Abstract: Background errors (BEs) for observable quantities are valuable for diagnostic analysis of the response of the data assimilation system to these observable quantities and play an important role in improving the variational data assimilation system. BEs are widely applied to assess impacts of observable quantities on analysis. The condition number of the Hessian matrix is determined by background errors for observable quantities, observation errors and observation count number. The background errors of observable quantities can also be used in the procedure of background check in data quality control. However, the background errors are specified in terms of those quantities that lead to a compact formulation of the background term Jb, i.e. the balanced stream function, unbalanced Exner pressure, velocity potential and specific humidity in GRAPES 3DVar system. It is not clear how the magnitudes of these background errors can be compared with various observation errors. The formulations of control variable randomization method in GRAPES are illustrated by applying the observation operators of GRAPES 3DVar system to a set of random vectors drawn from a population whose probability density function is given by an assumed background error covariance. This method is applied to estimate the background error for AMSU-A radiance data in grid-point space. The background error for radiance data is then applied in its quality control scheme. The results of forecast experiments show that more radiance data are assimilated using the new quality control scheme, which has a positive effect on geopotential height forecast in both the southern and northern Hemisphere. A statistically significant improvement in the anomaly correlation scores for geopotential height simulation in the southern Hemisphere at all forecast time is obtained. More than 0.2 day of forecast skill of geopotential height at 500 hPa is obtained in southern Hemisphere.