In realistic calculations of the vertical propagation of Rossby waves one must take into account the vertical variation of density. Carry through the calculation leading to the Charney–Drazin condition, either using pressure

(or log-pressure) co-ordinates or using the anelastic version of quasigeostrophy, using (5.65) with ρ = ρ₀ exp −z/H. Show that the condition for propagation analogous to (6.44) becomes

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