Giscience Theory Based Assessment of Spatial Disparity of Geodetic Control Points Location

International Journal of Geo-Information

Article GIScience Theory Based Assessment of Spatial Disparity of Geodetic Control Points Location

Elzbieta Bielecka , Krzysztof Pokonieczny * and Sylwia Borkowska Faculty of Civil Engineering and Geodesy, Military University of Technology, 2 gen. Sylwestra Kaliskiego St., 00–908 Warsaw 46, Poland; [email protected] (E.B.); [email protected] (S.B.) * Correspondence: [email protected]

Received: 3 February 2020; Accepted: 1 March 2020; Published: 3 March 2020

Abstract: Geodetic networks provide a spatial reference framework for the positioning of any geographical feature in a common and consistent way. An even spatial distribution of geodetic control points assures good quality for subordinate surveys in mapping, cadaster, engineering activities, and many other land administration-oriented applications. We investigate the spatial pattern of geodetic control points based on GIScience theory, especially Tobler’s Laws in Geography. The study makes contributions in both the research and application fields. By utilizing Average Nearest Neighbor, multi-distance spatial cluster analysis, and cluster and outlier analysis, it introduces the comprehensive methodology for ex post analysis of geodetic control points’ spatial patterns as well as the quantification of geodetic networks’ uniformity to regularly dense and regularly thinned. Moreover, it serves as a methodological resource and reference for the Head Office of Geodesy and Cartography, not only the maintenance, but also the further densification or modernization the geodetic network in Poland. Furthermore, the results give surveyors the ability to quickly assess the availability of geodetic points, as well as identify environmental obstacles that may hamper measurements. The results show that the base geodetic control points are evenly dispersed (one point over 50 sq. km), however they tend to cluster slightly in urbanized areas and forests (1.3 and 1.4 points per sq. km, respectively).

Keywords: geodetic control network; Poland; GIScience; point pattern analysis; Ripley’s K-function; kernel density; Moran statistics; LISA; cluster analysis

1. Introduction Geodetic control networks are widely used for investigating and monitoring any geographical features and phenomena. They are of great priority to many human actions, like geodetic and geophysical measurements, surveying, civil and environmental engineering, GIS development, and gathering spatial data. These networks provide a series of accurate positional measures that cover the analyzed area, thus delivering a time-continuous infrastructure enabling studying and tracking of crustal deformation [1], as well as seismic and geomorphologic landform activities (e.g., [2–4]). The ground stability of geodetic control points provides quality to the results of geometric measures, enables an accurate and detailed description of land topography, and changes relative to Earth processes, natural hazards, and climate change [5]. Control surveys serve as the basis for initiating or reviewing subordinate surveys for property boundary delineation [6], route and construction planning [7,8], engineering object displacements [9], cadastral and topographic mapping [10], as well as many environmental applications and cultural heritage preservation and monitoring [11,12]. They are indispensable as a reference framework for land administration systems, especially for georeferencing spatial objects [13–15]. Many scholars point out that the production and quality control of any geographical data and products requires references to the base geodetic network that realizes the CRS (Coordinate Reference System) and provides the consistent frame for GNSS users [5,16,17].

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Hence, the base geodetic control points (thereinafter refed as BGCPs) are of utmost importance for georeferencing of manuscripts of historical maps [11,18,19] or images from unmanned aerial vehicles [20]. Geodetic control points should cover an area relatively evenly to enable accurate and cost-effective measurements [21–23]. Although there is a variety of studies considering the design and densification of geodetic control networks [16,24,25] as well as investigating the influence of topographic objects that hinder the visibility of the horizon, interfere with satellite signals, and, finally, affect the quality of geodetic control stations’ positioning [26–28], a profound analysis of the spatial pattern of geodetic control points still requires investigation. The problem of geospatial distribution of geodetic control points was previously discussed in several publications [29–31]. However, these studies were concerned with the detail (third-order) of geodetic network point analyses in relatively small (less than 200 sq. km) rural areas. The results, related to surveying units and then grouped according to land use types, showed that geodetic control points are scattered with significantly visible groupings along roads, railways, and built-up areas. Moreover, the number and density of geodetic control points depend on the development of the area in question, and 35% to 50% depend on the land cover, mainly in locations of built-up areas, roads, and railways [30,31]. The density of geodetic control points is specified by the National Mapping Agencies. In Poland, all requirements for geodetic control networks are included in the Regulation of the Ministry of Administration and Digitization [32] implementing the Geodetic and Cartographic Law of the Polish Parliament. The document, like many other national regulations [33–36], assumes that in order to ensure an appropriate accuracy of survey measurements, the country’s territory should be covered evenly by high-order geodetic control networks. The anticipated network density is, in general, expressed by the inter-point distance or the density of the geodetic control points, and varies between counties, depending on their level of development [37]. The objective of this study was to investigate the spatial pattern of the geodetic control points of the Base National Geodetic Network (BNGN) in Poland, in particular, by performing an ex-post analysis of the uniformity of spatial distribution and determination of factors that disturb the assumed evenness. This is the first comprehensive study covering the entire country using GIScience methods, i.e., incremental spatial statistics, cluster and density analysis, as well as first and second order statistics. This study makes contributions in both research and applications. Based on a GIScience theoretical background, it introduces a comprehensive methodology for ex post analysis of geodetic control points’ spatial pattern as well as the quantification of geodetic network uniformity into regularly dense and regularly thinned. The conducted tests of the first and second order statistics provide, in the form of graphs and maps, exhaustive information on the spatial distribution type (regular, random, or clustered) of the geodetic points. The study is intended to be a methodological resource and reference for the National Mapping Agency and the Head Office of Geodesy and Cartography for the maintenance, as well as the further densification or modernization, of the base geodetic network in Poland. Furthermore, the results give surveyors the ability to quickly assess the availability of geodetic points, as well as identify environmental obstacles that may hamper measurements. Moreover, the method of investigating the spatial pattern of the BGCPs could be applied in any country or region, and after a small modification, on any man-made point feature of which the location is assumed to not be distributed randomly. The remainder of the article is structured as follows: Section2 provides an overview of the National Geodetic Control Network in Poland, Section3 presents the area and data used, the fundamentals of the point pattern analysis, and steps in data analyzing, Sections4 and5 describe the obtained outcomes in detail and provide discussion with the results, and finally, Section6 concludes this study.

2. Overview of the National Geodetic Control Network in Poland The control networks in Poland, maintained by the Head Office of Geodesy and Cartography, are designed and established according to the Geodetic and Cartographic Law [38] and the pertinent ISPRS Int. J. Geo-Inf. 2020, 9, 148 3 of 20 implementation rules established by the Ministry of Administration and Development [32]. Information about geodetic control points is stored in spatial databases, and includes the point number and unique identifier, coordinates, survey uncertainty, and information about their source, type of monumentation, and topographic details (e.g., location, access details, sketch plans); enabling the recovery or reconstruction of the point in terrain, and allowing the maintenance of the basic control network. The geodetic network in Poland consists of points of the horizontal and the vertical networks. The horizontal network is hierarchical and comprises three orders of geodetic control networks. The main criterion for assigning a geodetic control point to the appropriate network order is the accuracy of determining its position, expressed as the mean error. The fundamental (first-order) network consists of 127 GNSS stations that belong to the Active Geodetic Network–European Position Determination System (ASG-EUPOS) out of which 24 are located in the neighboring countries [39]. These stations meet the criteria established by the Subcommittee EUREF and provide an average density of one point per 20,000 km2. The base geodetic control is the second-order geodetic network providing the density of one point per 50 km2. The first and second-order geodetic networks, according to the Ministry Regulation [32], form the so called base (main) geodetic network in Poland [40]. All points belonging to these networks are monumented and have precisely measured positions (0.01 m for horizontal position and 0.02 m for geodesic height [32]) as they form the basis for determining the positions of other points. All BGCPs should be situated on stable ground, far from sources of electromagnetic interference or surface vibrations (e.g., caused by heavy traffic), objects that cause reflection of satellite signals (e.g., water reservoirs, flat metal surfaces, walls, wire fences, high antenna towers), as well as terrain barriers above 10 degrees over the horizon. The detailed geodetic network is a third-order control with 1,378,383 points and the average density of control points of ca. one point per 22.5 ha. The mean error of the third-order point’s location is in the range from 0.05 to 0.10 m, however for newly established points it should be less than 0.07 m. The control points are accurately tied to at least three reference geodetic controls. The geodetic control networks are the backbone of the Polish Spatial Information Infrastructure [40,41].

