Modifying Stokes' function to reduce the error of geoid undulation computations

Errors in computations of the geoid undulation, which determines the position of the geoid with respect to a reference ellipsoid, introduced by various modifications of the Stokes' function in the Stokes integral formula for the undulation are examined in light of currently available harmonic coefficients. The variants considered include the conventional Molodenskii truncation theory, in which integration is limited to a spherical cap, and the variations suggested by Molodenskii (1958) and Meissl (1971). In computations of the undulation from gravity anomalies in a spherical cap and terrestrial and satellite harmonic potential coefficients (GEM 9 and GEM 10B), it is shown that either of the modifications to the conventional Molodenskii theory results in substantial reductions in truncation errors, with the simpler modification of Meissl even providing superior results in certain circumstances.