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Despite being in use for more than 150 years, the error accumulation in precise levelling has not yet been completely clarified. It is believed that the error accumulation in this method is proportional to the square root of the levelling length. The first goal of this article is to demonstrate that this belief is not always scientifically proven. The second aim is to show that it is likely that a better adjustment decision will be missed if inverse distance weighting with a power parameter equal to one is automatically applied. Using linear regression analysis the measuring data of the Second Levelling of Finland is analysed. An inadequacy of the relationship between the absolute values of the differences between both measurements of the elevations in the levelling lines and their length is shown, which is due to heteroscedasticity. In order to obtain a homoscedastic model, the other two models are constructed. Based on the regression analysis results, the network is adjusted using three types of weights. The adjustment with traditional weights has produced significantly greater mean errors of the nodal benchmarks than both variants based on weights, which are functions of the absolute values of the line elevations.

Gravity recovery and climate experiment (GRACE) and GRACE Follow-On (GRACE-FO) are Earth’s gravity satellite missions with hydrological monitoring applications. However, caused by measuring instrumental problems, there are several temporal missing values in the dataset of the two missions where a long gap between the mission dataset also exists. Recent studies utilized different gap-filling methodologies to fill those data gaps. In this article, we employ a variety of singular spectrum analysis (SSA) algorithms as well as the least squares-harmonic estimation (LS-HE) approach for the data gap-filling. These methods are implemented on six hydrological basins, where the performance of the algorithms is validated for different artificial gap scenarios. Our results indicate that each hydrological basin has its special behaviour. LS-HE outperforms the other algorithms in half of the basins, whereas in the other half, SSA provides a better performance. This highlights the importance of different factors affecting the deterministic signals and stochastic characteristics of climatological time series. To fill the missing values of such time series, it is therefore required to investigate the time series behaviour on their time-invariant and time-varying characteristics before processing the series.

In this work, the determination of the discrepancy between the Ecuadorian Vertical Datum (EVD) and the International Height Reference System (IHRS) is presented. The vertical offset was estimated at the EVD based on the fixed geodetic boundary value problem approach. The focus of the experiment was the determination of the anomalous potential in the EVD, which in turn enable determination of the respective geopotential value. Taking a geopotential space-based approach, two estimates of the EVD offset with respect to the IHRS were obtained that amount to −1.51 and −1.61 m 2 /s 2 .

The geoid-quasigeoid separation (GQS) traditionally uses the Bouguer anomalies to approximate the difference between the mean gravity and normal gravity along the plumb line. This approximation is adequate in flat and low elevation areas, but not in high and rugged mountains. To increase the accuracy, higher order terms of the corrections (potential and gravity gradient) to the approximation were computed in Colorado where the 1 cm geoid computation experiment was conducted. Over an area of 730 km by 560 km where the elevation ranges between 932 and 4,385 m, the potential correction (Pot. Corr.) reaches −0.190 m and its root mean square (RMS) is 0.019 m. The gravity gradient correction is small but has high variation: the RMS of the correction is merely 0.003 m but varies from −0.025 to 0.020 m. In addition, the difference between the Bouguer gravity anomaly and gravity disturbance causes about a 0.01 m bias and a maximum correction of 0.02 m. The total corrections range from −0.135 to 0.180 m, with an RMS value of 0.019 m for the region. The magnitude of the corrections is large enough and is not negligible considering today’s cm-geoid requirement. After the test in Colorado, the complete GQS term is computed in 1′ × 1′ grids for the experimental geoid 2020 (xGEOID20), which covers a region bordered by latitude 0–85° north, longitude 180–350° east. Over the land areas, the RMS of the GQS is 0.119 m and the maximum reaches 1.3 m. The RMS of the GQS increases with respect to the height until 4,000 m, then decreases unexpectedly. At the highest peaks (5,500–6,000 m) of Denali and Mount Logan, the RMS of the GQS ranges between 0.08 and 0.189 m. The small GQS at these high peaks are caused by steep slopes around the peaks that produce large Pot. Corr. caused by the topography. In addition, the higher order correction terms reach half of a meter in those peaks.

New gravity and precise levelling measurements have been performed throughout the Hong Kong territories to modernize a vertical geodetic datum that is currently realized by heights of levelling benchmarks defined in the Hong Kong Principal Datum (HKPD). Modernization of the HKPD involved delivering various products, including new detailed geoid and quasigeoid models and newly determined orthometric and normal heights of levelling benchmarks. In this study, we present the result of gravimetric quasigeoid modelling. The method used to compute a detailed gravimetric quasigeoid model is based on the finite-element method to solve the geodetic boundary-value problem with oblique derivative boundary conditions considered directly at computational nodes on the discretized Earth’s topography. The result of a gravimetric quasigeoid modelling shows a good agreement with a geometric quasigeoid model at the Global Navigation Satellite System (GNSS)-levelling benchmarks. The standard deviation of differences between the gravimetric and geometric quasigeoid heights of ±3.3 cm is compatible with the expected accuracy of gravity, levelling, and GNSS measurements.

