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So i know that there are diurnal patterns for virtual potential temperature that can be described conceptually (such as $\frac{\partial \theta_v}{\partial z}\approx 0$ in the mixed layer and $\frac{\partial \theta_v}{\partial z} >0$ in the entrainment zone). I know there are similar relationships seen for moisture. Is there a similar concept for $\ce{[O_3]}$?

For example, is $\frac{\partial \ce{[O_3]}}{\partial z}>0$, $\approx0$ or $<0$ in the entrainment zone? What about the residual layer? Nocturnal inversion? And so on.

References would be appreciated.

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