EVALUATION OF THE EUROPEAN GRAVIMETRIC GEOID/QUASIGEOID EGG97 OVER THE LITHUANIAN TERRITORY

Transcription

1 Geodezija ir Kartografija ISSN: (Print) (Online) Journal homepage: EVALUATION OF THE EUROPEAN GRAVIMETRIC GEOID/QUASIGEOID EGG97 OVER THE LITHUANIAN TERRITORY Dr-Ing. H. Denker, E. Paršeliūnas, Dr-Ing. H. Denker & E. Paršeliūnas To cite this article: Dr-Ing. H. Denker, E. Paršeliūnas, Dr-Ing. H. Denker & E. Paršeliūnas (1999) EVALUATION OF THE EUROPEAN GRAVIMETRIC GEOID/QUASIGEOID EGG97 OVER THE LITHUANIAN TERRITORY, Geodezija ir Kartografija, 25:4, To link to this article: Published online: 11 Sep Submit your article to this journal Article views: 93 Full Terms & Conditions of access and use can be found at

2 ISSN Geodezija ir kartografija, 1999, XXV t., Nr.4 Geodesy and Cartography, 1999, Vol XXV, No 4 UDK EV ALUATION OF ТНЕ EUROPEAN GRA VIМETRIC GEOШ/QUASIGEOШ EGG97 OVER ТНЕ LIТНUANIAN TERRITORY Н. Denker, Е. Par eliiinas 1. Introduction The European Gravimetric Geoidlquasigeoid EGG97 was computed at the lnstitut fiir ErdmessШlg (IfE), University of Hannover (Germany) [1,2]. Since 1990 IfE is acting as the computing centre of the lnternational Association of Geodesy (IAG), Subcommission for the Geoid in Europe. The EGG97 gridded geoid values are stored on standard CD-ROM's, which were delivered to agencies and persons, who provided gravity andlor terrain data for the calculation of the geoid. The point gravity data and а 1 km х 1 km Digital Terrain Model (DТМ) for the Lithuanian territory were prepared Ьу the Geodetic lnstitute of Vilnius Technical University and transferred to IfE in Lithuanian specialists were very interested in the European Gravimetric Geoid project, because Lithuania is close to the centre of the computation area and thus an accurate geoid model could Ье expected. The evaluation strategy was to compare the geoid model against GPS ellipsoidal heights on levelling benchmarks. А set of the 70 most reliaьle benchmarks of blgh precision levelling lines of the Unified Precise Levelling Network (Кronstadt Height Datum) was chosen. The RМS difference for tbls set is 62 mm for the Ьias fit and 22 mm for the Ьias and tilt fit. Thus the EGG97 model performs very well and can Ье used for large-scale heighting applications in Lithuania. 2. The European Gravimetric Geoid EGG97 The geoidlquasigeoid models are given in the form of gridded Шldulations. Тhе computation of these Шldulations was done using gravity (Fig 1) and terrain data (Fig 2) as well as а g1obal high degree spherical harmonic model in а remove-restore procedure. For the long wavelength gravity field information the geopotential model EGM96 complete to degree and order 360 was employed [3]. The short wavelength gravity field components were modelled using -the residual terrain model (RТМ) reduction, where the:feference topography was constructed Ьу а 15' х 15' moving average filter. The input gravity and terrain data were transformed to а common reference system (WGS horizontal coordinate system, IGSN71 gravity system, UELN height system, GRS80 normal gravity formula) whenever this was possiьle. The terrestrial gravity data were merged with gravity data derived from ERS-1 in some marine areas with sparse ship data. All gravity observations were transformed into residual gravity anomalies and gridded Ьу least squares prediction in а 1.0' х 1.5' grid covering the area 25N - 77N and 35W Е. The field transformation from residual gravity to residual height anomalies was done Ьу the spectral combination technique together with а 1D FFT procedure and а detailedlcoarse grid approach to further speed up the calculations. For the spectral combination technique the error degree variances of EGM96 and the terrestrial gravity data were used. 167

3 Fig 1. Locations of gravity data stored in lfe database [2] Fig 2. Digital Terrain Models stored in lfe database [2] 168

