Reverse Engineering Official Croatian Geoid Model by CLGE

STUDENT CONTEST 2016

The CLGE Students' Contest 2015 – 2016 Category: I. Geodesy, Topography fifth edition

Reverse Engineering Official Croatian Geoid Model Using Computer Program for Datum Transformation and Python

Grubišić Franka, Mihoković Viktor, Zalović Luka

fgrubisic@geof.hr, vmihokovi@geof.hr, lzalovic@geof.hr

Faculty of Geodesy University of Zagreb

Address Offices in Brussels : Rue du Nord 76, BE – 1000 Bruxelles. Tel +32/2/217.39.72 Fax +32/2/219.31.47 E-mail: maurice.barbieri@clge.eu - www.clge.eu EU-Transparency Register of interest representatives - 510083513941-24

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb Viktor Mihoković, Faculty of Geodesy, University of Zagreb, 3rd year Undergraduate studies, vmihokovi@geof.hr Luka Zalović, Faculty of Geodesy, University of Zagreb, 3rd year Undergraduate studies, lzalovic@geof.hr Franka Grubišić, Faculty of Geodesy, University of Zagreb, 2nd year Undergraduate studies, fgrubisic@geof.hr

REVERSE ENGINEERING OFFICIAL CROATIAN GEOID MODEL USING COMPUTER PROGRAM FOR DATUM TRANSFORMATION AND PYTHON

ABSTRACT The official Croatian geoid model HRG2009 was developed as a surface for conversion of GNSSderived ellipsoidal heights into (normal) orthometric heights. Geoid undulation and orthometric height differences aren’t publicly available in the Republic of Croatia, that is, it is integrated into a computer program for official datum transformation and geoid interpolation, T7D. This paper demonstrates the procedure of creating a new geoid model, derived from T7D, using a set of 288113 randomly chosen measurements and high-level open source programming language, Python, as well as it delivers the comparison of HRG2009 and our reverse engineered determined geoid model.

KEYWORDS geoid, Croatian model, T7D, open source, python, undulation

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

CONTENT 1. Introduction ........................................................................................ 3 2. Official Croatian Geoid Model HRG2009 ........................................... 3 3. Computer Program For Official Datum Transformation And Geoid Interpolation ........................................................................................... 6 3.1. Grid Model Transformation .......................................................................... 6 3.2. User Application ........................................................................................... 8

4. Process Of Extrapolation Of Undulation From T7D ......................... 10 4.1. Defining Grid Points .................................................................................... 10 4.2. Getting Point Undulation Values Using T7D .............................................. 11 4.3. Testing The Newly Obtained Geoid File ..................................................... 13

5. Interpretaion Of The The Results ..................................................... 15 6. Future Plans ...................................................................................... 17 7. Conclusion ......................................................................................... 17 9. References ........................................................................................ 18

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

1. INTRODUCTION

The official Croatian geoid model HRG2009 is a new geoid model for the area of Republic of Croatia. Even though it is used for different purposes, its primary purpose is precise height definition using modern GNSS technology. Consequently, CROPOS (Croatian Positioning System) has been upgraded in 2011. with a new function which enables real-time transformation of ellipsoidal heights into (normal) orthometric heights using HRG2009 geoid GRID and Trimble Transformation Generator Software. The geoid file by itself is not publicly available to use in Croatia, but it is implemented in the official computer program for datum transformation and geoid interpolation – T7D. T7D model and user application have been developed in order to calculate the transformation between the old geodetic datum – Hrvatski državni koordinatni sustav, HDKS (Croatian State Coordinate System, CNCS) on Bessel ellipsoid in the new and official geodetic datum – Croatian Terrestrial Reference System (HTRS96) on GRS80 ellipsoid. As a research, in this paper possibilities like extrapolating the undulation, that is, the geoid file, from official program for transformation in the Republic of Croatia (T7D), have been tested. As for the tool used in the research – of course the necessary T7D, used for transformation HTRS96/ETRS89 à HDKS/Bessel and printing results into a detail list, open-source programming language Python for scripting (generating grid points, reading undulations, interpolation, joining the undulation values to the initial point values) and MO Excel for statistical analysis.

