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), the Gaussian and the Supergauss function based on the CMA-MESO (China Meteorological Administration Mesoscale Model). Results from the single-point test indicate that when using the u- and v-components as background error covariance, all the three correlation models can provide a reasonable representation of the wind field horizontal correlations, resulting in a coherent distribution of analysis increments. The Soar and Supergauss functions gain more information on meso- and micro-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 function. Moreover, the Soar and Supergauss function can effectively increase the analysis information on meso- and micro-scales in the lower atmosphere, significantly improving precipitation forecast accuracy in central Henan. The two options resolve the problems related to the unrealistically westward shift and underestimation of precipitation, leading to more consistency between observations and simulations. Compared to the Gauss correlation function, the Soar correlation function improves the ETS score for 3 h accumulated precipitation forecast, particularly for heavy rainfall, which is meaningful for forecasting extreme precipitation events. For the 24 h precipitation forecast scores over 6 d period, the Supergauss function has a higher ETS but larger BIAS and false alarm compared to the Soar correlation function. Overall, the Soar correlation function shows certain advantages in meso- and micro-scales analyses, yet it still has limitations when compared to Supergauss models. Further research is needed to apply multiscale methods to enhance the performance of the Soar correlation function.