Improving GPS time series for geodynamic studies

Accurate and stable time series of geodetic parameters can be used to help in understanding the dynamic Earth and its response to global change. The Global Positioning System, GPS, has proven to be invaluable in modern geodynamic studies. In Fennoscandia the first GPS networks were set up in 1993. These networks form the basis of the national reference frames in the area, but they also provide long and important time series for crustal deformation studies. These time series can be used, for example, to better constrain the ice history of the last ice age and the Earth s structure, via existing glacial isostatic adjustment models. To improve the accuracy and stability of the GPS time series, the possible nuisance parameters and error sources need to be minimized. We have analysed GPS time series to study two phenomena. First, we study the refraction in the neutral atmosphere of the GPS signal, and, second, we study the surface loading of the crust by environmental factors, namely the non-tidal Baltic Sea, atmospheric load and varying continental water reservoirs. We studied the atmospheric effects on the GPS time series by comparing the standard method to slant delays derived from a regional numerical weather model. We have presented a method for correcting the atmospheric delays at the observational level. The results show that both standard atmosphere modelling and the atmospheric delays derived from a numerical weather model by ray-tracing provide a stable solution. The advantage of the latter is that the number of unknowns used in the computation decreases and thus, the computation may become faster and more robust. The computation can also be done with any processing software that allows the atmospheric correction to be turned off. The crustal deformation due to loading was computed by convolving Green s functions with surface load data, that is to say, global hydrology models, global numerical weather models and a local model for the Baltic Sea. The result was that the loading factors can be seen in the GPS coordinate time series. Reducing the computed deformation from the vertical time series of GPS coordinates reduces the scatter of the time series; however, the long term trends are not influenced. We show that global hydrology models and the local sea surface can explain up to 30% of the GPS time series variation. On the other hand atmospheric loading admittance in the GPS time series is low, and different hydrological surface load models could not be validated in the present study. In order to be used for GPS corrections in the future, both atmospheric loading and hydrological models need further analysis and improvements.Satelliittipaikannusjärjestelmä GPS (Global Positioning System) on osoittautunut arvokkaaksi työkaluksi maapallon dynamiikkaa tutkittaessa. GPS:n avulla voidaan tutkia maankuoren liikkeitä sekä lyhyillä että pitkillä ajanjaksoilla. Lyhytaikaisista liikkeistä voidaan esimerkiksi ennakoida maanjäristyksiä tai tulivuorenpurkauksia, kun taas pitkistä aikasarjoista pystytään laskemaan tektonisten laattojen liikkeitä sekä jääkauden aiheuttaman maannousun nopeuksia. Nykyisiä maannousunopeuksia eli muinaisten jääkausien vaikutuksia havaitsemalla voidaan pyrkiä ymmärtämään nykyisen ilmaston lämpenemisen vaikutuksia maapalloon. Jotta saataisiin mahdollisimman luotettavia tuloksia GPS-aikasarjoista on häiriötekijät saatava mahdollisimman vähäisiksi. Tässä väitöskirjassa GPS-aikasarjoja on käytetty kahden ilmiön tutkimiseen. Ensimmäinen on neutraalin ilmakehän aiheuttama GPS-signaalin viivästyminen. Toinen ilmiö on nimeltään ympäristön aiheuttama pintakuormitus, eli tässä tapauksessa Itämeren, ilmakehän ja maavesien muuttuvien massojen aiheuttama maankuoren deformaatio. Nämä ilmiöt riippuvat toisistaan. GPS-laskennassa epätarkka ilmakehäkorjaus voi vaimentaa ympäristökuormituksesta johtuvaa todellista maankuoren liikettä, ja todellinen maankuoren liike voidaan puolestaan tulkita virheelliseksi ilmakehäkorjaukseksi. Ymmärtämällä näiden ilmiöiden syyt ja seuraukset GPS-aikasarjojen tarkkuutta ja vakautta voidaan parantaa. Neutraalin ilmakehän aiheuttamaa signaalin viivästymistä mallinnetaan GPS-ohjelmissa usein yksinkertaisten ilmakehämallien avulla. Tässä työssä on käytetty numeerisesta sääennusteesta laskettuja vinoviiveitä. Vertasimme useita GPS-aikasarjoja, jotka on laskettu käyttäen erilaisia ilmakehämalleja, kuvausfunktioita sekä myös vinoviiveitä. Lasketut vinoviiveet on korjattu suoraan GPS-havaintoihin, jolloin laskennassa ilmakehäkorjaus voidaan ottaa pois päältä. Vinoviiveitä käyttämällä saadaan yhtä hyviä tuloksia kuin perinteisellä zeniittiviive-kuvausfunktio-yhdistelmällä. Kannettavat yksitaajuusvastaanottimia käyttävät laitteet voisivat erityisesti hyötyä tästä menetelmästä. Maankuoren ympäristökuormitusta tutkittiin käyttämällä globaaleja maavesimalleja, globaaleja ilmakehämalleja sekä paikallista mallia Itämerelle. Eri tekijöiden kuorman aiheuttama deformaatio poistettiin GPS-aikasarjoista, ja vaikutusta aikasarjojen keskihajontaan tutkittiin. Tuloksista huomattiin, että kuormitustekijät näkyvät GPS-aikasarjoissa. Eri maavesimalleissa oli huomattavia eroja samoilla asemilla, parasta mallia ei pystytty valitsemaan. Myös ilmakehän kuormitus kaipaa lisätutkimuksia

