There is something about inverse square laws which makes them break down at extremities. Einstein showed this in the past with General Relativity. The inverse square law for calculating irradiance from a star is a direct consequence of conservation of energy. However, it is an approximation which fails to be generally applicable.

I was fortunate to get a chance to work on a project that makes a case about how inverse square law breaks down beyond a particular latitude on the planet and suggests a new numerical model that can supersede it. The adjacent figure shows the latitudinal zone where we see a deviation from the inverse square law. 

This work is currently under peer-review. A previous preprint of the work can be seen here.