= Log-pressure quasi-geostrophic potential vorticity
{title2=$q=\nabla_h^2\psi+e^{z/H}\partial_z(e^{-z/H}f_0^2\psi_z/N^2)+\beta y$}
In a <log-pressure coordinate>, <quasi-geostrophic potential vorticity> uses density-weighted vertical stretching. For stratification $N^2=RS/H$ and <geostrophic flow> $\mathbf u_g=(-\psi_y,\psi_x,0)$, the inviscid equation is $D_gq/Dt=0$. Combining horizontal <vorticity> balance with the thermal equation eliminates <ageostrophic flow> and gives this conservation law.
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