The united geodetic vertical network of Latvia and Lithuania.

Aleksejenko, Ivars ; Sakne, Janis ; Kalinka, Maris 等

1. Introduction

The existing levelling networks of Latvia and Lithuania are a part of the United Precise Levelling Network (UPLN). They were developed after the Second World War and no longer fit the nowadays requirements of geodetic control of the countries. Consequently, the project of the Fundamental Vertical Network of Lithuania was initiated (Parseliunas et al. 1998; Buga et al. 1999; Krikstaponis et al. 2007; Zakarevicius et al. 2008). The network was observed in 1998-2007. Connections to Polish and Latvian networks were observed in 2007-2010. Projection and construction works of the Latvian National First Order Levelling Network (NFOLN) commenced in 2000 and finished in 2010 (Celms, Kaminskis 2005; I, II and II 2000). Currently, computing of the networks continues, and discussions on the vertical reference system adoption in each country are taking place as well.

Following the Resolution of the European Reference Frame (EUREF) Symposium adopted in Bad Neuenahr-Ahrweiler in 1998 (Augath et al. 2000)--requesting to extend and improve the Vertical Network around the Baltic Sea--both Latvian and Lithuanian geodesists included the new state levelling networks to the United European Levelling Network (UELN) (Ernsperger, Kok 1986; Lang, Sacher 1995; Sacher et al. 1998, 1999; Parseliunas et al. 2000).

In order to unify the geodetic datums of Latvia and Lithuania and have a reliable basis for geodynamic studies, it was decided to connect both levelling networks (Parseliunas et al. 2000; Krikstaponis et al. 2011). Thus, the new first order levelling lines Butinge-Rucava, Joniskis-Eleja and Turmantas-Demene were observed by Latvian and Lithuanian geodesists in 2007-2010. An adjustment of the joint united vertical network was carried out. The main results achieved are presented in this paper.

2. An overview of the Latvian vertical network

Development of the Latvian National First Order Levelling Network (NFOLN) commenced in 2000, and field measurements were finished in 2010 (Celms, Kaminskis 2005). Geodetic measurements were taken by specialists of the Latvian Land Service in 2000-2005 and the Latvian Geospatial Information Agency in 2006-2010. The development of the network and geodetic measurements were undertaken on the basis of technical requirements "I, II and III classes of levelling instruction" (I, II and II 2000). The NFOLN consists of 15 loops of precise levelling lines (Fig. 1).

[FIGURE 1 OMITTED]

To develop the network, geodetic and gravimetric observations were performed. The general requirement to not exceed the RMS error of 0.5 mm/km of the measured height differences was followed in the course of development of the National First Order Levelling Network.

Digital levels Leica NA3003, Zeiss DiNi12, Zeiss Ni002 and Trimble DiNi0.3 and invar rods with bar code scales Wild GPCL3, Zeiss LD13, Zeiss LD11 and gravimeters Scintrex CG-3 and CG-5 were used for measurements. All levelling lines were divided into sections. Section length amounted to approx. 0.5 km in an urban area and approx. 2 km in a rural area. Every section was levelled forwards and backwards.

Differences in section height were corrected adjusting the calibration of levelling rods and temperature. Staff readings were reduced to the staff calibration temperature or +20[degrees]C. The temperature correction was computed using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

where [DELTA]h--measured height difference; [k.sub.rod]--rod length thermal dependency; [k.sub.termal]--thermal expansion coefficient; [t.sup.o.sub.m] - mean temperature during measurements; [t.sup.o.sub.cal]--calibration temperature.

The refraction effect was minimized by keeping an equal sight distance from a level to a rod (the maximum sight distance was 40 m, but usually--36 m) and by carrying out measurements at mornings and evenings.

Corrections due to non-homogeneity of the gravitational field were computed on the basis of parameters of real and normal gravitational fields. The gravimetric data and normal gravitational field GRS 80 were used for this purpose (Kaminskis, Forsberg 1996). The gravity acceleration was measured along the precise levelling lines. The distance between gravimetrically measured benchmarks was approximately 1 km in urban areas and 2 km in rural areas. All gravimetric measurements were connected to the Second Order Gravimetric Network, which is constraint by the First (Absolute) Order Network and is realized in IGSN71. No special correction for the tidal effect due to the Moon and the Sun was applied so far.

Geopotential numbers are determined in GRS 80 normal field, applying the new European gravity system and evaluating non-linearity of GRS 80 normal field equipotential surfaces (Moritz 1988). Normal correction computed from formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

where [g.sub.71]--gravity value measured in the IGSN71 system; [h.sub.ik]--measured height difference; [H.sub.v]--mean normal height between points; [[gamma].sub.80]--GRS 80 normal field gravity value on rotation telluroid surface:

[[gamma].sub.80] - [[gamma].sub.0] -0.3086 * H, (3)

where H--point height rounded till meter. GRS 80 normal field gravity value [[gamma].sub.0] computed using the following formula:

[[gamma].sub.0] = 97802.7 x (1 + 0.0053024 * [sin.sup.2] B - 0.0000058 * [sin.sup.2] 2B), (4)

where B--geodetic latitude in the LKS-92 system.