3. Materials and Methods 3.1. Area of Investigation and Data Used The study covers Poland, a central European country with the total area of 312,679 km2. Poland has the eighth largest and one of the most dynamic economies in the European Union [42]. It is highly developed both socially and economically, with a Gini coeﬃcient equal to 26.8 [43]. Simultaneously, the country holds a very high (33rd) worldwide position in the Human Development Index (0.865) [44]. The country is generally agricultural and ﬂat, with more than 76% of the territory below 200 m above mean sea level. Agricultural land covers 60.2% of its surface, followed by forests and bushes that take as much as 30.7%; water—2.1%; wastelands—about 1.5%; and built-up and urbanized areas—5.5%. Among the built-up and urbanized land, communication areas have the largest share of about 56% [45]. Data used in the study are summarized in the Table1 and described below.

Table 1. Spatial data characteristics.

Data Set Abbreviation CRS 1 Data Format Date Data Provider Base National Central Geodetic and Geodetic BNGN ETRS89 txt 2016 Cartographic Network Documentation Centre CORINE Land Copernicus Land CLC ETRS89 shape 2018 Cover Monitoring Service Vector Smart Polish Military VmapL2 WGS84 VPF 2018 Map level 2 Geography Directorate 1 Coordinate Reference System. ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 4 of 20 ISPRS Int. J. Geo-Inf. 2020, 9, 148 4 of 20 1 Coordinate Reference System. Coordinates of the 6723 BGCPs stations were obtained from the Central Geodetic and Cartographic Coordinates of the 6723 BGCPs stations were obtained from the Central Geodetic and Documentation Centre, in Warsaw. The points’ coordinates are given both in ETRS89 and Cartesian Cartographic Documentation Centre, in Warsaw. The points’ coordinates are given both in ETRS89 coordinate system “PL1992” (the EPSG code 2180). The geographic locations of points are shown in and Cartesian coordinate system “PL1992” (the EPSG code 2180). The geographic locations of points Figure1a. are shown in Figure 1a.

(a) (b)

Figure 1. Poland: (a) Base geodetic control points (BGCPs) location; (b) CORINE Land Cover. Figure 1. Poland: (a) Base geodetic control points (BGCPs) location; (b) CORINE Land Cover. The CORINE Land Cover (CLC) delivers information on the biophysical characteristics of the The CORINE Land Cover (CLC) delivers information on the biophysical characteristics of the Earth’s surface and its changes derived on visual interpretation of satellite images. The land cover Earth’s surface and its changes derived on visual interpretation of satellite images. The land cover nomenclature is hierarchical, including three levels of thematic details grouped in five major land nomenclature is hierarchical, including three levels of thematic details grouped in five major land cover types: Artificial, agricultural, forests and semi-natural areas, wetlands, water bodies, with 44 cover types: Artificial, agricultural, forests and semi-natural areas, wetlands, water bodies, with 44 classes at the third, most detailed level. The CLC data is available from COPERNICUS land monitoring classes at the third, most detailed level. The CLC data is available from COPERNICUS land services [46] free of charge. The CORINE Land Cover (Figure1b) data was used to investigate monitoring services [46] free of charge. The CORINE Land Cover (Figure 1b) data was used to a relationship between BGCPs’ density and land cover. investigate a relationship between BGCPs’ density and land cover. VmapL2 delivers vector-based geospatial data at medium resolution (1:50,000). Data are structured VmapL2 delivers vector-based geospatial data at medium resolution (1:50,000). Data are in nine thematic layers, i.e., boundaries, elevation, hydrography, industry, physiography, population, structured in nine thematic layers, i.e., boundaries, elevation, hydrography, industry, physiography, transportation, utilities, vegetation [47]. The study utilized data on road and rail networks, as subsets population, transportation, utilities, vegetation [47]. The study utilized data on road and rail of the transportation layers. networks, as subsets of the transportation layers. 3.2. Research Hypotesis and Methods 3.2. Research Hypotesis and Methods Based on an in-depth literature and national regulation review, we hypothesized that the spatial patternBased of the on basean in-depth geodetic literature control points and national in Poland regu dependslation on review, the scale we of hypothesized investigation. that Country-wide the spatial patternit could of be the perceived base geodetic as regularly control dispersed,points in Poland although, depends locally on it the is regularlyscale of investigation. densified or Country- regularly widethinned. it could Moreover, be perceived based on as CLC regularly and VmapL2 dispersed, data, although, we discover locally the BGCPs it is regularly that are locateddensified in theor regularlysignal interference thinned. Moreover, zone due to based environmental on CLC and factors, VmapL2 such data, as water we reservoirs,discover the heavy BGCPs traffi thatc paved are locatedroads, electricityin the signal lines, interference and other zone geographical due to envi features.ronmental This factors, is of such particular as water importance reservoirs, for heavy both trafficsurveyors paved and roads, mapping electricity authorities, lines, and because other some geographical advanced features. measurement This is and of particular calculation importance techniques for both surveyors and mapping authorities, because some advanced measurement and calculation

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techniques for measuring BGCP position should be recommended. CLC data allows also to for measuring BGCP position should be recommended. CLC data allows also to investigate dependence investigate dependence between the Thiessen polygons’ area and shape and the land cover structure. between the Thiessen polygons’ area and shape and the land cover structure. The hypothesis was proven using GIS tools based on Tobler’s laws of geography, in particular, The hypothesis was proven using GIS tools based on Tobler’s laws of geography, in particular, the first law that states ‘everything is related to everything else, but near things are more related than the first law that states ‘everything is related to everything else, but near things are more related than distant things’. This law serves as the basic concept for spatial statistical methods that are vastly distant things’. This law serves as the basic concept for spatial statistical methods that are vastly relevant for spatial analyses and modeling, e.g., global and local indicators of spatial autocorrelation relevant for spatial analyses and modeling, e.g., global and local indicators of spatial autocorrelation (Moran’s I, Anselin Local Moran’s I), and spatial interpolation (kernel density estimation). The second (Moran’s I, Anselin Local Moran’s I), and spatial interpolation (kernel density estimation). The second law (‘the phenomenon external to an area of interest affects what goes on inside’) emphasizes spatial law (‘the phenomenon external to an area of interest affects what goes on inside’) emphasizes spatial heterogeneity, particularly scale-dependent concentration and decentralization [48]. heterogeneity, particularly scale-dependent concentration and decentralization [48]. The BGCPs spatial pattern was investigated by testing complete spatial randomness using The BGCPs spatial pattern was investigated by testing complete spatial randomness using nearest-neighbor analysis and Ripley’s K-function, and global Moran’s I statistics. The regularity of nearest-neighbor analysis and Ripley’s K-function, and global Moran’s I statistics. The regularity geodetic point locations analysis was based on morphological parameters (area, shape and nearest of geodetic point locations analysis was based on morphological parameters (area, shape and distance between two adjacent polygons) of Thiessen polygons generated from the BGCPs. As a nearest distance between two adjacent polygons) of Thiessen polygons generated from the BGCPs. foundation for the quantification of the geodetic network evenness into regularly dense and regularly As a foundation for the quantification of the geodetic network evenness into regularly dense and thinned cluster, the outlier analysis (Anselin Local Morans I) was implemented. The adopted regularly thinned cluster, the outlier analysis (Anselin Local Morans I) was implemented. The adopted methodological framework is briefly shown in Figure 2. methodological framework is briefly shown in Figure2.

