I’m trying to create a photorealistic Earth Atmosphere. Several papers written on the topic of atmospheric scattering state that our atmosphere’s density has an exponential fall off, with most of it in the 25% of the roughly 100km of its visible height.

How can I implement exponential fall off into the density of the volume scatter node? ColorRamp node doesn’t seem to have exponential gradation. RGB Curves might not be precise enough. Is there a way to implement an exponential math function to control the volume density’s interpolation/gradation?

The gradient texture has a quadratic and quadratic sphere falloff (exponent of 2)

Alternatively - just use the linear or spherical falloff and multiply it with a math node set to “power” - then set your exponent to whatever you want it to be.