The observed height differences were corrected by temperature and calibration, so the corrected height differences for forward and backward levelling were computed. Mean height difference values were computed and corrected by normal correction [f.sup.80.sub.ik] and the final height differences were computed for all lines of the Latvian National First Order Levelling Network lines.

All levelling lines were reduced to common epoch 2000.0. The empirical Latvian land uplift model was taken into account.

The empirical land uplift model was calculated comparing height differences of common points in two levelling campaigns. The first was measured in 1929-1939 and the second in 2000-2010. The empirical model for Latvia showed the land uplift rate of 2 mm per year if to compare the majority of north-western and south-eastern areas.

For each nodal point, the speed of the land uplift was calculated and a correction for the measured height difference of a line to the common epoch was computed using a formula (5). Every section was corrected proportionally to the length of levelling.

[h.sub.ep] = [h.sub.m] + ([t.sub.ep] - [t.sub.m]) * ([v.sub.end] - [v.sub.start]), (5)

where [h.sub.m]--measured height difference of line corrected by temperature and staff calibration; [t.sub.ep]--common reduction epoch 2000.0; [t.sub.m]--epoch of measurements taken in the middle of a year; [v.sub.end]--speed of the land uplift at the end point; [v.sub.start]--speed of the land uplift at the start point.

The Latvian NFOLN was adjusted using the program HOENA (Schoch 1995).

The allowed misclosures of closed loops (Table 1) were computed with the help of the following formula:

[f.sub.h] = 2 * [m.sub.0] [square root of L], (6)

where [m.sub.0]--a priori standard deviation of point heights in mm; L--the loop perimeter in km.

Misclosures closest to the allowable value were obtained in loops 5 and 12. Exact reasons are unknown, but we could guess, that misclosure in the loop No 5 emerge because lines of the polygon go through the centre of the capital city Riga, cross river Daugava in two places and river Lielupe in two places as well.

One cross of Daugava is over the Rock Bridge in the centre of Riga but the second one is between moles in the harbour. River Lielupe is crossed over the Lielupes Bridge at the entrance to the city of Jurmala and near the mouth of the Riga Gulf.

The misclosure in the loop No 12 resulted from the lack of experience, because the loop consists of levelling lines, which were established from the very start of all levelling works and depend on local geodynamic individuality. In Soviet times, this polygon did not offer the best results either, thus geodesists made some re-measurements.

Here are the parameters of the adjustment of the Latvian NFOLN with one fiducial point (point code 014--A):

   --Number of fixed points:          1,

   --Number of unknowns:              1889,

   --Number of measurements:          1904,

   --Degrees of freedom:              15,

   --Standard deviation (from         0.870 kgal * mm/km,
     results of the adjustment):

   --A-posteriori standard            0.889 kgal * mm,
     deviation referred to
     a levelling distance of 1 km
     (based on actual misclosures):

   --The mean value of the standard   1.11 kgal * mm,
     deviation of the adjusted
     geopotential differences:

   --The mean value of the            8.18 kgal * mm,
     standard deviation of the
     adjusted geopotential heights:

   --The greatest value of the        12.47 kgal * mm,
     standard deviation of the
     adjusted geopotential heights:

   --The average redundancy:          0.008.

The adjustment of geopotential height differences of enlarged UELN including new Latvian and Lithuanian levelling networks was performed as an unconstrained adjustment linked to the reference point No 13600 in Amsterdam, the geopotential height of which was set to 0.70259 kgalxm, with normal height at 0.71599 m. The data for initial points of Latvian (Table 2) and Lithuanian (Table 4) vertical networks was received from this adjustment. These datum points were used in the adjustment of the united vertical network of Latvia and Lithuania.

3. An overview of the Lithuanian vertical network

The development of the Lithuanian National Geodetic Vertical First Order Network (NGVN) extended from 1998 till 2007 (Parseliunas et al. 1998; Buga et al. 1999; Krikstaponis et al. 2007). The contracting authority for the network establishment was the National Land Service under the Ministry of Agriculture. The Lithuanian National Geodetic Vertical Network was established following the technical regulation on Requirements for the Lithuanian National Geodetic Vertical Network. The latest requirements on development of vertical networks were considered (European ... 2000; Ihde, Augath 2000). The NGVN consists of 5 loops of precise levelling lines (Fig. 2).

To develop the network, data of the geodetic and gravimetric observations were used. Geopotential heights of points were determined from results of the precise levelling and gravimetric data. The ellipsoidal heights of the network points were obtained by means of the GNSS positioning.

The general requirement to not exceed the RMS error of 0.5 mm/km of measured height differences was followed in the course of development of the National Geodetic Vertical First Order Network.

