Hotine's geopotential formulation: revisited

Hotine's (1969) partially nonsingular geopotential formulation is revisited to study its utility for the computation of geopotential acceleration and gradients from high degree and order expansions. This formulation results in the expansion of each Cartesian derivative of the potential in a spherical harmonic series of its own. The spherical harmonic coefficients of any Cartesian derivative of the potential are related in a simple manner to the coefficients of the geopotential. A brief overview of the derivation is provided, along with the fully normalized versions of Hotine's formulae, which is followed by a comparison with other algorithms of spherical harmonic synthesis on a CRAY Y-MP. The elegance and simplicity of Hotine's formulation is seen to lead to superior computational performance in a comparison against other algorithms for spherical harmonic synthesis.