ACCURACY OF GLOBAL GEOID HEIGHT MODELS IN LOCAL AREA: TESTS ON CAMPANIA REGION (ITALY)

Transcription

1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 3, March 2018, pp , Article ID: IJCIET_09_03_105 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed ACCURACY OF GLOBAL GEOID HEIGHT MODELS IN LOCAL AREA: TESTS ON CAMPANIA REGION (ITALY) P. Maglione Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale - Isola C4, 80143, Napoli (Italy) C. Parente Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale - Isola C4, 80143, Napoli (Italy) A. Vallario Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale - Isola C4, 80143, Napoli (Italy) ABSTRACT Nowadays GPS technology permits to reach millimeter or sub-millimeter horizontal relative accuracy levels over very long distances (up to hundreds of kilometers). The vertical GPS accuracy is more difficult to obtain. In addition, because GPS heights are referred to ellipsoid, their transformation into orthometric heights requires the use of a geoid model that influences with its accuracy the quality of the results. Usually a local geoid model is characterized by a high level of accuracy, but often it has a fee. Global geoid models are free available and their accuracy is to test in the local area where they are to use so to evaluate their suitability for the user purposes. This paper is aimed to compare different Global Geoid Models testing their accuracy on Campania region (Italy). Particularly, models respectively named EGM84, EGM96 and EGM2008, are considered and tested on 18 points corresponding to GNSS Permanent Stations in Campania. For the best resulting model, the EGM2008, a solution to improve further its performance is adopted. Keywords: Geoid, Global Geoid Height model, local accuracy and Campania region. Cite this Article: P. Maglione, C. Parente and A. Vallario, Accuracy of Global Geoid Height Models in Local Area: Tests on Campania Region (Italy), International Journal of Civil Engineering and Technology, 9(3), 2018, pp editor@iaeme.com

2 Accuracy of Global Geoid Height Models in Local Area: Tests on Campania Region (Italy) 1. INTRODUCTION Global Positioning System (GPS), widely used for satellite based navigation and topographic survey, provides three dimension (3D) coordinates of points referred to the global geocentric orthogonal system World Geodetic System-84 (WGS-84) (El-Rabbany, 2002; Gopi, 2005; Hofmann-Wellenhof, 2012). The global coordinates X, Y, Z that determine the position of a point in a 3D space, are generally transformed into ellipsoidal coordinates ϕ, λ, h that are respectively ellipsoidal latitude, longitude and height (Li et al, 2010; Feltens, 2008; Civicioglu, 2012). The ellipsoidal height is transformed to orthometric or geoidal height (H) using the well-known formula (Heiskanen and Moritz, 1967; Featherstone et al, 1998; Kotsakis and Sideris, 1999; Fotopoulos, 2003; Pepe and Prezioso, 2015): where N is the geoid undulation (or geoid height), the vertical separation between the geoid and the ellipsoid. The relationship between H, h and N is shown in figure 1. Figure 1 Relationship between orthometric height (H), ellipsoidal height (h) and geoid undulation (N) The knowledge of geoid undulations N is necessary to solve the problem (Erol and Çelik, 2004; Srinivas et al. 2012). Orthometric heights are useful for many purposes, e.g. they permit to build Digital Terrain Model (DTM) referred to sea level (Maglione et al, 2014). A geoid model can be derived by an Earth Gravitational Model (EGM) that is a set of geopotential coefficients used in a spherical harmonic expansion to create a global potential surface that coincides with Mean Sea Level (MSL) (Pavlis et al, 2007; Sjöberg and Bagherbandi, 2017). This surface fluctuates above and below the reference ellipsoid surface established by WGS84. Commonly the acronym EGM is used also to indicate geoid model as well as undulation model derived by global earth gravitational model. Even if it depends on the specific model, usually the accuracy of EGM evaluated in a limited region of the Earth is lower than that associated to a local geoid obtained for the same area with other techniques, e.g. by GPS/levelling data (Kiamehr and Sjoberg, 2005; Merry, 2009; Alothman et al, 2014). For consequence, not to affect the accuracy of orthometric heights using an inappropriate undulation model, the EGM must be tested on the study area so to define the limits of its usage. In this paper the accuracies of three geoid height models, respectively named EGM84, EGM96 and EGM2008, are estimated on Campania region (Italy) and a fast solution to fit the best of them on the study area so to enhance its performance is proposed. The paper is editor@iaeme.com

