The geoid and its horizontal derivatives, the deflections of the vertical, play an important role in the adjustment of geodetic networks. In the one-dimensional (1D) case, represented typically by networks of orthometric heights, the geoid provides the reference surface for the measurements. In the two-dimensional (2D) adjustment of horizontal control networks, the geoidal undulations N and deflections of the vertical ξ, η are needed for the reduction of the measured quantities onto the reference ellipsoid. In the three-dimensional (3D) adjustment, N and ξ, η are basically required to relate geodetic and astronomic quantities. The paper presents the major gravimetric methods currently used for predicting ξ, η and N, and briefly intercompares them in terms of accuracy, efficiency, and data required. The effects of N, ξ, η on various quantities used in the ID, 2D, and 3D network adjustments are described explicitly for each case and formulas are given for the errors introduced by either neglecting or using erroneous N, ξ, η in the computational procedures.
