Robust calibration with stochastic emulators: hydrological model parameter estimation under uncertain rainfall conditions

Traditional calibration methods in hydrological models result in parameter values that can compensate for aleatory uncertainties in model forcings (such as rainfall, temperature, evapotranspiration, or pesticide application dates). Ignoring aleatory uncertainty can lead to subsequent model simulations being less reliable for taking operational decisions or predicting hazardous events (e.g., peaks of water pollution or floods). Robust calibration can better handle these uncertainties, but usually requires extensive model simulations, making it impractical for physically based environmental models. To overcome these issues, we use a new metamodeling approach using stochastic emulation. This method is non-intrusive, meaning it does not need a predefined structure for the forcing space. Once validated, the stochastic emulator is used to evaluate different robust estimators at low cost, allowing for the selection of the most suitable one for the specific problem. We demonstrate this approach using the PESHMELBA hydrological model for pesticide transfer. We construct and validate the stochastic emulator, and compare robust estimators to traditional calibration. Results show that robust calibration enhances the model's reliability under rainfall uncertainty. This methodology can be applied to any model and forcing uncertainty, making it relevant for other applications in complex technological systems, or environmental models where aleatory uncertainties are inherent.