## 1 Introduction
Connecting nodes have to be identified to link several independent networks of vertical movements. A solution to this problem was proposed by [20]. An analysis of unadjusted vertical movement changes  
Figure 1: Leveling network (blue triangles) and distribution of GNSS stations (red frames). Source: many.geoportal.gov.pl. on selected leveling lines used to estimate the maximum distance between nodal points and GNSS permanent stations was conducted. Therefore, points from a double-leveling network and a network of GNSS stations ASG EUPOS (Active Geodetic Network - European Position Determination System) can be considered as corresponding to the same nodal point (pseudo-nodal point). These points should less than 10 km apart. Connecting nodes are defined to simultaneously adjust independent networks of vertical movements and to generate a cartographic model of the vertical movements of the Earth's crust. The model can also be developed with the use of interpolation methods. In this study, a least-squares collocation was selected as the optimal method due to the use of geophysical data, differences in the spatial and temporal distribution of network points, and the possible presence of anisotropy and data trends. This group of methods involves kriging and its modification, namely co-kriging, which was developed for modeling surfaces based on several datasets. Co-kriging interpolation with a variogram (semivariogram) analysis was deployed in this study. This advanced method supports the evaluation of data during the selection of interpolation algorithm parameters. The relationships between data are modeled to adjust for the effect of extreme values and derive skeleton lines [21; 22; 23; 24]. Variogram analyses are performed to determine the correlations between the location of network points and point values. Variogram analyses support the description of anisotropic directions, the magnitude of nugget effects, and the variance. The selection of the optimal variogram significantly influences the quality of the generated model. An excessive variance could be indicative of low-quality data that requires additional processing. The nugget effect denotes undesirable local extremes in the process of modeling the vertical movements of the Earth's crust. These extremes have to be reduced or eliminated to obtain an accurate cartographic model. Data analyses also provide information about the homogeneity of datasets, which is particularly important in hybrid models of vertical crustal movements (for example models that rely on leveling data and GNSS data). Statistical analyses are performed before and after interpolation to assess the quality of the model and its applicability for research. In this study, the information about the relative vertical movements of the Earth's crust was acquired from precision leveling campaigns and GNSS measurements on the territory of Poland (465 points). Poland is situated in Central Europe, and its landform is influenced by glacial movements and, to a minor extent, plate tectonics and geological events caused mainly by fossil mining. The characteristics of the existing maps (cartographic models) of vertical crustal movements on the territory of Poland are presented in Table 1. None of the existing models describe anisotropy or nugget effects, and none of them combine leveling data with GNSS data.