This work proposes a Bayesian non-informative reconstruction of virtual state variables in the representation of stormwater total suspended solids pollutographs by the traditional wash-off models, based on 255 rainfall events measured in a 185 ha French urban catchment. Results from event-based analyses revealed the missing representation of an essential process in the traditional rating curve (RC) model (simplest wash-off model) for 56% of the rainfall events. The unsatisfactory performances of the RC model are found to be not necessarily linked to antecedent dry weather conditions, as assumed by a great number of accumulation/wash-off models. Statistical tests suggest that non-representable rainfall events by the RC model are randomly distributed in time. The proposed Bayesian reconstructions of a potential process missed by the RC model exhibit a suitable identifiability at an intra-event scale. However, these reconstructions are not interpretable from the traditional accumulation/wash-off notions, i.e. in terms of a unique state of virtual available mass over the catchment that is decreasing over time, due to their high unrepeatability regarding their shape and their low prediction capacity for other rainfall events.