A Simple Approach to Account for Stage–Discharge Uncertainty in Hydrological Modelling

The effect of stage–discharge (H-Q) data uncertainty on the predictions of a MIKE SHE-based distributed model was assessed by conditioning the analysis of model predictions at the outlet of a medium-size catchment and two internal gauging stations. The hydrological modelling was carried out through a combined deterministic–stochastic protocol based on Monte Carlo simulations. The approach considered to account for discharge uncertainty was statistically rather simple and based on (i) estimating the H-Q data uncertainty using prediction bands associated with rating curves; (ii) redefining the traditional concept of residuals to characterise model performance under H-Q data uncertainty conditions; and (iii) calculating a global model performance measure for all gauging stations in the framework of a multi-site (MS) test. The study revealed significant discharge data uncertainties on the order of 3 m³ s⁻¹ for the outlet station and 1.1 m³ s⁻¹ for the internal stations. In general, the consideration of the H-Q data uncertainty and the application of the MS-test resulted in remarkably better parameterisations of the model capable of simulating a particular peak event that otherwise was overestimated. The proposed model evaluation approach under discharge uncertainty is applicable to modelling conditions differing from the ones used in this study, as long as data uncertainty measures are available.