2. OFFICIAL CROATIAN GEOID MODEL HRG2009

In preparation of the computation of a new geoid, following research have been carried out: 1. analysis of recent global geopotential models (GGM) based on CHAMP and GRACE missions (Hećimović i Bašić 2005a, 2005b, Liker i dr. 2008), preparation for the upcoming mission GOCE (Hećimović i Bašić 2005c), and

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

special examination and testing of the newest EGM2008 solution (Pavlis i dr. 2008), 2. collection and quality control of much larger number of available data for gravity (Bašić i Hećimović 2006), 3. creation and 3''x3'' DMR-a data from the Shuttle Radar Topography Mission (SRTM) for the purpose of calculating the effects of the Earth’s topographic gravity field (Bašić i Buble 2007), 4. establishment of the Basic Gravimetric Network, EUVN i EUVN_DA (Bašić i dr. 2006c, Grgić i dr. 2007), which will be used for the purposes of independent control, 5. analysis of height differences between the old and the new height datum (Bašić i dr. 2006a, 2006b), 6. establishment of over 500 new GNSS/levelling points across Croatia in 2009. for the purpose of better absolute orientation of the new geoid, but also the independent audit quality check of HRG2000 (the previous Croatian geoid model). As a method of calculation, due to the relatively small number of measured data (anomalies of free air, with the help of satellite altimeter or GPS / levelling invention of geoid undulations) method of collocation by least squares (Least Squares Collocation, LSC), is used. The long-wave structure of the Earth's field acceleration gravity have been taken from the global geopotential model EGM2008, powered medium part of the spectrum comes from the used discrete terrestrial data and shortwave and ultrashortwave part are modelled with the help of high-resolution digital-terrain model, with the use of "remove-restore" normal procedure of calculation (Bašić 2011). To assess the quality of the new quasi-geoid model, HRG2009, two ways of estimating accuracy have been used - internal and external. Firstly, the internal accuracy through comparisons with 495 GNSS / levelled undulations, used in the calculations themselves, was done. The method demonstrated interoperability which is extraordinarily high (Figure), because the standard deviation is only 2.7 cm (with a mean difference almost zero), indicating above all the well-chosen methodology and

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

implementation of computing, but also the high reliability of the new solutions geoid of 2-3 cm over most of the Croatian mainland. After that, the external (independent) quality score of a new geoid was done, through its comparison with 59 GNSS / levelled undulations that were not used for computing HRG2009 geoid (Bašić, 2001). This comparison confirms that enviable absolute accuracy of the new geoid surface on the Croatian mainland is achieved, because the standard deviation is 3.5 cm (with a mean difference almost zero), confirming on the basis of the independent control data the high reliability of the new solution geoid.

Figure 2: Height differences of HRG2000 and HRG2009

Improvement of the new geoid in relation to the old HRG2000 solution (Bašić, 2001) is more than obvious because it achieved 71% reduction in the standard deviation compared with GNSS / levelling points.

STUDENT CONTEST 2016 The CLGE Studentsâ&#x20AC;&#x2122; Contest 2015-2016 Category: Geodesy | GrubiĹĄiÄ&#x2021; Franka, MihokoviÄ&#x2021; Viktor, ZaloviÄ&#x2021; Luka Faculty of Geodesy University of Zagreb

3. COMPUTER PROGRAM FOR OFFICIAL DATUM TRANSFORMATION AND GEOID INTERPOLATION

T7D GRID model transformation is based on the comfort shift date (Helmert 7 parameter transformation) using a unique transformation parameters and additional translation based on grid distortion model (Figure 3). The unique transformation parameters are calculated according to Bursa-Wolf algorithm whose equations are based on the geocentric Cartesian coordinate system.

Figure 3: Helmert 7 parametar transformation and distortion model.

After applying the Helmert spacious 7-parameter transformation, the resulting coordinates further improve with distortion repairs from a single grid which consists of a rectangular box dimensions: = 46.6 Â° NORTH, SOUTH = 42.0 Â°, with a step of 60 '', and WEST = 13.0 Â°, EAST = 19.5 Â° with steps of 90 '' (PremuĹžiÄ&#x2021; and Ĺ ljivariÄ&#x2021; 2011).

