Development of the Finnish Height Conversion Surface FIN2005N00

With the new Finnish height system, N2000, came the need for a new national height conversion surface, with which ellipsoidal EUREF-FIN heights, as measured with GPS in Finland, can be transformed into N2000 heights, as measured by levelling. The conversion surface was calculated by fitting a correction surface to the Nordic NKG2004-geoid model using 50 EUVN-DA-points, for which both levelled and GPS-determined heights were available. Polynomial surfaces with varying degrees were fitted to the data, as well as least-squares collocation surfaces using varying parameter values The surfaces were analysed using cross-validation. Collocation surfaces performed better than the polynomial surfaces, resulting in smoother surfaces and better fit statistics. Best results were obtained using a correlation length of 200 km and 2 cm noise level in the least-squares collocation. The resulting surface was added to the NKG2004 geoid model to form the new height conversion surface for Finland: FIN2005N00. The standard deviation of the cross-validation residuals indicates that with the new surface heights can be converted with an accuracy better than 2 cm

Suomen geoidimallit ja niiden käyttäminen korkeuden muunnoksissa

Geoidimallien käyttö on viime vuosina lisääntynyt huomattavasti. Kansallisen geoidimallin, tai oikeammin muunnospinnan avulla voidaan GPS:llä mitatut ellipsoidiset korkeudet muuntaa vaaituiksi korkeuksiksi kansallisessa korkeusjärjestelmässä. Tiedotteessa esitellään Suomen alueen geoidimallit ja niiden käyttö. Suomen alueella merkittävimmät globaaliset geoidimallit ovat OSU91A, EGM96 ja GGM02. Alueelliset geoidimallit ovat eurooppalainen EGG97-malli ja Pohjoismaisen geodeettisen komission geoidityöryhmän laskemat mallit NKG89, NKG96 ja NKG2004. Suomen alueen vanhat geoidimallit ovat astrogeodeettinen Bomford 1970 ja painovoimahavaintoihin perustuva FIN95-malli. Nykyisin Suomessa käytössä olevat geoidimallit ovat FIN2000 ja FIN2005N00. FIN2000-malli on muunnospinta jolla EUREF-FIN-koordinaatistossa GPS:llä mitatut ellipsoidiset korkeudet voidaan muuntaa N60-korkeusjärjestelmän mukaisiksi vaaituskorkeuksiksi. FIN2000-malli on laskettu sovittamalla korjauspinta NKG96-geoidimalliin 156 GPS/vaaituspisteiden avulla. Mallin tarkkuus on 3 cm ja suurimmat muunnosvirheet voivat olla 9 cm. FIN2005N00 on uusin valtakunnallinen malli. Tällä muunnospinnalla EUREF-FINkoordinaatistossa GPS:llä mitatut ellipsoidiset korkeudet voidaan muuntaa N2000-korkeusjärjestelmän mukaisiksi vaaituskorkeuksiksi. Mallin pohjana on NKG2004-geoidimalli, johon on laskettu korjauspinta 50 EUVN-DA (European Vertical Reference Network – Densification Act) GPS/vaaituspisteiden avulla. Mallin tarkkuus on 2 cm ja suurimmat muunnosvirheet voivat olla 6 cm. FIN2000- ja FIN2005N00-mallit ovat saatavissa hila-muotoisina EUREF-FIN-koordinaateissa. Hilasta voidaan laskea halutulle pisteelle geoidikorkeus bi-lineaarisella interpolointimenetelmällä. Alueellisilla GPS/vaaituspisteillä voidaan määrittää kansallisesta mallista paikallinen muunnospinta maantieteellisissä EUREF-FIN koordinaateissa tai haluttaessa tasokoordinaateissa.Over the years the use of geoid models has increased considerably. Using a national geoid model, or better said a transformation surface, ellipsoidal heights, as measured by GPS, can be transformed into heights in the national height system, as measured by levelling. This publication gives an overview of the geoid models available for Finland and their use. Global geoid models of importance for Finland are OSU91, EGM96, and GGM02. Important regional models are the European model EGG97 and the Nordic models NKG98, NKG96, and NKG2004 calculated by the working group on geoid determination of the Nordic Geodetic Commission. Old Finnish models are the astro-geodetic geoid model Bomford 1970 and the FIN95 model, which is based on gravity observations. At present, two geoid models are used in Finland: FIN2000 and FIN2005N00. The FIN2000 model is a transformation surface with which ellipsoidal coordinates, measured with GPS in the EUREF-FIN reference frame, can be transformed into leveled coordinates in the N60 height system. The FIN200 model was calculated by fitting a correction surface to the NKG96 model using data of 156 GPS/levelling points. The accuracy of the model is 3 cm and the biggest transformation errors can be 9 cm. The newest model for Finland is FIN2005N00. With this transformation surface ellipsoidal heights, measured with GPS in the EUREF-FIN reference frame, can be transformed into leveled heihts in the N2000 height system. The model is based on the NKG2004 geoid model to which a correction surface was fitted using the data of the 50 EUVN-DA (European Vertical Reference Network – Densification Act) GPS/levelling points. The accuracy of the model is 2 cm and largest transformation errors can be 6 cm. The FIN2000 and FIN2005N00 models are available in grid-formats in EUREF-FIN coordinates. Geoid heights for points can be calculated from the grids using bi-linear interpolation. When local GPS/levelling data is available a local transformation surface can be determined from a national model. This can be done either in EUREF-FIN coordinates or optionally in projected coordinates