Updated GNSS velocity solution in the Nordic and Baltic countries with a semi-automatic offset detection method

In Fennoscandia, the Glacial Isostatic Adjustment (GIA) causes intraplate deformations that affect the national static reference frames. The GNSS-determined velocities are important data for constraining the GIA models, which are necessary for maintaining the national reference frames. The Nordic Geodetic Commission (NKG) has published a dense and consistent GNSS station velocity solution in 2019, and we present now an update of the solution covering additional 3.5 years of data. Undetected positional offsets are the main factor decreasing the accuracy of the velocity estimates. We developed a method for the semi-automatic offset detection to improve the quality of our solution. The results show that we could correctly detect 74% of the manually determined offsets, and the undetected offsets would have caused a median 0.1 mm/y bias in trend. The method pointed out some otherwise unnoticed offsets and will decrease the need for manual analysis in the future. The updated velocity solution especially improves the velocity estimates of the newly established stations and the quality of the velocity estimates in Baltic countries. The formal uncertainties estimated using the power-law plus white noise model were at a median of 0.06 and 0.15 mm/y for horizontal and vertical velocities, respectively. However, we concluded that the systematic velocity uncertainties due to the reference frame alignment were approximately at the same level

Past and Future Sea Level Changes and Land Uplift in the Baltic Sea Seen by Geodetic Observations

We have studied the land uplift and relative sea level changes in the Baltic Sea in northern Europe. To observe the past changes and land uplift, we have used continuous GNSS time series, campaign-wise absolute gravity measurements and continuous tide gauge time series. To predict the future, we have used probabilistic future scenarios tuned for the Baltic Sea. The area we are interested in is Kvarken archipelago in Finland and High Coast in Sweden. These areas form a UNESCO World Heritage Site, where the land uplift process and how it demonstrates itself are the main values. We provide here the latest numbers of land uplift for the area, the current rates from geodetic observations, and probabilistic scenarios for future relative sea level rise. The maximum land uplift rates in Fennoscandia are in the Bothnian Bay of the Baltic Sea, where the maximum values are currently on the order of 10 mm/year with respect to the geoid. During the last 100 years, the land has risen from the sea by approximately 80 cm in this area. Estimates of future relative sea level change have considerable uncertainty, with values for the year 2100 ranging from 75 cm of sea level fall (land emergence) to 30 cm of sea-level rise.Peer reviewe

Probabilistic projections and past trends of sea level rise in Finland

We explore past trends and future projections of mean sea level (MSL) at the Finnish coast, in the northeastern Baltic Sea, during the period 1901–2100. We decompose the relative MSL change into three components: regional sea level rise (SLR), postglacial land uplift, and the effect of changes in wind climate. Past trends of regional SLR can be calculated after subtracting the other two components from the MSL trends observed by tide gauges, as the land uplift rates obtained from the semi-empirical model NKG2016LU are independent of tide gauge observations. According to the results, local absolute SLR trends are close to global mean rates. To construct future projections, we combine an ensemble of global SLR projections in a probabilistic framework. In addition, we use climate model results to estimate future changes in wind climate and their effect on MSL in the semi-enclosed Baltic Sea. This yields probability distributions of MSL change for three scenarios representing different future emission pathways. Spatial variations in the MSL projections result primarily from different local land uplift rates: under the medium-emission scenario RCP4.5/SSP2-4.5, for example, the projected MSL change (5 % to 95 % range) over the 21st century varies from −28 (−54 to 24) cm in the Bothnian Bay to 31 (5 to 83) cm in the eastern Gulf of Finland

New Tidal Analysis of Superconducting Gravimeter Records at Metsähovi, Finland

Superconducting gravimeters are the most sensitive instruments for monitoring gravitational changes. At the Metsähovi Geodetic Research Station in southern Finland, a superconducting gravimeter has been operating since 1994. It can be used to monitor crustal loading effects affecting the other geodetic measurements made at the station. Gravimeters iGrav-013 and iOSG-022 replaced the old gravimeter SG-T020 at Metsähovi in 2016. The first step was to do a new local tidal gravity modelling for Metsähovi Geodetic Research Station based on the first 5.5 years of iGrav-013 and iOSG-022 superconducting gravimeter data. Here we present the first analysis of the gravity data and the results of tidal analysis of Earth body tides and ocean tidal loading

