Determination of radii of curvature for high resolution geoid models using the harmonic synthesis algorithm

Different types of radii of curvature were assessed for the geoid based on the GECO geopotential model, up to degree and order 2190. The route values of gravity and the three horizontal gravity gradients were computed based on such geopotential model and the angular velocity of the Earth. The investigation was performed on coarse global grids and finer grids covering the Egyptian territory. Respective latitudinal and longitudinal profiles for the geoidal radii were extracted. Comparisons were held with the radii of curvature on the WGS-84 ellipsoid, and with the geoidal radii derived from other models of lower resolutions. Unlike the ellipsoid, the values of the geoidal radii exhibited a rather irregular behaviour that is far from any geographical symmetry. The principal radii of the geoid do not generally occur along the meridian and prime-vertical directions. Such irregularities were found to be more exaggerated with higher degrees. At all investigated resolution levels, the signs of the principal radii assured the convexity of the geoid surface. This enabled to define, compute and compare the Gaussian mean radii for the geoid. The local residual geoidal radii showed a decaying spectral tendency. Also, the results implied that the utilized algorithm proved to be convergent.