Vertical advection of geopotential

The vertical advection of geopotential is simply discretized as

$${\dot\pi} \frac{\partial\Phi}{\partial\pi}\bigg\vert_k = -{\dot\p... ...i_{k} - \Phi_{k-1}} { {\overline{\pi}}_{d,k}-{\overline{\pi}}_{d,k-1} } \right)$$ (203)

Note that numerical tests revealed that there is virtually no impact of using a higher order flux form advection compared to the more simple standard second order approach given by Eq. 205, thus the model currently uses the relatively simple second order scheme by default.