Comparative evaluation of computationally efficient uncertainty propagation methods through application to regional-scale air quality models Sastry S. Isukapalli *† , Alper Unal ‡ , Sheng-Wei Wang † , and Panos G. Georgopoulos † Environmental and Occupational Health Sciences Institute (EOHSI), Piscataway, New Jersey, 08854 This work presents the comparative evaluation of two computationally efficient uncer- tainty propagation techniques: the Stochastic Response Surface Method (SRSM) and the High Dimensional Model Representation (HDMR) method. The evaluation is performed in relation to the applicability to these methods to complex numerical models, specifically those dealing with simulating regional-scale air quality. The air quality model used in the application case study is a Eulerian type three-dimensional grid-based model, and involves a large set of non-linear partial and ordinary differential equations to describe atmospheric transport and chemistry, thus making it impractical to use traditional Monte Carlo based techniques for performing uncertainty analysis. The application case study focuses on studying uncertainties in ozone levels estimated by a regulatory air quality model due to uncertainties in biogenic emissions of ozone precursors. Preliminary results show that 95th confidence interval for the peak ozone levels spans a range of over ±15% from the mean value, indicating significant uncertainties with respect to the health impact and regulatory compliance. Both the SRSM and HDMR methods provide similar estimates, thus serving to cross-validate each other, while requiring a small number of model simulations. I. Introduction Uncertainty characterization is an important step in the use of mathematical and computational models for decision making. For example, this is especially crucial when complex numerical simulation models are employed to evaluate different emissions reductions strategies for improving air quality. A systematic uncertainty analysis in such cases provides estimates of the range of uncertainties and the degree of confidence in alternative decisions. It also highlights important sources of uncertainty, which helps in directing resources for further studies and data gathering needs. The main steps in performing this analysis include identifying and characterizing input uncertainties, propagating the uncertainties through the model, and identifying key contributions of input uncertainties towards the uncertainty in the output metric of interest for decision making. Probabilistic uncertainty analysis is the most widely used approach for characterizing uncertainties in computational models. The traditional sampling-based approaches for probabilistic analysis, such as the Monte Carlo (MC) and Latin Hypercube Sampling (LHS) techniques 1 require a large number of model simu- lations. This often implies that usually either no uncertainty analysis is performed due to the computational burden, or that uncertainty analysis is performed using MC and LHS techniques with a small set of sample points (e.g., in the context of air quality modeling, one study 2 used 20 simulations to assess the impact of over 10 inputs; whereas another study 3 used 100 simulations to assess the impact of about 128 inputs). Some of the alternative approaches for conducting systematic uncertainty propagation include the first- and second-order reliability-based methods (FORM/SORM), 4 which focus on estimating the probability of fail- ure, or events corresponding to low probability; and the decoupled direct method (DDM), 5 which focuses on sensitivity analysis of the model. The FORM/SORM method requires a means to map the probability * Address for correspondence: sastry@ccl.rutgers.edu † EOHSI is a joint Insitiute of UMDNJ-RW Johnson Medical School and Rutgers, The State University of New Jersey ‡ Affiliated with Mactec, Inc., New Jersey 1 of 8 American Institute of Aeronautics and Astronautics