To describe the nature of hemispherical monthly mean geopotential height fields,several circulation indices,such as intensity of climate fields I_c,intensity of climate anomaly fields I_a,instability of climate fields I_us,are defined.Calculation and analysis are performed based on the monthly mean geopotential height fields from NCEP/NCAR 40a reanalysis datsets.Results suggest that the indices exhibit evident spatial-temporal structure and significant difference between Northern and Southern Hemisphere.The basic characterics of the climatology and anomaly of atmospheric geopotential height field are generally presented by the indices proposed.