The isobaric pattern in surface synoptic chart shows contours of space pressure surface. The global pressure surface is a spherical surface with concaves and convexes. The peaks, valleys and passes in the space pressure surface correspond to high pressure centers, low pressure centers and saddle points in surface synoptic chart. Although the locations of concaves and convexes in the spherical surface change with time, and the corresponding locations of high and low-pressure centers also change with time, the Euler characteristic of the spherical surface is a topology invariant, whose number is 2. Topologically, the Morse theorem states that if a gradient vector field on the spherical surface synoptic chart has many zeros, then (number of high pressure center) + (number of low pressure center)-(number of saddle point)=2. For any vector field, the extended theorem is called Poincare-Hopf theorem. This theorem is very important for weather prediction. The present paper shows application of this theorem in longitudinal flow, latitudinal flow, Hadley circulation, and three-cell circulation etc. Atmosphere scientists know for sure that global atmosphere motion follows not only the Navier-Stokes equation, but also the topological theorem.