Equifinality and automatic calibration: What is the impact of hypothesizing an optimal parameter set on modelled hydrological processes?

Abstract

Accepting the concept of equifinality may result in larger uncertainty associated with model predictions than that of the optimal parameter set paradigm. Despite the existence of uncertainty characterization methods, the semi-distributed hydrological model HYDROTEL has been used within the latter paradigm. What is the impact of hypothesizing an optimal parameter set? This paper focuses on the assesment of the impact of equifinality of calibration parameters with respect to modelled hydrological variables and indices, namely: (1) daily flows; (2) seasonal 7- and 30-day low flows, and maximum flow; (3) snow water equivalent (SWE); (4) shallow ground water variations; and (5) actual evapotranspiration. This assessment is presented for 10 southern Québec watersheds of the St. Lawrence River. The watershed models were calibrated and validated for 1982–1991 and 1991–2002, respectively. Automatic calibration was performed using the dynamically dimensioned search (DDS) algorithm based on the maximization of two objective functions (OFs): (1) the Kling–Gupta efficiency and (2) the Nash-log. DDS was executed to calibrate 12 hydrological parameters for one optimization trial for each watershed and each OF with a budget of 5000 model runs. To analyze parameter uncertainty and resulting equifinality, 250 sets of parameters were extracted from each trial run. Calibration performances for both OFs were between 0.75 and 0.95, while the selected 250 best sets of parameters had OF values differing by less than 1%. Results showed that the overall OF uncertainty was larger than the parameter uncertainty for all modelled processes except the SWE. Nevertheless, seasonal results suggested parameter uncertainty could be greater than OF uncertainty for specific seasons or years, although it was not possible to make a general outcome stand out. In particular for impact studies where the variables of interest are not daily flows but rather hydrological indices or variables, parameter uncertainty will need to be accounted for.