4 The primary result of the computations is а quasigeoid model because the input (gravity) data were referring to the surface of the Earth. In principle the Molodensky correction terms for the terrain reduced data have to Ье considered. In the EGG97 model these correction terms were neglected, because the maximum values reach only 0.01 m in medium high mountains up to 1000 m, and 0,1 m in high mountains up to 4000 m, respectively. Furthermore, due to the applied mathematical models the computed height anomalies refer to an ideal (mean Earth) ellipsoid. Hence а zero order undulation correction of -0,5 m was applied in order to refer the final undulations to GRSSO (value taken from the literature and from GPS!leveling comparisons in Europe). In addition, а correction from the non-tidal system (used in the EGM96 model) to the zero tide system (recommended Ьу IAG) was applied [4]. Thus, the final quasigeoid values refer to the zero tide system and а geocentric ellipsoidal reference system based on the GRS80 constants. 3. Evaluation of the geoid EGG97 over the Lithuanian territory The geoidlquasigeoid EGG97 model is given Ьу two files: G 1 OM15M.BIN geoidlquasigeoid grid file with а resolution of 1 О' х 15' for the area 25N- 77N and 35W -67,5Е; G60S90S.BIN geoid/quasigeoid grid file with а resolution of 1,0' х 1,5' for the area 25N- 77N and 35W -ЗЗЕ. For the Lithuanian territory the evaluation of the EGG97 model was based on а GPS!levelling data set. The main efforts were directed towards the determination of а reliaьle set of benchmark heights. The existing old levelling network is а part of the Uni:fied Precise Levelling Network (UPLN) lines which were observed during the period So it is very difficult to estimate the accuracy of the normal heights. Some lines are also included in the new Lithuanian Vertical Network and were observed in [5). The national GPS network was the basis for the positioning of the benchmarks of the :first and second order levelling lines. А realistic accuracy of the ellipsoidal heights was calculated from the differences of the coordinates from two sessions. In this way an accuracy of 2 cm was obtained. In total, 120 benchmarks were observed, from which the 70 most reliaьle stations were chosen for the geoid evaluation and fitting [6, 7]. The data ofthe benchmarks are presented in ТаЬlе 1. А constant of 15 cm was added to the normal heights for the conversion between the Normal Amsterdamsch Peil and Кronstadt Height Datum [8]. The following abbreviations are used in the taьles: Не - ellipsoidal height, Нn- normal height, N[GPS]- GPS undulation, N[GRV]- gravimetric undulation, N[GR_B]- gravimetric undulation after Ьias correction, N[GR_BT]- gravimetric undulation after Ьias and tilt correction, dno=(n[gps]-n[grv])- discrepancies before fit, dn1=(n[gps]-n[gr_b])- residuals after Ьias fit, dn2=(n[gps]-n[gr_bt])- residuals a:fter Ьias and tilt :fit. Statistics of the discrepences between the GPS!levelling data and both quasigeoid representations are given in ТаЬlе 2 and 3. The comparisons were done using а Ьias fit as well as а Ьias and tilt fit. 169

5 ТаЬiе 1. GPS/levelling benchmarks No. Benchmark code Order of Yearof Нn,m Latitude Longitude He,m N[GPS],m levelling levelling 1 24S ,633 55, , ,322 24, S , S , , ,865 24, , , , S , ,734 24, S , , S ,100 55, , S , S ,934 55, , , S , ,802 24, S , , S , , , S , , , S ,427 55, ,919 24, S , , ,295 24, S ,66899 Ш , S , , S , , ,840 23, S-! ,921 53, , ,826 26, ,213 54, , V! , ,535 26, VIOOII , , , VI , V ,010 54, , V , , S , , , ,602 54, ,43451!02,890 25, , , ,293 25, S-8! ,590 54, , V ,127 54, , , , , ,154 23, S ,81749!09,496 23, S , , S , , ,883 23, S !843 23, ,666 23, ,392 23, ,201 56, , ,206 23, ,013 56, , !,932 22, S , ,952 23, ,376 25, ,089 54, S , ,261 24, S , , ,739 24, VI ,132 55, , , ЗV ,218 54, , ,150 24, V , !8 24, V !69 54, ,098 24, S ,995 55, , V , , , S--! , , , S ,6!975 24, ,985 22, S ,177 54, , ,745 25, , , ,461 25, S ,812 54, , V , , , V , , V , , S , , , , , , , S ,048 56, , , S ,038 54, !29 173,688 23, , , ,859 22, S , , ,435 55, ,295 21, ! , , АЕ , , S , , , АЕ 2! ,520 55, ,

