In the numerical modeling of groundwater solute transport, explicit solutions may be obtained for the concentration field at any future time without computing concentrations at intermediate times. The spatial variables are discretized and time is left continuous in the governing differential equation. These semianalytical solutions have been presented in the literature and involve the eigensystem of a coefficient matrix. This eigensystem may be complex (i.e., have imaginary components) due to the asymmetry created by the advection term in the governing advection-dispersion equation. Previous investigators have either used complex arithmetic to represent a complex eigensystem or chosen large dispersivity values for which the imaginary components of the complex eigenvalues may be ignored without significant error. It is shown here that the error due to ignoring the imaginary components of complex eigenvalues is large for small dispersivity values. A new algorithm that represents the complex eigensystem by converting it to a real eigensystem is presented. The method requires only real arithmetic.

The problem of identifying unknown aquifer dispersivities in two‐dimensional transient groundwater contaminant transport from given observations on the concentration field is addressed. This inverse problem is formulated as a general nonlinear programing problem, the purpose of which is to minimize the discrepancy between calculated and observed values of the concentration field. The method of quasilinearization is used to linearize the above problem, and the inverse algorithm becomes the solution of a sequence of linear programs that converge to the solution of the original nonlinear problem. The finite elements method in conjunction with finite differencing is used to discretize the governing differential equations which are then used as constraints for the optimization (mathematical programing) problem stated above. The effect on the inverse problem of the choice of observation points, objective function, number of finite elements, size of time step, and observation errors is studied. The proposed identification algorithm is shown to be fast, stable, and accurate.

Underpressures (subhydrostatic heads) in the Paleozoic units underlying the Great Plains of North America are a consequence of Cenozoic uplift of the area. Based on tectonostratigraphic data, we have developed a cumulative uplift history with superimposed periods of deposition and erosion for the Great Plains for the period from 40 Ma to the present. Uplift, deposition, and erosion on an 800 km geologic cross-section extending from northeast Colorado to eastern Kansas is represented in nine time-stepped geohydrologic models. Sequential solution of the two-dimensional diffusion equation reveals the evolution of hydraulic head and underpressure in a changing structural environment after 40 Ma, culminating in an approximate match with the measured present-day values. The modeled and measured hydraulic head values indicate that underpressures increase to the west. The 2 to 0 Ma model indicates that the present-day hydraulic head values of the Paleozoic units have not reached steady state. This result is significant because it indicates that present-day hydraulic heads are not at equilibrium, and underpressures will increase in the future. The pattern uncovered by the series of nine MODFLOW models is of increased underpressures with time. Overall, the models indicate that tectonic uplift explains the development of underpressures in the Great Plains.

This report contains listings of model input values for the simulation of three-dimensional groundwater flow in the Tesuque aquifer system in northern New Mexico using a modular, three-dimensional, finite-difference, groundwater flow model. The original simulations were done in 1980 using a mathematical, three-dimensional, finite-difference, groundwater flow model. Conversion of the mathematical model to the modular model was done in 1988.