Establishment of a corrective geoid surface by spline approximation of Iranian GNSS/levelling network

The performance of the gravimetric geoid models is usually evaluated by comparison of geoid heights with the GNSS/levelling derived geoid. But the GNSS/levelling network can be infected by significant systematic biases and random errors, especially in large and uneven areas. This contribution addresses the challenging problem of the corrector surface development along with the elimination of biases. To this end, fitting an appropriate geometric surface to the GNSS/levelling geoid heights is required, which is accomplished by applying the least squares B-spline approximation theory to the GNSS/levelling data. In addition, the 3D affine transformation is used to detect systematic effects of the GNSS/levelling network compared to a global geoid model. This strategy is applied to the adjustment of the Iranian GNSS/levelling network. A significant tilt is observed across the country ranging from −0.35 m to 0.04 m. The entire study area is divided into four zones and the corrector surfaces are obtained in each zone. The accuracy of three global geoid models, EGM2008, EIGEN-6C4 and SGG-UGM-1, along with that of the Iranian regional geoid model IRG2016, are then investigated based on the raw GNSS/levelling heights and the corrector surfaces. The evaluations show the reliable results regarding the corrector surfaces against the raw data set. All geoid models show their maximum RMSE values of discrepancies in the mountainous zones and their minimum RMSEs in the zones having lower variety in topography. This indicates that the irregular topographies are not well detected by the global models over the study area.