To prepare the mobile application for the ongoing update of the control network, it is necessary to define detailed procedures for dealing with the points database. These procedures concern the determination of the methodology of making an inventory of the existing database and then the determination of the rules for updating the control network using the developed application. This part describes a practical verification of Metrica for collecting control points data and showing specific cases in the collection and sharing of such data. There were created field inspections using nine different criteria on the set of selected points. Analysis shows that a large part of the points need to be reviewed once again, and its description needs to be updated.

Since the 1960s, the analysis of disturbed satellite orbits to infer Earth’s gravity field functionals has been an important element in determining the Earth’s gravitational field. The long wavelengths of the gravitational field are recovered through the analysis of non-Keplerian variations in the orbital path of artificial satellites, from their tracking from ground stations (Satellite Laser Ranging, Doppler Orbitography and Radiopositioning Integrated by Satellite, and Precise Range And Range-Rate Equipment), from satellite-to-satellite tracking, or by microwave interferometry. In addition, differences in gravitational acceleration in three mutually orthogonal dimensions can be determined by employing a differential accelerometer carried on artificial satellites (satellite gravity gradiometry, SGG). Satellite gravimetry provides global information (long wavelengths) of the Earth’s gravitational field, which is the fundamental basis for the implementation of Global Geopotential Models (GGMs). The GGMs are one of the key tools for the representation of the Earth’s gravity field and, therefore, for the establishment of a Global Height System (i.e., International Height Reference System), whose fundamental reference surface is defined in terms of a geopotential value. In this study, the validation of high-resolution GGMs (coefficients up to degree 2190) was performed based on their performance in Ecuador by comparing geoid heights estimated by the GGMs with the corresponding values derived from Global Navigation Satellite System/leveling records. Furthermore, geopotential values from the GGMs are compared with the corresponding value obtained for the Ecuadorian Vertical Datum by solving the fixed geodetic boundary value problem. The obtained results indicated that the precision of the high-resolution GGMs does not reach the established requirements for the geopotential computation in the International Height Reference Frame fundamental stations.

The use of orthometric height in geodetic applications provides elevations on the physical topographic surface of the earth rather than ellipsoidal heights that are not in conformity with the physical topography. Global positioning system (GPS)/levelling produces ellipsoidal heights that are not consistent with levelled heights above mean sea level. The study provides a practical solution of using the GPS levelling approach or the geoidal heights aimed at providing local orthometric height. Many research studies were conducted with a view of finding a viable solution to the derived orthometric heights. It was revealed that the research studies conducted were found lacking in the use of only lower order numerical solutions models, which limit the accuracy derived from the model, the use of online post-processing, RTKlib, and other non-precise software to obtain the coordinates of the stations used in the derivation of orthometric. Finally, the use of gravimetric data, with its temporal variation problem, poses a threat to the derivation of orthometric height, so also to the accuracy of the developed model. Considering factors while developing models for orthometric heights improves the accuracy in achieving required heights for geodetic applications and aids in fast-tracking mapping.

The transformation of coordinates between different geodetic datums has been a common practice within the geospatial profession. Relating different geodetic datums mostly involves the use of conformal transformation techniques, which could produce results that are not very often satisfactory for certain geodetic, surveying, and mapping purposes. This has been attributed to the inability of the conformal models to resolve the lack (non-exhaustivity) and the heterogeneity of double points existing within the Algerian local geodetic networks. Indeed, the Algerian geodetic network is divided into two main zones completely different in accuracy and points exhaustivity. The North is better and well defined in precision; on the other hand, the South is poorly defined because of the lack of heterogeneity of the points. Mathematical algebraic methods give closed-form solutions to geodetic transformation problems, requiring a high-level computer programming background. In everyday usage, the closed-form solutions are much simpler and have a higher precision than earlier procedures. Thus, it can be predicted that these new solutions will find their place in practice. The present work deals with an important theoretical problem of geodesy: we are looking for a mathematical dependency between two spatial systems using common pairs of points whose coordinates are given in both systems. In geodesy and photogrammetry, the most often used procedure to move from one coordinate system to another is the 3D, seven-parameter similarity transformation (Bursa–Wolf, Molodensky–Badekas, and Helmert).

The book “ Physical Geodesy ” by Martin Vermeer is written in a proper pedagogic way with a simple and complete text, good examples, conceptual questions and excellent exercises at the end of each chapter. This book is a suitable reference for educational purposes in Physical Geodesy from the bachelor to higher levels of education.

