Abstract: Using the twodimensional shallow water equation model and model simulated dat a, a set of numerical experiments were conducted to evaluate the im pacts of three different specification schemes of the background error covarianc e matrix on the fourdimensional variational (4DVAR) data assimilation in the c a se of different observation densities and observation errors. The three schemes are as follows: (1)for a single control variable, the background error covarian ce is assumed to be a diagonal matrix; (2) the background error covariance is si mplified to a Gaussian form with the homogeneous and isotropic assumptions; (3) the background error covariance is restructured through using the ensemble forec asts and the solving of the inverse of the background error covariance matrix is carried out by using the singular value decomposition (SVD) technique. The resu lts show that the background error covariance plays an important role in 4DVAR d ata assimilation. When the observational spatial density is not high enough, the re is no satisfied analysis available if the background error covariance matrix is simply reduced to a diagonal matrix. The Gaussian filter scheme has the abili ty to improve the analysis accuracy, but this it is sensitive to the length scal e of background error correlations. The third method shows a stable performance. In this method, the background error covariance matrix is calculated implicitly so the computation of the inverse of background error covariance matrix is avoi ded. When observations are sparse or large errors exist in the observations, the third method will behave better compared to the other two methods.