# The Impact of Gravity on Different Height Systems: A Case Study on Mt. Medvednica
## 1 Introduction  
To investigate the influence of gravity on different height systems, this study combined GNSS, leveling, and gravimetric measurements. Global Navigation Satellite Systems (GNSS) represent a collective term for all the satellite systems used for navigation and positioning. GNSS measurements provided positional coordinates for points that servedas reference markers for gravimetric measurements and geometric leveling. Considering the level of accuracy required to validate the hypothesis, precise geometric leveling was employed, which is recognized as the most accurate method for determining height differences in geodesy. Geometric leveling operates within the real field of gravity, where even under ideal conditions, the sum of height differences in a closed leveling loop would not be exactly zero due to the influence of the leveling path.  
The main objective of this study is to analyze how gravity affects different types of heights derived from leveling, such as orthometric, normal, and normal-orthometric heights. The methodology involves comparing these height types by integrating precise geometric leveling data with gravity measurements along a steep terrain profile. GNSS was used exclusively to establish horizontal positions and support the stabilization of benchmarks, while gravity data enabled the determination of corresponding height systems.  
To address this, gravimetric measurements were incorporated alongside leveling measurements, allowing the integration of gravity data with height differences. The study area was chosen to maximize the observable effects of gravity, which generally becomes more pronounced at greater height differences. Measurements were conducted along the Sljeme Road on the Mt. Medvedrica region of the City of Zagreb, Croatia, where the decrease in gravity with increasing altitude could be systematically analyzed. The fieldwork started in the foothills near the Sljeme Tunnel, continued along the Bliznec Road and the winding Sljeme Road, and concluded near restaurant Stara Lugarnica at the summit. The terrain was first reconnoitered to determine suitable locations for stabilizing benchmarks along the measurement trajectory. The GNSS-determined positional coordinates of these points were referenced to the official positional reference coordinate system of Croatia, the Croatian Terrestrial Reference System 1996 (HTRS96) (EPSG:4888).  
After determining the coordinates of the benchmarks, leveling and gravimetric measurements were carried out. To ensure the highest accuracy of precise geometric leveling, the instruments used--leveling staffs and levels--were tested in accordance with the Croatian standardized norm HRN ISO 17123-2:2004.  
The results of the leveling measurements, including their adjustments, were expressed in the Croatian Height Reference System 1971 (HVRS71) (EPSG:5610), while gravimetric measurements and their subsequent adjustments were presented in the Croatian Gravimetric Reference System 2003 (HGRS03). This integrated approach allowed for a comprehensive analysis of the impact of gravity on various height systems and provided insights into the relationship between leveling measurements and gravity field variations.