Digital levels Leica NA3003, invar precise staffs bar coded staffs Wild GPCL-3, GPS receivers Ashtech Z12, Z-Surveyor, Trimble 5700 and gravimeters La Coste & Romberg were used for measurements. All levelling lines were divided into sections. Every section was levelled forwards and backwards. The field measurements of height differences were corrected adjusting the calibration of staffs and temperature. The refraction effect was also taken into account. Corrections due to non-homogeneity of gravitational field were computed on the basis of parameters of real and normal gravitational fields. Sufficiently accurate gravimetric data and normal gravitational fields of Helmert and GRS 80 were used for this purpose. Gravitational acceleration measurements in control gravimetric first order network were performed with La Coste & Romberg gravimeters. Gravimetric observations were tied to the Lithuanian National Zero Order Gravimetric Network, at stations, the absolute gravitational acceleration of which was measured (Parseliunas et al. 2010b).

Tides are caused by the tidal effect of the Moon and the Sun (Petroskevicius 2000, 2004; Torge 1989; Petraskevicius et al. 2008). They result in periodic fluctuation of height difference between the Earth surface points. On the Lithuanian territory, for the points separated by 2.5 km, the change in height difference caused by the Moon may vary from -0.18 mm to 0.18 mm; and that caused by the Sun - from -0.07 mm to 0.07 mm. There are two maximums and minimums during the day time. The largest effect of both celestial bodies is during the full and young Moon phases. Tidal corrections SMS for the height differences were computed using the following formulas:

[[delta].sub.MS] = [[delta].sub.M] + [[delta].sub.S], (7)

where [[delta].sub.M]--correction due to the Moon and

[[delta].sub.M] = [v.sub.M] S cos ([A.sub.M] - A), (8)

[[delta].sub.S]--correction due to the Sun:

[[delta].sub.S] = [v.sub.S] S cos ([A.sub.S] - A), (9)

S--line between points of the vertical network in km; [v.sub.M] and [v.sub.S]--deflection of the vertical due to the Moon and the Sun; [A.sub.M] and [A.sub.S]--azimuths of the Moon and the Sun, A--azimuth between the points.

[FIGURE 2 OMITTED]

Staff readings were reduced to the staff calibration temperature of +20[degrees]C (Putrimas 1999; Skeivalas 2000; Skeivalas et al. 2009; Zakarevicius, Puziene 2010; Krikstaponis 2001, 2002; Parseliunas et al. 2010a). The temperature correction was computed with the help of the following formula:

[[delta].sub.t] = [a.sub.m] x [alpha] /2.93, (10)

where [a.sub.m]--staff reading; [alpha]--equation of temperature dependency of staff invar strip of 2.93 m, which common expression is

[alpha] = [k.sub.1] ([t.sub.m] - 20[degrees]) + [k.sub.2], (11)

where [k.sub.1] and [k.sub.2]--coefficients of equation of staff length thermal dependency, determined at the Finnish Geodetic Institute; [t.sub.m]--temperature of invar strip during the levelling.

Staff readings were corrected by staff calibration corrections:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (12)

Height difference at the station:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)

where [a.sub.m] and [p.sub.m]--backsight and foresight staff readings; [[delta].sup.a.sub.t] and [[delta].sup.p.sub.t]--temperature corrections for backsight and foresight readings; [[delta].sup.a.sub.k] and [[delta].sup.p.sub.k]--calibration corrections for backsight and foresight readings.

Height differences were corrected for refraction

[[delta].sub.r] = A [DELTA]t [S.sup.2] [h'.sub.s], (14)

where A--coefficient; [DELTA]t--temperature difference between heights [Z.sub.2] and [Z.sub.1] above the ground; S--length of collimation line; [h'.sub.s]--height difference at the station.

Coefficient A was computed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (15)

where c--coefficients; [Z.sub.0]--levelling instrument height. Values used: [Z.sub.0] = 1.5 m, [Z.sub.1] = 1.0 m, [Z.sub.2] = 2.0 m. The coefficient c was taken from intermediate values derived from the second order conformal transformation.

To determine normal height differences of points, it is necessary to evaluate non-paralellity of normal field equipotential surfaces as well as real and normal field non-coincidence. For this purpose, normal corrections for height differences determined by levelling in real gravity field were computed (Petraskevicius 2004; Petraskevicius et al. 2008). The gravity value [g.sub.71r] of the European system at the marks height of the first order network points were computed on the basis of Bouguer anomalies [([g.sub.p] - [[gamma].sub.H]).sub.2,3], taken from the gravity map, scale 1:200 000. The gravity value [g.sub.71z] at the surface was derived from the formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (16)

where [g.sub.P]--free fall acceleration in the Potsdam system; [[gamma].sub.H]--normal gravity value of the Helmert's field at the telluroid; [H.sub.z]--approximate normal height of the earth's surface; [delta] = 2.3 g/[cm.sup.3]--the density of the Earth's crust; [[gamma].sup.0.sub.H] - normal gravity value at the ellipsoid surface, from the Helmert's formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (17)

where [B.sub.42]--geodetic latitude in the coordinate system of 1942.

