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Development of a precise local quasigeoid model for the city of Krakow - QuasigeoidKR2019

Banasik Piotr, Bujakowski Kazimierz, Kudrys Jacek, Ligas Marcin

Reports on Geodesy and Geoinformatics

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2020

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Vol. 109

25--31

EN

A geoid or quasigeoid model allows the integration of satellite measurements with ground levelling measurements in valid height systems. A precise quasigeoid model has been developed for the city of Krakow. One of the goals of the model construction was to provide a more detailed quasigeoid course than the one offered by the national model PL-geoid2011. Only four measurement points in the area of Kraków were used to build a national quasigeoid model. It can be assumed that due to the small number of points and their uneven distribution over the city area, the quasigeoid can be determined less accurately. It became the reason for developing a local quasigeoid model based on a larger number of evenly distributed points. The quasigeoid model was based on 66 evenly distributed points (from 2.5 km to 5.0 km apart) in the study area. The process of modelling the quasigeoid used height anomalies determined at these points on the basis of normal heights derived through levelling and ellipsoidal heights derived through GNSS surveys. Height anomalies coming from the global geopotential model EGM2008 served as a long-wavelength trend in those derived from surveys. Analyses showed that the developed height anomaly model fits the empirical data at the level of single millimetres – mean absolute difference 0.005 m. The developed local model QuasigeoidKR2019, similar to the national model PL-geoid2011, are models closely related to the reference and height systems in Poland. Such models are used to integrate GNSS and levelling observations. A comparison of the local QuasigeoidKR2019 and national PL-geoid2011 model was made for the reference frame PL-ETRF2000 and height datum PL-KRON86-NH. The comparison of the two models with respect to GNSS/levelling height anomalies shows a triple reduction in the values of individual quartiles and a mean absolute difference for the developed local model. These summary statistics clearly indicate that the accuracy of the local model for the city of Krakow is significantly higher than that of the national one.

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Validation of European Gravimetric Geoid models in context of realization of EVRS system in Poland

Marjańska Dorota, Olszak Tomasz, Piętka Dominik

Geodesy and Cartography

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2019

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Vol. 68, no. 2

329--347

EN

In this study, several variants create and choose of a local quasi-geoid model in Poland have been considered. All propositions have a source in European Gravimetric Geoid models – EGG2008 and EGG2015, which are purely gravimetric models of reference surface. In the course of this work, each model has been analyzed in various ways: without any corrections, by parallel shifting of residuals, by the 7-parameter conformal transformation and by fitting residuals by 4- and 5-parameter trigonometric polynomials. Eventual corrections were based on points of national GNSS/levelling networks (EUVN, EUVN_DA, POLREF, EUREF and ASG-EUPOS eccentric points). As a final result of this study, a comparison of the accuracy of selected models has been carried out by RMSE statistics and maps showing spatial distribution of residuals and histograms. Validation has shown that the maximum achievable accuracy of the EGG models is approximately 2 cm for the ETRF2000 reference system and approximately 8 cm for ETRF89. In turn, fitting with the use of different mathematical methods results in an improvement of the standard deviation of residues to the level of 1.3–1.4 cm. The conclusions include an evaluation of considerations for and against the use of models based only on EGG realizations and, on the other hand, fitted to the points of Polish vertical network. Its usefulness is strictly connected with needs of the definition of up to date quasi-geoid model for the new realization of heights system in Poland, based on EVRF2007 frame.

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Validation of GOCE gravity field models over Poland using the EGM2008 and GPS/levelling data

Godah W., Kryński J.

Geoinformation Issues

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2011

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Vol. 3, no. 1(3)

5-17

EN

Since the mid of 2010, global geopotential models based on GOCE mission data became available. The first two releases of GGMs contained four different solutions while in the third release only two solutions have been generated. In the presented study the available GOCE-derived gravity field models were evaluated in terms of height anomalies and gravity anomalies over Poland with the use of the respective functionals calculated from the EGM2008 geopotential model as well as height anomalies at 184 stations of high precision GPS/levelling control traverse. The fit of GOCE gravity field models with the EGM2008 in terms of height anomalies and gravity anomalies measured with a standard deviation is below 10 cm, and 3 mGal, respectively. Their fit with GPS/levelling height anomalies at the stations of GPS/levelling control traverse is at the level of 10 cm. The results obtained indicate some improvement of the consecutive releases of GOCE gravity field models.

