Extending Monte Carlo Simulations to Represent and Propagate Uncertainties in Presence of Incomplete Knowledge: Application to the Transfer of a Radionuclide in the Environment

This work is devoted to some recent developments in uncertainty analysis of environmental models in the presence of incomplete knowledge. The classical uncertainty methodology based on probabilistic modeling provides direct estimations of relevant statistical measures to quantify the uncertainty on the model responses thanks to a nice mixing between Monte Carlo simulations and the use of efficient statistical treatments. However, this approach may lead to unrealistic results when not enough information is available to specify the probability distribution functions (pdfs) of input parameters. For example, if a fixed (i.e., the pdf is a Dirac distribution) variable is unknown between $a$ and $b$ , the proper way to model this knowledge is to consider a set of ${\delta }_c$ distributions (a ${\delta }_c$ distribution means that the probability that the parameter is equal to $c$ is $1$ and $0$ elsewhere), $c$ belonging to $[a,b]$ . This is quite different from assume an equidistribution. Thus, to respect the real state of knowledge in industrial applications, a new modeling based on the theory of evidence is introduced. It allows an extension of classical Monte Carlo simulations by relaxing assumptions related to the choice of probability distribution functions and possible dependencies between uncertain parameters. To illustrate the principle of our modeling, a comparison with the probabilistic modeling is given in the case of the transfer of a radionuclide in the environment.