Forward uncertainty Propagation methods propagate uncertainty using prior assumptions about the different sources of uncertainty without the use of additional evaluation data. The assumptions that need to be made normally include prior distributions for parameters and other inputs. No model evaluation is necessary to apply forward uncertainty propagation although forward uncertainty propagation is often applied to an optimal model after a calibration exercise or some “best estimate” model. It is evident that for nonlinear models the results of a forward uncertainty propagation will depend on the model assumed, as well as the prior assumptions about the parameter and input uncertainties.

Methods:

• Error propagation equations

• Monte Carlo propagation

• Reliability methods

• Fuzzy and imprecise methods

Questioning Forward Uncertainty Analysis

Forward feeding uncertainty analysis is based on no comparison against any measured data. It has to assume that all the approximations made are correct or negligible and that the methodology and model are a valid/reasonable representative of the real physical system. This assumption may be based on past performance within different set-ups or the hypothesis that the system is physically correctly represented. Uncertainties which are inhereit in the modelling process do question the fundamental possibility of such assumptions. Therefore, such analyses should be associated with a caveat that the results are conditional on the uncertainties assumed a priori. However, the methodology is vital in the model development phase as well as in conditions in which no or not enough measurements can be acquired. Moreover, in situation in reliability problems of unobserved or unrepeatable events it is the only alternative (see discussion in Hall and Anderson (2002). However, model evaluation and conditioning should be carried out whenever observations to check model predictions are available.

References and Further Reading

Hall, J.W. and Anderson, M.G., 2002. Handling uncertainty in extreme or unrepeatable hydrological processes - the need for an alternative paradigm. Hydrological Processes, 16(9): 1867-1870.