3.1. GRID MODEL TRANSFORMATION

The process of transformation between the initial (original) and final (target) coordinate system is displayed in matrix form: đ?&#x2018;żđ?&#x2018;Ş = đ?&#x2019;&#x2022; + đ?&#x2018;&#x161;đ?&#x2018;šđ?&#x2018;żđ?&#x2018;°

Address Offices in Brussels : Rue du Nord 76, BE â&#x20AC;&#x201C; 1000 Bruxelles. Tel +32/2/217.39.72 Fax +32/2/219.31.47 E-mail: maurice.barbieri@clge.eu - www.clge.eu EU-Transparency Register of interest representatives - 510083513941-24

where: đ?&#x2018;żđ?&#x2018;Ş â&#x20AC;&#x201C; three-dimensional vector coordinates of the target system, đ?&#x2018;żđ?&#x2018;° â&#x20AC;&#x201C; three-dimensional vector coordinates in the original system, đ?&#x2019;&#x2022; â&#x20AC;&#x201C; translation vector, đ?&#x2018;&#x161; â&#x20AC;&#x201C; the scale factor, đ?&#x2018;š â&#x20AC;&#x201C; rotation matrix.

Figure 3.1: Grid interpolation principle

The unknown value in the observed point T is calculated from the known values in the surrounding four points (T1, T2, T3 and T4) as the closest point of GRID. To calculate the unknown point value T, the method of bilinear interpolation is used, as described expressions (1) and (2):

đ?&#x203A;żđ?&#x153;&#x2018;+ = đ?&#x2018;&#x17D;- + đ?&#x2018;&#x17D;. đ?&#x2018;&#x2039; + đ?&#x2018;&#x17D;0 đ?&#x2018;&#x152; + đ?&#x2018;&#x17D;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x152;

expression (1)

đ?&#x203A;żđ?&#x153;&#x2020;+ = đ?&#x2018;?- + đ?&#x2018;?. đ?&#x2018;&#x2039; + đ?&#x2018;?0 đ?&#x2018;&#x152; + đ?&#x2018;?2 đ?&#x2018;&#x2039;đ?&#x2018;&#x152;

expression (2)

where the expression (1) is the term for calculating transformation by geodetic latitude, and the expression (2) is an expression for calculating the transformation of the geodetic longitude.

đ?&#x2018;&#x17D;- = đ?&#x203A;żđ?&#x153;&#x2018;. , đ?&#x2018;&#x17D;. = đ?&#x203A;żđ?&#x153;&#x2018;0 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2018;. , đ?&#x2018;&#x17D;0 = đ?&#x203A;żđ?&#x153;&#x2018;8 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2018;.

, đ?&#x2018;&#x17D;2 = đ?&#x203A;żđ?&#x153;&#x2018;. + đ?&#x203A;żđ?&#x153;&#x2018;2 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2018;0 â&#x2C6;&#x2019;

đ?&#x203A;żđ?&#x153;&#x2018;8 expression (3) đ?&#x2018;?- = đ?&#x203A;żđ?&#x153;&#x2020;. , đ?&#x2018;?. = đ?&#x203A;żđ?&#x153;&#x2020;0 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2020;. , đ?&#x2018;?0 = đ?&#x203A;żđ?&#x153;&#x2020;8 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2020;. , đ?&#x2018;?2 = đ?&#x203A;żđ?&#x153;&#x2020;. + đ?&#x203A;żđ?&#x153;&#x2020;2 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2020;0 â&#x2C6;&#x2019; đ?&#x203A;żđ?&#x153;&#x2020;8 expression (4)

đ?&#x2018;&#x2039;=

9: ;9< 9= ;9<

,đ?&#x2018;&#x152;=

>: ;>< >;><

expression (5)

In expressions (3), (4) and (5), the coefficients ai, bi, X and Y are defined, and they with the expressions (1) and (2) make the calculation of the transformation. To get the height distortion in point T, coefficients of latitude and longitude, Î´Îť and Î´Ď&#x2020; are replaced with coefficients of height Î´h, which means that for altitude distortion we get a new set of parameters ci. The principle of bilinear interpolation within grid does not change, that is, it is the same for all five components within the T7D distortion model (geoid undulation, the shift to the east, the shift to the north, along the normal shift height dH, the transformation between the old and the new height system).

