The spatial and temporal variability of sensitivities has a significant impact on parameter estimation and sampling design for studies of solute transport in porous media. Physical insight into the behavior of sensitivities is offered through an analysis of analytically derived sensitivities for the one-dimensional form of the advection-dispersion equation. When parameters are estimated in regression models of one-dimensional transport, the spatial and temporal variability in sensitivities influences variance and covariance of parameter estimates. Several principles account for the observed influence of sensitivities on parameter uncertainty. (1) information about a physical parameter may be most accurately gained at points in space and time with a high sensitivity to the parameter. (2) As the distance of observation points from the upstream boundary increases, maximum sensitivity to velocity during passage of the solute front increases and the consequent estimate of velocity tends to have lower variance. (3) The frequency of sampling must be "in phase" with the S shape of the dispersion sensitivity curve to yield the most information on dispersion. (4) The sensitivity to the dispersion coefficient is usually at least an order of magnitude less than the sensitivity to velocity. (5) The assumed probability distribution of random error in observations of solute concentration determines the form of the sensitivities. (6) If variance in random error in observations is large, trends in sensitivities of observation points may be obscured by noise and thus have limited value in predicting variance in parameter estimates among designs. (7) Designs that minimize the variance of one parameter may not necessarily minimize the variance of other parameters. (8) The time and space interval over which an observation point is sensitive to a given parameter depends on the actual values of the parameters in the underlying physical system. iNTRODUCTION In studies of solute transport in porous media based on the advection-dispersion equation, the concept of sensitivity plays an important role in parameter estimation and sampling design. A "sensitivity" is a partial derivative, which represents the change in solute concentration resulting from a change in a model parameter. The purpose of this paper is to describe the behavior of these sensitivities in time and space under varying conditions, to offer physical explanations of their observed behavior, and to relate this behavior to parameter estimation and the sampling design problem. The present analysis deals with one-dimensional transient transport under the assumption of steady flow, although the methods described and conclusions drawn are applicable to more complex problems. While sophisticated techniques have been applied to parameter estimation (although primarily for the flow problem), little attention has been paid to how the choice of location and time of field observations influences the outcome of the estimation process. A methodical analysis of this question is known in a...

The National Water-Quality Assessment (NAWQA) Program is designed to describe the status and trends in the quality of the Nation's ground-and surface-water resources and to provide a sound understanding of the natural and human factors that affect the quality of these resources. To meet its goals, the program will integrate information about water quality at different spatial scales local, study unit, and regional and national and will focus on water-quality conditions that affect large areas or are recurrent on the local scale. As part of the program, study-unit investigations will be conducted in 60 areas throughout the Nation to provide a framework for national and regional water-quality assessments. The study-unit investigations will consist of intensive assessment activity of 4 to 5 years duration followed by 5 years of less intensive activity. Twenty study units will be in an intensive datacollection and analysis phase during each fiscal year (FY), and the first cycle of intensive investigations covering the 60 study units will be completed in FY2002. National and regional assessments of ground-and surface-water quality will be provided from issue-oriented findings of nationally consistent information from the study units. By including study units (60) that cover both a large part of the United States and diverse hydrologic systems that differ in their response to natural and human factors, the NAWQA Program ensures that many critical water-resources and water-quality concerns or issues can be addressed by comparative studies that are national and regional in scale.

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A methodology is developed for discrimination among models of transient solute transport in porous media. The method utilizes nonlinear regression on observations of solute concentration. Discrimination requires comparisons of model predictions to observations, systematic error in residuals, stability in parameter estimates from regression on different observation sets, and other measures of model fit among hypothesized models of transport. The set of observations of solute concentration to which models are fitted strongly influences the assessment of these discrimination criteria. The most desirable observation set for discrimination amplifies the weaknesses of those models that appear to describe existing conditions but are in fact unsuitable for prediction. The inadequacies of various observation sets are illustrated in four examples of discrimination between one‐dimensional models of solute transport. Our purpose in these examples is to understand the physical, deterministic basis of sampling design for model discrimination. In addition to physical attributes such as transport processes, boundary conditions, and flow geometry, the assumed distribution of random error in the regression model is also treated as a model attribute to be tested by the designed experiment. A common problem in field studies occurs when the set of available observations does not include sufficient information with which to discriminate among hypothesized models, hence supporting the need to design a second round of sampling specifically for discrimination. A proposed objective function in the sampling design problem favors design points at locations and times when two hypothesized transport models display the greatest differences in predicted concentration. Two hypothetical examples demonstrate the effectiveness of the objective function and the application of the discrimination criteria.

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