MERGING OF THE 
SLOVENI AND AUSTRIAN 
STATE COORDINATE 
SYSTEMS AND DIGITAL 
TE N ODELS 
Dalibor Radovan, M.Se. 
Institute of Geodesy and Photogrammetry of the 
Faculty of Civil Engineering and Geodesy, Ljubljana 
Doc.Dr. Bojan Stopar 
Faculty of Civil Engineering and Geodesy - Department of 
Geodesy, Ljubljana 
Received for publication: 29 September 1997 
Prepared for publication: 29 September 1997 
Abstract 
Slovenian and Austrian national coordinate systems are 
described comparatively. The parameters for spatial 
calculation between them were calculated for the purpose of 
transformation of the Austrian digital terrain model into the 
Slovenian state plane coordinate system. The Austrian model 
was interpolated and merged with the Slovenian digital 
terrain model into a grid with a cel! size of 100 x 100 m. 
Keywords: Austria, digital terrain model, interpolation, 
national coordinate system, Slovenia, transformation 
1 PURPOSE 
By agreement with the Viennese Bundesamt fuer Eich- und Vermessungswesen (BEV), the Surveying and Mapping Authority of the Republic of Slovenia 
(SMA) purchased a part of the digital terrain model (DTM) covering the Austrian 
national territory almost up to Linz in the west, up to the Hungarian boundary in the 
east and almost up to Salzburg and Wiener Neustadt in the north. The surface area 
of this territory is about 30 percent greater than the surface area of Slovenia. The 
merging of the Austrian and Slovenian DTMs, which was performed by the Institute 
of Geodesy and Photogrammetry in cooperation with the Faculty of Civil 
Engineering and Geodesy, Ljubljana (Radovan, Stopar, 1996, Radovan et al., 1977), 
would have been a relatively simple task had they not been made in two different 
coordinate systems with different geodetic and projection bases. Parameters for the 
calculation (transformation) of the position of points between the two national 
coordinate systems were not known; therefore, their mathematical comparison was 
necessary prior to merging the models. 
Geodetski vestnik 41 (1997) 4 
2 NATIONAL COORDINATE SYSTEM 
he coordinate systems of Slovenia and Austria in which national geodetic surveys 
are performed differ in their position, orientation and scale in both horizontal 
and vertical directions. Therefore, for example, a random point on the state 
boundary between the two countries has different coordinates and altitudes in the 
two systems, even though it was surveyed reliably from both sides. The reasons for 
this discord lie in inevitable errors in the astronomical orientation of triangulation 
networks and differences in the elevation systems and cartographic projections of the 
two countries. The coordinate systems are therefore local - they are valid only for 
the territory of each individual country. Let us now examine their properties in 
slightly more detail. 
The two horizc,mtal coordinate systems share a common reference plane which approximates the Earth's geoid, i.e. Besell's rotation ellipsoid which was 
determined in 1841. They also have in common the starting triangulation point of 
Hermannskogel in Vienna, but the astronomical orientations ofthe two 
triangulations are not equal due to different improvements of primary results. Similar 
considerations apply to the two elevation systems which, however, do have a common 
starting point - bench mark near the automatic tide gauge in Trieste, on the Sartorio 
quay. 
he cartographic projections in the two countries are equal as regards their 
mathematical basis, but their parameters are very different. Their projection is 
Gauss-Krueger projection, the x axis of which (in Slovenia) is the projection of the 
central meridian of zone 5, 15° east of Greenwich. The line scale of points on the 
central meridian equals 0,9999 for geodetic practice in Slovenia. The Austrian 
national coordinate system consists of three meridian zones, and therefore three 
rectangular coordinate systems with central meridians of zones 28°, 31 ° and 34° east 
of Ferro, whereby the difference between the initial meridians of Greenwich and 
Ferro is expressed with a rounded Albrecht constant, A = AFerro - AGreenwich = 
-17°40'00", while the line scale ofpoints on the central meridian equals 1,0000. The 
projection systems of individual zones are named M28, M31 and M34. 
3 DIGITAL TERRAIN MODEL 
DTM of Slovenia is a regular grid of quadratic cells 100 x 100 m in size 
100). The grid is parallel to the axes of the national rectangular system. 
Data in the original were written into blocks of 1 x 1 km with 100 altitude values per 
block. Each block has only one pair of coordinates (y GK' x
0
K), which refers to the SW 
corner of the block. It is possible to calculate the coordinates of individual cells in a 
very simple manner. The altitudes are stated in whole metres. The accuracy of the 
Slovenian DTM 100 was assessed by comparing the model with altitudes of geodetic 
points with regard to frequency and amplitude properties of the terrain. The values 
are as follows (Radovan, 1991): 
o 3,3 m for level terrain 
o 9,0 m for uneven terrain 
o 16,1 m for very uneven terrain and 
o 10,0 m for the DTM as a whole. 
