Abstract: The horizontal correlation function of background error in three-dimensional variational data assimilation (3DVar) determines the extent to which observational information propagates across grid points and influences the analysis at various spatial scales. This study explores the application of the second-order auto-regressive (Soar), Gaussian and Supergauss function based on the CMA-MESO system. The result from the single-point test indicates that when using the u and v-component as background error covariance, three correlation models provide a more reasonable representation of the wind field horizontal correlations, resulting in a more coherent distribution of analysis increments.The Soar and Supergauss functions gain more information on meso- and small-scales compared to the Gaussian components. Numerical simulations of the extreme rainstorm event reveal that the Soar and Supergauss function achieve a closer alignment with actual circulation and moisture fields compared to the Gauss correlation function. Moreover, the Soar and Supergauss function can effectively increase the analysis information on meso- and small-scales in the lower atmosphere, significantly improving precipitation forecast accuracy in the center of Henan. It resolves problems related to the westward and weaker bias in precipitation forecast, thus the intensity and the fields are well simulated. As a result, compared to the Gauss correlation function, the Soar correlation function improves scores ETS for 3-hour accumulated precipitation, particularly in heavy rainfall, which is meaningful for forecasting extreme precipitation events. For the 24-hour precipitation scores over 6 days, the Supergauss function has a higher score ETS but larger BIAS and false alarms compared to the Soar correlation function.