Figure 2. Schematic flowchart of the methodological framework. Figure 2. Schematic flowchart of the methodological framework. 3.2.1. Point Pattern Analysis 3.2.1.Point Point pattern Pattern analysis Analysis (PPA) is a set of methods for the investigation of spatial arrangements of pointsPoint in space, pattern usually analysis two-dimensional, (PPA) is a set and of methods could be for expressed the investigation as a set X = of{x spatialD} where arrangements D, the study of 2 ∈ region,points in is aspace, subset usually of R , atwo-dimensional, two-dimensional and Euclidean could be space expressed [49]. Diggle as a set [50 X] defined= {x ∈ D} a where spatial D, point the patternstudy region, as a set is of a locations,subset of irregularlyR2, a two-dimensional distributed withinEuclidean a study space region, [49]. Diggle which [50] have defined been generated a spatial bypoint random pattern mechanisms. as a set of locations, Moreover, irregularly he formulated distributed the three within basic a simplified study region, spatial which point have patterns: been Completegenerated spatialby random randomness mechanisms. (CSR), Moreover, regularity, he and formulated clustering the that three are basic very usefulsimplified at an spatial early stagepoint ofpatterns: spatial analysis.Complete Literature spatial randomness presents many (CSR), methods regularity, of spatial and clustering point pattern that analysis,are very classifieduseful at byan Cressieearly stage [51] inof fivespatial main analysis. categories: Literature Quadrat presents methods, many distance methods methods, of spatial kernel point estimators pattern of intensity,analysis, nearestclassified neighbor by Cressie distribution [51] in functions, five main and categories: K-function Quadrat analyses. meth As noticedods, distance by [52], eachmethods, method kernel has itsestimators pros and of cons, intensity, and works nearest well ne forighbor certain distribution datasets orfunctions, regions. and K-function analyses. As noticed by [52],Three each methods, method namely: has its pros Kernel and density, cons, and nearest works neighbor well for analysis, certain anddatasets Ripley’s or regions. K-function, were usedThree to examine methods, the spatialnamely: geodetic Kernel controldensity, point neares patternt neighbor in this analysis, study. They and areRipley’s briefly K-function, described below.were used Kernel to examine density, athe nonparametric spatial geodetic estimation, control belongspoint pattern to the localin this density study. techniques They are briefly based ondescribed a first-order below. property Kernel density, of the pattern, a nonparametric which concerns estimation, itself withbelongs the to variation the local of density the observations’ techniques densitybased on across a first-order a given area property [53]. The of kernelthe pattern, method wh computesich concerns a localized itself with density the for variation subsets of thethe studyobservations’ area; the density sub-regions across overlap a given one area another, [53]. The providing kernel method a moving computes sub-region a localized window, density defined for as subsets of the study area; the sub-regions overlap one another, providing a moving sub-region

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a kernel. The density, λ(s), at s (a vector location anywhere in R and s1, ... , sn are the vector locations of the n observed events) is estimated as [54]:

n X 1 s s λˆ (s) = k − i (1) τ 2 τ i=1 where, k() represents the kernel weighting function; s, the center of moving window; and τ, which is greater than 0, the bandwidth. Deng et al. [55] demonstrated that the choice of the bandwidth τ has a critical impact on the results of density analysis. As noticed by Gatrell et al. [54], increasing the bandwidth results in smoothening of the spatial variation in intensity, while its reduction results in an increasingly ‘spiky’ estimate. The nearest neighbor analysis and Ripley’s K-function belong to the distance methods. They explore how the points are distributed relative to one another (a second-order property of the point pattern) as opposed to how the points are distributed relative to the study extent [56–58]. The PPA is tested against the hypothesis of complete spatial randomness, under which the spatial pattern is a realization of a Poisson point process. An average nearest neighbor (ANN) analysis measures the average distance from each point in a given area to its nearest point which compares to the distances between nearest points and distances that would be expected on the basis of chance. If the average distance is less than the average for a hypothetical random distribution, the distribution of the analyzed features is considered clustered. If the average distance is greater than a hypothetical random distribution, the features are considered dispersed [59]. The nearest neighbor analysis, developed in 1950 [54], is one of the oldest distance statistics. The null hypothesis, tested by the two-tail test of CRS, is rejected if and only if: [zANN] > zp/2 (2) where, zANN—observed distribution of analyzed sample of points, zp—standard normal distribution, and p—the signiﬁcance level. A zANN value lower than zp shows that the analyzed point pattern is more clustered, while a value larger than zp/2 indicates a pattern more dispersed than random. The K-function, known as Ripley’s K-function, examines all inter-point distances instead of computing separate nearest neighbors. It illustrates how the spatial clustering or dispersion of point change when the neighborhood size changes. For data analysis, the variance stabilized Ripley K-function, called the L function, is generally used (Equation (3)): v t PN PN A i=1 i=1,j,1 ki.j L(d) = (3) πN(N 1) − where, d—the distance, N—total number of points (features), A—the total area, and ki,j—a weight connected with edge correction function. Particularly, in this study, Ripley’s K function counts the number of neighboring BGCPs found within a given distance of each individual point. The number of observed neighboring BGCPs is then compared to the number of points that are expected based on a completely spatially randomness. The advantage of the function is that it allows for the investigation of how BGCPs point pattern distribution is changing with scale. However, it should be remembered that patterns are suspect at larger distances due to edge eﬀects.

3.2.2. Thiessen Polygons Measuring the evenness of the BGCPs’ spatial location is based on the analysis of the area and shape of Thiessen polygons formed over the geodetic points’ site. Thiessen polygons, also called Voronoi diagrams, define individual areas of influence around each of a set of points, hence any location within a Thiessen polygon is closer to its linked point than to any other [60]. This property has caused that Thiessen polygons are perceived as a proper construct to test the CSR hypothesis as ISPRS Int. J. Geo-Inf. 2020, 9, 148 7 of 20 well as the regularity of spatial distribution [61,62]. In considering the equal division characteristics of the Thiessen polygon in spatial tessellation, the method can be used to investigate such issues as nearest points, proximity, adjacency, and accessibility analyses [63]. The shape indices (SI) of Thiessen polygons were calculated according to the equation, firstly introduced by [64]: P SI = (4) 2 √πA where, P—denotes the perimeter of the Thiessen polygon, and A—the area of the polygon. The SI value 1.128 refers to the square-shaped polygon, while the value 1 denotes a circle-shaped. The diversities in the shape, area, and land cover structure of Thiessen polygons were measured by the coefficient of variation, CV (coefficient of disparity), a dimensionless number that quantifies the degree of variability relative to the mean [65]: σ CV = 100% (5) µ where, CV is the coefficient of variation, σ—the standard deviation, and µ—the mean. Clusters of small and big Thiessen polygons were found by analyzing the statistical distribution of the area and shape of the polygons. The diversity of Thiessen polygons land cover structure, expressed as percentage of artificial areas, agriculture, forest and bushes, water bodies, and marshes, as well as land cover diversity (i.e., number of classes—NC) and fragmentation (i.e., number of patches—NP), was assessed by the statistical measures of central tendency, position, and dispersion (mean, median) and the coefficient of disparity (CV).

3.2.3. Spatial Autocorelation, Cluster and Outlier Analysis Spatial autocorrelation on the entire study area was investigated by the Global Moran’s I index according to Equation (6) [66].

Pn Pn n i=1 j wij(yi y) yj y I = − − (6) P P 2 n n n w (y y) i=1 j ij i − where, n is the number of attributes; yi is the attribute value in region i; yj is the attribute value in region j; y is the mean value of the attribute in the study site; and wij are weights according to the neighborhood of the attributes. Moran’s I values closer to 1 indicate negative or inverse spatial − autocorrelation between the Thiessen polygons’ morphological parameters, i.e., adjacent Thiessen polygons are characterized by dissimilar parameters values. The values closer to +1 indicate positive or direct spatial autocorrelation and highlight the regions with similarly high or low attribute values. Moran’s I value 0 shows a global spatial randomness pattern of distribution. The local indicator of spatial autocorrelation of Thiessen polygons was explored by the means of Anselin Local Moran’s I (LISA) statistics in line with Equation (7) [67]:

Pn (yi y) j=1(yi y) = − − Ii P 2 (7) n (y y) /n j=1 i − where, n is the number of attributes; yi is the attribute value in region i; yj is the attribute value in region j; y is the mean value of the attribute in the study site. LISA is generally used for the decomposition of Moran’s statistics, the global measures of autocorrelation. The results, presented as a choropleth map, depict (by the COType attribute) statistically significant (95 percent confidence level) cluster of high values (HH) and low values (LL), as well as outlier where a high/low value are surrounded by low/high values (HL/LH). Based on the COTtype attributes’ values, the regularly dense and regularly thinned BGCPs’ patterns were defined. ISPRS Int. J. Geo-Inf. 2020, 9, 148 8 of 20

The regularly dense cluster (RD) is the sum of the Thiessen polygons that belong to the subset formed by the COType LL of the Thiessens’ area (LLAREA) and nearest neighbor distance between 2 geodetic points (LLNND) minus the Thiessen polygons of shape index (SI) value lower than SI < SI-σ , i.e., SI outliers (SIout), as seen in the Equation (8). The elimination of very irregular polygons makes it possible to exclude the polygons that are adjacent to the country border, thus eliminating the edge eﬀect [54]. The regularly thinned cluster (RT) is composed of the Thiessen polygons which COType attribute of an area and a nearest neighbor ﬁelds take value HH (Equation (9)).

RD = (LL LL ) SIout (8) AREA ∪ NND \ RT = HH HH (9) AREA ∪ NND) The RD regions with a closer location between BGCP (LL) and RT—more distant (HH)—are shown on a map. This map, available as a web application, could help surveyors to assess the cost and duration of measurement work. ArcGIS 10.5 and Statistica 13.1 were used for conducting the spatial and statistical analysis.

