Autoconvective Lapse Rate
From hydrostatic equilibrium and the ideal gas law,
P = Rg (z) T(z) we have
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
But T(z) and
![rho](https://pds-atmospheres.nmsu.edu/images/rho2.gif)
![Gamma](https://pds-atmospheres.nmsu.edu/images/Gamma.gif)
![ident](https://pds-atmospheres.nmsu.edu/images/ident.gif)
![geq](https://pds-atmospheres.nmsu.edu/images/geq.gif)
then d/dz
0. Thus, the autoconvective
criteria is that when the density increases with altitude the
atmosphere will be forced to convectively adjust and this
condition is met when
![Gamma](https://pds-atmospheres.nmsu.edu/images/Gamma.gif)
![ident](https://pds-atmospheres.nmsu.edu/images/ident.gif)