My hypothesis is as both pressure and temperature increases the surface will increase.
If we simplify to an ideal gas that doesn't undergo phase changes, PV = nRT.
I don't see a "surface" involved anywhere unless you make it the surface area of the volume that contains the gas. If we assume a sphere, then surface area will increase with volume. If the number of moles of the gas remain the same, the equation predicts
1) presure going up and temperature constant means volume decreases (inverse relationship), and
2) Temperature going up and pressure constant means volume increases (normal relationship)
Your hypothesis has both an inverse and normal relationship so there is going to be some cancellation of effects.
Are you more interested in the atmosphere (macro level) or are you more interested in things that can be done in the lab (micro level).
If you are more interested in things that can be done in a lab, then that opens areas of investigation to state changes and thermodynamics.