English: Plot of both the annual and monthly-averaged Stokes zonal meridional mass stream function based on 1991-2020 mean monthly meridional winds from NCEP-NCAR Reanalysis 1.

Given the latitude ${\displaystyle \phi }$ and the pressure level ${\displaystyle p}$, the Stokes stream function characterizing the Hadley circulation is given by

${\displaystyle \psi (\phi ,p)={\frac {2\pi a\cos \phi }{g}}\int _{0}^{p}[v(\phi ,p)]\,dp}$

where ${\displaystyle a}$ is the radius of Earth, ${\displaystyle g}$ is the acceleration due to the gravity of Earth, and ${\displaystyle [v(\phi ,p)]}$ is the zonally averaged meridional wind at the prescribed latitude and pressure level. NCEP-NCAR Reanalysis 1 includes meridional winds for a limited set of pressure levels; for this plot, the meridional wind data was first linearly interpolated to the domain [10 hPa, 1000 hPa] at 1 hPa intervals. The streamlines sketch the direction of mass flow, assuming that the vertical component is given by ${\displaystyle {\frac {\partial \psi }{\partial p}}}$ and the horizontal component is given by ${\displaystyle -{\frac {\partial \psi }{\partial \phi }}}$.

The timeseries plot at bottom gives the maximum absolute value of the stream function for both the Northern Hemisphere and Southern Hemisphere Hadley cells by month. The cell in the winter hemisphere is strongest, and the cells are weakest near the equinoxes.