4. Results

4.1. General Characteristic of BGCPs’ Location The Base Geodetic Control Network in Poland comprises 6723 points, including 103 ASG-EUPOS stations. The geographical points location highly (with the coefficient of determination equals to 0.92) corresponds to the main land cover type, namely: Artificial areas, agriculture, forest, and bushes (see Table2 and Figure3a). As many as 57.37% of BGCPs are situated on agricultural land, 30.78% in forest, and 5.65% in urban areas. There are relatively few points on pastures and meadows. This could be explained by the difficulty of maintaining a point’s monumentation stability in lands with high flood risk and variable groundwater levels, which, according to [68], is typical for Polish meadows and pastures, located mainly in river valleys.

Table 2. Global density of BGCPs over CORINE land cover types.

Number of BGCPs Density Density CORINE Land Cover Types Area [km2] (Frequency) BGCPs/1km2 BGCPs/50 km2 Artiﬁcial area 452 17,605 0.026 1.284 Agriculture, including: 3417 179,307 0.019 0.953 Arable land 2931 128,966 0.023 1.136 Pastures and meadows 486 50,341 0.010 0.483 Forest 2692 96,209 0.028 1.399 Bushes 141 5669 0.025 1.243 Others (e.g., bare rock, 21 6701 0.003 0.157 dispersed vegetation) Poland 6723 312,544 0.022 1.076

The average density of the BGCPs in Poland amounts to 1.08 point per 50 km2 and is in line with the national regulation [32]. A total of 6256 points are situated no further than 200 m from the transportation network (Table3, Figure3b), of which as many as 343 (5.1%) are within a 20 m bu ﬀer around paved roads, and two points are closer than 20 m from the railway. ISPRSISPRS Int. Int. J. J. Geo-Inf. Geo-Inf. 20202020,, 99,, x 148 FOR PEER REVIEW 99 of of 20 20

(b) (a)

Figure 3. Location of BGCPs: ( (aa):): Number Number of of BGCPs BGCPs per per CORINE CORINE land land cover cover type; ( b): Number Number of of BGCPs near transport network. Table 3. The number of BGCPs in the vicinity of land cover objects. Table 3. The number of BGCPs in the vicinity of land cover objects. The Buffer Number of BGCPs Number of BGCPs Number of BGCPs Number of BGCPs Number of Number of Number of BGCPs TheZone Buffer [m] Near Roads Near Railways NumberNear Water of BGCPs Bodies Near Electricity Lines BGCPs Near BGCPs Near Near Electricity Zone10 [m] 157 0Near Water 2 Bodies 19 20Roads 343 Railways 2 5Lines 33 1050 157 966 0 22 15 2 103 19 20100 343 1853 2 69 60 5 215 33 50200 966 3094 22 168 21915 474103 total 6256 261 301 844 100 1853 69 60 215 200 3094 168 219 474 totalThe relatively close6256 (up to 200 m) distance 261 of as much as 30193.05% of geodetic control 844 points to paved roads makes them easily accessible to surveyors, which is undoubtedly a great advantage of the BaseThe Geodetic relatively Control close Network (up to 200 in terms m) distance of its use of andas much maintenance. as 93.05% of geodetic control points to pavedNevertheless, roads makes there them is easily a set of accessible 383 BGCPs to locatedsurveyors, no furtherwhich thanis undoubtedly 20 m from environmentala great advantage objects of thethat Base could Geodetic provide Control significant Network disruption in terms of an of electromagnetic its use and maintenance. signal, and finally, decrease the accuracy of positioningNevertheless, (see Tablethere3 is and a set Figure of 3834). BGCPs located no further than 20 m from environmental objectsLocal that density could provide of BGCPs significant varies from disruption 0.2 to 3.65 of points an electromagnetic over 50 km2 and signal, shows and places finally, of higher decrease and thelower accuracy point density,of positioning which (see are underlinedTable 3 and inFigure red and 4). orange in the kernel density map (Figure5a). A significantLocal density increase of inBGCPs the density varies of from geodetic 0.2 to points 3.65 ispoints observed over in 50 major km2 metropolitanand shows places agglomerations of higher and lower heavily point industrialized density, which regions, are suchunderlined as mining in red areas and (Figure orange5b). in the kernel density map (Figure 5a). AThe significant highest density increase is observedin the density in the Upperof geodetic Silesian points Polycentric is observed Metropolitan in major Area metropolitan (from 3 to agglomerations3.5 points per 50 and km heavily2) followed industrialized by Warsaw, regions, Lodz, Wroclaw,such as mining Szczecin, areas Bydgoszcz-Torun-Grudziadz, (Figure 5b). tri-citiesThe metropolitanhighest density areas, is observed where thein the density Upper of Silesian BGCPs variesPolycentric from Metropolitan 1.2 to 2.85 points Area per (from 50 km3 to2 . 3.5The points lowest per values 50 km (less2) followed than 0.5 by over Warsaw, 50 km2 )Lodz, are mainly Wroclaw, found Szczecin, in the Southern Bydgoszcz-Torun-Grudziadz, Pomerania Lakelands, tri-citiesSandomierz metropolitan and Nida areas, Basins, where as well the as density the North of BGCPs Polesie varies Plain, from which 1.2 are to mostly2.85 points agricultural per 50 km and2. Theforested lowest regions values with (less a highthan share0.5 over of natural 50 km2) vegetation are mainly and found relatively in the sparselySouthern populated Pomerania areas, Lakelands, and the Sandomierzpercentage of and urbanized Nida Basins, areas loweras well than as the 1.17 North (Figure Polesie5b). Plain, which are mostly agricultural and forested regions with a high share of natural vegetation and relatively sparsely populated areas, and the percentage of urbanized areas lower than 1.17 (Figure 5b).

ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 10 of 20

ISPRSISPRS Int.Int. J.J. Geo-Inf.Geo-Inf. 20202020,, 99,, 148x FOR PEER REVIEW 10 10 ofof 2020

(b) (a) (b) (a) Figure 4. Poland: (a) BGCPs located in near vicinity of express roads, water reservoirs, or electricity lines;Figure (b 4.) zoomPoland: to selected (a) BGCPs BGCPs located exposed in near to vicinitysignal disruption of express (upper roads, waterleft express reservoirs, road, orupper electricity right Figure 4. Poland: (a) BGCPs located in near vicinity of express roads, water reservoirs, or electricity electricitylines; (b) zoomline, bottom to selected left—dense BGCPs urban, exposed bottom to signal right—forest disruption and (upper water left reservoir). express road, upper right lines; (b) zoom to selected BGCPs exposed to signal disruption (upper left express road, upper right electricity line, bottom left—dense urban, bottom right—forest and water reservoir). electricity line, bottom left—dense urban, bottom right—forest and water reservoir).

(a) (b) Figure 5. Poland:(a) (a) Local density of BGCPs; (b) level of urbanization(b (in) percent). Figure 5. Poland: (a) Local density of BGCPs; (b) level of urbanization (in percent). 4.2. Point Pattern Analysis Figure 5. Poland: (a) Local density of BGCPs; (b) level of urbanization (in percent). 4.2. Point Pattern Analysis The null hypothesis presuming Complete Spatial Randomness (CSR) for BGCPs’ pattern analysis was4.2. ThePoint rejected, null Pattern usinghypothesis Analysis Average presuming Nearest NeighborComplete tools. Spatial The RandomnesszANN score amounts(CSR) for to BGCPs’ 1.39, with pattern a 99% 𝑧 analysisconﬁdenceThe was null level, rejected, hypothesis which using indicates presumingAverage that Nearest there Complete is lessNeighbor than Spatial 1% tools. likelihoodRandomness The that score the(CSR) dispersed amounts for BGCPs’ patternto 1.39, pattern ofwith the aBGCPs 99% confidence could be level, the result which of indicates random chancethat there and is thatless than the points 1% likelihood are dispersed that the over dispersed the territory pattern of analysis was rejected, using Average Nearest Neighbor tools. The 𝑧 score amounts to 1.39, with a 99% confidence level, which indicates that there is less than 1% likelihood that the dispersed pattern

ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 11 of 20 of the BGCPs could be the result of random chance and that the points are dispersed over the territory of Poland. The observed mean nearest inter-point distance equals 5.583 km, while the expected amounts to 4.013 km. Moreover, the coefficient of variation CV amounts to 21.66%, which means that the nearestISPRS distancesInt. J. Geo-Inf. 2020between, 9, x FOR BGCPs PEER REVIEW do not vary significantly (see Figure 6). 11 of 20 ISPRS Int. J. Geo-Inf. 2020, 9, 148 11 of 20

of the BGCPs could be the result of random chance and that the points are dispersed over the territory of Poland.Poland. The The observedobserved mean mean nearest nearest inter-point inter-poin distancet distance equals 5.583equals km, 5.583 while km, theexpected while the amounts expected amountsto 4.013 to 4.013 km. Moreover, km. Moreover, the coeﬃ thecient coefficient of variation ofCV variationamounts CV to amounts 21.66%, which to 21.66%, means thatwhich the means nearest that the nearestdistances distances between between BGCPs do BGCPs not vary do signiﬁcantly not vary significantly (see Figure6). (see Figure 6).

