= Stretched coordinates for quasi-geostrophic inversion
{title2=$Z=(N/|f|)z,\quad Q-f=\psi_{xx}+\psi_{yy}+\psi_{ZZ}$}
For constant nonzero <Coriolis parameter> and positive constant <buoyancy> <frequency>, the anisotropic <quasi-geostrophic potential vorticity> operator becomes the ordinary three-dimensional <Laplacian> in the displayed coordinates. Its decaying whole-space inverse is $\psi(\mathbf X)=-\int[Q(\mathbf X')-f]/(4\pi|\mathbf X-\mathbf X'|)\,d^3X'$. Boundary or far-field data are needed to exclude arbitrary harmonic additions.
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