Gravity value [g.sub.71r] at the mark height H was computed as follows:

[g.sub.71r] = [g.sub.71z] + dg. (18)

If [H.sub.z] > H, then

dg = 0,3086dh - 2 * 0,0419[delta]dh, (19)

where dh = [H.sub.z] - H.

If [H.sub.z] < H, then

dg = -0,3086dh, (20)

where dh = H - [H.sub.z].

[FIGURE 3 OMITTED]

Normal height difference in LKS 94 (the Lithuanian Coordinate System of 1994) was determined in the GRS 80 normal field, applying the new European gravity system and evaluating the non-linearity of GRS 80 normal field equipotential surfaces (Moritz 1988). Normal correction was computed using the formula (2), therefore the GRS 80 normal field gravity value [[gamma].sup.0.sub.80] was computed as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (21)

where [B.sub.94]--geodetic latitude in the LKS 94 system; normal gravity value at the equator on equipotential ellipsoid surface [[gamma].sup.0.sub.80e] = 978032.67715 mGal; [e.sub.80]--the first eccentricity of ellipsoid; [e.sup.2.sub.80] = 0.00669438002290; coefficient [k.sub.80] = 0,001931851353.

The mean normal gravity value between ellipsoid and telluroid for the territory of Lithuania: [[gamma].sub.80v] = 981 500 mGal.

Free air gravity anomaly of vertical network points:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (22)

where atmospheric gravity correction (Petraskevicius 2004)

[[delta]g.sub.a] = 0,874 - 0,99 * [10.sup.-4] H + 0,356 * [10.sup.-8] [H.sup.2] (23)

and height correction (H in metres) (Torge 1989)

[[DELTA][gamma].sub.80] = -0,30877(1 - 0,00142[sin.sup.2] [B.sub.94])H + 0,75 * [10.sup.-7] [H.sup.2]. (24)

Observed height differences were corrected by temperature, calibration, refraction and tidal corrections, so the corrected height differences for forward and backward levelling were computed. Mean height difference values were computed and corrected by the normal correction [f.sup.80.sub.ik] and the final height differences were computed.

In summer of 2007, the NGVN was integrated into the UELN (Fig. 3) (Krikstaponis et al. 2011).

Data preparation was divided into a number of steps:

--Computing the gravity values of benchmarks and heights differences,

--Computing the geopotential height differences and geopotential heights of benchmarks,

--Preliminary control and adjustment of the single Lithuania levelling network,

--Detecting the connections with levelling networks of neighbouring countries,

--Encoding the nodal benchmarks according to the coding system of the UELN,

--Adjustment of the total UELN,

--Calculation of normal heights of benchmarks,

--Comparison of the received normal heights with normal heights of the national height system.

Later, the NGVN of Lithuania was also adjusted using the program HOENA (Schoch 1995).

The misclosures of the closed loops are presented in Table 3.

All actual misclosures are below the allowable values. This proves that the right method was used to determine the normal height difference and that fieldworks were of the highest quality. Therefore, the misclosure in the loop No 3 is close to the allowable misclosure. Exact reasons are unknown, but we could guess, that big misclosure results from geodynamic processes, because the levelling lines were established in different epochs: 1998, 2005 and 2006.

Below are the parameters of the adjustment of the new NGVN of Lithuania with one fiducial point (point code 73S-0271):

   --Number of fixed points:              1,

   --Number of unknowns:                  1381,

   --Number of measurements:              1454,

   --Degrees of freedom:                  73,

   --Standard deviation (from             0.187 kgal * mm/km,
     the results of adjustment):

   --A-posteriori standard deviation      0.722 kgal * mm,
     referred to a levelling distance
     of 1km (based on actual
     misclosures):

   --The mean value of the standard       0.22 kgal * mm,
     deviation of adjusted
     geopotential differences:

   --The mean value of the standard       2.02 kgal * mm,
     deviation of adjusted
     geopotential heights:

   --The greatest value of the standard   2.73 kgal * mm,
     deviation of adjusted
     geopotential heights:

   --Average redundancy:                  0.050.

All datum points of the NGVN are presented in Table 4. These datum points were used in the adjustment of the United Network of Latvia and Lithuania.

4. Adjustment of the United Vertical Network of Latvia and Lithuania

In order to unify the geodetic datums of Latvia and Lithuania, to have the reliable basis for geodynamic studies, it was decided to connect both levelling networks. Consequently, the new first order levelling lines Butinge-Rucava, Joniskis-Eleja and Turmantas-Demene were observed by Latvian and Lithuanian geodesists in 2007-2010. Some data on connecting levelling lines are presented in Tables 5 and 6.

The United Geodetic Vertical Network of Latvia and Lithuania was adjusted using the program HOENA developed by the Leipzig department of Bundesamt fur Kartographie und Geodasie (Schoch 1995). The adjustment of geopotential height differences of the United Levelling Network was performed as a constrained adjustment linked to the datum points presented in Tables 2 and 4.

