Mathematical processing of results of determining geodetic distances between landslides and infrastructure objects in different coordinate systems

The purpose of this study is to develop a method for calculating the orthodromic distance between displacement points in the WGS84 geodetic coordinate system using the QGIS and ArcGIS Pro GIS environments. The study utilizes the Geodesic parameter, which has been the standard for ArcMap (since version 9.0) and ArcGIS Pro environments, providing the shortest distances on an ellipsoid. In this work, the tool is used not as a new feature, but as a basis for comparing the accuracy of calculations in different coordinate systems. The focus is on accuracy, automation of calculations, and verification of results for their subsequent use in analyzing the spatial structure of landslide processes. Methodology. The work employs a geodetic (orthodromic) method, which accounts for the ellipsoidal shape of the Earth and ensures high accuracy in calculations, unlike the plane Euclidean approach. The calculations were performed in ArcGIS Pro using the Generate Near Table tool, which enables the determination of the shortest distances between sets of spatial objects. The analysis was performed in four coordinate systems: WGS84 geographic, UCS-2000 national, rectangular flat coordinate system UTM Zone 35N, and historical SK-42 (Gauss-Krüger, zone 5). Additionally, the results were verified using the classic Vincent formula, implemented through the geopy.distance.geodesic library, which made it possible to compare ArcGIS Pro algorithms with reference to geodetic calculations. Results. The results confirm the high accuracy of ArcGIS Pro's built-in algorithms, as the difference between software calculations and classical formulas does not exceed one millimetre. This demonstrates the feasibility of applying the Geodesic method to scientific and applied tasks in the field of geoinformation analysis. Research has shownthat the choice of coordinate system significantly affects the accuracy of spatial measurements. Using planar methods or inappropriate projections can lead to errors of several tens of metres.  This is especially dangerous when modelling risks for transport infrastructure in mountainous areas. Scientific novelty and practical significance.  The novelty of the research lies not in the use of the Geodesic parameter itself (it has long been implemented in ArcGIS), but in the comprehensive analysis of measurements in different coordinate systems. It includes comparison with planar methods and verification using classical geodetic formulas to assess the accuracy of measurements from infrastructure objects to landslide areas. The practical significance of the research lies in its potential applications for automated spatial analysis of landslide risks, modeling the vulnerability of transport infrastructure, and planning protective measures effectively.The proposed approach can be integrated into the geoinformation systems of local authorities, surveyors, and engineers to enhance the accuracy of calculations and informed management decisions in complex geospatial environments.

geodetic distances; landslides; road infrastructure; coordinate systems; geodetic method; ArcGIS Pro; Vincent's formula
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