Effective model background error covariance representation is crucial in both meteorological and chemical data assimilation. A large number of species included in chemical transport models and various chemical reactions among the species make formulation of background error covariances in chemical data assimilation more complex and challenging. Currently, ozone predictions for the U.S. are operationally generated from the National Air Quality Forecast Capability (NAQFC) at National Oceanic and Atmospheric Administration (NOAA). NOAA is also testing developmental predictions of fine particulate matter (PM2.5). The NAQFC experimental ozone predictions and developmental PM2.5 predictions are used in the NMC (National Meteorological Center, now National Centers for Environmental Prediction) approach for estimation of model error statistics. In the NMC approach, differences between two NAQFC forecasts are used as surrogates for model errors. The model error covariance is studied in detail to reveal how the model errors are correlated in space, in time, and between different atmospheric constituents. We also estimate model error statistics using Hollingworth-Lönnberg approach based on AIRNow ozone and PM2.5 hourly measurements. Results from the two approaches are then compared. Several different representations of the background error covariances are implemented in data assimilation experiments with two different schemes, optical interpolation (OI) and three-dimensional variational (3D-Var) method. The truncated singular value decomposition (TSVD) regularization is performed to invert the covariance matrix efficiently. The impact of chemical data assimilation is evaluated using the AIRNow measurements, which are neither used in Hollingworth-Lönnberg approach nor assimilated. The effect of different background error covariance representations and its implication in future air quality forecasts are discussed.