3.2. USER APPLICATION

T7D model and user application have been developed in order to carry out the transformation from the old geodetic datum - the Croatian State Coordinate System (HDKS) on the Bessel ellipsoid in the new official geodetic datum - Croatian Terrestrial Reference System (HTRS96) on the GRS80 ellipsoid. In the user application, it is possible to carry out five different transformations: HDKS / Bessel, HTRS96 / ETRS89, ITRF94 / 96/97 ITRF2000 and ITRF2005, which can be

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

recorded as different sets of coordinates: the flat NEZ / ENH, XYZ Cartesian and ellipsoidal in sexagesimal DMS or decimal DEG or GON arched formats.

Figure 3.2: Functionality scheme of T7D

The program contains data for geoid undulation allocated in the new date and distortion position allocated in the old Bessel ellipsoid (y, x GK projection), as well as height distortions in the new height system (HVRS71) and their differences with regard to the old legacy network II. NVT (Trieste <> HVRS71) (Premužić and Šljivarić 2011). The new geoid model HRG2009 implemented in the program allows easy transition from ellipsoidal to orthometric heights, while the model transformation HTMV2009 (Rožić 2009) is used to transform heights Trieste ↔ HVRS71.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

4. PROCESS OF EXTRAPOLATION OF UNDULATION FROM T7D

The aim of this project was to create a geoid file in txt format that will consist of three columns: geodetic longitude, latitude and geoid undulation. We chose that format because it is quite simple to work with such files in Python scripts. Geodetic longitude and latitude in every row represent coordinates of grid point, while the third value is geoid undulation on that point. All the parameters are chosen to correspond to those used in HRG2009 geoid model. The regular grid is made of 288113 points with grid resolution of 30”x45”, which covers the area of approximately 1x1 km. Area of computation was taken to cover the entire territory of Croatia, which is from 42 to 46 degrees of geodetic latitude and from 13 to 19.5 degrees of geodetic longitude.

Complete procedure of creating and testing the geoid file can be divided into 3 steps: 1. Defining grid points 2. Getting point undulation values using T7D 3. Testing the newly obtained geoid file

4.1. DEFINING GRID POINTS

In order to get grid points record, Python script was written. It was used to write every point from defined boundaries (42-46.6 and 13-19.5), with a 30” latitude and 45” longitude shift. Complete script is shown in Figure 4.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

Figure 4: Python script – defining GRID points

Output file consist of two columns in which points coordinates are written. The record contains

288113

points.

4.2. GETTING POINT UNDULATION VALUES USING T7D

T7D software has an option to export so called “detail list” after HTRS96 - HDKS transformation is carried out. In this list, coordinates of points in both coordinate systems, ellipsoidal and normal-orthometric heights in vertical datums Trieste and HVRS71 and geoid undulations for every point are recorded.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

One example of detail list is given in Figure 4.2.

Figure 4.2: Detail list

Since T7D can handle limited number of points (about 30000), the record was divided into 10 smaller lists, which were then imported into T7D one at the time. HTRS96 was set as input datum, while the output datum was HDKS. Chosen coordinate set was ellipsoidal

sexagesimal

DMS.

Transformation between those datums is not significant by itself. It was only done for the purpose of creating and exporting detail list which contains information we needed. After each of 10 records were imported into T7D and the transformation was done, we managed to get 10 detail lists. Next step was “pulling out” geoid undulation information for every grid point, and writing it into our first record which contains grid point coordinates. It was done using another Python script. Since the undulation value in every detail list is situated in the same “position”, that “position” can be defined in our script and used to copy-paste the geoid undulation data into output txt file. Using this procedure, the txt file containing only geoid undulations for every grid point was created. After that, it was necessary to copy those undulations into our grid points record and the geoid file “Geoid.txt” was formed.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

Figure 4.2.1: Python script for reading undulations from detail lists

4.3. TESTING THE NEWLY OBTAINED GEOID FILE

After we created our geoid file, it was necessary to test it in a way to determine the accuracy of the results obtained using our geoid file compared to T7D undulations. For the purposes of testing, open-source GIS software QGIS 2.6. Brighton and MO Excel were used. Complete test was divided into 2 parts. Every test used 30000 randomly selected points created in the territory of our country. First step was defining ETRS89 as project coordinate system in QGIS. After that, we imported a vector layer of our country which was previously downloaded from http://www.diva-gis.org web site. Creation of test points was done inside QGIS interface by clicking on Vector - Research Tools - Random points. This tool opens a window where parameters like number of random points and vector layer must be defined. We dividing our test into 2 parts because of the difficulties QGIS faces while creating such amount of points. What is more, 30000 points seems to be logical choice because T7D is also limited to that number of points. After the program created 30000 points, they were exported to csv. file format. That file was than opened using MO Excel.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

Figure 4.3: Vector Layer of Croatia in QGIS

Since the exported coordinates were in decimal degrees format, we had to convert them to DMS coordinate format. It was done using the functions of MO Excel. Coordinates

were

then

exported

.txt

file

and

imported

T7D.

