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Within the context of the Air Quality Model Evaluation International Initiative Phase 2 (AQMEII2) project, this part II paper performs a multi-model assessment of major column abundances of gases, radiation, aerosol, and cloud variables for 2006 and 2010 simulations with three online-coupled air quality models over the North America using available satellite data. It also provides the first comparative assessment of the capabilities of the current generation of online-coupled models in simulating column variables. Despite the use of different model configurations and meteorological initial and boundary conditions, most simulations show comparable model performance for many variables. The evaluation results show an excellent agreement between all simulations and satellite-derived radiation variables including downward surface solar radiation, longwave radiation, and top-of-atmospheric outgoing longwave radiation, as well as precipitable water vapor with domain-average normalized mean biases (NMBs) of typically less than 5% and correlation coefficient (R) typically more than 0.9. Most simulations perform well for column-integrated abundance of CO with domain-average NMBs of -9.4% to -2.2% in 2006 and -12.1% to 4.6% in 2010 and from reasonably well to fair for column NO2, HCHO, and SO2, with domain-average NMBs of -37.7% to -2.1%, -27.3% to 59.2%, and 16.1% to 114.2% in 2006, respectively, and, 12.9% to 102.1%, -25.0% to 87.6%, -65.2% to 7.4% in 2010, respectively. R values are high for CO and NO2 typically between 0.85 and 0.9 (i.e., R-2 of 0.7-0.8). Tropospheric ozone residuals are overpredicted by all simulations due to overestimates of ozone profiles from boundary conditions. Model performance for cloud-related variables is mixed and generally worse compared to gases and radiation variables. Cloud fraction (CF) is well reproduced by most simulations. Other aerosol/cloud related variables such as aerosol optical depth (AOD), cloud optical thickness, cloud liquid water path, cloud condensation nuclei, and cloud droplet number concentration (CDNC) are moderately to largely underpredicted by most simulations, due to underpredictions of aerosol loadings and also indicating high uncertainties associated with the current model treatments of aerosol cloud interactions and the need for further model development. Negative correlations are found for AOD for most simulations due to large negative biases over the western part of the domain. Inter-model discrepancies also exist for a few variables such as column abundances of HCHO and SO2 and CDNC due likely to different chemical mechanisms, biogenic emissions, and treatments of aerosol indirect effects. Most simulations can also capture the inter-annual trend observed by satellites between 2006 and 2010 for several variables such as column abundance of NO2, AOD, CF, and CDNC. Results shown in this work provide the important benchmark for future onlinecouple air quality model development. (C) 2014 Elsevier Ltd. All rights reserved.