Figure 6. Histogram of nearest inter-BGCPs distance.

Figure 6. Histogram of nearest inter-BGCPs distance. Ripley’s K function (FigureFigure 7) 6. is Histogram estimated of nearest for distances inter-BGCPs up distance. to 20 km, in 1 km increments, and Ripley’s K function (Figure7) is estimated for distances up to 20 km, in 1 km increments, indicates twoRipley’s different K function departures (Figure from7) is estimated randomness. for distances up to 20 km, in 1 km increments, and and indicates two diﬀerent departures from randomness. indicates two different departures from randomness.

K Function Clustered K Function ExpectedK ObservedK Clustered ExpectedK ObservedK Confidence Env. 22000 Confidence Env. 22000 20000 20000 18000 18000 16000 16000 14000 14000 12000 L(d) 12000L(d) 10000 10000 8000 8000 6000

6000 4000 4000 2000 2000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 Distance 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000Dispersed18000 19000 20000 Distance Figure 7. The arrangement of BGCPs over the range of distances (in meters).Dispersed The blue line denotes the expected distance, and the red line—the observed distance. Figure 7. TheFigure arrangement 7. The arrangement of BGCPs of BGCPs over over thethe range range of distances of distances (in meters). (in Themeters). blue line The denotes blue the line denotes expected distance, and the red line—the observed distance. the expectedAt the distance,distances andfrom the 2 up red to line—the 7 km, typical observed for base distance. geodetic control networks, L(d) lies below the expectedAt the distance distances value from (higher 2 up to than 7 km, expected typical for approximately base geodetic control 2000 m) networks, and indicates L(d) lies statistically below Atsignificant thethe distances expected (with distancethefrom level 2 value ofup confidence to (higher 7 km, than of typical expected99%) evidence for approximately base of geodeticregular 2000 dispersion m)control and indicates of networks, geodetic statistically points. L(d) Atlies below longersigniﬁcant distances (with (greater the level than ofconﬁdence 7 km) L(d) of 99%)lies evidenceabove the of regularexpected dispersion distance, of geodeticindicating points. spatial the expectedAt distance longer distances value (greater (higher than than 7 km) expected L(d) lies aboveapproximately the expected 2000 distance, m) indicatingand indicates spatial statistically significantclustering. (with Inthe general, level ofat nearconfidence distances, of the 99%) BGCP evidences are expected of regular to be dispersiondispersed, as of the geodetic number ofpoints. At points within a given distance of each individual point is small, as the distance increases, each BGCP longer woulddistances typically (greater have more than neighb 7 km)ors, henceL(d) theylies areabove clustered. the expected distance, indicating spatial clustering. In general, at near distances, the BGCPs are expected to be dispersed, as the number of points within4.3. Thiessen a given Polygons distance Morphology of each and individualLand Cover Structure point is small, as the distance increases, each BGCP would typically have more neighbors, hence they are clustered.

4.3. Thiessen Polygons Morphology and Land Cover Structure

ISPRS Int. J. Geo-Inf. 2020, 9, 148 12 of 20 clustering. In general, at near distances, the BGCPs are expected to be dispersed, as the number of points within a given distance of each individual point is small, as the distance increases, each BGCP would typically have more neighbors, hence they are clustered. ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 12 of 20 4.3. Thiessen Polygons Morphology and Land Cover Structure TheThe analysisanalysis ofof thethe ThiessenThiessen polygonspolygons areaarea andand shapeshape alsoalso emphasizesemphasizes thatthat thethe distributiondistribution ofof BGCPsBGCPs inin PolandPoland is is generally generally dispersed. dispersed. The The shape shape of of polygons, polygons, expressed expressed as as the the shape shape index index (Eq.4), (Eq.4), is almostis almost equal. equal. The The SI values SI values vary vary from from 0.095 0.095 to 0.935 to (range0.935 (range 0.840), 0.840), with the with mean the of mean 0.826, of and 0.826, median and ofmedian 0.840 (seeof 0.840 Table (see4, andTable Figure 4, and8a). Figure Moreover, 8a). Moreover, 50% of polygons 50% of polygons are characterized are characterized by the SI by index the SI thatindex ﬂuctuates that fluctuates from 0.812 from (lower 0.812 quartile)(lower quartile) to 0.863 to (upper 0.863 quartile).(upper quartile). H-spread H-spread (IQR) amounts (IQR) amounts to 0.051, showingto 0.051, veryshowing low very dispersion, low dispersion, which is also which visible is also in thevisible CV in index the value,CV index equal value, to 8.45. equal The to exclusion 8.45. The ofexclusion polygons of neighboringpolygons neighboring the country the bordercountry entails border even entails smaller even diversiﬁcationsmaller diversification of the SI, of whichthe SI, underlineswhich underlines the almost the almost double double reduction reduction of the CV of the index CV from index 8.45% from to 8.45% 4.48%. to 4.48%.

(b) (a)

FigureFigure 8.8. ThiessenThiessen polygons’polygons’ distribution:distribution: (a)) ShapeShape histogram;histogram; ((bb)) areaarea histogram.histogram.

The analysis of the Thiessen polygons’ size distribution indicates little deviation from the normal The analysis of the Thiessen polygons’ size distribution indicates little deviation from the normal distribution. The mean equals 46.48 km2, and the median is 46.64km2. Skewness (0.051) shows the distribution. The mean equals 46.48 km2, and the median is 46.64km2. Skewness (0.051) shows the fairly symmetric character, with a little longer right tail, while kurtosis (0.896) indicates the fewer and fairly symmetric character, with a little longer right tail, while kurtosis (0.896) indicates the fewer and less extreme outliers than in the normal distribution. The area of 50% polygons ranges from 3.685 to less extreme outliers than in the normal distribution. The area of 50% polygons ranges from 3.685 to 46.636 km2, and 90% does not exceed 64.4 km2 (Figure8b). The coe fficient of disparity (CV) of the 46.636 km2, and 90% does not exceed 64.4 km2 (Figure 8b). The coefficient of disparity (CV) of the polygons’ area amounts to 32.4% and emphasizes their medium differentiation. polygons’ area amounts to 32.4% and emphasizes their medium differentiation. The analysis of land cover structure in the Thiessen polygons reveals high diversity, emphasized The analysis of land cover structure in the Thiessen polygons reveals high diversity, emphasized by the CV coefficient, which varied from 285.18% for water bodies to 47.76% for agriculture areas. by the CV coefficient, which varied from 285.18% for water bodies to 47.76% for agriculture areas. The land cover dispersion in dense urban areas (CV = 166.16) is higher than in sparsely urbanized ones The land cover dispersion in dense urban areas (CV = 166.16) is higher than in sparsely urbanized (CV=123.97) and was followed by forested lands (CV = 76.35). On average, the number of CLC classes ones (CV=123.97) and was followed by forested lands (CV = 76.35). On average, the number of CLC (NC=9) is nearly four times lower than the number of patches (NP = 34), which suggests that the classes (NC=9) is nearly four times lower than the number of patches (NP = 34), which suggests that landscape heterogeneity is lower than its fragmentation. Moreover, there were some polygons covered the landscape heterogeneity is lower than its fragmentation. Moreover, there were some polygons entirely by one land cover patch (NP amounts to one). On average, 53.4% of the area of Thiessen covered entirely by one land cover patch (NP amounts to one). On average, 53.4% of the area of polygons is agricultural, followed by forests (32.4%). Urban areas occupy about 6.6%, and dispersed Thiessen polygons is agricultural, followed by forests (32.4%). Urban areas occupy about 6.6%, and settlement 2.8%. Water bodies (lakes and rivers) cover only 2.1%. dispersed settlement 2.8%. Water bodies (lakes and rivers) cover only 2.1%.

Table 4. Morphology and land cover characteristics of Thiessen polygons (confidence level 95%).

