What is Relative, planetary and absolute vorticity?

For a horizontal velocity $(u, v)$, the relative vorticity is the vertical component of the curl of the velocity relative to the ground, $\zeta = \partial v/\partial x - \partial u/\partial y$, positive for anticlockwise rotation seen from above. The planetary vorticity is the vertical component of the vorticity of the Earth’s rotation, $2\Omega\sin\varphi = f$. The absolute vorticity is their sum, $\zeta + f$.