(Translated by https://www.hiragana.jp/)
№ 88 (2018) | Видавництво Львівської політехніки

№ 88 (2018)

ADAM ŁYSZKOWICZ 1, ANNA BERNATOWICZ 2
1 Department of Air Navigation, Faculty of Navigation, Polish Air Force University
2 Department of Geodesy, Faculty of Civil Engineering, Environmental and Geodetic Science Koszalin University of Technology
ABSOLUTE SEA LEVEL CHANGES AT THE TIDE GAUGE STATION
IN WŁADYSŁAWOWO USING DIFFERENT TIME SERIES SOFTWARE PACKAGES
https://doi.org/10.23939/istcgcap2018.02.013
This paper presents geocentric sea level changes at the tide gauge station in Władysławowo, Poland. These changes have been calculated from the time series of GNSS and tide gauge observations. For the estimation of the geocentric sea level trend computer software packages Hector, GITSA, GGMatlab, and Statistica have been used. The results show that all the software packages give a similar value of absolute sea level changes in Władysławowo and it is estimated at a rate of around 3 mm/year. The examined computer programs are featured by a different degree of visualization and the simplicity of use. A significant difficulty is to prepare the required data format and the installation of the computer program in the software environment e.g. Matlab. Finally, it can be concluded that the Hector software package, due to the simplicity of input data preparation, that the possibility of on-line calculations and the selection of different error models are very useful for the analysis of time-series of geophysical phenomena like sea level changes. The least recommended for this type of analysis of time series is the Statistica software package.
Key words: mean sea level, tide gauge, satellite GNSS observations.
Література – 30.

UDC 528.2
B. DZHUMAN
Department of Higher Geodesy and Astronomy, National University Lviv Polytechnic, 12, S. Bandera str., Lviv, 79013, Ukraine, ph. +38 (068) 7632139, е-mail teojuman@gmail.com
MODELING OF THE REGIONAL GRAVITATIONAL FIELD USING FIRST
AND SECOND DERIVATIVE OF SPHERICAL FUNCTIONS
https://doi.org/10.23939/istcgcap2018.02.005
Aim. The main task of the geodesy is to determine the shape and size of the Earth and its changes over time. An integral part of determining the shape and size of the Earth is the construction of a geoid surface model, both global and regional. Today larger and more precise arrays of input data (geopotential functionals) appear to construct such a model, methods for their processing are rapidly becoming generated. One of such methods is an extention in a series of spherical functions on a spherical trapezium. Since the functionals of the gravitational field are mostly obtained using the differentiation operator, for the use of this method it is necessary to investigate the first and second derivatives of spherical functions on a spherical trapezium, which is the purpose of this work. Method. Spherical functions on a spherical trapezium can not be presented in explicit form, nor do they have simple recurrence relations. To calculate them, the extention in a hypergeometric series should be used. Therefore, to calculate the first and second derivative from the above-mentioned functions, the derivative from the hypergeometric series should be used. Results. As a result of certain mathematical transformations, we obtain an expression for finding the first and second derivatives of spherical functions on a spherical trapezium, as well as a comparatively obtained result with spherical Legendre functions of the first kind. The scientific novelty and practical significance. The expression for the first and second derivative of spherical functions on a spherical trapezium was first determined. The result obtained with the spherical Legendre functions of the first kind is comparative. This enables the use of such functions as a basic system of functions on a spherical trapezium for modelling of regional gravitational or magnetic fields.
Key words: spherical functions, spherical trapezium, first and second derivative.

Література – 18.

