Can Parameter Estimation Be Improved by Optimizing Data Use and Analysis?

Monday, April 12, 2010: 12:05 p.m.
Tabor Auditorium (Westin Tabor Center, Denver)
Otto Strack Sr., Ph., D. , Civil Engineering, University of MInnesota, Minneapolis, MN
Randal J. Barnes, Ph.D. , Civil Engineering, University of MInnesota, Minneapolis, MN
Bonnie Ausk , Civil Engineering, University of MInnesota, Minneapolis, MN
The objective of this paper is to examine whether current parameter estimation techniques may be improved by examining inverse modeling analyses published over the past sixty years. Inverse modeling concerns the mathematical problem of solving for aquifer parameters; e.g., Pasquier and Marcotte (2007) consider transient three-dimensional flow in a single aquifer. The mathematical problem concerns, for isotropic hydraulic conductivity, a first-order partial differential equation in terms of the hydraulic conductivity. The solution to the inverse problem requires that the field of piezometric heads be fully known throughout the domain to such an extent, that the first and second-order partial derivatives of the piezometric heads can be assumed to be accurate and the value of either discharge or hydraulic conductivity be known at one point per streamline. The hydraulic conductivity can then be computed at all points of that streamline. Conditions in real aquifers rarely meet the requirements of inverse modeling; these methods, although mathematically precise and well-defined, have limited use in practice. We will adhere to the convention to differentiate between "parameter estimation" and "inverse modeling". Parameter estimation is the process that is commonly applied to a numerical model, such as MODFLOW, using a package for parameter estimation, such as PEST. We investigate whether lessons learned from the inverse modeling approaches can be applied to parameter estimation. We pose the question whether the trend to increase the number of observations to define an increasingly detailed pattern of transmissivity values improves models, or, whether better results are obtained by limiting the number of parameters, and by optimizing the use of data available, and, finally, what can realistically be expected in terms of reliable results in parameter estimation. We discuss various such issues, and illustrate some ideas with examples.