The misclosures of the connecting loops are presented in Table 7.

The actual misclosures are below the allowable values and that proves the high quality of the geodetic measurements performed both by Latvian and Lithuanian geodesists. Below are the parameters of the adjustment of the United Vertical Network of Latvia and Lithuania:

   --Number of fixed points:              26,

   --Number of unknowns:                  3281,

   --Number of measurements:              3397,

   --Degrees of freedom:                  116,

   --Standard deviation                   0.534 kgal * mm/km,
     (from the results of adjustment):

   --A-posteriori standard deviation      0.816 kgal * mm,
     referred to a levelling distance
     of 1km (based on actual
     misclosures):

   --The mean value of the standard       0.65 kgal * mm,
     deviation of adjusted
     geopotential differences:

   --The mean value of the standard       2.75 kgal * mm,
     deviation of adjusted
     geopotential heights:

   --The greatest value of the standard   4.54 kgal * mm,
     deviation of adjusted
     geopotential heights:

   --Average redundancy:                  0.034.

Results of the variance component estimation are given in Table 8.

Adjusted geopotential numbers and normal heights of the border points are presented in Table 9.

5. Conclusions

1. The first step was made in preparation for establishment of the United Vertical Network of Latvia and Lithuania. The levelling data of both countries fit each other with a better than 1 mm accuracy. Misclosures of common loops are 6.76 and 2.47 mm.

2. The accuracy of the United Vertical Network of Latvia and Lithuania (the standard deviation is 0.534 kgal * mm/km) is at the same level as that of vertical networks of the greatest part of other countries participating in the UELN project.

3. Differences between the United Vertical Network of Latvia and Lithuania and the UPLN height systems at the border points amount to approx. 15 cm.

4. The adjustment results are basic for high accuracy over boundary civil engineering projects.

5. The adjustment results of the United Vertical Network of Latvia and Lithuania could serve as a basis for the adoption of vertical (height) systems of both countries.

Acknowledgements

The National First Order Levelling Network of Latvia is under construction by the initiative of the Latvian Geospatial Information Agency, which implements the governmental politics in the field of geodesy.

The Lithuanian Vertical Network was developed by the Institute of Geodesy, VGTU, under contracts with the National Land Service No 98-3271 and No 2733-MA/68.

Calculations regarding the United Vertical Network of Latvia and Lithuania were performed using resources of the Geodetic Laboratory of the Science Centre for Civil Engineering, VGTU.

Received 25 October 2011; accepted 21 March 2012

doi: 10.3846/20296991.2012.679800

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Schoch, H. 1995. Beschreibung des Programmsystems HOENA. Institut fur Angewandte Geodasie. Leipzig. Marz 1995. 12 p. (draft).

Skeivalas, J. 2000. Research of refraction influence for levelling, Geodezija ir kartografija [Geodesy and Cartography] 26(4): 160-163.

Skeivalas, J.; Parseliunas, E.; Putrimas, R.; Slikas, D. 2009. Kodiniu niveliavimo matuokliu kalibravimo tikslumas taikant kovariacines funkcijas, Geodezija ir kartografija [Geodesy and Cartography] 35(2): 43-46. ISSN 1392-1541.

Torge, W. 1989. Gravimetry. Berlin, New York: de Gruyter. 465 p.

Zakarevicius, A.; Puziene, R. 2010. Ismatuotu auksciu redukavimas ivertinat vertikaliuosius Zemes pavirsiaus judesius, Geodezija ir kartografija [Geodesy and Cartography] 36(2): 50-56.

Zakarevicius, A.; Sliaupa, S.; Parseliunas, E.; Stanionis, A. 2008. Deformation of geodetic network based on GPS data in the Baltic region, Geodezija ir kartografija [Geodesy and Cartography] 34(4): 122-126. http://dx.doi.org/ 10.3846/1392-1541.2008.34.122-126

Ivars Aleksejenko (1), Janis Sakne (2), Maris Kalinka (3), Martins Reiniks (4), Ausra Kalantaite (5), Boleslovas Krikstaponis (6), Eimuntas Kazimieras Parseliunas (7), Petras Petroskevicius (8), Povilas Viskontas (9)

(1,2) Latvian Geospatial Information Agency, O. Vaciesa street 43, LV-1004 Riga, Latvia (3,4) Riga Technical University, Kalku street 1, LV-1658 Riga, Latvia (5,6,7,8,9) Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania

E-mails: (1) ivars.aleksejenko@lgia.gov.lv; (2) janis.sakne@lgia.gov.lv; (3) maris.kalinka@rtu.lv; (4) martins.reiniks@rtu.lv; (5) ausra.kalantaite@vgtu.lt; (6) boleslovas.krikstaponis@vgtu.lt; (7) eimis@vgtu.lt (corresponding author); (8) petras.petroskevicius@vgtu.lt; (9) povilas.viskontas@vgtu.lt

Ivars ALEKSEJENKO. M. Sc. Eng. Latvian Geospatial Information Agency., Dept of Geodesy and Cartography, O. Vaciesa iela 43., LV-1004 Riga, Latvia. Ph +371 2 61 65 5678, Fax +371 6 706 4209, e-mail: ivars.aleksejenko@lgia.gov.lv.

