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U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2007–5237

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Limitations and Appropriate Use of Models

The transect and study-area simulation models were developed to generate a better understanding of the fate and transport of nitrate from on-site wastewater systems at multiple scales. The study-area model also may be used to help evaluate alternative options for management of nitrate loading from on-site wastewater systems. Limitations of the modeling software, assumptions made during model development, and results of model calibration and sensitivity analysis all are factors that constrain the appropriate use of these models and highlight potential future improvements.

A simulation model is a means for testing a conceptual understanding of a system. Because ground-water flow systems are inherently complex, simplifying assumptions must be made in developing and applying model codes (Anderson and Woessner, 1992). Models solve for average conditions (for example, head or nitrate concentrations) within each cell using parameters which are interpolated or extrapolated from measurements, and (or) estimated during calibration. Practical limitations on model size, and hence minimum cell size, are imposed by the size and speed of available computers. More commonly, however, it is the availability of data to define the system that limits the scale and accuracy of the model. In light of this, the intent in developing the simulation models was not to reproduce every detail of the natural system, but to portray its important characteristics in sufficient detail to provide a useful tool for testing the conceptual model and evaluating alternative management options.

Simulation Models

The study-area simulation model is a decision-support tool for evaluating the effects of wastewater management alternatives on ground-water and surface-water quality at the neighborhood to watershed scale. The study area and transect models are not capable of simulating nitrate concentrations at individual wells; however, the transect model (which has more than twice the lateral resolution of the study-area model) has sufficient detail to approximately simulate the location of nitrate plumes.

The ground-water flow system was assumed to be at steady-state, meaning that the velocity and direction of ground-water flow did not change with time. Water-level variation occurs seasonally and over the long term in response to stresses like climatic variation. The variation can change the velocity, and possibly direction, of ground-water flow over periods ranging from hours to years depending on the cause; a change in river stage might affect the system for hours to days whereas an extended drought might have effects that last for months to years. These changes in the flow system could have effects on the fate and transport of nitrate not represented by the simulation models. The simulation models are designed to evaluate the long-term effects of options for management of nitrate loading. The models should not be used to evaluate short-term changes without considering the possible effects of changes in the ground-water velocity distribution from the steady-state conditions represented in the models.

The location of the boundary between the oxic and suboxic parts of the ground-water system was mapped based on dissolved oxygen concentrations in 256 wells sampled as part of a synoptic sampling of private wells by ODEQ and Deschutes County in June 2000. Because denitrification is assumed to occur at the oxic-suboxic boundary and nitrate concentration below the boundary (in the suboxic zone) is specified as zero, simulated nitrate concentrations near and below the boundary are sensitive to location. Uncertainty in the boundary location will result in uncertainty in simulated nitrate concentrations. The distribution of wells used to map the boundary was generally good for a study area this size, however, the boundary location is less certain in some areas. For example, there were fewer wells available to constrain the location of the boundary near the margin of the model area and near streams. In these areas, model results should be evaluated with respect to the effects of uncertainty on simulated nitrate concentrations.

The ground-water discharge to evapotranspiration process is simulated by the study-area model and accounts for the mass of water lost from the system where deep-rooted plants extract ground water for transpiration and where ground water is shallow enough to be evaporated from bare soil. Plants also may take up nutrients dissolved in ground water; however, the rate of uptake is highly variable and poorly understood in non-agricultural settings. Nutrients and other solutes are not removed by evaporation and this process results in concentration of solutes in ground water. For this study, there was no basis for partitioning the mass of ground water discharged by ET into its transpiration and evaporation components and it was assumed that no nitrate was taken up with the mass of water discharged by ET. This assumption may bias simulated nitrate concentrations toward high values in areas where ET is a significant part of ground-water discharge.

Management Model

Because the NLMM was developed using optimization methods with the study-area simulation model, the NLMM is subject to the same limitations listed for the study-area model. However, additional factors should be considered when using the management model that relate to how the management problem is formulated.

The sensitivity analysis of the NLMM presented in this report illustrates how closely optimal solutions are tied to the definition of the management problem. The NLMM solutions were shown to be highly dependent on the value of the maximum nitrate concentration constraint and on the number, location, and depth of specified constraints. Assignment of the constraints is an important part of developing a strategy for protecting ground-water resources.

The management problem for this study was formulated with the objective of minimizing the amount of reduction in nitrate loading that would be required to meet specified water-quality goals within management areas. Management area boundaries were defined using the township and section lines of the Public Land Survey System (PLSS) and included areas ranging from 160 to 640 acres. The management-area boundaries do not coincide with the hydrologic, geologic, and geochemical boundaries that control the nitrate loading capacity of the system. The loading capacity for some management areas may be strongly controlled by loading in part of the area close to where constraints were specified. Large differences in computed optimal reduction requirements can occur across management-area boundaries even though there may be little difference in lot densities, recharge, depth of the suboxic zone, or other factors that affect loading capacity. Users of the NLMM need to be cognizant of the effects of problem formulation on results and interject knowledge of on-the-ground conditions when using model results to support management decisions.

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