PL

Od połowy 2010 roku są udostępnione globalne modele geopotencjału opracowane na podstawie danych z misji GOCE. Pierwsze dwie generacje modeli geopotencjału z misji GOCE zawierały cztery różne rozwiązania podczas gdy trzecia - składała się zaledwie z dwóch rozwiązań. Jakość dostępnych modeli pola siły ciężkości z misji GOCE została w niniejszym opracowaniu oceniona w wyniku porównania obliczonych z nich anomalii wysokości i anomalii grawimetrycznych z odpowiednimi funkcjonałami obliczonymi z modelu geopotencjału EGM2008 oraz z anomaliami wysokości 184 stacji precyzyjnego satelitarno-niwelacyjnego trawersu kontrolnego. Odchylenia standardowe różnic anomalii wysokości i anomalii grawimetrycznych pomiędzy uzyskanymi z opracowanych na podstawie danych z misji GOCE modeli geopotencjału i z modelu EGM2008 wynoszą odpowiednio 10 cm i 3 mGal. Dopasowanie modeli geopotencjału z misji GOCE do anomalii wysokości satelitarno- niwelacyjnego trawersu kontrolnego kształtuje się również na poziomie 10 cm. Uzyskane wyniki wskazują na poprawę w kolejnych generacjach modeli geopotencjału z misji GOCE.

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Study on choice of global geopotential model for quasigeoid determination in Poland

Krynski J., Lyszkowicz A.

Geodezja i Kartografia

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2005

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Vol. 54, no 1

17-36

EN

The choice of global geopotential model used in remove-restore technique for determination of regional quasigeoid from gravity data may affect the solution, in particular when the accuracy is supposed to reach a centimetre level. Global geopotential model plays also an important role in validating heigh anomalies at GPS/levelling sites that are used for the estimation of the external accuracy of quasigeoid models. Six different global geopotential models are described in the paper. Three kinds of numerical tests with use of terrestrial gravity data and GPS/levelling height anomalies were conducted. The first one concerned comparison of height anomalies at GPS/levelling sites in Poland with corresponding ones computed from various geopotential models. In the second on the terrestrial gravity anomalies in Poland and neighbouring countries were compared with corresponding gravity anomalies computed from global geopotential models. Finally the quasigeoid models obtained from gravity data with use of different global geopotential models were verified against corresponding height anomalies at GPS/levelling sites in Poland. Data quality was discussed and best fitting global geopotential model in Poland was specified.

PL

Wybór globalnego modelu geopotencjału użytego w procedurze remove-restore w procesie wyznaczania regionalnej quasigeoidy ma wpływ na rozwiązania, w szczególności, gdy oczekuje się dokładności centymetrowej. Globalny model geopotencjału odgrywa także istotną rolę w określaniu jakości anomalii wysokości wyznaczonych z pomiarów GPS na punktach o znanej wysokości normalnej, które używane są do określenia zewnętrznej dokładności modeli quasigeoidy. W pracy podano charakterystykę 6 globalnych modeli geopotencjału. Przeprowadzono trzy rodzaje testów numerycznych modeli geopotencjału, w których wykorzystano naziemne dane grawimetryczne oraz anomalie wysokości na punktach sieci POLREF i EUV52. Pierwszy test dotyczył porównania anomalii wysokości na punktach sieci POLREF i EUVN52 z odpowiadającymi anomaliami wysokości obliczonymi z różnych globalnych modeli geopotencjału. W ramach drugiego testu dokonano porównania anomalii grawimetrycznych z obszaru Polski i krajów sąsiednich z odpowiadającymi anomaliami grawimetrycznymi obliczonymi z globalnych modeli geopotencjału. Trzeci test obejmował porównanie modeli quasigeoidy obliczonych przy użyciu różnych globalnych modeli geopotencjału z anomaliami wysokości na punktach sieci POLREF i EUVN52. Na podstawie uzyskanych wyników dokonano oceny jakości danych grawimetrycznych oraz anomalii wysokości na punktach sieci POLREF i EUVN52 oraz wskazano najlepiej pasujący do obszaru Polski globalny model geopotencjału.