Impact of the numbers of observations and calibration parameters on equifinality, model performance, and output and parameter uncertainty

The level of model complexity that can be effectively supported by available information has long been a subject of many studies in hydrologic modelling. 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 Soil and Water Assessment Tool model. In the experiments, the number of observations was increased by expanding the 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 different numbers of observations. The calibration quality was quantified with statistics calculated based on the ‘behavioural’ parameter sets, identified using 1% and 5% cut-off thresholds in a generalized likelihood uncertainty estimation 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. Copyright © 2015 John Wiley & Sons, Ltd.

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