Total modeling uncertainty may be defined in terms of the difference between numerical simulations and physical observations of the same phenomena. As such it includes both experimental uncertainty and uncertainty associated with the modeling process itself. Experimental uncertainty arises from variability in the experimental setup, measurement variability and variability in the processing of raw data. Modeling uncertainty (associated with the modeling process itself) arises from the variability in modeling assumptions and methods that parameterize a solution, as well as the parameter values themselves.
This presentation will describe recently developed methods for quantifying total modeling uncertainty for linear and nonlinear systems. Examples will be presented that show how covariance matrices of total modeling uncertainty have been derived from comparisons of specific numerical simulations with test data, and how that uncertainty has been propagated through models to evaluate the predictive accuracy of numerical simulations generically similar to those from which the total modeling uncertainty was derived. To demonstrate the validity of the process, predicted uncertainty bands on numerical simulations will be compared with test data.