Geodetski vestnik 41 (1997) 4 
The data for the DTM was acquired cartometrically with linear interpolation of 
altitudes from contour lines presented on the basic topographical maps at 1:5 000 
and 1:10 000 scales, and for a smaller area on the topographical map at 1:25 000 
scale. The data are accessible at the SMA in severa! different ASCII formats as 
individual points, profiles and grid blocks. 
the other hand, the purchased DTM of Austria is a regular quadratic grid of 
50 x 50 m in size, except for 100 x 100 m for certain places close to the 
Hungarian state boundary. By agreement between the SMA and BEV, only the less 
dense model of 100 x 100 m may be used in Slovenia. The DTM grid is locally 
parallel with the projection of central meridians of zones M28, M31 and M34, which 
means that individual parts are rotated in relation to each other. The data on 
altitudes were acquired photogrammetrically by analytical evaluation of stereo 
overlaps and later processed by interpolation and expressed in m with two decimal 
points. Accorcling to BEV, the accuracy of the model is approximately 1 to 2 m for 
fiat terrain and 10 to 15 for forested and hilly terrain. The DTM is distributed in 
severa! forms: it was received as recorded by trigonometric sections in 320 ASCII 
datafiles, each of which had a header with metadata which determined numerous 
properties of individual blocks and format details. Control between sections was 
ensured by overlapping marginal profiles. 
4 TRANSFORMATION BETWEEN THE TWO NATIONAL COORDINATE SYSTEMS 
order to ascertain the position of the two national coordinate systems relative to 
other, their common geodetic points are needed, the position of which is 
known in both systems. As expected, these were given only for the immediate vicinity 
of the Slovenian-Austrian state boundary as boundary points and points for the 
boundary surveying grid. The state boundary between Slovenia and Austria is divided 
into 27 sections which run from the triple boundary with Hungary to the triple 
boundary with Italy. Each of them is a rounded whole, within the framework of 
which technical geodetic work is performed for the determination of the position of 
boundary points. For each boundary section, surveying and calculations are 
performed separately in each country. After harmonisation and removal of any 
discords, official boundary records are adopted which also contain a list of points 
verified by both sides. Point coordinates are thus determined in both national 
coordinate systems and are officially valid. 
there are only seven boundary sections with coordinates harmonised in 
manner. For these sections, coordinates were taken from official boundary 
records of the Department for State Boundary of the SMA. For other boundary 
sections, coordinates were taken from lists of trigonometric points of the Department 
of Basic Activities of the Geodetic Institute of Slovenia and from BEV. On the 
Austrian side, common points were given in zones M31 and M34, which additionally 
complicated the procedure. Initially, trial transformation was performed by boundary 
section to reveal errors and discords in <lata, and la ter severa! different types of plane 
and spatial transformations between the Slovenian and the Austrian systems were 
performed. The best, and theoretically most suitable, results were obtained by a 
Geodetski vestnik 41 (1997) 4 
spatial 7-parametric transformation which can be performed only in a 3D Cartesian 
coordinate system (X, with the following sequence of steps: 
o Gauss-Krueger plane coordinates of common points Y GK and Xrn<. in the 
Slovenian coordinate system and both Austrian meridian zones are 
analytically transformed into ellipsoid geographical coordinates Aand <p. 
o Each pair of geographical coordinates (A, <p) is assigned a known altitude H. 
o Such a triplet of ellipsoid coordinates (A, <p, is analytically translated into 
spatial quasigeocentric coordinates (X, · 
o Spatial 7-parametric transformation is performed by comparing the common 
points of zone 5 and zones M31 and M34. This yields transformation 
parameters between the two systems which were assessed by levelling: 
(X, Z)calculated from M31 and M34 zones H (X, Z)calculated from zone 5 
111 common pojnts were used for the assessment of transformation parameters; of 
which on the Austrian side 29 were in the western zone of M31 and 82 were in the 
eastern zone of M34. The mean error of transformation is 0,192 m. The plane 
deviations were lower than 1 m on almost all common points; they mostly ranged 
about 0,2 m. An analysis of elevation deviations on extreme corners of the Austrian 
DTM showed that even in the most unfavourable positions they did not exceed 1,5 
m. Since the distribution of common points along the boundary is non-homogeneous 
and approximately colinear, it was assessed that parameter accuracy entirely satisfies 
its purpose, i.e. the transformation of the Austrian DTM. The parameters of reverse 
transformation from the Slovenian to the Austrian system were also assessed by 
levelling, with similarly accurate results. 
