## 2 Materials and Methods
### GNSS and Leveling Data Integration  
Based on the literature [6; 7; 8; 9; 10; 11; 12], data integration methods for determining the vertical movements of the Earth's crust can be divided into five approaches. In all approaches, the data are vertical movements at points (GNSS stations, nodal benchmarks) or between points. A brief description of the main requirements and capabilities of these methods is shown below:  
* _Data averaging_: Vertical movements must be determined at the same points with known uncertainty in their determination, the same reference level used and measurement in similar time intervals; under certain assumptions, vertical movements can be determined at close points. Possibilities--vertical movements determined from GNSS data (from various calculation strategies) as well as vertical movements determined from double leveling from different measurement epochs can be used as data.
* _Transformation_: Vertical movements must be determined at the same points, but not for the entire set--only for adjustment points--and one reference system should be adopted--secondary (reference); under certain assumptions, vertical movements can be determined at close points, similarly to adjustment points (pseudo-nodal points). Possibilities--vertical movements determined from GNSS data (from different calculation strategies), vertical movements at nodal and intermediate benchmarks, and hybrid data (GNSS vertical movements and vertical movements at benchmarks) can be used as data, the data can have different temporal and spatial resolution, and adjustment points can be individually selected.
* _Interpolation_: Vertical movements should be related to the same reference level. Possibilities--vertical movements determined from GNSS data (from various computational strategies), vertical movements at nodal and intermediate benchmarks, and hybrid data (GNSS vertical movements and vertical movements at benchmarks) can be used as data; the data may have different temporal and spatial resolutions. The vertical movements do not have to be determined at the same points. It is possible to weight observations.
* _Adjustment of the hybrid network_: The sets should have a network structure, vertical movements should be determined between adjacent points for each adopted set  
Figure 6: Vertical movements between neighboring ASG-EUPOS stations (source: [5]).  
separately with known uncertainty, common points should be defined, and a defined reference level should be defined. Possibilities--vertical movements determined from GNSS data (from different calculation strategies), and vertical movements between nodal benchmarks and hybrid data (vertical movements between GNSS stations and vertical movements between nodal benchmarks) can be used as data, the data can have different temporal and spatial resolution, adjustment points can be selected individually, and the reference level may be adopted individually.
* A fifth approach may combine all four of the above assumptions in various configurations.  
From the above, two methods are most suitable for this article: hybrid network transformation and adjustment. The same reference point was adopted. The following computational strategy was adopted:  
* Test adjustment of the DLN (double-leveling network) and GTN (GNSS triangulation network) networks separately.
* Adjustment of the hybrid network (DLN+GTN), common points (nodal points) 50 adopted from [17]--version 1.
* Transformation of absolute GNSS vertical movements [5] at ASG-EUPOS stations to relative vertical movements determined from the DLN adjustment, common points (nodal points) 50 adopted from [17]--version 1.
* Statistical evaluation of hybrid network adjustment and transformation.
* Re-adjustment of the hybrid network based on common points with the best match between the hybrid network and transformation vertical movements, without points showing self-motions or VLM movements [5]--(version 2).
* Transformation based on common points as in point 5.
* Statistical evaluation of the results.