The beginning of radars goes back to the 1930s where its main boost was related to the second world war. Nowadays, the techniques associated with radars are focused around a vast variety of civil, geodetic, and military applications. The development of the synthetic aperture principle, in the 1950s and 1960s, gave birth to a lot of new applications, and together with the technological progress of the last decades, the technique of interferometry with synthetic aperture radar (SAR) data became one of the most powerful ones for sensing remotely, with high quality and a vast spatial coverage. We used Sentinel-1 data and the differential interferometry SAR (DinSAR) technique to map and measure the surface deformation related to the 2015 Mw 8.3 Illapel earthquake (Chile). We also validated the results, by analysing the temporal variation of coordinates acquired from global navigation satellite system observations and projecting them in the geometry of the SAR system. Using this application we prove the DinSAR technique to be useful and powerful for the observation and analysis of surface deformation caused by the release of stress during the Mw 8.3 Illapel earthquake. It proved to be an efficient tool to detect and map the surface deformation with high spatial resolution in an approximate area of 20,000 km 2 .

Coordinates in global reference frames are becoming more and more common in positioning whereas most of the geospatial data are stored in registries in national reference frames. It is therefore essential to know the relation between global and national coordinates, i.e., the transformation, as accurately as possible. Officially provided pan-European transformations do not account for the special conditions in the Nordic and Baltic countries, namely crustal deformations caused by Glacial Isostatic Adjustment. Therefore, they do not fulfill the demands for the most accurate applications like long-term reference frame maintenance. Consequently, the Nordic Geodetic Commission (NKG) has developed customized and accurate transformations from the global ITRF to the national ETRS89 realizations for the Nordic and Baltic countries. We present the latest update, called the NKG2020 transformation, with several improvements and uncertainty estimates. We also discuss its significance and practical implementation for geodetic and geospatial communities.

During the 1950s–1970s, there were three geodesy professors in Sweden. Before and after that period the only such position was at KTH in Stockholm. One in the triple proposed the creation of the Nordic Geodetic Commission, which was realized in 1953 and still exists in much the same form as originally proposed.

The International Height Reference System (IHRS) was defined by the International Association of Geodesy in 2015. Since then, the international geodetic community has been working on the specification and establishment of its realisation, the International Height Reference Frame (IHRF). This frame will primarily be realised by geopotential numbers (or physical heights) in a sparse global reference network. In Sweden, only one such global station is planned. Regional and national realisations (or densifications) computed in accordance with the IHRS definition are needed to enable the best possible unification of height datums. The main purpose of this article is to make a case study for Sweden regarding the national realisation of IHRS and to investigate in what way preliminary IHRF differs from the current Swedish levelling-based realisation of the European Vertical Reference System, RH 2000. The two different quasigeoid models that we consider best over Sweden at the present time are used to compute the preliminary IHRS realisations in the study. The realisations are compared to each other and to RH 2000. It is shown that a very significant part of the difference to RH 2000 is due to the different postglacial land uplift epochs, permanent tide concepts, and zero levels. The standard deviation for the difference between one of the preliminary national IHRS realisations and RH 2000 is reduced from 75.5 to 19.2 mm after correction of the postglacial land uplift and permanent tide effects. The corresponding mean differences are –208.5 and –454.7 mm, respectively. The magnitude of the mean difference thus increases when the corrections in question are applied.

Satellite altimetry (SA) is one of the most valuable techniques that measure the sea level data at both the near-coast and offshore. There exists, however, multiple challenges and hindrances in determining and using accurate sea level data. The most pertinent is that evaluation of SA performance requires that all data sources (such as tide gauges (TG) and hydrodynamic models (HDMs)) refer to the same vertical datum. Thus, knowledge of the geoid (equipotential surface of the earth) is essential in linking different sources of sea level. Accordingly, this study examines performance of along-track data for three satellite missions (Sentinel-3A, Jason-3, and Sentinel-6A) to obtain realistic sea level variation and to determine the accuracy of the various missions in the complex area of the eastern Baltic Sea. The methodology consisted of utilizing SA, HDM, and TG data and a high-resolution geoid model. Results show that root-mean-square error (RMSE) varied for Jason-3 within a range of 1.68–50.14 cm, Sentinel 3A with a range of 2.8–46.27 cm, and Sentinel 6A with a range of 3.5–43.90 cm. Sentinel 6A was determined to be the most accurate and reliable satellite mission. Results also showed higher RMSE (15.7–46.2 cm) during (i) the seasonal sea ice month (e.g. March 2018); (ii) at locations of several islands (e.g. eastern section of Gulf); and (iii) at locations where rivers discharged into the Gulf (e.g. Nava, Kemi, Luga, and Neva rivers). These features tended to show up as peaks in the final results even though robust data processing for outliers were undertaken. These results suggests that improvements can still be made in the SA retrackers and also in the data-processing techniques utilized.

Geodetic advances in Estonia within the Nordic Geodetic Commission activity term 2018–2022 are reviewed. The new Estonian height and gravity systems and a new geoid model, EST-GEOID207, have been implemented. A national global navigation satellite system (GNSS) satellite data centre (ESTPOS) was established at the Estonian Land Board (ELB). ELB has also acquired instruments capable of detecting GNSS interference. ELB and Latvian Geospatial Information Agency conducted the Interreg-funded joint Estonian–Latvian cross-border project “Harmonization of Estonian and Latvian geodetic systems in the border areas” within 2021–2022.