Modelling the behaviour of a karst system catchment using non-linear hysteretic conceptual model

A two reservoir conceptual model with a hysteretic transfer function is proposed for hydrological modelling of karst catchments. The main features of the model are (i) a simple model for evapotranspiration based on potential rates, (ii) a non-linear, hysteretic discharge law accounting for the variations of connectivity in the soil/epikarst zone, (iii) a threshold-based discharge law accounting for the time variability of the active catchment area via losses to secondary springs. The structure of the model and the governing equations are proposed on the basis of physical considerations, with the underlying assumption that the model compartments, state variables and parameters should bear a physical reality. The model is applied to the karst system catchment of the Durzon spring (France). Model robustness is assessed by using only 1 year for calibration and 4 years for validation. A modified Nash–Sutcliffe criterion decreases from 91% to 87% between the calibration and validation phase, thus demonstrating the robustness of the model. The proposed model is compared to a model of similar complexity available from the literature, previously applied to similar catchments. The comparison indicates the superiority of the hysteresis-based model in terms of robustness and overall performance.