Abstract: The nodal sets (zero sets) of spherical harmonics divide the spherical surface into numerous small regions through their intersections and result in the emergence of vertices (V), edges (E), and faces (F). The relationship between these elements and the Euler characteristic (χ) of the spherical topology is given by χ = V - E + F = 2. If the flow field on the spherical surface is vortical, the physical interpretation of nodal sets is that the vertical vorticity on the sphere is zero. And Nodal sets divide the sphere into alternating regions of positive and negative vorticity, representing cyclones and anticyclones, respectively. For vortical fields consisting solely of zonal flow, the nodal sets coincide with both the locations of zero vertical vorticity and the latitude weighted maxima of the zonal flow. If the flow field on the spherical surface is a non-vortical gradient field, the zonal nodal set represents lines of constant potential or isobars. The meridional circulation, such as the north-south meridional flow, is perpendicular to the nodal set. The nodal set corresponds to regions of zero horizontal divergence, dividing the spherical surface into alternating patches of positive and negative horizontal divergence. Based on these considerations, the qualitative models of atmospheric circulations, such as meridional and zonal flows, Hadley circulation, and the three?cell circulation system with its associated planetary wind belts on the sphere can be inferred from a topological perspective. Subsequently, the models can be further validated through the properties of critical points in the flow field.