Insights on terrain roughness and density variations for geoid models and orthometric heights: A quantitative comparison in the Konya Closed Basin, Türkiye and Auvergne, France

Recent advancements in high-resolution Digital Elevation Models (DEMs) derived from Light Detection and Ranging (LiDAR) and satellite radar technologies have added a new dimension to the determination of height systems and geoid models. However, their benefits are limited by simplified assumptions inherited from past practices. In mountainous areas, taking into consideration of topography as the Bouguer plate or employing inaccurate terrain corrections can constitute to a problematic approach. Even though the gravity reduction procedures mentioned above have been enhanced in geoid determination studies, the Helmert orthometric heights based on them are still used in some countries such as Türkiye and Taiwan. It is inevitable that this contradiction will negatively affect geoid modelling studies that are intended to be verified or combined with Global Navigation Satellite System (GNSS)/levelling data. Another issue arises by ignoring density variations of topographic masses. Through a comparative analysis, this study reviews combined and individual impacts of terrain roughness and density variations on geoid models in the Konya Closed Basin (KCB) and the Auvergne regions, with a focus on their distinctive topographical characteristics. Using 1″ DEMs of the Shuttle Radar Topography Mission mission and 30″ UNB_TopoDensT lateral density models, we reveal that terrain corrections in gravity reductions significantly affect geoid heights, with deviations of up to 11.9 cm in KCB and 4.2 cm in Auvergne. Incorporating lateral density models has resulted in geoid height discrepancies of up to 26.8 cm in KCB and 6.7 cm in Auvergne. A validation strategy implemented through GNSS/levelling paths showed that terrain corrections markedly improved geoid model accuracy, particularly in relation to elevation. However, the contribution of the UNB_TopoDensT model to geoid accuracy is questionable in terms of accuracy. Notably, applying density values below 2.4 g cm-3 in high-altitude regions can lead to disruptive effects on geoid determination. This result is underscoring of the need on a realistic modelling of topographical densities in high elevated and rugged terrains. A further conclusion that emerged from these analyses is that gravimetric geoid models should be verified by rigorous orthometric heights, which are observed to fit them better at the 1-2 cm level, instead of the Helmert orthometric heights.