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In the uncertainty treatment framework considered, the intrinsic variability of the inputs of a physical simulation model is modelled by a multivariate probability distribution. The objective is to identify this probability distribution–the dispersion of which is independent of the sample size since intrinsic variability is at stake–based on observation of some model outputs. Moreover, in order to limit the number of (usually burdensome) physical model runs inside the inversion algorithm to a reasonable level, a nonlinear approximation methodology making use of Kriging and a stochastic EM algorithm is presented. It is compared with iterated linear approximation on the basis of numerical experiments on simulated data sets coming from a simplified but realistic modelling of a dyke overflow. Situations where this nonlinear approach is to be preferred to linearisation are highlighted.