6 ТаЬlе 2. EGG97 geoid model (G60S90S.BIN) comparisons for GPS/Ievelling data set No. Benchmark code NIGPS],m NIGRVl.m N[GR В],m NIGR BТl.m dno,mm dnl,mm dn2 mm ,689 24,651 24,618 24, , ,519 24,475 24,442 24, S , ,519 24, ,488 24,361 24, ,480 24,361 24,327 24, ,917 24, ,023 24,989 25, ,535 24, \ ,325 24, , \20 24, ,968 24, ,992 25, , ,930 23,908 23, ,001 23,949 23, , ,905 27,019 26, ,089 26,158 26,124 26, VI ,094 26,197 26, VI ,330 26,437 26, V\ ,892 25,983 25, \ V , V , ,713 25, , ,288 25, ,565 25,532 25, ,801 25,893 25, VI ,623 23,650 23,616 23, ,528 23, , ,776 24, о S ,474 23,443 23, , ,443 23,433 23,400 23, , о ,919 22,873 22,839 22, ,\ , ,658 25, , , S ,823 24,877 24, ,648 24,689 24,656 24, VJ ,467 24,510 24,476 24, V ,932 25,006 24,973 24, V ,865 24,924 24,890 24, V ,929 24,997 24,964 24, ,430 23,518 23,485 23, V ,149 24,\ S ,808 22,775 22, ,904 22, , S ,568 25,730 25,696 25, S ,367 25, о , V ,897 24, V ,074 25, V , S ,602 23,689 23, SOI ,168 22, ,870 22, , ,634 21,601 21, S , S , , S ,876 22,960 22, SOI058 21,860 21, , о 68 95S-16AE ,909 21, S , АЕ 21,945 22,012 21, NшnЬer of differences Mcan difference RМ8 difference ±70 ±62 ±22 Standard deviation of differences ±62 ±62 ±22 Мinimal difference Мaximal diffcrence

7 ТаЬiе 3. EGG97 geoid model (G10M15M.BIN) comparisons for GPS!Ievelling data set No. Benchrnark code N[GPS) N[GRV] N[GR В) N[GR ВТ) dno dni do2 1 24S , S...l , S ,519 24, S-! ! 24, S , ,326 24, S...l , S , S , s , , , S...! ,163 24, S ,003 24,972 24,982 ~ Зs--IO 25, ,991 25, s-OG20 24,492 24,463 24,431 24, SOII , S...l ,881 23, S...l ,930 23,898 23, ,999 23,930 23, S...I , S , , Vl , VIOO!I 26, ~ VI , , ~ V ,738 26,707 26,652 ~ V , S , s , ~ s ,303 25, S ,512 25,480 25, S , Vl , ,704 25,683 ~ ,625 23, ,528 23,542 23,510 23, S , ,761 24, S ,412 23, ,503 23,508 23,476 23, s-з775 23, ,978 22,946 23, , , {)204 25, , S ,039 26,084 26, S ,823 24,885 24,853 24,828 ~ S-45!0 24,648 24,682 24,650 24, VI ,467 24,502 24,470 24, V , ~ V , V ,929 24,999 24,967 24, , V , S ,824 22,792 22, s S , S ,071 24, ~ V , V ,046 24, V , ,679 23, S , S-{)781 ~2,870 ~934 22,903 22,901 ~ S-{) , S...I S , S , ,943 22, ~ SOI S ,975 21,943 21, S-16AE 21,872 21, , ,978 21, S...39AE ,987 21, Nшnber of differences Mean difference RМS difference ±69 ±61 ±26 Standard deviation of differences ±61 ±61 ±26 Мinimal difference Maximal difference