UDC 528.2./.3
S. SAVCHUK1, N. KABLAK2, A. KHOPTAR1*
1 * Department of Higher Geodesy and Astronomy of National University Lviv Polytechnic, 12, S. Bandera str., Lviv, 79013, Ukraine, tel.:+38(093)1107822, e-mail: alina.a.khoptar@lpnu.ua
2 Department of Urban Construction and Management, Uzhhorod National University, Uzhhorod, 88000, Ukraine.
COMPARISON OF APPROACHES TO ZENITH TROPOSPHERIC DELAY DETERMINATION BASED ON DATA OF ATMOSPHERE RADIO SOUNDING
AND GNSS OBSERVATION
https://doi.org/10.23939/istcgcap2018.02.024
Currently, Global Navigation Satellite Systems (GNSS) are increasingly used in atmospheric monitoring tasks. To determine tropospheric delays, two approaches are most often used: the calculation of atmospheric radio sounding data and the processing of GNSS observations. GNSS processing is, generally, based on two methods, namely precise point positioning (PPP) and double-differencing (DD). PPP is a potent data analysis instrument sensitive to a variety of parameters. This paper demonstrates that PPP can be used not only for positioning and navigation but also for other atmospheric monitoring tasks. Purpose. Realization of a comparative analysis of various approaches for tropospheric delays determination based on the results of GNSS observations processing by the PPP and DD methods, and on atmospheric radio sounding data. Methodology. The observation data from following GNSS stations were used: BUCU (Bucharest, Romania), GANP (Ganovce, Slovakia) and GLSV (Kyiv, Ukraine), as well as, located nearby, aerological stations 15420 (Bucharest, Romania), 11952 (Poprad-Ganovce, Slovakia), 33345 (Kiev, Ukraine). Therefore, in this work the zenith tropospheric delay ( ) determination is performed according to GNSS observation data using the PPP method with the application of the software package GIPSY-OASIS and the DD method by means of the Bernese GNSS Software and GAMIT-GLOBK software packages. The obtained results were compared with the corresponding radio sounding data. Results. The values obtained using different approaches correspond to a sub-centimeter level of accuracy with respect to radio sounding data, while the best results were obtained by the PPP method at Slovak stations (millimeter level), where the distance between the location of the aerological and GNSS stations is less than 1 km, i.e. they are in the same atmospheric conditions. This suggests that the PPP method provides a better level of accuracy and can be used precisely to determine tropospheric delays. Scientific novelty, practical significance. The technology of continuous atmospheric monitoring using GNSS stations and observations processing technology from these stations based on the absolute positioning PPP. The obtained results after their completion can be used in thoughtful investigations of tropospheric effects through GNSS observations and for numberous atmospheric monitoring applications.
Key words: precise point positioning (PPP), zenith tropospheric delay ( ), atmospheric radio sounding, GNSS-observation, atmospheric monitoring.

Література – 20.

UDC 528.9
Y. HOLUBINKA*, V. NIKULISHYN, R. SOSSA, M. YURKIV
Department “Cartography and geospatial modelling” of National University Lviv Polytechnic, 12, S. Bandera str., Lviv, 79013, Ukraine, tel. 067-78-26-582, *е-mail JuliaG@i.ua
INVESTIGATION OF THE ACCURACY OF PLANS OF LVIV IN 1844 AND 1931
https://doi.org/10.23939/istcgcap2018.02.033
Purpose of this work is the accuracy assessment of plans of Lviv in 1844 and 1931. Methodology. The main criterion for evaluation of the authenticity of the old plans is the study of their geometric accuracy, which is determined by the magnitudes of errors that arise when measuring lengths, angles, coordinates, and other cartometric attributes. For the investigation of accuracy, quantitative method used direct measurements of the lengths of lines and angles between two directions in the oldert and modern plans and analysis of these measurements based on the statistical theory of errors using the Gauss and Bessel formulas. Results. According to this methodology, for each plan, the mean square error of the distance, the angle of rotation, and the mean square error of the directional angles were determined. These characteristics made it possible to compare the errors of linear and angular variables of two time-varying and multi-scale plans of Lviv to each other and concluded that the plan of Lviv in 1931 is more accurate with respect to the angular measurements. Distortion distances are characteristic for both Lviv’s plans. Nevertheless, there was less relative mean square error is in the plan of 1931, despite its smaller scale. The calculated distortion coefficients of the lengths of lines and the amplitude of fluctuations of the boundary values of the scale denominator made it possible to carry out the analysis of distortion in different parts of the plan and to continue the study of the accuracy of the above-mentioned cartographic materials using graphical research methods that allowed us to evaluate and illustrate spatial variations of errors, as well as to detect and understand the facts and technical aspects of creating these cartographic works. Scientific novelty and practical significance. The determination of the geometric accuracy of the 1844 plans of Lviv, as a tool for scientific research, is relevant since it enables us to evaluate the cartographic publication as a result of human activity more objectively and fully. Numerical data obtained during such a research made it possible to compare the cartographic, documentary, and content values of old plans. The quantitative technique chosen in the study of Lviv’s old plans, based on direct measurements of the lengths of lines and angles between two directions, made it possible to compare the errors of linear and angular variables of time-varying and multi-scale plans of Lviv. Having been calculated in this research, this methodology can be used to evaluate the accuracy of other plans of Lviv and any other city.
Key words: old plan, theory of errors, length distortion, mean square error, Gauss formula, directional angle.

Література – 18.

