Abstract: The flow-dependent background error covariance between variables is important, yet traditional climatic background errors in variational systems are difficult to characterize such kind of information. Although 4DVar can implicitly evolve the initial background error covariance by tangent linear and adjoint models, it suffers from complex development, maintenance, and expensive computational costs, which are particularly prominent in high-precision scalable global atmospheric models. To avoid the tangent linear and adjoint models, the four-dimensional ensemble forecast error is introduced into the CMA global data assimilation system, and the H-4DEnVar assimilation scheme is developed. The batch cycling forecast experiments and typhoon forecast experiments are conducted and compared with the 4DVar scheme. Batch forecast experiments indicate that the introduction of the four-dimensional ensemble forecast error improves the analysis and significantly improves the global forecast performance; typhoon forecast experiments show that the flow-dependent background error in H-4DEnVar is the main reason for the reduction in typhoon track forecast error; the comparison with 4DVar reveals that H-4DEnVar exhibits essentially comparable forecast capability at 26% of the computational cost of 4DVar when the IO cost of the ensemble forecast error is considered. The H-4DEnVar assimilation scheme shows good analysis and forecast effects while avoiding the tangent linear and adjoint models, and provides a reference for achieving four-dimensional assimilation scheme without the tangent linear and adjoint models.