In this paper we discuss variational data assimilation using the STEM atmospheric Chemical Transport Model. STEM is a multiscale model and can perform air quality simulations and predictions over spatial and temporal scales of different orders of magnitude. To improve the accuracy of model predictions we construct a dynamic data driven application system (DDDAS) by integrating data assimilation techniques with STEM. We illustrate the improvements in STEM field predictions before and after data assimilation. We also compare three popular optimization methods for data assimilation and conclude that LBFGS method is the best for our model because it requires fewer model runs to recover optimal initial conditions.