Scientific Investigations Report 2006-5041
U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2006-5041
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A primary objective of this study was to identify, by geographic region, parameters important to the simulation of ground-water recharge. This objective was partially achieved. During specific periods, whether those periods are days, weeks, or months, specific parameters control the rate of recharge. In the seven watershed models, some of these important parameters indicate the role of climate and physiographic setting. In the Lost River and Big Creek watersheds and the three MOPEX watersheds, simulated recharge (and streamflow) was sensitive to small changes in air temperature. Periods of high precipitation include those periods in late autumn and early winter when temperatures are near the freezing point. In the North Fork Pheasant Branch watershed, the rate of recharge is limited in summer because most of the precipitation is lost to ET, but is greater in autumn and winter when ET is minimal. Parameters related to the density of tree cover in the summer and winter also affected recharge in that watershed.
Although the other study objectives were considered secondary, their results proved valuable to the development of future models. The value of a rigorous sensitivity analysis can (1) make the calibration process more efficient, (2) guide additional data collection, (3) identify model limitations, and (4) explain simulated results.
The standard version of PRMS has more than 125 parameters. Some of the empirical formulas alone contain four parameters. The abundance of model parameters can seem overwhelming to an inexperienced watershed modeler and daunting to even the most knowledgeable. Automated calibration of process-based watershed models is becoming increasingly popular and provides capabilities that help modelers take greater advantage of available data (Poeter and Hill, 1998). Several methods use multiple objective functions to calibrate the model’s simulation of streamflow and hydrograph shape (Boyle and others, 2000; Hogue and others, 2000) or streamflow and solar radiation, potential ET, and water balance (L.E. Hay, U.S. Geological Survey, written commun, 2005). The ability to identify the 2 or 5 or even 10 parameters most important to the simulation would greatly increase the efficiency of the calibration process.
Hill (1998) describes 14 methods and guidelines for effective model calibration, and several define the role of scaled sensitivities. Guideline 1 in Hill (1998), “Apply the principle of parsimony,” states the importance of beginning the calibration by estimating very few parameters and increasing complexity slowly. Completing a systematic sensitivity analysis before final model calibration would clearly identify parameters that have dominant control over the simulated results. The extra effort could eliminate over-parameterization and an ineffective approach toward calibration.
Nonlinear regression can be used directly to guide data-collection efforts. Tiedeman and others (2003) discussed the “value of improved information” (VOII) method to determine the model parameters most important to a given prediction. Data then can be collected about the flow-system features related to those parameters. Although the VOII method was beyond the scope of this study, the scaled sensitivities can be used in their most basic form to guide data collection. Simply, if the model is sensitive to a parameter, or a group of parameters, resources could be allotted to collect data on the most sensitive parameters and thereby efficiently reduce model uncertainty. Some of the parameters used in PRMS are physically based and can be measured in the field, such as tree-cover density, but most others are coefficients or maximum rates that partition or limit flow among the reservoirs. Parameters such as soil2gw_max or jh_coef cannot be measured in the field, but a high CSS would indicate that they warranted additional consideration. The type of sensitivity analysis detailed in this study could intimate which parameters could be set to default values (low CSS) and which parameters would require a more thorough investigation (high CSS).
A hydrologic flow model represents a complex, natural system with a set of mathematical equations that describe the system. Intrinsic to the model is the error and uncertainty associated with approximations, assumptions, and simplifications that must be made (Ely and Kahle, 2004). Sources of hydrologic modeling errors typically are (1) input data, (2) representation of physical processes by model algorithms, and (3) parameter estimation during the calibration procedure (Troutman, 1985). A rigorous sensitivity analysis helps identify the major source of errors.
A strength of PRMS and MMS is the modular nature of the code. A computer model could be customized to match the specific purpose and scope of a project by adding or deleting routines. The objective of the Hamden watershed model was to investigate wetland features. Modules were compiled to route flow to land-surface features first, limiting flow to the ground‑water reservoir. A watershed model in a similar setting, but without the wetland emphasis, would most likely yield significantly different results. In the mountainous watersheds of Washington State, the importance of snowmelt created the need for an additional parameter, groundmelt, to define the amount of snowpack that could infiltrate the soil. This parameter also may have been important in other snow-driven watersheds, such as North Fork Pheasant Branch or Hamden. The PRMS code used for the three MOPEX watershed models was identical and was reflected, in part, by the similarity of the parameter sensitivities of the Amite River, English River, and South Branch Potomac River watershed models.
Watershed models traditionally are calibrated using measured streamflow data as calibration targets. Some models benefit by the existence of a long period of record to constrain the model. Studies such as MOPEX and the International Association of Hydrologic Studies’ Predictions in Ungaged Basins are investigating methods to estimate a priori model parameters and reduce parameter uncertainty for watersheds with no streamflow measurements or other data to calibrate a model. An effort could be made to validate the simulation results by using available diagnostic statistics, such as DSS and CSS. Merely minimizing residuals between simulated and measured streamflow does not ensure that the flow processes in a watershed are properly simulated.
An examination of parameter sensitivities may provide information about why a model produces certain results. For example, is the scaled sensitivity a function of the parameter value, the modeling and calibration approach, or climatic limitations? The modeler can evaluate the parameter sensitivities and determine if the simulated model output is correct for the right reasons. In short, do the parameters with the highest and lowest CSS make hydrologic sense? If not, the model construction and calibration should be reconsidered.
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