3 P. Maglione, C. Parente and A. Vallario organized as follows. Section 2 illustrates data and methods: a very brief description of the main characteristics of each considered model is supplied. Section 3 presents and discusses the results of the tests carried out using as references the geoid undulations in 18 control points collected in the GNSS Permanent station network of Campania region. Section 4 concludes the paper. 2. MATERIALS AND METHODS 2.1. Study Area Located in Southern Italy, Campania has an area of 13,590 km 2 and includes three small islands (Ischia, Procida and Capri). Its coastline of 350 km on the Tyrrhenian Sea contains three gulfs (Naples, Salerno and Policastro). Close to the cost there is the Volcano Vesuvio (1,277 m) while the mountainous interior is disjointed into several massifs, e.g. Taburno (1,344 m), Partenio (1,573 m), Matese (Gallinola, 1,923 m), Monte Miletto (2,050 m). Two costal lowlands are present in Campania: the Volturn river basin and the Terra di lavoro (North of Naples), the plain of the lower Sele river (south of Salerno). The region is mostly hilly (50.8 %), in part mountainous (34.6%) and flat (14.6%). It extends roughly from E to E in longitude and from 39 59' 30.8" N to 41 30' 26.6" N in latitude EGM84 EGM84 is a gravitational model of the Earth provided as a set of normalized, geopotential coefficients to degree and order 180. A 30-minute worldwide geoid height model for the original WGS 84 ellipsoid is precomputed from EGM84. The coefficient and geoid height files have associated software and documents: three FORTRAN programs can interpolate from the grid supplying a geoid height at any given latitude and longitude. EGM84 was approved for official use by United States Department of Defense (DoD) as documented in DMA TR8350.2, Second Edition, 1 September 1991 (NGA, 2008). In figure 2 the extraction of EGM84 geoid height model concerning Italy and surrounding area is shown. Figure 2 EGM84 geoid height model: particular on Italy and surrounding area editor@iaeme.com

4 Accuracy of Global Geoid Height Models in Local Area: Tests on Campania Region (Italy) 2.3. EGM96 The EGM96 is a gravitational model of the earth provided as a set of normalized, geopotential coefficients to degree and order 360 (rather than 180 as EGM84). It results as composite solution including: a combination solution to degree and order 70; a block diagonal solution from degree 71 to 359; and the quadrature solution at degree 360. This model is produced in collaboration by the National Imagery and Mapping Agency, the NASA Goddard Space Flight Center, and the Ohio State University (Lemoine et al., 1998). A 15-minute worldwide geoid height file is precomputed from the EGM96. The coefficient and geoid height files have associated software and documents: a FORTRAN program, named F477, permits to calculate undulation based on geographic coordinates. EGM96 was approved for official use by DOD as documented in NIMA TR8350.2, Third Edition, 4 July 1997 (NGA, 2008). EGM96, integrating new available gravimetry data, has enhanced the previous continental geoid model; contributions has been provided by many countries, e.g. surveyed data from South America, Africa, and North America (Lemoine et al., 1998). In figure 3 the EGM96 geoid height model in the study area (Campania region) is shown. Figure 3 EGM96 geoid height model on Campania region and surrounding area 2.4. EGM2008 The EGM2008 is a gravitational model of the Earth, developed by a least squares combination of the ITG-GRACE03S gravitational model (with its associated error covariance matrix) and a 5'x5' grid of free-air gravity anomalies. This grid results by integrating terrestrial, altimetryderived, and airborne gravity data. Over areas where only lower resolution gravity data were available, their spectral content was enhanced with gravitational information derived by the editor@iaeme.com

5 P. Maglione, C. Parente and A. Vallario topography. EGM2008 is developed up to degree/order 2159 with some additional terms up to degree/order 2190 (Pavlis et al., 2012). Over areas covered with high quality gravity data, the differences between EGM2008 geoid undulations and independent GPS/Levelling values are on the order of ±5 to ±10 cm. In some areas higher values of discrepancies results, e.g. RMS of 79 cm in Saudi Arabia (Alothman et al., 2014). In figure 4 the EGM2008 geoid height model in the study area (Campania region) is shown. Figure 4 EGM2008 geoid height model on Campania region and surrounding area 2.5. Local Geoid Height Data for Comparison To test the accuracy of the three mentioned geoid height models on the study area, 18 GNSS permanent stations are considered: they are included in the network managed by Campania region for real time surveying service and their coordinates are precisely know in ETRF2000, the European Terrestrial Reference Frame (Crespi et al, 2005, Benciolini et al, 2008). The network was disegned to limit the distance between neighboring stations within 70 km. At present 16 stations are working and two are not operational; nevertheless both heights (orthometric and ellipsoidal) of each GNSS permanent station are known with millimeter accuracy, so geoid undulations can be calculated in 18 points. In figure 5 all GNSS permanent stations in the network of Campania region are shown editor@iaeme.com

