Least squares spherical harmonics approximation on the Cubed Sphere

The Cubed Sphere grid is an important tool to approximate functions or data on the sphere. We introduce approximation framework this based least squares and a suitably chosen subspace of spherical harmonics. main claim that for equiangular with step size π/(2N), relevant harmonics one all SH degree less than 2N. This choice, which matches Nyquist’s cutoff frequency along equatorial great circle, provides problem both well-posed well-conditioned. A series theoretical numerical results supporting fact are presented.