Author of more than 5 scientific publications. Participated in a number of international conferences.

Research interests: gravity field and measurements, height system and geopotential number, adjustment of geodetic network, quasi-geoids modelling, geodetic works in civil aviation.

Janis SAKNE. Latvian Geospatial Information Agency, Dept of Geodesy and Cartography, O. Vaciesa iela 43., LV-1004 Riga, Latvia. Ph +371 2 63 34 6512, Fax +371 6 706 4209, e-mail: janis.sakne@lgia.gov. lv.

Author of more than 2 scientific publications.

Research interests: levelling network and height system, adjustment of geodetic network, geodetic works in civil aviation.

Maris KALINKA. Assoc. Prof., Dr. Sc. Eng. Riga Technical University, Dept of Geomatics, Azenes iela 16/20., LV-1048 Riga, Latvia. Ph +371 6 708 9263, e-mail: maris.kalinka@rtu.lv.

Doctor of Science (2008).

Author of more than 20 scientific publications. Participated in a number of international conferences.

Research interests: terrestrial laser scanning, height system and geopotential number, adjustment of geodetic network.

Martins REINIKS. Assoc. Prof., M. Sc. Eng. Riga Technical University, Dept of Geomatic, Azenes iela 16/20., LV-1048 Riga, Latvia. Ph +371 6 708 9263, e-mail: martins.reiniks@rtu.lv.

Author of more than 10 scientific publications Participated in a number of international conferences.

Research interests: establishment of geodetic network, height and coordinate system, adjustment of geodetic network, spatial images.

Ausra KALANTAITE. Deputy Director of the Land Politics Department of the Ministry of Agriculture, Vilnius (Ph. + 370 5 2398 446), doctoral student at Vilnius Gediminas Technical University (Ph +370 5 274 4703), e-mail: ausra.kalantaite@vgtu.lt.

Graduated from Vilnius Gediminas Technical University (master of Geodesy and Cartography, 1997). Participation in projects: Development of the Land Parcel Identification System in Lithuania (2002-2003), Land Parcel Identification System and Block Database Update in Lithuania (2004-2006).

Research activities: digital mapping and GIS, digital elevation models, LIDAR.

Boleslovas KRIKSTAPONIS. Assoc. Prof., Dr. Dept of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail: boleslovas.krikstaponis@vgtu.lt.

Doctor at VGTU (2002).

Research interests: calibration of geodetic instruments, engineering geodesy.

Eimuntas Kazimieras PARSELIUNAS. Assoc. Prof., Dr at the Department of Geodesy and Cadastre, Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail: eimis@vgtu.lt.

Doctor of Science (1992).

The author of two teaching books and more than 50 scientific papers. Participated in a number of international conferences.

Research interests: graphs theory in geodesy, adjustment of geodetic networks, geoinformation systems, establishment of geodetic and gravimetric networks.

Petras PETROSKEVICIUS. Prof., Doctor Habil. Vilnius Gediminas Technical University. Dept of Geodesy and Cadastre, Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail: petras.petroskevicius@vgtu.lt.

Author of 1 monograph and more than 120 scientific publications. Participated in many international conferences.

Research interests: determination of the Earth's satellites orbits, research of the Earth's gravity field by means of satellite geodesy and gravimetric methods, establishment of geodetic and gravimetric networks.

Povilas VISKONTAS. Eng., Geodetic Institute, Vilnius Gediminas Technical University. Sauletekio al. 11, LT-10223 Vilnius, Lithuania. Ph +370 5 274 4703, Fax +370 5 274 4705, e-mail: povilas.viskontas@vgtu.lt.

Eng of Applied Geodesy at VGTU (1973).

Research interests: engineering geodesy, establishment of geodetic and gravimetric networks.

Table 1. Misclosures of loops of the Latvian NFOLN

Loop     Actual         Loop           Allowable
No.    misclosure,   perimeter,       misclosure,
        kgal x mm        km       [m.sub.0] = 1.0 mm

  1        -2.44       36.800            11.89
  2        -7.66       35.500            11.68
  3       -18.86      429.800            40.63
  4       -15.62      353.300            36.84
  5       -16.69       97.000            19.30
  6       -11.76      363.200            37.35
  7        +1.82       42.700            12.81
  8        -7.72       36.400            11.83
  9       -15.33      342.400            36.27
 10        +4.10      366.900            37.54
 11        -7.49      362.800            37.33
 12       +33.50      501.600            43.90
 13       +12.25      548.500            45.90
 14       +11.66      423.800            40.35
 15        -9.10      420.600            40.20