6 Accuracy of Global Geoid Height Models in Local Area: Tests on Campania Region (Italy) Figure 5 GNSS Permanent stations in Campania region 3. RESULTS AND DISCUSSION At first, the grid of each global model is considered without interpolation to carry out the geoid undulation in correspondence of every GNSS permanent station. In table 1 the statistics of the residuals (discrepancies between the geoid heights from global model and the effective ones of the GNSS permanent stations) are shown. The best performance is supplied by EGM2008 (RMS=0.267 m), the worst by EGM84 (RMS=1.174 m). Table 1 Statistics of the residuals between the geoid heights of the GNSS permanent stations and those supplied by each global model. Geoid Height Model Min Max Mean Standard deviation RMS EGM EGM EGM Then the geoid undulations in the considered points are derived by each global model using interpolation. Particularly, online geoid height calculator based on GeoidEval utility is used: supplying the position on standard input, this application prints out the corresponding heights of three geoids (EGM84, EGM96 and EGM2008) above the WGS84 ellipsoid on standard output. The position is given in latitude and longitude and the geoid undulation is returned in meters (Karney, 2014). Also in this case the results are compared with the geoid heights of the GNSS permanent stations; the statistics of the residuals are shown in table 2. Using the interpolation approach very little improvements are achieved and only for EGM84 and EGM editor@iaeme.com

7 P. Maglione, C. Parente and A. Vallario Table 2 Statistics of the residuals between the geoid heights of the GNSS permanent stations and those supplied by each global model using online GeoidEval utility Geoid Height Model Min Max Mean Standard deviation RMS EGM EGM EGM The geoid undulations supplied by EGM2008 remarks the presence of systematic error: the results can be performed subtracting mean value from all values. Considering the model without interpolation approach, the statistics of the residuals are shown in table 3. Table 3 Statistics of the residuals between the geoid heights of the GNSS permanent stations and those derived by EGM2008 removing the mean value of the early residuals (0.257 m) Geoid Height Model Min Max Mean Standard deviation RMS EGM CONCLUSIONS The experiments carried out in this work confirm the highest accuracy of EGM2008 compared to the other global models, i.e. EGM84 and EGM96. However they also remark that global geoid height models are often no suitable for local applications. In fact RMS values (1.157 m for EGM84, m for EGM96 and for EGM2008) resulting in Campania region are inappropriate for accurate survey and representation: centimeter accuracy supplied by GPS technology for ellipsoidal heights is degraded in the passage to orthometric heights because of the approximate estimation of the geoid undulation. Better results can be achieved if the EGM2008 is preventively adapted to the study area: for Campania region a vertical translation of the model is appropriate; in particular, m must be subtracted to the original value of each undulation. This project is a work in progress: more tests will be carried out on Campania region using a higher number of points presenting known undulation values, so to verify further the possibility to fit a global geoid height model on the considered area. ACKNOWLEDGEMENTS This paper presents results of experiments performed within the project New Geodetic Reference System and GNSS data quality. This project is supported by the University of Naples Parthenope. The authors are grateful to Prof. Raffaele Santamaria, recently died, for his useful suggestions in the first phase of this project. REFERENCES [1] El-Rabbany, A. Introduction to GPS: the global positioning system. Artech house, [2] Gopi, S. Global positioning System: Principles and applications. Tata McGraw-Hill Education, [3] Hofmann-Wellenhof, B., Lichtenegger, H., Collins, J. Global positioning system: theory and practice. Springer Science & Business Media, editor@iaeme.com

