So far I understood, geopotential $\Phi$ is just defined by
$$\vec \nabla \phi = \vec g$$
But because g can be taken to be constant within troposphere, it is nothing but
$$\Phi(z) = g \cdot z + C$$
So it is nothing more than height z multiplied by a constant. What is the benefit of it? These relations are trivial - is there anything I have overseen?
In this image one could equally say that minimum surface pressure corresponds to minimal height of constant pressure layers above.
