In modern variational data assimilation system,the background error covariance determines the space distribution of observation information and analysis increment balance between control variables.Based on the NMC(National Meteorology Centre) method,a new multivariable balance constraint operator is designed,and the forecast difference fields of WRF model from 2 June to 9 August 2009 are used to simulate the new background error covariance.In physical transformation,the multivariable balance constraint operator is built among control variables including relative humidity.The empirical orthogonal function method and the recursive filter are used to simulate the vertical and horizontal error covariances of control variables (ψ,χ_u,T_u,h_ru,p_su)^T, respectively.The results of single observation test show that observation information has been passed between the wet and dry variables with new background error covariance,and the increment distribution of relative humidity is similar to the temperature.