Forty-three years of absolute gravity observations of the Fennoscandian postglacial rebound in Finland

Postglacial rebound in Fennoscandia causes striking trends in gravity measurements of the area. We present time series of absolute gravity data collected between 1976 and 2019 on 12 stations in Finland with different types of instruments. First, we determine the trends at each station and analyse the effect of the instrument types. We estimate, for example, an offset of 6.8 μgal for the JILAg-5 instrument with respect to the FG5-type instruments. Applying the offsets in the trend analysis strengthens the trends being in good agreement with the NKG2016LU_gdot model of gravity change. Trends of seven stations were found robust and were used to analyse the stabilization of the trends in time and to determine the relationship between gravity change rates and land uplift rates as measured with global navigation satellite systems (GNSS) as well as from the NKG2016LU_abs land uplift model. Trends calculated from combined and offset-corrected measurements of JILAg-5- and FG5-type instruments stabilized in 15 to 20 years and at some stations even faster. The trends of FG5-type instrument data alone stabilized generally within 10 years. The ratio between gravity change rates and vertical rates from different data sets yields values between − 0.206 ± 0.017 and − 0.227 ± 0.024 µGal/mm and axis intercept values between 0.248 ± 0.089 and 0.335 ± 0.136 µGal/yr. These values are larger than previous estimates for Fennoscandia

Postglacial gravity change in Fennoscandia - three decades of repeated absolute gravity observations

For the first time, we present a complete, processed compilation of all repeated absolute gravity (AG) observations in the Fennoscandian postglacial land uplift area and assess their ability to accurately describe the secular gravity change, induced by Glacial Isostatic Adjustment (GIA). The dataset spans over more than three decades and consists of 688 separate observations at 59 stations. Ten different organisations have contributed with measurements using 14 different instruments. The work was coordinated by the Nordic Geodetic Commisson (NKG). Representatives from each country collected and processed data from their country, respectively, and all data were then merged to one dataset. Instrumental biases are considered and presented in terms of results from international comparisons of absolute gravimeters. From this dataset, gravity rates of change (g_dot) are estimated for all stations with more than two observations and a timespan larger than two years. The observed rates are compared to predicted rates from a global GIA model as well as the state of the art semi-empirical land uplift model for Fennoscandia, NKG2016LU. Linear relations between observed g_dot and the land uplift, h_dot (NKG2016LU), are estimated from the absolute gravity observations by means of weighted least squares adjustment (WLSA) as well as weighted orthogonal distance regression (WODR). The empirical relations are not significantly different from the modelled, geophysical relation g_dot = 0:03 - 0:163(+-0.016)h_dot. We also present a g_dot -model for the whole Fennoscandian land uplift region. At many stations, the observational estimates of g_dot still suffer from few observations and/or unmodelled environmental effects (e.g. local hydrology). We therefore argue that, at present, the best predictions of GIA-induced gravity rate of change in Fennoscandia are achieved by means of the NKG2016LU land uplift model, together with the geophysical relation between g_dot and h_dot

An Accuracy Assessment of Absolute Gravimetric Observations in Fennoscandia

We compare a suite of absolute gravimeters used to monitor the temporal changes of gravity at a number of sites in Fennoscandia. Direct comparisons are made from simultaneous observations at selected sites within and outside of the postglacial uplift region. We also compare results at sites visited by two instruments with some separation in time. We conclude from four years of data that gravity differences are obtained within an rms error of ± 3 Gal. The data reveal no systematic biases between the instruments, but occasional shifts from one year to another are noted. We consider that annual instrument comparisons are required to ensure data integrity in a regional observing program that extends over more than a decade