Table 2. Datum points of the Latvian NFOLN

No.   National   UELN      LKS-92 coordinates        Geopotential
      code       code                                number,
                                                     [m.sup.2] x
                                                     [s.sup.-2] x
                                                     [10.sup.-1]

 1    012--002   2110009   56[degrees] 56' 44.064'    2.239
                           23[degrees] 36' 46.210'
 2    007----4   2110262   56[degrees] 26' 16.597'   49.783
                           21[degrees] 33' 57.398'
 3    031---50   2110070   57[degrees] 46' 38.465'   48.937
                           26[degrees] 01' 18.304'
 4    001--766   2110238   57[degrees] 45' 7.924'     4.232
                           22[degrees] 35' 48.308'
 5    014----A   2110281   56[degrees] 57' 16.737'    5.156
                           24[degrees] 06' 43.893'
 6    038-3939   2110087   56[degrees] 50' 18.746'   138.716
                           26[degrees] 12' 7.821'
 7    040-1484   2110340   57[degrees] 29' 40.496'   153.926
                           27[degrees] 20' 18.772'
 8    049-1174   2110366   56[degrees] 25' 20.766'   128.130
                           28[degrees] 03' 20.514'
 9    034-2913   2110323   57[degrees] 51' 45.518'     6.093
                           24[degrees] 21' 31.032'
10    033-2083   2110322   58[degrees] 04' 32.081'    71.244
                           25[degrees] 11' 30.075'
11    042--538   2110347   57[degrees] 33' 08.763'    77.341
                           26[degrees] 39' 59.427'
12    006-1684   2110259   56[degrees] 04' 50.446'    10.980
                           21[degrees] 07' 22.582'
13    026-0718   2110301   56[degrees] 21' 55,157'    38.670
                           23[degrees] 40' 26,333'
14    046-2285   2110354   55[degrees] 42' 13,666'   136.431
                           26[degrees] 28' 03,768'
15    035-3433   2110326   57[degrees] 52' 27.015'     3.336
                           24[degrees] 21' 39.366'
16    044-2128   2110349   57[degrees] 46' 35.152'    50.146
                           26[degrees] 01' 23.200'

No.   National   Accuracy of     Normal    IGSN71 gravity
      code       geopotential    height,   acceleration,
                 number          m         m x [s.sup.-2]
                 in UELN
                 network,
                 [m.sup.2]
                 x [s.sup.-2]
                 x [10.sup.-1]

 1    012--002   0.0138            2.281   9.816420

 2    007----4   0.0139           50.715   9.816343

 3    031---50   0.0146           49.847   9.817236

 4    001--766   0.0147            4.310   9.817144

 5    014----A   0.0135            5.252   9.816479

 6    038-3939   0.0140          141.310   9.816187

 7    040-1484   0.0146          156.797   9.816766

 8    049-1174   0.0146          130.531   9.815665

 9    034-2913   0.0148            6.206   9.817452

10    033-2083   0.0154           72.568   9.817204

11    042--538   0.0149           78.782   9.817141

12    006-1684   0.0132           11.185   9.815799

13    026-0718   0.0129           39.394   9.816106

14    046-2285   0.0130          138.997   9.815243

15    035-3433   0.0148            3.398   9.817488

16    044-2128   0.0146           51.079   9.817232

Table 3. Misclosures of loops of the Lithuanian NGVN

Loop   Loop perimeter,       Actual            Allowable
 No.         km          misclosure, mm       misclosure,
                                          [m.sub.0] = 1.0 mm

 1          491.5             +4.29               43.4
 2          525.4            -14.80               44.9
 3          576.3            -32.83               47.0
 4          452.0            +11.66               41.6
 5          510.0             +3.04               44.2

Table 4. Datum points of the Lithuanian NGVN

No.   Name          National   UELN      LKS94 coordinates
                    code       code

 1    SIAULIAI      55S-0128   2412001   55[degrees]54'48.78202"
                                         23[degrees]22.17.18605"
 2    VILNIUS       73S-0271   2412002   54[degrees]39'11.30417"
                                         25[degrees]17'55.19158"
 3    MOLAS         25S-1522   2412004   55[degrees]43'47.23801"
                                         21[degrees]04'58.88606"
 4    ZELVIAI       26V10300   2412015   56[degrees]00'41.96954"
                                         21[degrees]06'20.64503"
 5    MIKYTAI       34V10201   2412020   55[degrees]07'54.06812"
                                         21[degrees]57'34.81749"
 6    JONAVA        64V--217   2412023   55[degrees]05'55.95392"
                                         24[degrees]16'20.64503"
 7    KAZLAI        53V12421   2412030   54[degrees]44'43.61659"
                                         23[degrees]28'14.25382"
 8    LAZDIJAI      52V-1021   2412038   54[degrees]13'18.96189"
                                         23[degrees]30'43.65627"
 9    PETRUNISKIS   85V-0739   2412055   55[degrees]43'08.70335"
                                         26[degrees]14'41.29362"
10    RADIKIAI      56V---11   2412065   56[degrees]12'13.21889"
                                         23[degrees]34'03.21221"

