Agnieszka Wnęk

Time series of Global Positioning System (GPS) station positions include signals whose characteristics vary over time. Therefore, in detailed analyses, methods dedicated to nonstationary time series should be used. In this study, the Complementary Ensemble Empirical Mode Decomposition (CEEMD) method was used to model trends in time series of GPS station positions and to verify their nonlinearity. As the CEEMD method does not provide equations for assessing the uncertainty of the determined trend, we propose to use the bootstrap method for this purpose. In this study, daily time series of the Up components of 25 GPS stations from seismic regions in Europe and from the Nevada Geodetic Laboratory (NGL) service were used. The determined trends were compared with the trends calculated using the Singular Spectrum Analysis (SSA) method and then interpreted in the context of earthquakes occurring in the vicinity of the station. In turn, the bootstrap method was used to estimate the mean standard deviations of trends determined by the CEEMD as well as SSA method. The conducted studies showed the usefulness of the CEEMD method for modeling trends in time series of GPS station positions, especially for stations where changes may occur on short time scales, visible as the local nonlinearity of the trend, mainly due to earthquake events. The bootstrap-estimated mean standard deviation values for the modeled nonlinear trends are at the level of 1–3 mm, depending on the station. In turn, the root mean square error (RMSE) estimated between the nonlinear trend determined by the CEEMD method and the linear trend fitted to it by the least squares method does not exceed 3 mm. The conducted research indicates that the CEEMD method can be successfully used to model locally nonlinear trends resulting from earthquakes, and the mean standard deviation of the estimated trends is relatively low.

The article proposes to combine a methods based on wavelet denoising (WDN) and Shannon entropy (DSE) for GNSS station position time series denoising and Complementary Ensemble Empirical Mode Decomposition (CEEMD) for the decomposition of the time series into frequency components, namely intrinsic mode functions (IMFs). First, we used WDN as well as DSE to denoise the GNSS time series. They were then decomposed with CEEMD, which is dedicated to analysing non-stationary time series. The proposed WDN + CEEMD and DSE + CEEMD methods were then employed to analyse several GNSS station position time series in Poland. We used daily time series of position residues for 15 GNSS stations of the EUREF Permanent Network (EPN) classified as the Polish national control network. The station time series were decomposed into IMF frequency components, of which IMF5 and IMF6 represented semi-annual and annual signals. We noted an annual oscillation for all the reference stations in the horizontal and vertical components. A semi-annual oscillation was found for all the stations only in the vertical component. The study confirms that the WDN + CEEMD as well as DSE + CEEMD method is capable of limiting the absorption of some noise by seasonal signals. The values of the spectral indices of the station position time series after subtracting the seasonal signals modelled by the WDN + CEEMD or DSE + CEEMD methods assumed values from the range of the power law noise model. GNSS station position time series analysis with WDN + CEEMD and DSE + CEEMD yielded satisfactory results and can be a good alternative for modelling time-dependent seasonal signals in GNSS time series, particularly the annual and semi-annual signals.

Soil sealing is a threat to soil and its ecosystem services. One of the main drivers of soil sealing is land degradation resulting from the expansion of urban areas, where it leads to such problems as the growing risk of flooding and local inundations, urban heat islands, or water shortages. The article focuses on analyses and quantification of the general degree of soil sealing in 2012–2018 in eight functional urban areas (FUA) in Poland, taking into account their division into the urban core (UC) and the commuting zone (CZ). We used the high resolution layer imperviousness density (HRL IMD) data to quantify soil sealing as well as data on land cover and land use with different spatial resolutions, i.e. from the European Urban Atlas project (UA) and the National Database of Topographic Objects (BDOT10k) to quantify artificial surfaces. The research determined the spatial differentiation of UCs and CZs in terms of the degree of soil sealing. We further observed higher average growth of sealed land in CZs. Quantitative and spatial analyses determined the spatial patterns of soil sealing in the FUA in Poland. Soil sealing intensified from 2012 to 2018. The process should be expected to continue in the coming years in light of the continuous transformation of vegetated areas into artificial ones. The conclusions should be considered valuable for the implementation of the spatial policy concerning sustainable land use and soil protection in suburban areas.

