Disentangling The Contribution of Precipitation and Epistemic Uncertainties on Streamflow Estimates from Hydrologic Models in The Canadian Prairies

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Abstract Precipitation estimates are subject to substantial errors, but their propagation into streamflow simulations remains an open question. This study uses a combinatorial approach to investigate this problem. First, the Raven hydrological modelling framework is used to identify behavioural model configurations by accounting for both parameter and structural uncertainties. Unlike conventional approaches using synthetic perturbations, we use empirically derived precipitation errors from 405 observed–estimated satellite and reanalysis-based pairs. The relationship between precipitation input errors and resulting streamflow errors (P–Q) is analyzed using two methods: the Random Forest model and precipitation elasticity analysis. Overall streamflow uncertainty is partitioned using Shannon entropy and Sobol indices. The methodology is applied to 16 Canadian Prairie catchments; the model is calibrated over 2008–2023 to obtain behavioural parameter sets, which are then used to simulate streamflow under 405 precipitation estimates for 2018–2023. Results show that precipitation-induced streamflow errors depend strongly on model parameterization, particularly as input errors increase. Behavioural parameter sets do not exhibit uniform error propagation despite similar calibration performance, highlighting the critical role of model configuration in shaping the P–Q error relationship. This relationship is captured through precipitation elasticity, with higher elasticity leading to greater error amplification. Furthermore, Shannon entropy decomposition reveals substantial precipitation–parameter interactions that are not fully captured by the Sobol method. Overall, our study shows that precipitation uncertainty strongly influences streamflow uncertainty in the Canadian Prairies, while commonly used performance metrics (KGE, NSE, etc) do not necessarily indicate model robustness to input errors.

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