Uncertainty quantification of pollutant source retrieval: comparison of Bayesian methods with application to the Chernobyl and Fukushima-Daiichi accidental releases of radionuclides

International audienceInverse modelling of the emissions of atmospheric species and pollutants has significantlyprogressed over the past 15 years. However, in spite of seemingly reliable estimates, theretrievals are rarely accompanied by an objective estimate of their uncertainty, except whenGaussian statistics are assumed for the errors, which is often an unrealistic assumption.Here, we assess rigorous techniques meant to compute this uncertainty in the context of theinverse modelling of the time emission rates – the so-called source term – of a point-wiseatmospheric tracer. Log-normal statistics are used for the positive source term prior andpossibly the observation errors; this precludes simple Gaussian statistics-based solutions.Firstly, through the so-called empirical Bayesian approach, parameters of the errorstatistics – the hyperparameters – are first estimated by maximizing their likelihood viaan expectation–maximization algorithm. This enables a robust estimation of a sourceterm. Then, the uncertainties attached to the retrieved source rates and total emission areestimated using four Monte Carlo techniques: (i) an importance sampling based on a Laplaceproposal, (ii) a naive randomize-then-optimize (RTO) sampling approach, (iii) an unbiasedRTO sampling approach, and (iv) a basic Markov chain Monte Carlo (MCMC) simulation.Secondly, these methods are compared to a more thorough hierarchical Bayesian approach,using an MCMC based on a transdimensional representation of the source term to reducethe computational cost.Those methods, and improvements thereof, are applied to the estimation of the atmosphericcaesium-137 source terms from the Chernobyl nuclear power plant accident in April andMay 1986 and Fukushima Daiichi nuclear power plant accident in March 2011. This studyprovides the first consistent and rigorous quantification of the uncertainty of these bestestimates