely reported), while hydraulic conductivity was taken at several (known) vertical points in each multilevel bore=-=hole flowmeter (see [2]-=-). We restricted ourselves to a two dimensional model of a horizontally oriented rectangular domain, D 1 , see figure (1). Two approaches were taken with the data. Since the domain is much longer and ... |

2 | Parameter Estimation in Groundwater Flow Models with Distributed and Pointwise Observations
- Fitzpatrick, Jeffris
- 1994
(Show Context)
Citation Context ...y to balance the two quantities (which vary by orders of magnitude depending on the units of measure used). For theoretical considerations concerning the solution of (1), and minimization of (3), see =-=[3]-=-, and the references therein. A crucial component of any problem of function estimation is compactness. In order to minimize (3) in a way that is stable with respect to perturbations in the data, we m... |