Quartile Std. Coef. Variables Mean Median Minimum Maximum Range Variance (Range) Dev. Var. [%] Thiessen polygons area 46.480 46.636 3.685 120.806 117.120 16.881 227.271 15.076 32.434 in km2 Shape index of Thiessen 0.826 0.840 0.095 0.935 0.840 0.004 0.005 0.070 8.450 polygons Heavily urbanized [%] 6.65 3.32 0.00 99.96 99.96 5.23 122.22 11.05 166.16

ISPRS Int. J. Geo-Inf. 2020, 9, 148 13 of 20

Table 4. Morphology and land cover characteristics of Thiessen polygons (conﬁdence level 95%).

Quartile Std. Coef. Variables Mean Median Minimum Maximum Range Variance (Range) Dev. Var. [%] Thiessen polygons area 46.480 46.636 3.685 120.806 117.120 16.881 227.271 15.076 32.434 ISPRS Int. J. Geo-Inf.in km2 2020, 9, x FOR PEER REVIEW 13 of 20 Shape index of Thiessen 0.826 0.840 0.095 0.935 0.840 0.004 0.005 0.070 8.450 polygons SparselyHeavily urbanized urbanized [%] [%] 2.79 6.65 1.70 3.32 0.00 0.00 99.96 37.11 99.96 37.11 5.23 3.22 122.22 11.97 11.05 3.46 166.16 123.97 AgricultureSparsely urbanized [%] [%] 53.40 2.79 57.51 1.70 0.00 0.00 37.1199.90 37.11 99.95 3.22 39.10 11.97 650.53 3.46 25.51 123.97 47.76 Forest andAgriculture bushes [%] 32.45 53.40 26.52 57.51 0.00 0.00 99.9099.98 99.95 99.98 39.10 35.64 650.53 613.72 25.51 24.77 47.76 76.35 WaterForest bodies and bushes [%] [%] 2.13 32.45 0.00 26.52 0.00 0.00 99.9897.54 99.98 97.54 35.64 1.88 613.72 36.78 24.77 6.06 76.35 285.18 Water bodies [%] 2.13 0.00 0.00 97.54 97.54 1.88 36.78 6.06 285.18 NC NC8.94 8.94 9.00 9.00 1.00 1.00 16.00 15.0015.00 2.002.00 3.603.60 1.901.90 21.23 21.23 NP NP33.90 33.90 32.00 32.00 1.00 1.00 109.00 108.00108.00 19.0019.00 232.67232.67 15.25 15.25 44.99 44.99

ArtificialArtificial land land (heavily (heavily and and sparsely sparsely urbanized), urbanized), onon average,average, occupies occupies 9.44% 9.44% of theof the Thiessen Thiessen polygons.polygons. However, However, the the smallest smallest polygons, polygons, with with an areaarea of of less less than than 16.5 16.5 km km2 (mean2 (mean2.0 − 2.0 std. std. dev.), dev.), − are coveredare covered by artificial by artificial surfaces surfaces in in 32.06%, 32.06%, while while for veryvery large large polygons polygons (bigger (bigger than than 77 km 772 km, mean2, mean 2.0 std. dev.) artificial land covers only 4.64% (see Figure9). The Pearson’s correlation coe fficient − 2.0− std. dev.) artificial land covers only 4.64% (see Figure 9). The Pearson’s correlation coefficient (PCC), equal to 0.28 (significant at p < 0.05000), indicates the weak downhill linear correlation (PCC), equal to −0.28− (significant at p < 0.05000), indicates the weak downhill linear correlation between the size of the polygons and acreage of urbanized areas. The level of urbanization, however, between the size of the polygons and acreage of urbanized areas. The level of urbanization, however, is moderately correlated with road density (PCC equals 0.50). Nevertheless, in small polygons, is moderately correlated with road density (PCC equals 0.50). Nevertheless, in small polygons, the the average share of urbanized and agricultural areas amounted to 30% and the average share of forests averageamounted share of to 20%,urbanized which showsand agricultural a fairly balanced areas land amounted cover structure. to 30% and the average share of forests amounted to 20%, which shows a fairly balanced land cover structure.

FigureFigure 9. 9.ThiessenThiessen polygons polygons –land covercover structure. structure. A moderate positive linear correlation (with the significant at p < 0.05) was observed between aA polygon’s moderate size positive and the linear number correlation of patches (with (PCC =the0.56), significant while, the at relationship p < 0.05) was between observed a polygon’s between a polygon’ssize and size the and area the of agriculturalnumber of landpatches was (PCC very weak= 0.56), (PCC while,= 0.14). the Likewise,relationship the linearbetween relationship a polygon’s size andbetween the thearea shape of agricultural index the land land cover was structure very we wasak similarly(PCC = 0.14). very weakLikewise, (PCC lowerthe linear than 0.15).relationship between the shape index the land cover structure was similarly very weak (PCC lower than 0.15). 4.4. Quantification of Geodetic Network Uniformity 4.4. QuantificationThe Thiessen of Geod polygons’etic Network variability Uniformity in size and shape analysis supported by cluster and outlier analysis (Anselin Local Moran’s I), and preceded by a global autocorrelation assessment, made it The Thiessen polygons’ variability in size and shape analysis supported by cluster and outlier possible to delineate the places of more or less densified geodetic networks. Global Moran’s I statistics, analysisbased (Anselin on Thiessen Local polygons’ Moran’s locations I), and and preceded attributes by values, a global such autocorrelation as area, shape, and assessment, nearest distance made it possibleto neighbor to delineate polygons’ the centroids, places of returned more positiveor less Idensified and z-score geodetic values (I =networks.1.06/z = 204.43, Global I = Moran’s0.24/z I statistics,45.18, based and Ion= 1.08Thiessen/z = 207.78, polygons’ correspondingly) locations withand aattributes 99% level values, of significance. such as This area, empowers shape, and − nearestrejection distance (with to aneighbor probability polygons’ greater thancentroids, 1%) of re theturned null hypothesis, positive I and assuming z-score that values the Thiessen (I = 1.06/z = 204.43,polygons I = 0.24/z characterised − 45.18, and by the I = attribute 1.08/z = being 207.78, analyzed correspond are randomlyingly) with distributed a 99% in level a study of areasignificance. that This empowers rejection (with a probability greater than 1%) of the null hypothesis, assuming that the Thiessen polygons characterised by the attribute being analyzed are randomly distributed in a study area that covered all of Poland.. Therefore, the spatial distributions of high and low area, shape, and NN distance (NNd) values are clustered. Such characteristics of the spatial distribution of polygons was the basis for further analysis, namely determining the type of the polygon clusters, due to the high/low values of the attribute of surrounding polygons (see Figure 10a–d). Out of 6723 polygons, 3914 (58.2%) created statistically significant clusters of autocorrelated polygons, characterized by the HH/LL or HL/LH area values. As much as 1234 Thiessen polygons (18.3%) create HH clusters (light red), and 1130 create LL clusters (light blue) (Figure 10a). The number of autocorrelated Thiessen polygons is less if the nearest distance between neighboring polygons is analyzed; a total of 2054, which is 30.6% of all polygons. As much 46.0% (945 points) form

ISPRS Int. J. Geo-Inf. 2020, 9, 148 14 of 20 covered all of Poland.. Therefore, the spatial distributions of high and low area, shape, and NN distance (NNd) values are clustered. Such characteristics of the spatial distribution of polygons was the basis for further analysis, namely determining the type of the polygon clusters, due to the high/low values of the attribute of surrounding polygons (see Figure 10a–d). Out of 6723 polygons, 3914 (58.2%) created statistically signiﬁcant clusters of autocorrelated polygons, characterized by the HH/LL or HL/LH area values. As much as 1234 Thiessen polygons (18.3%) create HH clusters (light red), and 1130 create LL clusters (light blue) (Figure 10a). The number of autocorrelated Thiessen polygons is less if the nearest distance between neighboring polygons is ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 14 of 20 analyzed; a total of 2054, which is 30.6% of all polygons. As much 46.0% (945 points) form LL clusters LLand clusters 870 (42.4%) and form870 (42.4%) HH clusters. form HH These clusters. Thiessen Th polygonsese Thiessen comprise polygons 14.1% comprise and 12.9% 14.1% of all and polygons, 12.9% ofrespectively. all polygons, If the respectively. shape (i.e., If the the SI) shape of polygons (i.e., the is SI) considered of polygons (Figure is considered 10c), polygons (Figure of 10c), LL and polygons HL are ofmainly LL and located HL are along mainly the countrylocated along border. the They country constitute border. 43.4% They of constitute autocorrelated 43.4% polygons, of autocorrelated and just polygons,10% of all ofand them. just A10% further of all 746 of them. polygons A furthe formr HH 746 clusters. polygons However, form HH LL clusters. and HL However, clusters are LL rather and HLsmall, clusters with anare average rather small, of 11 polygons,with an average so they of were 11 polygons, eventually so excluded they were from eventually further excluded analysis aimed from furtherat ﬁnding analysis local BGCPaimedThiessen at finding polygon local BGCP clusters. Thiessen polygon clusters.