The transformation was done once again and the results were written into a detail list, using the same procedure described in chapter 4.2. Using the previously mentioned Python script, the undulations were copied from detail lists and the file called “test1.txt”, containing test points coordinates and their undulations, was formed. Those undulations were used as referent. The same procedure was done with another set of 30000 test points for the file called “test2.txt”. The next step was writing new Python script that will be used to compute geoid undulations of test points based on our geoid file and bilinear interpolation method. Those undulation will then be compered to those exported from T7D. The script imports our geoid file and test file, after which it finds 4 closest grid points that surround the test point. By using interpolation methods integrated in Python module “scipy.interpolate”, geoid undulation of test point is calculated by using known

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

coordinates and undulations of grid points. This undulation is then written in a new txt. file.

Figure 4.3: Part of the code of Interpolation script

Data from that file is afterwards simply imported into Excel file where we had previously imported undulations calculated in T7D. By subtracting our undulations from referent T7D undulations, we got the undulation deviations. Since the massive amount of data that had to be processed using our Python script (geoid file containing 288113 points and test file containing 30000 points), we had to perform maximum script optimization, so it’s process wouldn't take too long. After optimization, our script could perform data processing within 30 seconds, which we considered to be quite satisfying time period.

5. INTERPRETAION OF THE THE RESULTS

When creating 30 000 points on top of vector layer representing republic of Croatia in QGIS, there is a possibility that small amount of points will be generated outside of Croatian border. The main reason is inadequate accuracy of borders defined in used vector layer. Those points were not taken into account when analysing data. The results of our interpolation script are values of undulations for test points. Those undulation values were imported into Excel and then compared with undulation values extracted from T7D for the same set of points. By subtracting our calculated value from reference T7D value, we compared those two sets of data. We tested our geoid file

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

with two different sets of points, with each containing just few points less then 30 000. The results of first test is shown on Figure 5.

Figure 5. The results of Test 1

As shown on Figure, we used 3 interpolation methods: bilinear interpolation, nearest neighbour interpolation and cubic interpolation. On top of that, we calculated arithmetic mean of all three values. All of those values were used with the aim of getting as much data for comparison in order to decide which method produces the best results. As expected, the best method was bilinear interpolation, since T7D itself uses that method for calculation. Naturally, only the results of bilinear interpolation were used in evaluating accuracy of our undulations. Both tests used a bit less then 30 000 points, with the total of almost 60 000 points, what can be considered a representative sample since it covers whole country area and distribution of points is completely random. A lot of pints of points in the first test (over 23 000) coincides with T7D undulations to the third decimal place (less then 1 millimetre accuracy). In second test that number is even a bit higher. In both of the tests there is a fair amount of points that differ by only 1 millimetre, while the maximum deviation in the first test was 4mm, and in the second one 5mm. Standard deviation of our undulations in relation to reference undulations in first test is 0.000043 m. Standard deviation in second test is 0.000034 m. Based on our sample and specified statistical indicators, we can conclude that we were able to get a model that fits the model of the geoid HRG2009.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

6. FUTURE PLANS

The next step would definitely be conversion of our ASCII format in some of the conventional geoid formats (GGF, GRD, BIN...). This could be done using one of the available programs for this type of conversion such as Hydromagic, which allows the conversion of a large number of geoid formats and offers the possibility of downloading free trial version. In addition, one of the possibilities is to send such a record to one of the photogrammetric software manufacturers who could make the conversion to TIFF format, which is very often used in processing programs photogrammetric data. After the conversion into a more conventional format, it would be possible to make further conversions into formats that are adapted by surveying software for field data collection, such as Topcon Field Magnet, Trimble Access, Leica Captivate, Carlson SurvCE and so on. This would enable further testing of the geoid file and possible modifications or adjustments.

