Identification of parameters in a linear equation of groundwater flow

Abstract

An inductive method is presented for evaluating parameters in a two-dimensional linear equation describing groundwater flow. The approach employs finite difference approximations, which can be simply programed for calculation by computer. Before illustrating the method, which is applicable to both stationary and time-dependent problems, the various types of data required for evaluation in general are systematically enumerated. An assumption is introduced limiting the local variability of T, the transmissivity, and its relation to apparently similar assumptions used elsewhere is discussed. The particular aquifer chosen for illustration is the chalk of the South Downs between the rivers Adur and Ouse. The parameters are calculated on the basis of cyclic data in which annual abstraction is about 30% of the total infiltration for the year. The method gives a match to the minimum and maximum water levels during the year to within 7%.

Calculation of aquifer parameters from sparse data

“…Cooley and Sinclair [1976] have stated that normal methods of contouring data manually also tend to smooth out permeability contrasts. In addition, experience with the direct solution proposed by Nutbrown [1975] has shown that the predicted values of transmissivity and storage coefficient are generally realistic but that discretization of boundary conditions such as occur at streams and leaky rivers is particularly difficult and may lead to unreasonable values of the computed aquifer properties. Neuman [1975] has shown that measured hydraulic heads rarely satisfy the assumed flow equation, which usually includes Depuit's assumption, and that employment of direct methods with an inadequate flow equation can induce errors in the computed aquifer parameters which overshadow their true values.…”

A method for estimating recharge and boundary flux from groundwater level observations / Méthode pour estimer la recharge des nappes souterraines et le flux aux limites à partir de l'observation du niveau des eaux souterraines

“…This coastal aquifer is typical of many encountered in semiarid regions in that recharge is restricted to known localized areas and although variable, follows a cyclical pattern. This last condition often allows a steady state formulation to be used (Nutbrown, 1975) and, in the case of the method described here, leads to estimates of the average recharge given average water levels.…”

“…The method outlined in this paper is particularly applicable to those semiarid regions where recharge, although variable, follows a cyclical pattern thus allowing a steady state formulation (Nutbrown, 1975) . The partial differential equation describing steady state groundwater flow can be approximated by a set of simultaneous equations with recharge as the dependent variable, water levels as the independent variable and the parameter of transmissivity as the coefficient matrix linking the two.…”

“…Considerable research has been undertaken into estimating the parameters of transmissivity and storage coefficient in deterministic groundwater models (Emsellem & de Marsily, 1971;Kleinecke, 1971;Cole, 1973;Nutbrown, 1975;Garay et al, 1976;Cooley, 1977 and1979;Smith & Piper, 1978;and others). Much less research has been directed to the equally important problem of estimating recharge and boundary fluxes.…”

Numerical identification of a spatially varying diffusion coefficient

“…Nelson [5] has devised a method for integrating the homogeneous version of (1) (i.e.,/ = 0) along its characteristics, and Frind and Pinder [3] have developed a finite element Galerkin technique. A finite difference approach has also been proposed by Nutbrown [6].…”