The paper by Gorelick et al. [1983] on the identification of groundwater pollution sources most certainly addresses a significant contemporary hydrologic problem. The approach that they describe could find application in detection of inputs to surface water systems as well as in detection of sources of groundwater pollution. Indeed, approaches similar to their steady state conservative model have been used recently in slightly different contexts.Woolhiser et al. [1979, 1982] developed a technique to estimate multiple inflows to a stream reach based on a quadratic programming solution to find the unknown inflow quantities that minimized the sum of squares of normalized errors for up to eight ion balance equations, subject to a water balance constraint and a nonnegativity constraint. They used Monte Carlo techniques to investigate the sensitivity of the solution to errors in the chemical analyses and stream flow measurements. Chemical element balances (CEB's) have also been used to identify sources of particulates for many elements which can be associated with specific types of air pollution sources [Kowalczyk et al., 1982]. According to the CEB model, the composition of particles at a receptor is a linear combination of concentration patterns of particles from contributing sources. Kowalczyk et al. [1982] determined source strength coefficients by a least squares fit to the observed concentrations of several "marker elements." Tsurumi [1982] utilized the multiple ion balance approach to estimate not only the relative proportions of sources present in a mixture but also the ranges of chemical composition of the sources of chemical constituents. His method requires several mixtures of the source waters at different proportions and uses an iterative least squares solution. The source compositions are also subject to an anion-cation balance constraint.The objective of all of these techniques is to select a subset of sources, from the set of physically feasible sources, which results in simulated concentrations representing the best match with a sample. "Best" is, of course, defined in terms of the objective function and imposed constraints. The works cited above can be viewed as extensions of earlier works in which it was assumed that stream water or groundwater is a mixture of solutions derived from different steady state origins, with no loss of dissolved species occurring before or after mixing [Piper, 1944;Pinder and Jones, 1969;Visocky, 1970;Hall, 1970; Sklash et al., 1976]. Previous works, however, have considered only models of complete mixing in a lumped system and have considered only conservative substances. Thus, the approach of Gorelick et al. This paper is not subject to U.S. copyright. Published in 1984 by the American Geophysical Union. Paper number 4W0423.[1983] is novel because it introduces a method to treat a distributed system by incorporating a groundwater solute transport model and a nonconservative tracer. The transient case had also not been considered previously.Although Gorelick et al. [198...

A mathematical model is developed describing moisture removal from soil by the roots of transpiring plants. The model uses a macroscopic extraction term in the one‐dimensional soil moisture flow equation. It describes both moisture removal by the plant and induced moisture movement through the soil. A numerical procedure based on the Douglas‐Jones predictor‐corrector method is used to solve the model, and solutions are compared with experimental data. The results indicate that extraction term models are computationally and physically feasible and give insight into the mechanics of the overall moisture extraction process.

An approximate numerical method to solve transient two‐dimensional unsaturated‐saturated subsurface flow problems is presented. Several one‐dimensional vertical unsaturated column models are linked to a one‐dimensional saturated flow model. The Dupuit‐Forchheimer assumptions are used for the saturated flow, and the unsaturated flow is assumed to be strictly vertical. The systems are linked because solutions of the equation governing unsaturated flow determine recharge and storage information used to solve the equation governing saturated flow. In addition, the position of the water table locates the lower boundaries of the unsaturated models. The solution of a test problem using a linked model is compared with results from a rigorous two‐dimensional model. The comparison is good at early times when recharge to the water table is small but poor at later times when recharge increases. Applications are then made to field‐size problems. Results compare closely with an actual groundwater hydrograph. In addition, a linked model is used to show that in a specific humid climate watershed the type of vegetation does not significantly affect the groundwater regimen, whereas in a given arid climate watershed the type of vegetation would determine whether groundwater recharge occurred. For field‐size problems where water table movement is relatively small, where the Dupuit‐Forchheimer assumptions are valid, and where lateral unsaturated flow is not important, the linked model offers an efficient approximate way to solve unsaturated‐saturated flow problems.

An efficient numerical technique is used to obtain solutions of the Boussinesq equation for problems of groundwater recession and groundwater flow in response to changes in stream stage. Comparison of the numerical results with the analytical solution of Boussinesq [1904] attests to the accuracy of the former. The solution of a recession problem indicates that the form of the Werner and Sundquist [1951] model of groundwater discharge recession is appropriate. The solution of a problem involving changing boundary conditions on an aquifer because of a flood wave provides data relative to groundwater outflow. A comparison with the results of Cooper and Rorabaugh [1963] evaluates the applicability of a linear model of unconfined flow.

The linear programing-superposition method is presented for ma, naging multiple sources of groundwater pollution over time. The method uses any linear solute transport simulation model to generate a unit source-concentration response matrix that is incorporated into a management model. This series of constraints indicates local solute concentration histories that will result from any series of waste injection schedules. The linear program operates on the matrix to arrive at optimal disposal schedules. An example demonstrates application of the method to maximizing groundwater waste disposal while maintaining water quality of local water supplies within desired limits. Flow field variations associated with waste injection are ignored as an approximation. Parametric programing is shown to be an important tool in evaluating waste disposal trade-offs at various injection sites over time. Mixed-integer programing permits restrictions to be placed upon the number of injection wells which may operate during given management periods.