Abstract: In this paper,the statistical technique is employed to establish a model for the precision estimation of the gravity and deformation variation caused by barometric pressure loading calculated with Green's function method.Using the data of atmospheric pressure recorded in China and its adjacent areas,we obtain the error constants of the data and the estimation of precision of the atmospheric gravity and deformation signals.Our results agree with those of detection of the atmospheric gravity signals using tidal gravity observations with high precision in different weather condition.This method can be also used in other similar physical models.At first,based on the comprehensive analysis of the Green's function of the earth's response to air-pressure loads and the errors caused by the numerical calculation,a statistical technique is used to set up the error estimation model of the barometric pressure data and their noise at every individual station.And then,this model is generalized to the case for a plane.The model of observing errors,expressed with average air-pressure data,is obtained.The method of error estimation in Stokes formula,developed by Moritz,is employed to establish the model of error transformation caused by convolution.In consideration of the errors of air-pressure data,the model of error transformation and the statistical characteristics of barometric pressure data,we obtain the relationship of the Earth's response to the barometric pressure loads and the air-pressure signals,errors due to discretion and observing errors.Finally,in the calculation of the Earth's response to the barometric pressure loads,the effects of different kinds of errors on the final results are determined. The continuous air-pressure observations,with four samples a day,recorded at more than 700 stations,selected from over 2000 ones,were employed in this study.The period of the observations spans January 1,1990 to December 31,1994.The covariance of the air-pressure variations between each two stations is analyzed,with the air-pressure variations as the random variables.The estimated values of the covariance (EVC) of the air-pressure variations between Wuhan and the adjacent stations were obtained.The surface distribution of EVC was derived based the station locations and their EVC.A transformation parameter ΔΣ,defined in this paper,and obtained by numerical integration of the surface distribution function of the covariance and division by the autocovariance estimation at a given station,is about 10⁶ km².We got the calculation deviations σ₁,reflecting the effects of the standard deviation of average atmospheric pressure upon the atmospheric gravity and deformation signals during sampling and unsampling periods,and σ₂,describing the effects of the atmospheric averaged signals standard deviation upon the atmospheric gravity and deformation signals.And then,the precision estimation of the calculation for the effects of barometric pressure upon the gravity and deformation is obtained. The results show that the precision of atmospheric correction to gravity is about ±0.103μGal for sampling period,and ±0.639μGal for unsampling period,respectively.Considering the fact that the observation precision of superconducting gravimeters is about ±0.2μGal,we can reach the conclusion that the former correction is effective,while the later one unreasonable.This agrees with the analysis of the Earth's tides in variant condition.