Geoidi ja maannousuun liittyvät painovoiman muutokset Suomessa

Defence is held on 23.4.2021 16:00 – 19:00 Remote: https://aalto.zoom.us/j/61678768590Positioning using Global Navigation Satellite Systems (GNSS) is widely used nowadays and it is getting more and more accurate. This requires also better geoid models for the transformation between heights measured with GNSS and heights in the national height system. In Finland heights are continuously changing due to the Fennoscandian postglacial rebound. Land uplift models are developed for the Fennoscandian land uplift area, not only for the vertical velocities, but also for the gravity change related to postglacial rebound. In this dissertation geoid studies were carried out in search of the geoid model that is most suitable for the conversion of GNSS heights in the EUREF-FIN coordinate system to heights in the Finnish height system N2000 on land as well as on sea. In order to determine the relationship between gravity change rates and vertical velocities, time series of absolute gravity measurements were analysed. Methods were tested for fitting a geoid model to GNSS-levelling data. The best method for Finland was found to be least-squares collocation in combination with cross-validation. The result was the height conversion surface FIN2005N00, the official model for Finland. Then, high-resolution global gravity field models were tested in geoid modelling for Finland. The resulting geoid models were better than the earlier geoid models for Finland. After correcting for an offset and tilt, the differences with other models disappeared. Also, a method was developed to validate geoid models at sea using GNSS measurements collected on a vessel. The method was successful and key elements were identified for the process of reducing the GNSS observations from the height of observation down to the geoid surface. Possible offsets between different types of absolute gravimeters were investigated by looking at the results of international comparisons, bi-lateral comparisons and of trend calculations. The trend calculations revealed significant offsets of 31.4 ± 10.9 μGal, 32.6 ± 7.4 μGal and 6.8 ± 0.8 μGal for the IMGC, GABL and JILAg-5 instruments. The time series of absolute gravity measurements at 12 stations in Finland were analysed. At seven stations reliable trends could be determined. Ratios between -0.206 ± 0.017 and -0.227 ± 0.024 μGal/mm and axis intercept values between 0.248 ± 0.089 and 0.335 ± 0.136 μGal/yr were found for the relationship between gravity change rates and vertical velocities. These values are larger than expected based on results of others. The knowledge obtained in the geoid studies will be of benefit in the determination of the next generation geoid models and height conversion surfaces for Finland. Before clear conclusions can be drawn from the absolute gravity results, more studies related to glacial isostatic adjustment, and longer high-quality time series from more stations in Finland, as well as the whole of the uplift area and its boundaries, are needed.Satelliittipaikannus (GNSS) on nykyään laajasti käytössä ja sen tarkkuus paranee koko ajan. Tämä vaatii myös parempia geoidimalleja, joita tarvitaan kun satelliittipaikannuksella mitattuja korkeuksia muunnetaan kansallisessa korkeusjärjestelmässä oleviksi korkeuksiksi. Suomessa korkeudet muuttuvat jatkuvasti jääkauden jälkeisen maannousun johdosta. Maannousumalleja kehitetään Fennoskandian maannousualueelle, ei pelkästään koordinaattien pystykomponentin nopeuksille, vaan myös jääkauden jälkeisen maannousuun liittyville painovoimamuutoksille. Tässä väitöskirjassa tehtiin geoiditutkimuksia etsittäessä geoidimallia, joka parhaiten sopii muuntamaan EUREF-FIN koordinaattijärjestelmässä olevat GNSS-korkeudet Suomen N2000- korkeusjärjestelmässä oleviksi korkeuksiksi sekä maalla että merellä. Absoluuttipainovoima-mittauksien aikasarjoja analysoitiin painovoiman muutosnopeuksien ja pystysuuntaisten nopeuksien väliseen suhteen määrittämiseksi. Geoiditutkimuksessa testattiin menetelmiä, joilla geoidimalli sovitaan GNSS-vaaitus aineistoon. Parhaaksi menetelmäksi Suomessa osoittautui pienimmän neliösumman kollokaatio yhdessä ristivalidoinnin kanssa. Tulos oli FIN2005N00-korkeuden muunnospinta, josta tuli Suomen virallinen geoidimalli. Seuraavaksi testattiin korkean resoluution globaaleja painovoimakenttämalleja Suomen geoidilaskennassa. Tuloksena olevat geoidimallit olivat parempia kuin aiemmat geoidimallit Suomen alueelle. Vakioeron ja kallistuksen poistamisen jälkeen erot muihin malleihin hävisivät. Lisäksi kehitettiin menetelmä, jolla geoidimalleja voidaan tarkistaa merellä laivan GNSS-mittauksien avulla. Menetelmä onnistui ja tunnistettiin keskeiset elementit prosessille, jolla muunnetaan GNSS havainnot mittauskorkeudelta geoidipintaan. Absoluuttigravimetrityyppien välisiä vakioeroja etsittiin tutkimalla kansainvälisten vertailujen, kahdenvälisten vertailujen ja trendilaskennan tuloksia. Trendilaskennan tulokset paljastivat merkittäviä vakioeroja IMGC, GABL ja JILAg-5 laitteille: 31.4 ± 10.9 μGal, 32.6 ± 7.4 μGal ja 6.8 ± 0.8 μGal. 12 aseman absoluuttipainovoimamittauksien aikasarjat analysoitiin ja seitsemälle asemalle saatiin luotettavat trendit. Painovoiman muutosnopeuksien ja pystysuuntaisten nopeuksien väliselle suhteelle estimoidut suhdeluvut vaihtelivat 0.206 ± 0.017 ja -0.227 ± 0.024 μGal/mm välillä ja akselin leikkausarvot 0.248 ± 0.089 ja 0.335 ± 0.136 μGal/v välillä. Nämä arvot ovat suurempia kuin odotettiin aikaisempien tulosten perusteella. Geoiditutkimuksista saatu tieto hyödynnetään Suomen seuraavien geoidimallien ja korkeuden muunnospintojen määrittämisessä. Ennen kuin absoluuttipainovoiman tuloksista voidaan tehdä selkeitä johtopäätöksiä, tarvitaan lisää maannousututkimusta ja pidemmät korkealaatuiset aikasarjat useammalta asemalta Suomesta, sekä koko maannousun alueelta ja sen reunalta