No.   Name          Geopotential   Accuracy of     Normal
                    number,        geopotential    height,
                    [m.sup.2] x    number in       m
                    [s.sup.-2] x   UELN network,
                    [10.sup.-1]    [m.sup.2] x
                                   [s.sup.-2] x
                                   [10.sup.-1]

 1    SIAULIAI      138.795        0.0127          141.402

 2    VILNIUS       211.797        0.0128          215.801

 3    MOLAS           4.590        0.0136            4.676

 4    ZELVIAI         9.126        0.0138            9.297

 5    MIKYTAI        16.370        0.0116           16.678

 6    JONAVA         67.575        0.0122           68.848

 7    KAZLAI         63.884        0.0112           65.090

 8    LAZDIJAI      129.529        0.0105          131.981

 9    PETRUNISKIS   142.250        0.0136          144.924

10    RADIKIAI       59.636        0.0134           60.754

No.   Name          IGSN71 gravity
                    acceleration,
                    m x

 1    SIAULIAI      9.815339

 2    VILNIUS       9.814334

 3    MOLAS         9.815498

 4    ZELVIAI       9.815762

 5    MIKYTAI       9.814947

 6    JONAVA        9.814745

 7    KAZLAI        9.814756

 8    LAZDIJAI      9.814077

 9    PETRUNISKIS   9.815321

10    RADIKIAI      9.815793

Table 5. Data on benchmarks of connecting levelling lines

UELN code          National    Approx. normal   Geodetic
                   benchmark   height, m        latitude
                   code

Butinge-Rucava

2412013            26V-6237     9.36900         56 03 09.97802
                   26V10238    11.72000         56 04 16.70929
                   21L-1684    11.02613         56 04 50.4464
Joniskis-Eleja

2412967            56V10051    39.89800         56 20 52.57184
2412066            56S-335     38.89700         56 21 42.24637
                   02L-0718    39.24405         56 21 55.1571

Turmantas-Demene
                   03L-0331    137.83819        55 42 44.9058
                   03L-2285    138.82556        55 42 13.6655
2413395            95V-0053    139.20100        55 41 29.00782

UELN code          Geodetic longitude

Butinge-Rucava

2412013            21 07 09.22163
                   21 07 19.04867
                   21 07 22.58237
Joniskis-Eleja

2412967            23 38 30.49239
2412066            23 39 28.86839
                   23 40 26.33

Turmantas-Demene
                   26 28 14.77
                   26 28 03.76
2413395            26 27 36.01

Table 6. Data on height differences of the connecting lines

Start point         End point   Distance, km   Height differences,
                                               m (Lithuanian
Butinge-Rucava                                 measurements

26V-1561            26V-6237    1.76           +3.20416
26V-6237            26V10238    2.08           +2.39474
26V10238            006-1684    1.1

Joniskis-Eleja

56V10049            56V10051    1.43            0.56092
56V10051            56S-335     1.88           -1.00096
56S--335            026-0718    1.50

Turmantas-Demene

046-0331            046-2285    1.21
046-2285            95V-0053    1.60
95V-0053            95S-295     0.35           +1.54210

Start point         Height differences,        Geopotential
                    m (Latvian measurements)   number, kgal
                                               x m
Butinge-Rucava

26V-1561                                       +3.14513
26V-6237            +2.3948                    +2.35063
26V10238            -0.8733                    -0.85721

Joniskis-Eleja

56V10049                                       +0.55060
56V10051            -1.00014                   -0.98255
56S--335            -0.37657                    0.36965

Turmantas-Demene

046-0331            +0.98737                   +0.96913
046-2285            +0.31743                   +0.31157
95V-0053            +1.54210                   +1.51363

Table 7. Misclosures of the connecting loops

Loop   Loop         Actual        Allowable
       perimeter,   misclosure,   misclosure,
       km           kgal x mm     [m.sub.0] = 1.0 mm

1      640.7        6.76          49.61
2      548.2        2.47          45.89

Table 8. Accuracy of levelling networks of Latvia and Lithuania

Country     Number of      Sum               Corrected sum
            measurements   of redundancies   of redundancies

Latvia      1904           14.5181            30.293
Lithuania   1493           18.5848            85.707
Sum         3397           33.1029           116.000

Country     Correction factor   A-posteriori
                                standard deviation
                                kgal x mm/km

Latvia      0.4793              0.6923
Lithuania   0.2168              0.4657
Sum

Table 9. Normal heights of border benchmarks

Point code   Geopotential number   Normal height   Standard deviation
             kgal x mm             m               kgal x mm

26V10238      11.83571              12.05762       0.52
006-1684      10.97960              11.18544       --
56S--335      38.30000              39.01728       0.63
026-0718      38.66980              39.39400       --
046-2285     136.43150             138.99660       --
95V-0053     136.74380             139.31492       0.64