8 4. Conclusions 1. The RМS difference for the GPS!levelling benchmarks set is 62 mm for the Ьias fit and 22 mm for the Ьias and tilt fit. 2. Тhе precision of the EGG97 geoidlquasigeoid in Lithuania is about 3 cm. 3. Тhе geoidlquasigeoid EGG97 model performs very well and can Ье used for large-scale heighting applications in Lithuania. References 1. Н. Denker, D. Behrend and W. Torge. The European Gravimetric Quasigeoid EGG96 // Proceed. IAG Symp. No.ll7 1 Gravity, Geoid and Marine Geodesy, Tokyo, Japan, Sept. 30- Oct. 5, 1996, р , Springer- Verlag, Berlin, Heidelberg, NewYork, Н. Denker, W. Torge. The European Gravimetric Quasigeoid EGG97 - an IAG supported continental enterprise // Proceed. IAG Scientific AssemЬley, Rio de Janeiro, Sept. 3-9, 1997, р. Berlin, Heidelberg, NewYork, , Springer-Verlag, 3. F. Lemoine, et al. The development of the NASA GSFC and DМAjoint geopotencial model // Proceed.IAG Symp. No Gravity, Geoid and Marine Geodesy, Tokyo, Japan, Sept. 30- Oct. 5, 1996, р. Verlag, Berlin, HeidelЬerg, NewYork, , Springer 4. R.H. Rapp, R.S. Nerem, С.К. Shum, S.M. Юosko, R.G. Williamson. Consideration of Permanent Тidal Deformation and Data Analysis for the Topex!Poseidon Мission, NASA ТМ , S. Kazakevi~itts, Р. Petro kevi~ius, А. Zakarevi~ius. On the priciples of Lithuanian Geodetic Vertical network estaьlishment // Geodezija ir kartografija (Geodesy and Cartography), Vilnius: Technika, 1999, Vol. XXV, No. 2. р S. Kazakeviaus, Е. Par eliiinas. Specifying the parameters of Lithuanian territory quasigeoid in 1998 /1 Geodezija ir kartografija (Geodesy and Cartography), Vilnius: Technika, 1999, Vol. XXV, No. 1, р R. Forsberg, Е. Parseliunas. The improvement ofthe geoid model oflithuania // Abstracts ofthe ПJGG ХХП General AssemЬley, Birrningham, July 19-30, р. А J. Ihde. Some remarks on geodetic reference systems in Eastem Europe in preparation of а geoid//bull. Geodesique, Vol.67, No. 2,1993. unifonn European Iteikta EUROPOS GRA VIМETRINIO GEOIOOIКV AZIGEOIOO EGG97 LIETUVOS TERПORIJOJE JVERTINIМAS Н. Denk.er, Е. ParJeliQnas Santrauka (lnstitut flir Erdmessung, IfE). Nuo 1990 m. IfE yra Tarptautines geodezijos asocijacijos pakomisio geoidui nustatyti Europoje skai~iavimo centras. EGG97 modelio tinkliniai duomenys, sura yti i standartinius kompaktinius diskus, i siuntinejami asmenims ir istaigoms, prisidejusiems sudarant geoido modeli. Lietuvos teritorijos gravimetrinius ir aulclciq duomenis renge VGТU Geodezijos institutas. Kadangi Lietuva yra beveik geoido apimamos teritorijos centre, galima tiketis gerч rezultatq. Geoido modelio ivertinimo startegija remiasi geoido duomenq palyginimu su GPS/niveliacijos duomenimis. Is Bendrojo precizinio niveliacijos tinklo (КronStato futstoko pradine reilclme) atrinkta 70 patikimiausiq geodeziniq zenklq grupe. Prie jq normaliniq auks~iч prideta 15 cm konstanta, kaip skirtumas tarp Bendrojo precizinio niveliacijos tinklo ir Europos bendrojo niveliacijos tinklo, su kuriuo susietas Europos geoido modelis, auks~iq. Analize parode, kad vidutine kvadratine skirtumq paklaida yra 62 mm, eliminavus tik geoido pavirsiaus polinki, ir 22 mm, eliminavus geoido pavirsiaus polinki. ir nuokrypi. Daroma isvada, kad geoido aukscius Lietuvos teritorijoje pagal Europos gravimetrini geoido modeli EGG97 galima apskaiciuoti 3 cm tikslumu. Todel modeli galima ir siuloma taikyti geodeziniams auks~iams nustatyti atliekant daugeli geodeziniq ir kartografiniq darbq. Heiner Denker. Dr-Ing. University of Hannover. Institut flir Erdmessung, Schneiderberg 50, D Hannover, Germany (tel , fax ). А graduate offachhochschule Oldenburg (1980). Dipl-Ing (University of Hannover, 1984). Цoctor (University of Hannover, 1988). Research training at the Ohio State University, (1989). Research interests: high resolution glob~ and local gravity field deterrnination, geoid modelling, computation of а continental geoid for Europe, three-dimensional networks, height deterrnination Ьу combination of GPS and levelling data, development of high-degree global and regionally tailored spherical harmonic models, use of satellite altimetry for geodetic and ocean circulation studies. Eimuntas Par elii1nas. Associate Professor, Doctor. Vilnius Gediminas Technical University. Dept of Geodesy. Saulёtekio al. 11, 2040 Vilnius, Lithuania (tel , fax ) А graduate of Vilnius Gediminas Technical University (engineer of geodesy, 1979). Doctor (Sankt-Petersburg Мining Institute, 1992). Research training at Moscow Engineering Institute for Geodesy, Aerosurveying and Cartography (1987); training course "The treatment of GPS observations" at Aalborg University (Denmark, 1993); training course "Gemini SCG in Lithuania" (Norway) according to the programme "Cooperation Land Refonn" (1993); training seminar "Coordinate Systems, GPS measurements, Geoid deterrnination" (Finish Geodetic Institute, 1994); training course in Norway according to the programme "Digital mapping Ьу photogrammetric means" (1995); training course in Sweden according to the programme "Digital orthophotomapping in Lithuania" (1995); advanced school "Algorithmic Foundations of Geographic Infonnation Systems" in Udine (Italy, 1996). Research interests: graphs theory in geodesy, treatment of geodetic networks, geoinformation systems. Europos gravimetrinis geoido!kvazigeoido modelis EGG97 apskai~iuotas Нanoverio universiteto.temes matavimq institute 173