Coupled watershed models that link a land-surface model (SWAT) with a groundwater flow model (MODFLOW) have more parameters and feedbacks than either component alone, yet they are still commonly calibrated against streamflow performance metrics alone. Acero Triana, Chu, Guzman, Moriasi and Steiner (2019) showed that such single-domain calibration can pass standard goodness-of-fit tests while leaving the coupled system physically misrepresented, and posed the follow-on question: evaluate the degrees of freedom of single-domain (e.g., SWAT, MODFLOW) and coupled-domain (e.g., SWATmf) hydrologic systems, i.e., determine what additional observational information, or what changes in model conceptualization, are required to sufficiently constrain such systems and reduce equifinality. The source's analysis also notes that fast surface runoff and slow groundwater response follow different characteristic times, which complicates calibration. The problem remains open: existing studies provide single-watershed techniques rather than a general quantification.

Background

Watershed-scale hydrology is often simulated with the Soil and Water Assessment Tool (SWAT), a semi-distributed model that divides a catchment into hydrologic response units (areas of common land use, soil and slope) and computes rainfall partitioning into evapotranspiration, runoff, soil storage, and percolation. Saturated groundwater flow is instead the domain of MODFLOW, a grid-based, three-dimensional finite-difference groundwater flow code. In the coupled SWAT-MODFLOW model (also written SWATmf), SWAT supplies water and chemical fluxes, such as recharge derived from soil-column percolation, to MODFLOW, while MODFLOW simulates aquifer flow and stream-aquifer exchange (Bailey et al., 2016). Such integrated models are widely used because neither component alone captures the bidirectional feedback between surface water and groundwater (Kallon et al., 2026).

Calibration is the process of adjusting model parameters, which cannot be measured directly everywhere, until simulated outputs match observations. Practice is anchored on goodness-of-fit statistics for streamflow, chiefly the Nash-Sutcliffe Efficiency (NSE, a normalized measure of model skill relative to the observed mean) and Percent Bias (PBIAS, the mean relative error); Moriasi et al. (2007) proposed widely used thresholds, e.g., NSE above 0.50 and PBIAS within plus or minus 25 percent for streamflow, below which a simulation is called 'satisfactory'. A long-standing concern is equifinality: many different parameter sets can reproduce the observed record acceptably well while representing internal processes (evapotranspiration, recharge, groundwater storage, baseflow) very differently (Beven, 2006). One way to phrase the issue, used by the source paper, is informational: a model has an effective number of degrees of freedom, and the observations used in calibration must supply enough information to constrain them; Nearing and Gupta (2015) formalized how to measure the quantity and quality of information that calibration data provide about model parameters.

Acero Triana et al. (2019) demonstrated the problem for coupled modeling at the Fort Cobb Reservoir Experimental Watershed (Oklahoma, USA). A SWAT model calibrated only on streamflow at three gauges met the conventional 'satisfactory' criteria (daily NSE 0.52-0.61, PBIAS from -4 to 14 percent), yet when the calibrated model was coupled to MODFLOW the resulting groundwater simulation was physically implausible, with excessive recharge and unrealistic simulated heads. They concluded that calibration must account for equifinality, model inadequacy, and constraint inadequacy, and that unsupervised optimization against single-domain metrics (e.g., the SUFI2 (Sequential Uncertainty Fitting, version 2) algorithm in the SWAT-CUP calibration package) can produce distorted parameters. The unresolved question they left, stated in their Conclusion, is to evaluate the degrees of freedom in single- (e.g., SWAT, MODFLOW) and coupled-domain (e.g., SWATmf) hydrologic systems in order to determine the additional information or changes in the model conceptualization that might be required to constrain such systems. Their analysis additionally observes that streamflow responses follow different temporal scales than subsurface domains, that the temporal scale of some processes may fall outside the chosen or available calibration period, and that calibration techniques do not account for the differences in velocity of water propagation across the domains, from daily surface runoff to seasonal and multi-year groundwater response.

Problem Statement

Quantify the degrees of freedom of hydrologic systems in single-domain (e.g., standalone SWAT or MODFLOW) and coupled-domain (e.g., SWATmf-class SWAT-MODFLOW) configurations, and determine what additional observational information, or what changes in model conceptualization, are required to sufficiently constrain such systems and reduce equifinality of the coupled model. Together these sub-goals define the target, each sought at the level of a general quantification that holds across configurations rather than only as a demonstration for a single watershed. Multi-domain observations (e.g., streamflow, groundwater levels, baseflow, recharge/percolation fluxes) and conceptualization changes such as fuller representation of feedback fluxes in the surface-subsurface coupling (in SWATmf, feedbacks from MODFLOW to SWAT were not considered) are illustrative examples of the information and conceptualization routes the question encompasses; no specific measure, data type, or method is prescribed. A system counts as sufficiently constrained, and its equifinality as reduced, when the observational information and the stated model conceptualization together identify the system's parameters (ruling out the alternative parameter sets that still reproduce acceptable single-domain goodness-of-fit) rather than leaving the coupling free to represent the internal fluxes in physically divergent ways. As background, the source's analysis notes that processes with widely different characteristic times (daily surface runoff versus seasonal and multi-year groundwater response) and differences in the velocity of water propagation across domains complicate calibration.

References

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