Pareto-Based Multi-Objective Calibration of a Hydrological Model Integrating Streamflow and Snow Cover Area

Abstract Accurate hydrological modeling in high-mountainous snow-dominated basins is essential for effective water resource management, particularly in climate change-sensitive regions. To better understand the processes that govern hydrological responses, model calibration against multiple variables offers a valuable approach for reducing parameter uncertainty and model equifinality. In data-scarce environments, simple lumped-parameter hydrological models that account for snow accumulation and melting processes are particularly useful. In this study, we used the Témez lumped hydrological model enhanced by the integration of a new semi-distributed snow module to simulate key snow-related processes. We performed a novel sensitivity analysis of the efficiency of the models depending on the adopted multi-objective functions within an automatic procedure to calibrate and validate the models. We evaluated three calibration approaches by varying the weight of the snow cover objective $$\:{w}_{S}$$ . The first procedure consisted of a single-objective calibration against streamflow alone. The other procedures applied multi-objective calibration against streamflow and snow cover, which differed in the performance metric used for the snow component: Nash-Sutcliffe efficiency and Kling-Gupta efficiency. The results demonstrated that incorporating snow cover data into the calibration process improved snow cover simulation without significantly compromising streamflow efficiency, except when the streamflow weight $$\:{w}_{Q}$$ was reduced to zero. Notably, the KGE-based approach yielded a better-defined Pareto front with a more robust snow cover efficiency and reduced bias. Our findings also revealed that snow-related parameters were highly sensitive to the inclusion of snow cover data. Key parameters exhibited substantial changes, with a reduction in variability of approximately 30%.