7. CONCLUSION

The aim of this project was to present the way in which one can extrapolate geoid file from the official program for the transformation of the Republic of Croatia, T7D, using open-source programming language Python. Using the method described in this paper, we have successfully created a geoid file of extreme accuracy, which in large part (on the basis of the test sample) coincides with that of the integrated program T7D. Deviations of undulations test points calculated using our files and those obtained by using T7D are extremely small and in practical terms negligible. It can be concluded that our geoid file could apply in practice, of course, provided that it is converted in some of the standard formats, such as GGF, GRD, BIN and others. Nowadays, geoid files have very great significance for the surveying profession. With the development of modern technologies of mass data collection (photogrammetry, laser scanning, mobile systems) it is possible to collect a large number of high-quality data in a short time. These details need to be displayed in an appropriate position and

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

height coordinate system. In most cases, the height of such data are ellipsoidal, since all modern systems of mass data collection method use GNSS positioning. It is necessary to transform those heights to the height system used in a particular country (usually orthometric or normal, in Croatia normal-orthometric), since the ellipsoid heights are rarely used in practice. The relationship between ellipsoidal and orthometric heights is exactly geoid undulation. Many of today's applications for processing mass data collection can use geoid file for the transformation of ellipsoidal heights to the appropriate systems. As in Croatia, geoid files are integrated into T7D and as such are not publicly available, it is not possible to carry out the transformation of height in such programs in this way. This can be a significant problem since such information, although of very high quality, is not complete. Such problems can be solved in different ways, but none is as fast and reliable as the use of the geoid file. While these technologies in Croatia have not yet become standard, it is expected that in the near future their use will become widespread. At that time, the problem given here will become a key issue and will have to be solved somehow.

9. REFERENCES

1. PREMUŽIĆ, M., & ŠLJIVARIĆ, M. (2010). T7D korisnička aplikacija. Zbornik radova, 2. 2. Rožić, N. (2006). Hrvatski transformacijski model visina. IZVJEŠĆA, 23. 3. Hećimović, Ž., & Bašić, T. (2005). Satelitska misija CHAllenging Minisatellite Payload (CHAMP). Geodetski list, 59(2), 129-147. 4. Hećimović, Ž., & Bašić, T. (2005). Satelitska misija Gravity Recovery and Climate Experiment (GRACE). Geodetski list, 59(3), 181-197. 5. Hećimović, Ž., & Bašić, T. (2005). Satelitska misija Gravity Field and Steady− State Ocean Circulation Explorer (GOCE). Geodetski list, 59(4), 253-265. 6. Pavlis, N. K., Holmes, S. A., Kenyon, S. C., & Factor, J. K. (2008). An earth gravitational model to degree 2160: EGM2008. EGU General Assembly, 13-18.

STUDENT CONTEST 2016 The CLGE Students’ Contest 2015-2016 Category: Geodesy | Grubišić Franka, Mihoković Viktor, Zalović Luka Faculty of Geodesy University of Zagreb

7. Bašić, T., & Hećimović, Ž. (2006). Latest geoid determinations for the Republic of Croatia. In IAG International Symposium Gravity, Geoid and Space Missions GGSM2004, Session (Vol. 3, pp. 83-92). 8. Bašić,

Tomislav,

Marko

Šljivarić,

and

Goran

Buble.

"Jedinstveni

transformacijski model HTRS96/HDKS." Izvješća o znanstveno-stručnim projektima iz 2005 (2004). 9. Grgić, Ilija, et al. "Fundamental gravity network of the republic of croatia in the function of control and improving of National and European Geoid Model."EUREF 2007 Symposium London. 2009. 10. Bašić,

T.,

Šljivarić,

M.,

Buble,

(2006).

Izrada

jedinstvenog

transformacijskog modela HTRS96/HDKS. Elaborat za Državnu geodetsku upravu Republike Hrvatske, 1-133. 11. Bašić, T., Šljivarić, M., & Buble, G. (2004). Jedinstveni transformacijski model HTRS96/HDKS. Izvješća o znanstveno-stručnim projektima iz, 2005. 12. Bašić,

Tomislav.

"Detaljni

model

geoida

Republike

Hrvatske

HRG2000."Izvješća Državne geodetske uprave o znanstveno-stručnim projektima iz(2000): 11-22. 13. DENKER, H., & BAŠIĆ, T. Europski gravimetrijski geoid EGG2008 i hrvatski geoid HRG2009.