UDC 332.3: 528.44
YU. HUBAR, L. VINARCHYK
The Department of Cadaster of Territory of National University Lviv Polytechnic, 12, S. Bandera str., Lviv, 79013, Ukraine,
tel. +38 (032) 2582631, email: Yurii.P.Hubar@lpnu.ua
METHODS FOR THE DETERMINATION OF EXTERNAL OBSOLESCENCE
OF THE COMMERCIAL REAL ESTATE-CASE STUDY
https://doi.org/10.23939/istcgcap2018.02.047
The purpose of the study. Solving the problem of the calculation of aggregate obsolescence of a real estate object in general and external obsolescence in particular, as being less investigated and described in scientific papers is a topical issue. A topical issue being investigated and described in scientific papers is the problem of calculating the aggregate obsolescence of a real estate object, particularly its external obsolescence. The drawback of the existing methods of determining the external obsolescence (except a paired comparison method) is the necessity of storing a great amount of selling or renting data, which is rather difficult within Ukrainian market conditions. Current methods used for the investigation of external obsolescence of commercial real estate which require less data are proposed [ISA, 2017; NSA-1, 2003; NSA-2, 2004]. Methodology. In the process of real estate valuation obsolescence is considered to be an important factor for the valuation of buildings by the cost approach and is determined as sacrifice of utility or loss in value, due to several possible causes [Kharryson, 1994; Ekkert, 1997]. The subject of the investigation and analysis shows a potential gross revenue received from leasing; revenue losses from rental payments; the possibility of gain contingency; and transaction costs, that comprise net operating income. In this case they should serve as a market proof of the level of the rate of return of the real estate being evaluated. The results. Today the value of external obsolescence of the real estate is determined with the use of a large amount of market data. In general, the market comparison is a key position in determining aggregate improvements and depreciation and the aggregate depreciation is the difference between replacement or renewal costs and market improvement value, and depreciated cost of replacement of land improvements is a difference between the selling prices of real estate and market land value. The investigations related to the development of new methods of the estimation of the external obsolescence of real estate have been carried out. In the paper it is proven that for the improvement of the evaluating methodology of real estate and determining its external obsolescence new methods should be applied, which will allow the real estate evaluators to avoid subjectivity in calculations and, subsequently, “legal deficiency” in obtained results. Scientific innovation. Existing methods of valuation of the external obsolescence do not always meet modern market demands and it is necessary to develop new methods having certain advantages over the methods being widely used in practice. The introduction of new methods of calculating the external obsolescence of commercial real estate is important for improving the valuation methodology for modern real estate market of Ukraine. Its practical significance. The investigations enable obtaining the mathematical dependences for determining the correct and scientifically grounded coefficients of the external obsolescence for the commercial real estate property objects. It is feasible to apply the investigations represented in the paper for determining the external deterioration of commercial real estate with the purpose of the calculation of depreciated costs of replacement or depreciated costs with further calculation of its market value [Hubar, 2014, Perovich & Hubar, 2016].
Key words: aggregate obsolescence, external obsolescence, commercial real estate, valuation of real estate, price of liquidation, improvement, production volume.

Література – 17.

UDC 528.4
YU. HUBAR, V. SAI, YU. KHAVAR, U. FARION
Department of Cadastre of Territory of National University Lviv Polytechnic, 12, S. Bandera str., Lviv, 79013, Ukraine, tel: +38 (032) 2582631, e-mail: Yurii.P.Hubar@lpnu.ua
ESTABLISHING THE ENVIRONMENTALLY SAFE WIDTH
OF PROTECTIVE RIPARIAN ZONE ALONG WATER BODIES
https://doi.org/10.23939/istcgcap2018.02.055
Aim. Establishing protective riparian zonesalong the riversides of the Shopurka river inside water protection zones at the territory of urban settlement Velykyy Bytchkiv for protecting surface water bodies from polluting and littering, as well as for saving their water content. The aim of the research is determining the safe protective riparian zonesof water bodies taking into account ecological factors. Methods. The research methodology consists in using the algorithm of determining the width of the protective riparian zone, which enables providing the science-baseddetermination of the width of the protective riparian zone of the water body depending on the types of sylva, granulometric composition of soils, slope expositionand type of soil treatment. Results. The proposed method of determining the optimal width of protective riparian allows justifying the topicality and necessity of its application. For the given river, the width of protective riparian has been determined according to the requirements of Water code of Ukraine and calculated in accordance with formula (1). It will allow the elimination of ambiguity of the determining the width of the protective riparian by the calculations made by the representatives of local water economy with the use of Water code of Ukraine and will facilitate the univocal determining the areas of protective riparian zones. Scientific topicality. Realization of the method of determining the width of the protective riparian according to the proposed algorithm and actual legal documents has shown that the aberration of the protective riparian along the river Shopurka is equal to 20 m. The area of the protective riparian according to the Water code equals 1.82 ha, but according to formula (1) is equal to 3.29 ha. Therefore, the total area of the protective riparian zone should be expandedby 1.47 ha. Practical importance. Determined area and boundaries of the protective riparian zones along the river Shopurka (Zakarpatsky region) will enable the systematic monitoring of the use of riparian soils to be conducted and facilitate the improvement of ecological and sanitary state of the river.
Key words: water protection zone, protective riparian, water body, water code, land code.

Література – 21.

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