8 Accuracy of Global Geoid Height Models in Local Area: Tests on Campania Region (Italy) [4] Li, Y.X., Zhang, J.H., Zhang, J.Q., Du, X. Direct transformation from geocentric cartesian coordinates to geodetic latitude and ellipsoidal height. Journal of Geodesy, 42, 2010, pp [5] Feltens, J. Vector methods to compute azimuth, elevation, ellipsoidal normal, and the Cartesian (X, Y, Z) to geodetic (φ, λ, h) transformation. Journal of Geodesy, 82(8), 2008, pp [6] Civicioglu, P. Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Computers & Geosciences, 46, 2012, pp [7] Heiskanen, W., Moritz, H. Physical Geodesy. W.H. Freeman and company, San Francisco and London, [8] Featherstone, W. E., Dentith, M. C., Kirby, J. F. Strategies for the accurate determination of orthometric heights from GPS. Survey Review, 34(267), 1998, pp [9] Kotsakis, C., Sideris, M. G. On the adjustment of combined GPS/levelling/geoid networks. Journal of Geodesy, 73(8), 1999, pp [10] Fotopoulos, G. An analysis on the optimal combination of geoid, orthometric and ellipsoidal height data. Ph.D. Dissertation. University of Calgary: Department of Geomatics Engineering, [11] Pepe, M., Prezioso, G. A Matlab geodetic software for processing airborne LIDAR bathymetry data. The International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, 40(5), 167. [12] Erol, B., Çelik, R. N. Modelling local GPS/levelling geoid with the assessment of inverse distance weighting and geostatistical kriging methods. Proceedings XX th ISPRS Congress, Istanbul, Turkey, [13] Srinivas, N., Tiwari, V. M., Tarial, J. S., Prajapti, S., Meshram, A. E., Singh, B., Nagarajan, B. Gravimetric geoid of a part of south India and its comparison with global geopotential models and GPS-levelling data. Journal of earth system science, 121(4), 2012, pp [14] Maglione, P., Parente, C., Santamaria, R., Vallario, A. Modelli tematici 3D della copertura del suolo a partire da DTM e immagini telerilevate ad alta risoluzione WorldView-2. Rendiconti Online della Società Geologica Italiana, 30, 2014, pp [15] Pavlis, N. K., Factor, J. K., Holmes, S. A. Terrain-related gravimetric quantities computed for the next EGM. Proceedings of the 1 st International Symposium of the International Gravity Field Service (IGFS), Istanbul, 2007, pp [16] Sjöberg, L. E., Bagherbandi, M. Modern Physical Geodesy. In: Gravity Inversion and Integration. Cham: Springer, 2017, pp [17] Kiamehr, R., Sjoberg, L. E. Comparison of the qualities of recent global and local gravimetric geoid models in Iran. Studia Geophysica et Geodaetica, 49(3), 2005, pp [18] Merry, C. EGM2008 evaluation for Africa. Newton s Bulletin, 4, [19] Alothman, A., Bouman, J., Gruber, T., Lieb, V., Alsubaei, M., Alomar, A., Fuchs, M., Schmidt, M. Validation of regional geoid models for Saudi Arabia using GPS/levelling data and GOCE models. In: Gravity, Geoid and Height Systems. Cham: Springer, 2014, pp [20] NGA - Office of Geomatics, EGM WGS 84 Version, [21] Lemoine, F. G., Kenyon, S. C., Factor, J. K., Trimmer, R.G., Pavlis, N. K., Chinn, D. S., Cox, C. M., Klosko, S. M., Luthcke, S. B., Torrence, M. H., Wang, Y. M., Williamson, R editor@iaeme.com

9 P. Maglione, C. Parente and A. Vallario G., Pavlis, E. C., Rapp, R. H., Olson, T. R. The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, [22] NGA - Office of Geomatics. NGA/NASA EGM96, N=M=360 Earth Gravitational Model, [23] Pavlis, N. K., Holmes, S. A., Kenyon, S. C., Factor, J. K. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of geophysical research: solid earth, 117(B4), [24] Crespi, M., Mazzoni, A., Colosimo, G. Global and local reference frames. Rendiconti Lincei, 26(1), 2015, pp [25] Benciolini, B., Biagi, L., Crespi, M., Manzino, A. M., Roggero, M. Reference frames for GNSS positioning services: Some problems and proposed solutions. Journal of Applied Geodesy, 2(1), 2008, pp [26] Charles Karney. Online geoid calculations using the GeoidEval utility, editor@iaeme.com