This article investigates the land use and land cover (LULC) mosaic as a function of distance to the city centre. The research area is four Functional Urban Areas (FUAs) of the capitals of Central European countries: Czechia (Prague), Poland (Warsaw), Slovakia (Bratislava), and Hungary (Budapest). The article presents LULC mix changes in these FUAs in the context of transformations in urban cores and commuting zones of capital city metropolises, which have large populations and prominent positions in the country or region. The study makes use of Urban Atlas LULC data for 2006, 2012, and 2018. LULC change was analysed using a hexagonal tessellation with the hexagon as the basic spatial unit. Spatial entropy (ENT) and Simpson’s Diversity Index (SIDI) were employed. The change in ENT and SIDI were determined as a function of distance to urban cores, as well as changes on the first level of Urban Atlas nomenclature for 2006–2012 and 2012–2018, as well as on the third level of nomenclature for 2012–2018. The research shows that changes from 2006 to 2012 were more considerable than from 2012 to 2018. It also revealed that, if LULC classes are considered on the first level of nomenclature, diversity in urban cores grows and then declines in commuting zones. An analysis of diversity on the third level of nomenclature demonstrated its decline with the growing distance to the urban core. It has also been demonstrated that the mean values of ENT and SIDI are approximately twice as high in urban cores as in commuting zones, indicating a plateau of the mean value of ENT and SIDI over the study period in urban cores compared to an increase in commuting zones around them. The conducted research will be helpful to urban planners and decision-makers in directing the further, inevitable development of metropolitan areas in accordance with sustainable environmental management.

The paper presents an assessment of the accuracy and precision of point positioning using a currently available online service for automatic post-processing (APPS) of GNSS observations made by the Polish Active Geodetic Network—European Position Determination System (ASG-EUPOS). The ASG-EUPOS network is part of the national EUPOS project and was selected for the study because of its substantial spatial reach in Europe. A modification to the current APPS algorithm is proposed to limit the number of baseline vectors used in positioning and change the method for adjusting post-processing results. Currently, the APPS of the ASG-EUPOS determines point coordinates based on the method for adjusting direct and equally accurate observations with the least-squares method (equally accurate method, EAM). The modification proposes to determine the coordinates based on post-processing results adjustment using the unequally accurate observations method (unequally accurate method, UAM). Our analysis diagnoses the uncertainty of the ASG-EUPOS’s APPS, and the modification optimises the adjustment. The proposed modification facilitates a much lower standard deviation of positioning in relation to reference positions. It is demonstrated that, if modified, the ASG-EUPOS service can provide automatic post-processing for 1 h GPS observations with a 1 s interval at 0.03 m accuracy for 99% of cases.

The land use mix (LUM) is among the critical issues in spatial planning because it can determine the occurrence and structure of various land use and cover types (LUC) and prevent any adverse patterns. The paper focuses on the LUM in functional urban areas (FUAs) in Czechia, Slovakia, Poland, and Hungary. The research employed Urban Atlas (UA) data on LUC in 2006 and 2012 to characterise LUM in the FUAs. The research follows the division of the FUA into the urban area (urban core, UC) and its functional surroundings (commuting zones, CZ). We further characterised the phenomena investigated for the entire country, region, and Europe using Corine Land Cover (CLC) data. The LUM was quantified with the entropy index (EI), dissimilarity index (DI), and multi-dimensional balance index (MBI). The EI demonstrated that the investigated FUAs went through more substantial LUM changes than the 27 European Union member states (EU27) from 2006 to 2012. Moreover, it has been demonstrated that LUM overspill was more intensive in CZs than in UCs on the regional and national levels. We found out that urbanised areas grew at the expense of agricultural areas in both UCs and CZs with similar dynamics in 2006–2012 in all the analysed countries.

We present the modeling of annual and semiannual signals in position time series of GNSS stations. The employed method is the Complementary Ensemble Empirical Mode Decomposition (CEEMD), dedicated to analyzing nonstationary and nonlinear signals. The input data were daily time series of position residuals for 25 stations of the EUREF Permanent Network (EPN) collected over 16 years. The CEEMD method was applied to decompose the GNSS time series into nine intrinsic mode functions (IMF1–IMF9). The set of the IMFs was divided into high- and low-frequency sets with mutual information entropy (MIE). IMF5 turned out to be the threshold for high- and low-frequency IMFs in most cases. Hence, IMF1 to IMF4 are considered functions of the high-frequency part of the signal, while IMF5 to IMF9 cover the low-frequency band. The spectral analysis demonstrated that IMF5 and IMF6 represent annual and semiannual signals, respectively, with time-dependent amplitudes. Therefore, IMF5 and IMF6 were used as seasonal oscillation models and juxtaposed with seasonal models from fitting periodic functions using the least-squares (LS) method as well as with the seasonal models obtained using singular spectrum analysis (SSA) decomposition. This way, the suitability of the CEEMD method for modeling seasonal signals in GNSS time series was verified. The calculated spectral index for the GNSS time series after subtracting seasonal models varies from − 1 to 0, which corresponds to the fractional Gaussian noise. The analyses provided new insight into GNSS time series by defining their time-dependent seasonal models as well as demonstrated the suitability of the CEEMD method for this purpose.

