Scientific Investigations Report 2006-5041
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006-5041
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Recharge is a vital component of the ground-water budget. As competition grows for limited water resources, water managers increasingly consider the ground-water system as a source for possible development. To aid in the decision-making process, managers look to numerical models as management tools. Recharge rates used in the numerical models are usually extremely important in calculating simulation results, and therefore, considerable effort must be spent quantifying the value.
Ground-water recharge estimation methods vary from extremely complex to relatively simple. Variably saturated flow models, such as VS2DT (Healy, 1990; Lappala and others, 1987), VS2DH (Healy and Ronan, 1996), or HYDRUS-2D (Simunek and others, 1999), that solve the Richards’ Equation for fluid flow are best suited to estimate recharge, but they require soil parameter data that are generally unavailable (Bauer and Vaccaro, 1987) or are too costly to obtain. Simpler methods, such as empirical relations based on precipitation and surficial geology (Woodward and others, 1995; Drost and others, 1999) or hydrograph separation (Rorabaugh, 1964; Rutledge and Daniel, 1994; Rutledge, 1998), do not characterize fluid flow processes. A ground-water budget is a useful tool but many components of the budget, such as precipitation, streamflow, and evapotranspiration (ET), must be measured directly. Methods using geochemical or radioisotope techniques can be costly and are best suited for long-term average recharge rates. Scanlon and others (2002) provide a comprehensive review of these and other recharge estimation methods.
The scale of application also limits these commonly used techniques. The methods simulate either at a point or site scale and must be extrapolated to a larger area or they simulate a single value for a large area, limiting the option to accurately scale down to a local area or to distribute recharge estimates spatially.
Another method for estimating ground-water recharge includes process-based models that compute distributed water budgets on a watershed scale (Leavesley and others, 1983; Bauer and Vaccaro, 1987). Cherkauer (2004) demonstrated that the method calculates accurate recharge rates at varying scales using readily available databases. The recharge component of these spatially distributed water budgets can then be used as input to numerical ground-water flow models (Hunt and others, 2001). These watershed models should be evaluated to determine which model parameters are the dominant controls in determining ground-water recharge. Determining which watershed-model parameters control recharge estimates would allow hydrologists to focus on compiling only the most relevant data in studies of regional ground-water recharge.
The U.S. Geological Survey (USGS) analyzed the sensitivity of simulated ground-water recharge to selected parameters in seven different applications of a precipitation-runoff watershed model representing distinctly different watersheds in humid regions of the United States. The objectives of the study were to determine: (1) which watershed-model parameters were the dominant controls in determining ground-water recharge; (2) if regional differences were in the sensitivity of ground-water recharge to watershed-model parameters; (3) if specific computer models used to simulate recharge affect parameter sensitivities; and (4) if objectives and approach of a study can affect ground-water recharge estimates and parameter sensitivities.
The study evaluated 16 watershed-model parameters common to all 7 watersheds, and an additional parameter common to 2 of the watersheds. Parameter sensitivities were determined using a nonlinear regression computer program to generate a suite of diagnostic statistics. These diagnostic statistics identify model parameters that are most important (greatest effect on simulated result [recharge]) for determining ground-water recharge, and compare and contrast the response of different types of hydrologic systems to those parameters. The study also assessed the usefulness of this type of sensitivity analysis in planning and carrying out watershed model studies and explaining the results.
Most modelers understand the importance of a sensitivity analysis in any modeling effort. Research on watershed modeling has advanced considerably, along with the awareness that computer-model algorithms and their associated model parameter sets are not unique and that infinite plausible mathematical representations exist (Vogel and Sankarasubramanian, 2003). Christiaens and Feyen (2002) provide a short overview of available sensitivity-analysis methods. However, these methods are not widely applied in watershed modeling.
Vogel and Sankarasubramanian (2003) used a generalized sensitivity analysis to derive analytical relations between the input (precipitation), output (streamflow), model error, and model parameters. They determined that a watershed model could be validated by reproducing those relations. Samanta and McKay (2003) used a Monte Carlo sampling strategy to determine the sensitivity of the model’s streamflow output to different values of hydrologically relevant parameters.
Downer and Ogden (2003) examined the effects of model complexity and parameter assignment in a coupled surface/subsurface hydrologic model and determined the model was insensitive to soil depth and most sensitive to saturated hydraulic conductivity. Martinez and others (2001) did a sensitivity analysis to determine the effects of increasing the number of soil layers in a land surface-atmosphere model on the water budget. The conclusions of Martinez and others (2001) differed from those of Downer and Ogden (2003). Martinez and others determined that (1) the water budget was sensitive to the number of layers in the soil profile during wet conditions, and (2) the sensitivity to the number of soil layers greatly exceeded the sensitivity to the range of saturated hydraulic conductivity. The conflicting results suggest that the role parameters play in different models and settings needs to be evaluated.
Christiaens and Feyen (2002) used the Latin hypercube approach to qualify and quantify uncertainty and sensitivity measures in the spatially distributed hydrological model. They evaluated the sensitivity of streamflow discharge, average soil water content, and ground-water elevation to soil hydraulic parameters. They determined that the correlation among parameters added significant complexity to the assessment of uncertainty and sensitivity.
Yobbi (2000) used 91 recharge-parameter zones derived from a surface-water model as input to a coupled ground-water flow model. A nonlinear least-squares regression method determined that the model simulations were relatively insensitive to any one recharge-parameter zone.
The various approaches, limited scope (one watershed simulation per analysis), and differing results make it impossible to draw broad conclusions concerning recharge sensitivity to parameters. The study presented in this report differs significantly by using a standard method to evaluate the parameters important to ground-water recharge in seven different humid region watershed models and attempting to draw general conclusions from the diagnostic statistics.
This report documents an analysis of the sensitivity of ground-water recharge to selected parameters in seven watershed models. The report (1) describes the seven watershed models, the nonlinear regression model used to calculate diagnostic statistics, and the sensitivity-analysis process, (2) evaluates the recharge-parameter sensitivities, (3) assesses the effects of regional differences, type of watershed model, and study objectives and approaches on sensitivity, and (4) discusses the importance of a rigorous sensitivity analysis. The analysis for each watershed model covered a 3-year simulation period.
The results of this study can help focus data-collection efforts in future studies that require watershed-scale estimates of ground-water recharge. An understanding of parameter sensitivities and correlations will make the calibration process more efficient. Future studies also could benefit from an understanding of regional differences in ground-water recharge processes and of the effect of the specific model code and objectives on parameter sensitivities.
The USGS Ground-Water Resources Program funded this work. Mark Mastin and John Vaccaro, USGS, Tacoma, Wash., Kevin Vining, USGS, Bismarck, N. Dak., Randall Hunt, USGS, Madison, Wis., and George Leavesley and Steve Markstrom, USGS, Denver, Colo., generously submitted their watershed models for evaluation in this study.
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