An investigation into the sensitivity of postglacial decay times to uncertainty in the adopted ice history

At the centres of previously glaciated regions such as Hudson Bay in Canada and the Gulf of Bothnia in Fennoscandia, it has been observed that the sea level history follows an exponential form and that the associated decay time is relatively insensitive to uncertainty in the ice loading history. We revisit the issue of decay time sensitivity by computing relative sea level histories for Richmond Gulf and James Bay in Hudson Bay and Ångerman River in Sweden for a suite of reconstructions of the North American and Fennoscandian Ice Sheets and Earth viscosity profiles. We find that while some Earth viscosity models do indeed show insensitivity in computed decay times to the ice history, this is not true in all cases. Moreover, we find that the location of the study site relative to the geometry of the ice sheet is an important factor in determining ice sensitivity, and based on our set of ice sheet reconstructions, conclude that the location of James Bay is not well-suited to a decay time analysis. We describe novel corrections to the RSL data to remove the effects associated with the spatial distribution of sea level indicators as well as for other signals unrelated to regional ice loading (ocean loading, rotation and global mean sea level changes) and demonstrate that they can significantly affect the inference of viscosity structure. We performed a forward modelling analysis based on a commonly adopted 2-layer, sublithosphere viscosity structure to determine how the solution space of viscosity models changes with the input ice history at the three study sites. While the solution spaces depend on ice history, for both Richmond Gulf and Ångerman River there are regions of parameter space where solutions are common across all or most ice histories, indicating low ice load sensitivity for these mantle viscosity parameters. For example, in Richmond Gulf, upper mantle viscosity values of (0.3-0.5)x10 21 Pa s and lower mantle viscosity values of (5-50)x10 21 Pa s tend to satisfy the data constraint consistently for most ice histories considered in this study. Similarly, the Ångerman River solution spaces contain a solution with an upper mantle viscosity of 0.3 × 10 21 Pa s and lower mantle viscosity values of (5-50)x10 21 Pa s common to 9 of the 10 ice histories considered there. However, the dependence of the viscosity solution space on ice history suggests that joint estimation of ice and Earth parameters is the optimal approach.Peer reviewe

Validating Geoid Models with Marine GNSS Measurements, Sea Surface Models, and Additional Gravity Observations in the Gulf of Finland

Traditionally, geoid models have been validated using GNSS-levelling benchmarks on land only. As such benchmarks cannot be established offshore, marine areas of geoid models must be evaluated in a different way. In this research, we present a marine GNSS/gravity campaign where existing geoid models were validated at sea areas by GNSS measurements in combination with sea surface models. Additionally, a new geoid model, calculated using the newly collected marine gravity data, was validated. The campaign was carried out with the marine geology research catamaran Geomari (operated by the Geological Survey of Finland), which sailed back and forth the eastern part of the Finnish territorial waters of the Gulf of Finland during the early summer of 2018. From the GNSS and sea surface data we were able to obtain geoid heights at sea areas with an accuracy of a few centimetres. When the GNSS derived geoid heights are compared with geoid heights from the geoid models differences between the respective models are seen in the most eastern and southern parts of the campaign area. The new gravity data changed the geoid model heights by up to 15 cm in areas of sparse/non-existing gravity data

Analyzing the 3D Deformation Induced by Non-tidal Loading in GNSS Time Series in Finland

Improving our understanding of non-tidal loading (NTL) in geodetic time series, especially at regional and local scales, holds paramount importance. This deeper comprehension enables accurate modeling and effective removal of NTL effects from the time series, consequently enhancing the overall stability and reliability of geodetic observations. In this study, we compared the performance of different loading products and investigated their impact on the 20-year time series of four permanent GNSS stations within the Finnish permanent GNSS network (FinnRef). We employed original GNSS time series data products generated by four different analysing centers. We qualitatively compared NTL corrections involving ten different combinations of different hydrological, non-tidal atmospheric, and non-tidal oceanic loading models to see how various loading configurations operate and how they affect the noise characteristics of GNSS 3D time series, and ultimately to figure out which models are the most realistic in Finland. We observed weighted RMS reduction rates of up to 20% for the vertical coordinate and up to 10% for the horizontal coordinate. Additionally, we identified a maximum annual amplitude reduction rate of 87.2%. The results demonstrate a substantial improvement through the integration of hydrological loading products derived from GRACE satellites in our study conducted over Finland