(a) (b) (c)

(d) (e)

Figure 10. Anselin Local Moran statistics: ( (aa)) Thiessen Thiessen polygons polygons area; area; ( (b)) nearest distance between BGCPs; ( c) Thiessen Thiessen polygons’ polygons’ shape index (SI); ( d) map map legend; legend; ( (e)) clusters clusters of of dense dense (red) (red) and and thinned thinned (green) Base Geodetic Network.

The largestlargest clusters clusters of of the the large large and and regular regular Thiessen Thiessen polygons polygons (HH COType (HH COType values of values the attributes of the attributesarea and shape), area and named shape), the named regularly the thinned regularly clusters thinned (RT), clusters are located (RT), are in the located North-West in the North-West (Pomerania (PomeraniaLakeland, Northern Lakeland, Podlasie Northern Plain), Podlasie East (east Plain), part ofEast Northern (east part Masovia of Northern Lowland), Masovia south-east Lowland), (Lublin south-east (Lublin and Roztocze Upland), South (Sandomierz Basin, Nida Basin, Wester Beskidy Foothills), and the central part (Masovia Lowland and Hills) of the country. The RT regions (shown in green Figure 10e) are mainly covered by forest, agriculture, or agricultural-forest lands, and occupy 92,644 km2 (29.7% of Poland). The regions of regularly densified geodetic control points (RD, presented in red, Figure 10e) are created by small, regularly shaped Thiessen polygons. They are composed of a smaller number of polygons than the RT regions (Table 5), and are more dispersed throughout the country territory, covering mainly urbanized areas, i.e., large agglomerations and accompanying industrial areas. Tiny RD clusters are located along the country’s border, mainly West (Odra river bands), North (along Baltic coastal zone), and South (the Sudetes, the Tatra Mountains and the Western and Eastern Carpathians). The two largest clusters are located in Silesia Upland and Oświęcim Basin as well as in the central part of the Masovia and

ISPRS Int. J. Geo-Inf. 2020, 9, 148 15 of 20

and Roztocze Upland), South (Sandomierz Basin, Nida Basin, Wester Beskidy Foothills), and the central part (Masovia Lowland and Hills) of the country. The RT regions (shown in green Figure 10e) are mainly covered by forest, agriculture, or agricultural-forest lands, and occupy 92,644 km2 (29.7% of Poland). The regions of regularly densiﬁed geodetic control points (RD, presented in red, Figure 10e) are created by small, regularly ISPRS Int. J. Geo-Inf.shaped 2020, Thiessen9, x FOR PEER polygons. REVIEW They are composed of a smaller number of polygons than the RT 15 regions of 20 (Table5), and are more dispersed throughout the country territory, covering mainly urbanized areas, PodlasieISPRS Lowlands. Int. i.e.,J. Geo-Inf. large RG 2020 agglomerations regions, 9, x FOR PEERcoverand REVIEW just accompanying 9.9% of the industrial country areas. and Tinycomprise RD clusters 16.8% are of located all Thiessen 15 along of 20 the country’s border, mainly West (Odra river bands), North (along Baltic coastal zone), and South (the polygons. When it comes to the polygons’ size, RD regions are more homogeneous than RT clusters, PodlasieSudetes, Lowlands. the TatraRG regions Mountains cover and just the 9.9% Western of the and country Eastern Carpathians).and comprise The 16.8% two of largest all Thiessen clusters are because Thiessen polygons’ area ranges from 3.68 to 46.44 km2 with an average value of 27.35 km2, polygons.located When in it Silesia comes Upland to the andpolygons’ O´swi˛ecimBasin size, RD asregions well as are in themore central homogeneous part of the Masoviathan RT andclusters, Podlasie 2 while, becausein RT, is Lowlands.Thiessen takes values polygons’ RG regions from area 9.29 cover ranges to just 120.80 9.9%from km of3.68 the(see to country 46.44 Table km and 5).2 with comprise an average 16.8% of value all Thiessen of 27.35 polygons. km2, while, inWhen RT, is it takes comes values to the from polygons’ 9.29 to size, 120.80 RD km regions2 (see areTable more 5). homogeneous than RT clusters, because Table 5. DescriptiveThiessen polygons’ characteristics area ranges of regularly from 3.68 thinned to 46.44 cluster km2 (RT)with and an average regularly value dense of 27.35 cluster km (RD)2, while, in 2 regions.Table RT, 5. is Descriptive takes values characteristics from 9.29 to of 120.80 regularly km thinned(see Table cluster5). (RT) and regularly dense cluster (RD) regions. BGN RegularityTable 5. Descriptive Type characteristics of regularly thinned RT cluster (RT) and regularly RD dense cluster Number ofBGN(RD) Thiessen regions.Regularity polygons Type 1504 RT RD 1130 Number of Thiessen polygons 1504 1130 Area in kmBGN2 (in Regularity %) Type 92,643.9 RT (29.7) 30,920.1 RD (9.9) 2 Area in km (in %) 2 92,643.9 (29.7) 30,920.1 (9.9) Thiessen polygonsNumber min of Thiessen area in polygons km 9.29 1504 3.68 1130 Thiessen polygons min area in km2 9.29 3.68 Thiessen polygonsArea max in area km2 (inin %)km2 92,643.9120.80 (29.7) 30,920.1 46.44 (9.9) Thiessen polygons max area in km2 2 120.80 46.44 Thiessen polygonsThiessen mean polygons area min in area km in2 km 61.609.29 27.26 3.68 ThiessenThiessen polygons polygons mean max area area in in km km2 2 120.8061.60 27.26 46.44 Thiessen polygons mean area in km2 61.60 27.26

ThiessenThiessen polygonsThiessen polygons polygonsarea area frequency area frequency frequency distributiondistributiondistribution

