Abstract: The anomaly of height fields is set up based on the temporal decomposition of these fields, and even continuations from hemisphere to globe at certain level in certain month are made. During the study, two kinds of monthly averaged geopotential fields dataset is used, namely 2.5° by 2.5° resolution even rectangular grid data and spherical function coefficient data derived from 1958—1997 NCEP/NCAR reanalyzed geopotential height fields dataset. Firstly based on the previously defined intensity index of climate anomaly fields (I_a), it demonstrates the intensity variations of hemispheric anomaly fields at the different height and seasons, and the differences between Northern and Southern Hemisphere are also investigated. Then according to the low-dimension and low-order characteristics of the spherical function spectrum in the hemispherical geopotential height anomaly fields, hemispherical circulation anomaly is divided into four types:hemispherical homogeneous anomaly, zonal homogeneous anomaly, ultra-long and long wave scale anomaly. The corresponding variance contributions (R′₀₀, R′₀, R′_ul, R′_l) are also calculated respectively by using spherical function coefficient data with the wavenumber of m≥0, k≤6. Finally the variations and their hemispheric differences of the four anomalies above as the function of height and seasons are discussed in detail.The main results are as follows:① I_a shows a yearly periodic oscillation and is stronger in winter than in summer. The index always increases with the height, especially in winter. However in summer I_a has a weak high (low) value center near the tropopause (the upper stratosphere) respectively. The difference between the two hemispheres is that the seasonal variation of I_a in the Southern is weaker than the Northern at the troposphere. ② For the spectral structure of the anomaly circulations, there are some obvious changes from the troposphere to the stratosphere. In the troposphere the ultra-long wave circulation is predominant. Hemispherical homogeneous anomaly (Long wave scale anomaly) is not important in the troposphere (stratosphere) respectively. ③ The characteristics of the variance contributions of the Northern Hemisphere can be concluded that in January, R′₀₀ at all the levels are very little (less than 10%); R′_l is only significant in the troposphere; R′₀ and R′_ul predominate at all the levels, whereas R′_ul(R′₀) is more important in the troposphere (stratosphere), and in July, R′₀₀ dominates in the medium and upper stratosphere; R′₀ takes second place; R′_ul and R′_l are predominant in the troposphere with equivalent magnitude. ④ For the Southern Hemisphere, in July, R′₀₀(R′_l) in the troposphere (stratosphere) is very little; just as the January's situation in the Northern Hemisphere, R′₀ and R′_ul are dominant through the atmosphere; R′_ul is a little larger. In January, the characteristics in the stratosphere are similar to July's situation in Northern Hemisphere. The difference is that R′_ul and R′₀ dominate through the troposphere with the comparable im portance.