This paper presents an engineering approach to the thermal challenge problem defined by Dowding et al. (this issue). This approach to model validation is based on a multivariate validation metric that accounts for model parameter uncertainty and correlation between multiple measurement/prediction differences. The effect of model parameter uncertainty is accounted for through first-order sensitivity analysis for the ensemble/validation tests, and first-order sensitivity analysis and Monte-Carlo analysis for the regulatory prediction. While sensitivity based approaches are less computational expensive than Monte-Carlo approaches, they are less likely to capture the far tail behavior of even mildly nonlinear models.
The application of the sensitivity based validation metric provided strong evidence that the tested model was not consistent with the experimental data. The use of a temperature dependent effective conductivity with the linear model resulted in model predictions that were consistent with the data. The correlation structure of the model was used to pool the prediction/measurement differences to evaluate the corresponding cumulative density function (CDF). Both the experimental CDF and the predicted CDFs indicated that the regulatory criterion was not met.