NN distance mean value in m 6789 3770 NN distanceNN distance mean mean value value in m in m 6789 6789 3770 3770 Base Geodetic Network densification and thinning also emphasize the shortest distances between Base Geodetic Network densification and thinning also emphasize the shortest distances Base Geodeticadjacent Network (near neighbor) densification points, which and ranges thinning from 5840also to emphasize 20,580 m in RTthe clusters, shortest and distances from 145 to between adjacent (near neighbor) points, which ranges from 5840 to 20,580 m in RT clusters, and from between adjacent5560 (near in RD neighbor) clusters. Distances points, below which 500 ranges m occur from in Upper 5840 Silesia,to 20,580 in areas m in threatened RT clusters, by landand surfacefrom 145 to 5560deformation in RD clusters. related Distances to hard coal below mining. 500 m occur in Upper Silesia, in areas threatened by land 145 to surface5560 in deformationRD clusters. related Distances to hard below coal 500mining. m occur in Upper Silesia, in areas threatened by land surface deformation5. Discussion related to hard coal mining. 5. DiscussionNew technological advances in GIScience have made it easier to justify Tobler’s laws of geography. 5. Discussion NewNow, technological we are able advances to measure in almostGIScience everything, have made but theit choiceeasier ofto technologyjustify Tobler’s and methodslaws of has Newgeography. technologicala significant Now, we advances impact are able on theinto measureGIScience result of almost the have analysis everything, made and it final easierbut conclusions. the to choice justify of Tobler’s Tobler’stechnology laws laws giveand of the background for GIScience theory, while GIS software provides tools for spatial analysis. In our study, geography.methods Now, has awe significant are able impact to measure on the resultalmost of everything,the analysis andbut finalthe conclusions.choice of technology Tobler’s laws and Tobler’s laws of geography are read as a statement about the form of geodetic control points’ spatial give the background for GIScience theory, while GIS software provides tools for spatial analysis. In methods has aarrangement, significant particularlyimpact on inthe the result sense of of similarity.the analysis Regardless and final of theconclusions. nature and Tobler’s type of geodetic laws our study, Tobler’s laws of geography are read as a statement about the form of geodetic control give the backgroundcontrol networks, for GIScience their task theory, is to createwhile a GIS basis software for determining provides the positiontools for of spatial various analysis. objects on In the points’ spatial arrangement, particularly in the sense of similarity. Regardless of the nature and type our study, Tobler’sEarth’s laws surface. of Preferably,geography the are entire read area as concerneda statement should about be coveredthe form at aof uniform geodetic density control with of geodetic control networks, their task is to create a basis for determining the position of various points’ spatiala arrangement, simultaneously particularly adjusted network in the of controlsense of survey similarity. stations. Regardless Both ANN andof the Ripley’s nature K-function and type are objects on the Earth’s surface. Preferably, the entire area concerned should be covered at a uniform best suited to analyzing the type of spatial distributions. They help avoid the modifiable areal unit of geodeticdensity control with a networks,simultaneously their adjusted task is tonetwork create of a controlbasis for survey determining stations. Both the ANNposition and of Ripley’s various objects on the problemEarth’s [surface.69] as they Preferably, treat space asthe continuous, entire area without concerned constraining should data be within covered any regionsat a uniform or units, K-functionand, are contrary best tosuited the quadrat to analyzing method, the they type are free of fromspatial statistical distribution bias causeds. They by datahelp aggregation avoid the [ 70]. density with a simultaneously adjusted network of control survey stations. Both ANN and Ripley’s modifiableNevertheless, areal unit problem Ripley’s K[69] and as NN they functions treat space describe as continuous, different aspects without of constraining a point process. data In within particular, K-functionany regions are best or units,suited and, to contrary analyzing to the the quadrat type method,of spatial they distribution are free froms. statisticalThey help bias avoid caused the modifiableby data areal aggregation unit problem [70]. [69]Nevertheless, as they treat Ripley’s space K asand continuous, NN functions without describe constraining different aspects data within of a any regionspoint process.or units, In and, particular, contrary pr toocesses the quadrat with the method, same K(t) they func aretion free may from have statistical different bias nearest- caused by dataneighbor aggregation distribution [70]. Nevertheless, functions, and Ripley’svice versa. K and NN functions describe different aspects of a point process.As stated In particular, in many national processes regulations with the and same standa K(t)rds, thefunc spacingtion may of the have higher-order different stations nearest- neighborcan distributionvary from 5func to tions,16 km and [23,33,71]. vice versa. The conducted research proved that, in Poland, such requirements are fulfilled, with the mean observed interstation distance equal to 5.6 km. Moreover, As stated in many national regulations and standards, the spacing of the higher-order stations each geodetic control point should be monumented with substantial stable survey monuments, and can vary from 5 to 16 km [23,33,71]. The conducted research proved that, in Poland, such situated far from sources of electromagnetic interference and ground vibration [5,25,32]. The analysis requirementsrevealed are that fulfilled, these requirements with the mean are fulfilled,observed alth interstationough, 5.7% distanceof the base equal geodetic to 5.6 control km. Moreover, points, each geodeticwhich are control located point in theshould near be vicinity monumented of geographical with substantial features thatstable could survey provide monuments, significant and situateddisruption far from of sources electromagnetic of electromagnetic signal, have interfer to be moencenitored and onground a regular, vibration short-term [5,25,32]. basis Thein order analysis to revealedensure that a thesehigh accuracy requirements of their areposition. fulfilled, although, 5.7% of the base geodetic control points, which are located in the near vicinity of geographical features that could provide significant disruption of electromagnetic signal, have to be monitored on a regular, short-term basis in order to ensure a high accuracy of their position.

ISPRS Int. J. Geo-Inf. 2020, 9, 148 16 of 20 processes with the same K(t) function may have different nearest-neighbor distribution functions, and vice versa. As stated in many national regulations and standards, the spacing of the higher-order stations can vary from 5 to 16 km [23,33,71]. The conducted research proved that, in Poland, such requirements are fulfilled, with the mean observed interstation distance equal to 5.6 km. Moreover, each geodetic control point should be monumented with substantial stable survey monuments, and situated far from sources of electromagnetic interference and ground vibration [5,25,32]. The analysis revealed that these requirements are fulfilled, although, 5.7% of the base geodetic control points, which are located in the near vicinity of geographical features that could provide significant disruption of electromagnetic signal, have to be monitored on a regular, short-term basis in order to ensure a high accuracy of their position. The review of world-wide scientific literature concerning geodetic points’ location, as well as international and national regulation on network design and monumentation, revealed that intertwining between global, high-, and low-order networks is clearly visible. This is due to the growing demand for high-precision location measurements of objects, especially engineering, which is ensured by GNSS-based measurement techniques and methods [71]. Therefore, there is a clear tendency to place detailed geodetic control points (low-order) in a position that maximizes the use of various measurement techniques, especially those that are intended for use in GNSS observations [21,28,72]. High-order geodetic stations are dispersed regularly [25,39,73,74], and this evenness is only slightly disturbed in densely urbanized areas [23] or those with challenging environmental conditions [75]. At the local level, based on Poland as a case study, the clustered distribution and its relation to land cover/land use is evident and well documented [22,29,30], and the analysis revealed high clustering along roads, water courses, and in dense urban areas. High-order geodetic control networks, with regularly dispersed reference stations, define the geodetic reference system in Poland [16]. To the contrary, local, detailed networks, that are a part of land administration systems, are tailor-made to the covered area, and are suitable for performing local measurements, including surveying deformations and the necessity to monitor engineering structure [28,72]. They are inevitably designed to match local purposes and scale. Scale is, de facto, a fundamental concept in any analysis concerned with spatial pattern and processes [48,66] as the patterns and processes of spatial objects have an implicit scale of variation. As noticed by Goodchild [76,77], scale is often perceived as an alternative dimension to interpret the patterns and processes. Scale also implicite relates to land policy, especially in land administration domain systems and models [15,78]. Scale dependent variation of BGCPs’ spatial pattern is shown by Ripley’s K-function and spatial autocorrelation. Furthermore, the spatial pattern of geodetic control networks is locally hampered by environmental features or processes (e.g., surface deformation as a result of mining, vicinity of water reservoirs, sky obstruction by a forest canopy) and changes from regular to densified or thinned.

6. Conclusions The novelty of this study relied on quantifying the observed dispersed spatial pattern of the base geodetic control points (BGCPs) into regularly dense and regularly thinned, depending on a cluster and outlier analysis. The rules and principles of designing geodetic control networks are well recognized and described in the literature, but mainly as theoretical, numerical examples. Our research examines the spatial distribution of geodetic control points monumented within the frame of the base geodetic network in Poland. Hence, it has a broader context and provides some results concerning the spatial pattern of the BGCPs in Poland, which slightly changes within scales. The spatial dispersion of the BGCPs was documented by an ANN analysis, one of the oldest spatial statistics. The z-score of 1.39 for the ANN analysis, placed in the tail of normal distribution, provides clear evidence for dispersion. This dispersion was confirmed by the second-order spatial statistic, namely the Ripley’s K-function, which shows that at the near distances from 2 to 7 km, which are typical lengths in base geodetic ISPRS Int. J. Geo-Inf. 2020, 9, 148 17 of 20 networks. This leads to the conclusion that the assumed uniform distribution of BGCPs over the country’s territory has been achieved, however, in regions where the inter-point distance equals 2 km on average, a considerable densification of BGCPs is observed. Only 6% of the BGCPs could be influenced by environmental obstacles, such as close vicinity to express roads, water reservoirs, or electricity lines. Moreover 452 points are located in artificial areas, where the satellite signals may be disturbed in multiple ways. All these points should be monitored regularly to ensure that their coordinates are determined accurately. The presented research faces challenges in examining the configuration of Polish base geodetic control points by means of advanced spatial pattern methods, especially in analyzing the distribution of basic control network points. The achieved results could serve the scientific community and also land surveyors. They could be helpful at the survey planning stage because they show the accessibility of points in terms of inter-point distance, geometric distribution, and environmental conditions in the vicinity of stations. The originality of the research lies in its complex approach to analyzing the density of geodetic control points and the evenness of their spatial distribution. Although the methods used are well known and widely described in the literature, their combination is an added value, especially for the National Mapping Agency that is responsible for geodetic control networks maintenance as well as for surveyors. Ultimately, the goal of the present research is not only to quantify the uniformity of spatial distribution of the base geodetic control points in Poland, but also to find environmental obstacles that hamper the assumed regular dispersed distribution and, finally, to provide methodological fundamentals enabling to conduct the analytical procedure for geodetic control points spatial pattern assessment.

Author Contributions: Conceptualization, E.B. and K.P.; Formal analysis, E.B., K.P. and S.B.; Methodology, E.B.; Visualization, S.B.; Writing—original draft, E.B. and K.P.; Writing—review & editing, E.B. and K.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Institute of Geospatial Engineering and Geodesy, Faculty of Civil Engineering and Geodesy, Military University of Technology. Acknowledgments: The CORINE Land Cover data was derived from Copernicus Land Monitoring web site, while the BGCPs coordinates from the Head Office of Geodesy and Cartography. Conflicts of Interest: Authors declare no conflict of interest.

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