5 MERGING OF THE DTMs 
Using the estimated transformation parameters, the Austrian DTM was recalculated into the Slovenian coordinate systern. Extensive preparatory and 
finishing work needed to be carried out, which included the following activities: 
o transcription of 320 datafiles with the Austrian DTM into a sirnple ASCII 
record without redundant rnetadata, 
o levelling of the altitude of DTM points on the edges of neighbouring blocks 
which differed due to the interpolation of original photogrammetric data, 
o merging of 320 levelled datafiles into two datafiles for zones M31 and M34, 
o levelling of the altitude of DTM point pairs with insufficient tolerance 
distance between thern in the area where the DTM grids frorn zones M31 
and M34 overlapped (but were not parallel), 
o merging the two DTM datafiles frorn zones M31 and M34 into a single 
comrnon one, 
o spatial transformation of the common datafile of the Austrian DTM into the 
Slovenian coordinate system with given parameters, 
o non-linear interpolation of the transformed Austrian DTM into the grid and 
format of the Slovenian DTM 100, 
o cutting of the interpolated Austrian DTM to match the state boundary and 
elimination of superfluous points in the Slovenian territory, 
o merging of the Slovenian and Austrian DTMs into a common datafile, 
Geodetski vestnik 41 (1997) 4 
• transcript of the merged DTM into the standard form which is used by the 
SMA far distribution, 
• positional and elevation control of contact of cells on the state boundary by 
hypsometric axonometric mapping. 
6 PROPER'fIES OF THE MERGED DTM 100 
Table 1 presents the basic properties of the existing DTM 100 and the model merged in the described manner. 
Datafile size 4,1 MB 9,5MB 
No. of non-empty blocks (by 1 km2) 21.270 48.999 
No. of altitudes 2.093.161 4.863.672 
Range of altitudes (m) 1- 2.864 1- 3.321 
Minimum Y coordinate (m, zone 5) 5.375.000 5.354.000 
Minimum X coordinate (m, zone 5) 5.030.000 5.030.000 
Maximum Y coordinate (m, zone 5) 5.624.000 5.624.000 
Maximum X coordinate (m, zone 5) 5.194.000 5.272.000 
Area size in E-W direction (km) 249 270 
Area size in N-S direc.tion (km) 164 242 
Table 1: Properties of the Slovenian and merged Slovenian-Austrian DTM 
The Slovenian DTM is located in zone 5 in its entirety. Zone 5 stretches on the 
latitude of Slovenia approximately 127 km towards the east and west from the central 
meridian. It can be established from Table 1 that the new merged DTM reaches 146 
km to the west, which exceeds the width of zone 5 by 19 km. Due to this, the line 
scale in the Gauss-Krueger projection increases on the western edge from the 
allowable 1,000100 to 1,000161. This means that the relative projection accuracy of 
length is 1:6 150 instead of the allowed 1:10 000, while line deformation is 1,6 dm/km 
instead of 1 dm/km. Even without further analysis, it can be established with regard 
to the estimated accuracy of both the Austrian and the Slovenian part of the DTM 
that projection deformation is negligible. Therefore, the model may be stored in only 
one zone, i.e. zone 5, which is also more practical. 
6 CONCLUSION 
over the world, traditional national coordinate systems are still almost 
local, that is, dependent on the orientation of the reference ellipsoid. 
In times of universal globalisation of international economic cooperation, however, 
such systems are becoming an obstacle for undisturbed work even outside the scope 
of geodesy. Numerous international activities such as naval and air navigation are 
introducing global coordinate systems, e.g. WGS 84, GRS 80, ITRS and ETRS, 
rather than using local ones. The project for the connection of the Austrian and 
Slovenian coordinate systems is one of the first steps required for undisturbed 
Geodetski vestnik 41 (1997) 4 
cooperation with our northern neighbours in this field. Even though it was intended 
for the merging of two DTMs, transformation parameters are sufficiently accurate 
for the majority of geocoded data exchanges. 
authors hereby gratefully acknowledge the assistance of their colleagues from 
Department of Basic Work of the Geodetic Institute of Slovenia for <lata and 
information on geodetic points in boundary sections. 
Literature: 
Radovan, D., Korekture in analiza natančnosti digitalnega modela reliefa Slovenije (DMR 100). 
Ljubljana, Client Republiška geodetska uprava, Contractor Inštitut za geodezijo in 
fotogrametrijo FGG, 1991 
Radovan, D., Stopar, B., Transformacija med slovenskim in avstrijskim državnim koordinatnim 
sistemom. Ljubljana, Client Geodetska uprava Republike Slovenije, Contractor Inštitut za 
geodezijo in fotogrametrijo FGG, 1996 
Radovan, D. et al., Spojitev slovenskega in avstrijskega digitalnega modela reliefa. Ljubljana, Client 
Geodetska uprava Republike Slovenije, Contractor Inštitut za geodezijo in fotogrametrijo FGG, 
1997 
Review: Dušan Miškovi(; (in preparation) 
Marjan Podobnikar 
Geodetski vestnik 41 ( 1997) 4