Simulations of large-scale physical systems are often affected by the uncertainties in data, in model parameters, and by incomplete knowledge of the underlying physics. The traditional deterministic simulations do not account for such uncertainties. It is of interest to extend simulation results with ``error bars'' that quantify the degree of uncertainty. This added information provides a confidence level for the simulation result. For example, the air quality forecast with an associated uncertainty information is very useful for making policy decisions regarding environmental protection. Techniques such as Monte Carlo (MC) and response surface are popular for uncertainty quantification, but accurate results require a large number of runs. This incurs a high computational cost, which maybe prohibitive for large-scale models. The polynomial chaos (PC) method was proposed as a practical and efficient approach for uncertainty quantification, and has been successfully applied in many engineering fields. Polynomial chaos uses a spectral representation of uncertainty. It has the ability to handle both linear and nonlinear problems with either Gaussian or non-Gaussian uncertainties. This work extends the functionality of the polynomial chaos method to Source Uncertainty Apportionment (SUA), i.e., we use the polynomial chaos approach to attribute the uncertainty in model results to different sources of uncertainty. The uncertainty quantification and source apportionment are implemented in the Sulfur Transport Eulerian Model (STEM-III). It allows us to assess the combined effects of different sources of uncertainty to the ozone forecast. It also enables to quantify the contribution of each source to the total uncertainty in the predicted ozone levels.