Air quality models simulate the fate of atmospheric pollutants using a set of algebraic and differential equations based upon the physical laws of science. Inevitably, model performance is influenced by errors and uncertainties introduced into the model by the parameterization schemes and the input data. Many sampling methods (e.g., the Monte Carlo method) have been widely used for model uncertainty calculations. When the model is complex, these methods require substantial computer resources and human effort for executing and managing model runs. Moreover, these methods provide only partial information unless every model run is executed with a complete set of input data. These disadvantages can be overcome with two techniques described in this paper: an automatic differentiation technique for calculating sensitivity and a statistical method for calculating the propagation of uncertainty in air quality models. These methods are demonstrated using a one-dimensional advection model.