A method of estimating parameters and assessing reliability for models of steady state groundwater flow: 1. Theory and numerical properties

Abstract

A new nonlinear least squares solution for the Hydrogeologic parameters, sources and sinks, and boundary fluxes contained in the equations approximately governing two‐dimensional or radial steady state groundwater motion was developed through use of a linearization and iteration procedure applied to the finite element discretization of the problem. Techniques involving (1) use of an iteration parameter to interpolate or extrapolate the changes in computed parameters and head distribution at each iteration and (2) conditioning of the least squares coefficient matrix through use of ridge regression techniques were proven to induce convergence of the procedure for virtually all problems. Because of the regression nature of the solution for the parameter estimation problem, classical methods of regression analysis are promising as an aid to establishing approximate reliability of computed parameters and predicted values of hydraulic head. Care must be taken not to compute so many parameters that the stability of the estimates is destroyed. Reduction of the error variance by adding parameters is desirable provided that the number of degrees of freedom for error remains large.

The minimum structure solution to the inverse problem

“…One of the earliest applications was given by Jahns [1966]. In groundwater hydrology a well-known approach is the nonlinear regression method [Cooley, 1977]. In 2263…”

“…One of the earliest applications was given by Jahns [1966]. In groundwater hydrology a well-known approach is the nonlinear regression method [Cooley, 1977] In applications, it is desirable to achieve the maximum resolution of log conductivity that is possible consistent with the mathematical model. For example, in a finite element formulation it is preferable to allow every element to have a different log conductivity; in analytical formulations that involve no discretization, one may view log conductivity as a function defined over the domain occupied by the formation, which in an intuitive sense is equivalent to a vector with infinite entries (i.e., mathematically speaking, a function is a point in a Hilbert space the same way that a vector is a point in a Euclidean space).…”

Geohydrological studies for nuclear waste isolation at the Hanford Reservation. Volume II. Final report

“…uncertainty in hydrological. models hae been considered by Freeze (975); Tang and Pinder (1977); Cooley (1977);Ge1har (1974);McMillan (1966), Neuman et a1. (1976);and Warren (1961).…”

Hydrogeology and simulation of water flow in strata above the Bearpaw Shale and equivalents of eastern Montana and northeastern Wyoming

“…Values of the array factor were perturbed by a small amount and the system's response was observed. The application of these techniques to the analysis of ground-water systems has been discussed by Draper and Smith (1966), Cooley (1977), and Durbin (1978) and has been documented by Garabedian (1984). Garabedian applied a finitedifference based parameter-estimation model to the Snake River plain aquifer.…”