How do observations and parameters influence equifinality?

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modeling. In particular, distributed parameter models tend to be regarded as overparameterized because of numerous parameters used to describe spatially heterogeneous hydrologic processes. However, it is not clear how parameters and observations influence the degree of overparameterization, equifinality of parameter values, and uncertainty. This study investigated the impact of the numbers of observations and parameters on calibration quality including equifinality among calibrated parameter values, model performance, and output/parameter uncertainty using the SWAT model. In the experiments, the number of observations was increased by expanding calibration period or by including measurements made at inner points of a watershed. Similarly, additional calibration parameters were included in the order of their sensitivity. Then, unique sets of parameters were calibrated with the same objective function, optimization algorithm, and stopping criteria but the different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioral’ parameter sets, identified using 1 and 5% cut-off thresholds in a GLUE framework. The study demonstrated that equifinality, model performance, and output/parameter uncertainty were responsive to the numbers of observations and calibration parameters; however the relationship between the numbers, equifinality, and uncertainty was not always conclusive. Model performance improved with increased numbers of calibration parameters and observations, and substantial equifinality did neither necessarily mean bad model performance nor large uncertainty in the model outputs and parameters.