The paper analyses the accuracy of the determination of normal heights in the national spatial reference system using the PL-geoid-2011 quasi-geoid model. The heights were determined using the PL-EVRF2007-NH normal height system. The paper discusses the results of a measurement experiment consisting in measuring 8 points with the use of the Network Real Time Kinematic (NRTK) technique and the Virtual Reference Station (VRS) surface correction generated on the basis of the TPI NETpro commercial network of reference stations and with the use of two global satellite systems (GPS, GLONASS). In the experiment, three measurement schemes were evaluated in relation to the number of measurement epochs recorded above the designated point, as well as the order of recording points. The conducted measurement experiment allowed to determine which of the proposed schemes guarantees the best accuracy from the point of view of establishing a height measurement network with the use of the NRTK technique and VRS corrections. The tests showed that it is possible to determine the height difference between points using the NRTK technique and the VRS method with an accuracy of 0.01m. However, to ensure adequate accuracy, elevation differences must be defined as the differences of the measured heights and should be determined several times and based on independent measurements at the beginning and end of the levelling section. Thus, determining elevation differences with the use of the NRTK VRS technique may be particularly effective in areas with large differences in height, where the determination of elevation differences with the use of classical methods is time-consuming. The obtained elevation differences require tying to the points of the height control network with the use of classical methods

Land-use and cover change (LUCC) impacts global environmental changes. Therefore, it is crucial to obtain cross-national level LUCC data that represents past and actual LUCC. As urban areas exhibit the most significant dynamics of the changes, accompanied by such processes as urban sprawl, it seems desirable to take into account LUCC information from such areas to acquire national level information. The paper analyses land-use changes (LUCs) in urban areas in Czechia, Poland, and Slovakia. The analysis is based on functional urban area (FUA) data from the European Urban Atlas project for 2006 and 2012. The area of urbanised land grew at the expense of agricultural areas, semi-natural areas, and wetlands over the investigated period in all three countries. The authors determined LUC direction models in urban areas based on the identified land-use change. The proposed LUC direction models for the investigated period and area should offer national level LUC data for such purposes as modelling of future changes or can be the point of reference for planning analyses. The paper proposes the following models: mean model, median model, weighted mean model where the weight is the urbanised to vegetated area ratio, and weighted mean model where the weight is the share of urbanised areas. According to the proposed LUC models, areas considered as urbanised grow in FUAs on average in six years by 5.5900‰ in Czechia, 7.5936‰ in Poland, and 4.0769‰ in Slovakia. Additionally, the change models facilitated determination of a LUC dynamics ratio in each country. It reached the highest values in Poland and the lowest in Slovakia.

Information on landscape structure is an important issue for sustainable development and for making correct spatial planning decisions. Therefore, studies providing information on the diversity and changes of land cover and land use in a selected area are currently an important research topic. In addition to quantitative-qualitative statistics, spatial entropy is increasingly used to assess the degree of diversity of land cover and land use. This paper aim was to determine the diversity of objects within the land cover classes in the years 2014, 2017 and 2020, with a focus on built-up areas, in three districts bordering the city of Kraków, i.e. the Wieliczka, Kraków and Proszowice districts, located in the Małopolskie Voivodeship in Poland. In order to perform the analysis with the appropriate spatial resolution, a hex grid was used to determine the diversity of objects in the built-up area class. For this reason, data on land cover from the BDOT10k national database of topographic objects were used. The analyses followed the division into classes and objects defined in the structure of the BDOT10k database. The degree of diversity was determined using the Entropy Index and Herfindahl-Hirschman Index. Changes in the diversity of built-up areas were observed especially in areas located in close proximity to the border of Kraków, as well as on its eastern and south-eastern sides. A significant relationship was also observed between the increase in diversity of objects in the built-up area class and the immediate proximity of roads.