On an Earth ellipsoid best-fitted to the Earth surface

Historically, the mean Earth ellipsoid is obtained by fitting an ellipsoid of revolution to the geoid. Such an ellipsoid, however, does not necessarily best fit the physical surface of the Earth due to the existence of topography outside the geoid. In this paper, we present a purely geometrically defined Earth ellipsoid that best fits the physical surface of the Earth so that the resulting ellipsoidal height attains minimum global mean square value. Using a global digital terrain model and a global geopotential model, the size, shape and position of such an Earth ellipsoid have been numerically estimated.