Uncertainty is inherent in the modelling of any physical processes. Regarding hydrological modelling, the uncertainty has multiple sources including the measurement errors of the stresses (the model inputs), the measurement errors of the hydrological process of interest (the observations against which the model is calibrated), the model limitations, etc. The typical techniques to assess this uncertainty (e.g., Monte Carlo simulation) are computationally expensive and require specific preparations for each individual application (e.g., selection of appropriate probability distribution). Recently, data-driven methods have been suggested that attempt to estimate the uncertainty of a model simulation based exclusively on the available data. In this study, two data-driven methods were employed, one based on machine learning techniques, and one based on statistical approaches. These methods were tested in two real-world case studies to obtain conclusions regarding their reliability. Furthermore, the flexibility of the machine learning method allowed assessing more complex sampling schemes for the data-driven estimation of the uncertainty. The anatomisation of the algorithmic background of the two methods revealed similarities between them, with the background of the statistical method being more theoretically robust. Nevertheless, the results from the case studies indicated that both methods perform equivalently well. For this reason, data-driven methods can become a valuable tool for practitioners.
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