Abstract This study addresses the crucial detection of offsets in GNSS time series for accurate velocity estimations, vital in geosciences and engineering. Existing methods are challenged by correlated noise and can suffer from over-segmentation or high false positive rates. A novel methodology is proposed that combines a modified bilateral filter and an adapted implementation of the Pruned Exact Linear Time (PELT) algorithm, optimizing the detection of abrupt changes in the presence of complex noise. The technique was evaluated using a set of 3450 synthetic time series and 45 real time series from Global Navigation Satellite System (GNSS) stations located in Northern Europe. In the synthetic time series, the success threshold of 80 % was exceeded for the horizontal component with offsets of 1.2 mm, and the 90 % threshold for offsets of 1.4 mm. For the vertical component, 80 % success was achieved with offsets of 4 mm and 90 % with offsets of 5 mm. Regarding the real time-series, success percentages of 87.1 % were obtained for the East component, 74.4 % for the North component, and 74.2 % for the vertical component (Up). This hybrid technique enhances the identification of real offsets in GNSS time series, simplifying monitoring and paving the way for fully automated workflows.

Abstract In America, height systems were established during the twentieth century by connecting the leveling network to a tide gauge. In 1997, the Geodetic Reference System for the Americas (former Geocentric Reference System for South America) created Working Group III, called Vertical Datum, to assist in establishing a unified vertical reference system for the Americas. In this context, this article aims to trace the evolution of height systems in America, especially South America, and present the current situation in the region to contribute to the International Height Reference Frame. A brief chronological description of the systems of South American countries and the efforts developed by Working Group III over the past 25 years is presented. A bibliometric study assesses the scientific community’s involvement in this field. The results revealed that some countries have been standing out in engagement in recent years. Finally, an evaluation is performed between recent global geopotential models and a regional gravity field model at the 17 stations that comprise the International Height Reference Frame in Latin America. The results indicate that the Andes region requires efforts in gravity densification and improvement of global models.

Abstract This note presents formulas to evaluate a spherical harmonic model of Earth’s gravitational potential for essential gravimetric quantities without spherical and linear approximation. Typically, 10–13 significant digits of numerical accuracy for such computations are obtained over the globe using EGM2008 with FORTRAN 77 code that is also provided.

Abstract 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.

Abstract 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.

Abstract RTKLIB which is an open source Global Navigation Satellite Systems (GNSS) software has gained rapid acceptance among Surveying professionals thanks to recent developments in UAS (Unmanned Aerial System) technology. RTKLIB enables standard and precise point positioning (PPP) in real-time and post-processing modes to be performed. As such, UAS users utilize this software to analyze GNSS data collected by GNSS systems on UAS. By being versatile and free, RTKLIB is commonly used by many; however, it is not the only freely available GNSS software. There are also freely available online GNSS data processing software running on servers. These online GNSS data processing services provide data processing in static, kinematic and rapid static modes. Because UAS collect data in kinematic mode, in this study, kinematic data processing by aforementioned software (CSRS-PPP, GAPS and APPS) is analyzed. The results coming from these software are compared against the results produced by photogrammetric software (Agisoft Metashape and Pix4Dmapper). The aim of this practical project is to produce generalizable knowledge about the performance of these software. It is found out that RTKLIB and CSRS-PPP achieved cm-level precision. Yet, GAPS and APPS achieved dm-level precision both for horizontal and vertical coordinates. This study demonstrates the precision and accuracy expected from these software if they are used for kinematic GNSS data processing.

Abstract The direct geodetic problem is regarded on the biaxial and triaxial ellipsoid. A known solution method suitable for low eccentricities, which uses differential equations in Cartesian coordinates and Taylor series expansions of these coordinates, is advanced in view of its practical application. According to previous works, this approach has the advantages that no singularities occur in the determination of the coordinates, its mathematical formulation is simple and it is not computationally intensive. The formulas of the solution method are simplified in the present contribution. A test of this method using an extensive test data set on a biaxial earth ellipsoid shows its accuracy and practicability for distances of any length. Based on the convergence behavior of the series of the test data set, a truncation criterion for the series expansions is compiled taking into account accuracy requirements of the coordinates. Furthermore, a procedure is shown which controls the truncation of the series expansions by accuracy requirements of the direction to be determined in the direct problem. The conducted tests demonstrate the correct functioning of the methods for the series truncation. However, the considered solution method turns out to be significantly slower than another current method for biaxial ellipsoids, which makes it more relevant for triaxial ellipsoids.

Abstract The GRACE mission has demonstrated a tremendous potential for observing mass changes in the Earth system from space for climate research and the observation of climate change. Future mission should on the one hand extend the already existing time series and also provide higher spatial and temporal resolution that is required to fulfil all needs placed on a future mission. To analyse the applicability of such a Next Generation Gravity Mission (NGGM) concept regarding hydrological applications, two GRACE-FO-type pairs in Bender formation are analysed. The numerical closed loop simulations with a realistic noise assumption are based on the short arc approach and make use of the Wiese approach, enabling a self-de-aliasing of high-frequency atmospheric and oceanic signals, and a NRT approach for a short latency. Numerical simulations for future gravity mission concepts are based on geophysical models, representing the time-variable gravity field. First tests regarding the usability of the hydrology component contained in the Earth System Model (ESM) by the European Space Agency (ESA) for the analysis regarding a possible flood monitoring and detection showed a clear signal in a third of the analysed flood cases. Our analysis of selected cases found that detection of floods was clearly possible with the reconstructed AOHIS/HIS signal in 20% of the tested examples, while in 40% of the cases a peak was visible but not clearly recognisable.

Abstract In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre).

Abstract Least-squares estimates are trustworthy with minimal variance if the correct stochastic model is used. Due to computational burden, diagonal models that neglect correlations are preferred to describe the elevation dependency of the variance of GPS observations. In this contribution, an improved stochastic model based on a parametric function to take correlations between GPS phase observations into account is presented. Built on an adapted and flexible Mátern function accounting for spatiotemporal variabilities, its parameters can be fixed thanks to Maximum Likelihood Estimation or chosen apriori to model turbulent tropospheric refractivity fluctuations. In this contribution, we will show in which cases and under which conditions corresponding fully populated variance covariance matrices (VCM) replace the estimation of a tropospheric parameter. For this equivalence “augmented functional versus augmented stochastic model” to hold, the VCM should be made sufficiently largewhich corresponds to computing small batches of observations. A case study with observations from a medium baseline of 80 km divided into batches of 600 s shows improvement of up to 100 mm for the 3Drms when fully populated VCM are used compared with an elevation dependent diagonal model. It confirms the strong potential of such matrices to improve the least-squares solution, particularly when ambiguities are let float.