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In this study, we show that pollutants of emerging concern are, by nature, prone to the emergence of epistemic uncertainty. We also show that the current uncertainty quantification methods used for pollutant modelling rely almost exclusively on parameter uncertainty, which is not adequate to tackle epistemic uncertainty affecting the model structure. We, therefore, suggest a paradigm shift in the current pollutant modelling approaches by adding a term explicitly accounting for epistemic uncertainties. In a proof-of-concept, we use this approach to investigate the impact of epistemic uncertainty in the fluctuation of pollutants during wet-weather discharge (input information) on the distribution of mass of pollutants (output distributions). We found that the range of variability negatively impacts the tail of output distributions. The fluctuation time, associated with high covariance between discharge and concentration, is a major driver for the output distributions. Adapting to different levels of epistemic uncertainty, our approach helps to identify critical unknown information in the fluctuation of pollutant concentration. Such information can be used in a risk management context and to design smart monitoring campaigns., Competing Interests: The authors declare no conflicts of interest., (© 2024 The Authors This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).)