Geoid and postglacial rebound related gravity change in Finland

Positioning using Global Navigation Satellite Systems (GNSS) is widely used nowadays and it is getting more and more accurate. This requires also better geoid models for the transformation between heights measured with GNSS and heights in the national height system. In Finland heights are continuously changing due to the Fennoscandian postglacial rebound. Land uplift models are developed for the Fennoscandian land uplift area, not only for the vertical velocities, but also for the gravity change related to postglacial rebound. In this dissertation geoid studies were carried out in search of the geoid model that is most suitable for the conversion of GNSS heights in the EUREF-FIN coordinate system to heights in the Finnish height system N2000 on land as well as on sea. In order to determine the relationship between gravity change rates and vertical velocities, time series of absolute gravity measurements were analysed. Methods were tested for fitting a geoid model to GNSS-levelling data. The best method for Finland was found to be least-squares collocation in combination with cross-validation. The result was the height conversion surface FIN2005N00, the official model for Finland. Then, high-resolution global gravity field models were tested in geoid modelling for Finland. The resulting geoid models were better than the earlier geoid models for Finland. After correcting for an offset and tilt, the differences with other models disappeared. Also, a method was developed to validate geoid models at sea using GNSS measurements collected on a vessel. The method was successful and key elements were identified for the process of reducing the GNSS observations from the height of observation down to the geoid surface. Possible offsets between different types of absolute gravimeters were investigated by looking at the results of international comparisons, bi-lateral comparisons and of trend calculations. The trend calculations revealed significant offsets of 31.4 ± 10.9 μGal, 32.6 ± 7.4 μGal and 6.8 ± 0.8 μGal for the IMGC, GABL and JILAg-5 instruments. The time series of absolute gravity measurements at 12 stations in Finland were analysed. At seven stations reliable trends could be determined. Ratios between -0.206 ± 0.017 and -0.227 ± 0.024 μGal/mm and axis intercept values between 0.248 ± 0.089 and 0.335 ± 0.136 μGal/yr were found for the relationship between gravity change rates and vertical velocities. These values are larger than expected based on results of others. The knowledge obtained in the geoid studies will be of benefit in the determination of the next generation geoid models and height conversion surfaces for Finland. Before clear conclusions can be drawn from the absolute gravity results, more studies related to glacial isostatic adjustment, and longer high-quality time series from more stations in Finland, as well as the whole of the uplift area and its boundaries, are needed