European Vertical Reference System Influence in Latvia

Till 1 December, 2014, in Latvia the heights were determined in Baltic Normal Height System 1977. The national height system is determined by the Cabinet of Ministers and internal laws. Now for the change of the national height system to reconcile it with the European Vertical Reference System, amendments to the laws and regulations have been developed, but so far only the amendment to the Geospatial Information Law is in force, the amendment to the regulation of the Cabinet of Ministers is still not approved. This amendment declares the Latvia Height System based on the European Vertical Reference System in Latvia as the national height system. For height transformation, there is a transformation formula for each European country. After calculations it is seen that height difference between Baltic Normal Height System 1977 and European Vertical Reference System depends on point location in the territory (coordinates). This unequal height difference between both height systems will cause unequal height values on border connection points between Baltic countries. The aim of the research is to evaluate the European Vertical Reference System in Latvia. To reach the aim the following tasks are set: 1) to evaluate the components of transformation formulas; 2) using the transformation formulas to calculate height differences between Baltic Normal Height System 1977 and the European Vertical Reference System realization EVRF2007 for the territory of Latvia and also between Baltic Normal Height System 1977 and the Latvia Normal Height System; 3) to get height differences in the European Vertical Reference System on the borderlines of Latvia - Estonia and Latvia - Lithuania.


Introduction
Levelling network is a forming element of the national height system. Levelling network ensures realization of various functions in the national economy. Using the Class I levelling results for any kind of transformations, it is necessary to know the accuracy of the established levelling network (Celms et al., 2013). Since 1 December 2014 Latvia uses the realization of the European Vertical Reference System in Latvia -Latvia Normal Height System as the national height system. Lithuania and Estonia still use Baltic Normal Height System 1977 as the national height system. In Latvia this is 2 To whom any correspondence should be addressed. Amendment to the regulations by the Cabinet of Ministers determines the Latvia Normal Height System LAS-2000,5, the transformation formula for the Latvia Normal Height System and its parameters. The transformation formula and some of its parameters are the same as the transformation formula and parameters for EVRF2007 realization in the territory of Latvia. For unknown reasons, for the territory of Latvia slope in the direction of the meridian a 2 = 7.99066182789555 E -0008 m and slope in the direction perpendicular to the meridian a 3 = -9.48289473646151 E -0008 m are different from all parameters for EVRF2007. The amendment defines these two parameters in meters, but probably it must be a mistake, because parameters a 2 and a 3 can be determined in radians or seconds. For the calculations of height difference, the authors of research adopted the values of both parameters in radians.

Results and discussion
After applying the transformation formula, height difference between Baltic Normal Height System 1977 and the European Vertical Reference System is not a constant value in the entire territory of Latvia, it differs from 135 mm in the south-east part of the country to 169 mm in the north-west part of the country (see figure 1) and depends on point location in the territory (coordinates).

Figure 1. Height difference between Baltic Normal Height System 1977 and the European Vertical
Reference System realization EVRF2007 for the territory of Latvia.
After calculations using the parameters for Latvia Normal Height System, the height differences between Baltic Normal Height System 1977 and Latvia Height System are from 125 mm in the southeast part of the country to 173 mm in the north-west part of the country (see figure 2). The differences constitute 48 mm, which is higher than primarily determined by EVRF2007.  In the European Coordinate Reference Database it is also possible to calculate the height difference between Baltic Normal Height System 1977 and the European Vertical Reference System realization EVRF2007 for the territory of Lithuania and Estonia. Figure 3 shows the results of the calculation.

Figure 3. Height difference between Baltic Normal Height System 1977 and the European Vertical
Reference System realization EVRF2007 for the territory of Lithuania, Latvia, Estonia and locations of transformation points P 0 .
As seen in figure 3, in Lithuania the difference between height systems changes in the southnorth direction and will be 80 mm in the south part till 150 mm in the north part of the country. In Estonia the difference between height systems changes in the same direction as in Latviafrom 185 mm in the south-east part till 207 mm in the north-west part of the country.
As it is seen in figure 3, there is one serious problemthe European Vertical Reference System will cause unequal height values at border connection points (see figure 4)on the state border the height difference of the same point in the height system of Latvia and Estonia or Latvia and Lithuania can reach 33 mm (see table 1).    Table 1 shows the height difference of 1 st class leveling network border connection points. On Latvia -Estonia border, height difference in the European Vertical Reference system realization EVRF2007 in both countries will be from 32.0 to 33.9 milimetres, but on Latvia -Lithuania border connection point heights in Latvia and Lithuania in the European Vertical Reference System realization EVRF2007 will be from -0.5 mm to 19.6 mm. So the same point on the border will have different height value in each country's realization of the European Vertical Reference System EVRF2007. There will be no more height connections between the Baltic countries.
For the practical testing, 2 geodetical points were mesaured with the GNSS instruments at the same time-Latvia 1 st class leveling network point 1727 and Lithuania 1 st class leveling network point 10284. Point 1727 is situated at about 5 km from Latvia -Lithuania border line and point 10284at 12 km (see figure 5). The measurements were made in the static mode for 3 hours.  Height System 1977 (database information) and the European Vertical Reference System realization EVRF2007, the results are almost the same. The reason for the same result is almost equal height difference between Baltic Normal Height System and the European Vertical Reference System realization EVRF2007 for the territory of Latvia and Lithuania in this area. It can be also seen in table 1 where the height difference of point 718 located in the same area in both systems in both countries is just 0.5 mm.