Volume 11, Issue 1

Arne Bjerhammar is well known worldwide mainly for his research in physical geodesy but also for introducing a new matrix algebra with generalized inverses applied in geodetic adjustment. Less known are his developments in geodetic engineering and contributions to satellite and relativistic geodesy as well as studies on the relation between the Fennoscandia land uplift and the regional gravity low. Most likely part of his research has contributed to worldwide political relaxation during the cold war, which deed was honored by a certificate of achievement awarded by the Department of Research of the US army as well as the North Star Order by the King of Sweden. Arne Bjerhammar’s pioneer scientific production, in particular on a world geodetic system, towards what would become GPS, as well as relativistic geodesy, is still of great interest among the worldwide geodetic community, while the memories and spirit along his outstanding academic deeds have more or less fainted away from his home university (KTH) only a decade after he passed away.

Detection and quantification of sea level accelerations at tide gauge stations are needed for assessing anthropogenic contributions to the climate change. Nonetheless, uniform or non-uniform sea level accelerations/decelerations are particularly di˚cult to discern partly because of their small magnitudes and partly because of the low frequency sea level variations as confounders. Moreover, noisy excursions in the observed sea level variations also exacerbate reliability of estimated sea level accelerations. This study explores the uniformity of a sea level acceleration graphically that is left unmodeled in the residuals of a least squares solution using cumulative sum charts. Key West, USA tide gauge station’s record is studied for a demonstration. The cumulative sum charts of the residuals of a rigorous kinematic model solution without the acceleration parameter revealed its crisp and uniform signature experienced at this station since 1913.

The impact of the earth’s atmospheric layers, particularly the troposphere on Global Navigation satellite system (GNSS) signals has become a major concern in GNSS accurate positioning, navigation, surveillance and timing applications. For precise GNSS applications, tropospheric delay has to be mitigated as accurately as possible using tropospheric delay prediction models. However, the choice of a particular prediction model can signifi-cantly impair the positioning accuracy particularly when the model does not suit the user’s environment. A performance assessment of these prediction models for a suitable one is very important. In this paper, an assessment study of the performances of five blind tropospheric delay prediction models, the UNB3m, EGNOS, GTrop, GPT2w and GPT3 models was conducted in Ghana over six selected Continuously Operating Reference Stations (CORS) using the 1˚x1˚ gridded Vienna Mapping Function 3 (VMF3) zenith tropospheric delay (ZTD) product as a reference. The gridded VMF3-ZTD which is generated for every six hours on the 1˚x1˚ grids was bilinearly interpolated both space and time and transferred from the grid heights to the respective heights of the CORS locations. The results show that the GPT3 model performed better in estimating the ZTD with an overall mean (bias: 2.05 cm; RMS: 2.53 cm), followed by GPT2w model (bias: 2.32cm; RMS: 2.76cm) and GTrop model (bias: 2.41cm; 2.82cm). UNB3m model (bias: 6.23 cm; RMS: 6.43 cm) and EGNOS model (bias: 6.70 cm; RMS: 6.89 cm) performed poorly. A multiple comparison test (MCT) was further performed on the RMSE of each model to check if there is significant difference at 5% significant level. The results show that the GPT3, GPT2w and GTrop models are significantly indifferent at 5% significance level indicating that either of these models can be employed to mitigate the ZTD in the study area, nevertheless, the choice of GPT3 model will be more preferable.

The coastal marine gravity field is not well modelled due to poor data coverage. Recent satellite altimeters provide reliable altimetry observations near the coast, filling the gaps between the open ocean and land. We show the potential of recent satellite altimetry for the coastal marine gravity modelling using the least squares collocation technique. Gravity prediction error near the coast is better than 4 mGal. The modelled gravity anomalies are validated with sparse shipborne gravimetric measurements. We obtained 4.86 mGal precision when using the altimetry data with the best coastal coverage and retracked with narrow primary peak retracker. The predicted gravity field is an enhancement to EGM2008 over the coastal regions. The potential improvement in alti- metric marine gravity will be beneficial for the next generation of EGM development.

The Geocentric Datum of Australia 2020 (GDA2020) is Australia’s new and much improved national datum. It is based on a single, nationwide least squares network adjustment that rigorously propagates uncertainty. This paper explores three options to include Network Real-Time Kinematic (NRTK) observations and their Positional Uncertainty (PU) in the survey control network of New South Wales (NSW) via the GDA2020 state adjustment. In the first option, PU is empirically estimated based on a dataset of more than 1,500 observations to obtain values that can be uniformly applied to all NRTK observations. In the second option, PU is calculated for each NRTK observation, based on the coordinate quality indicators provided by the Global Navigation Satellite System (GNSS) equipment. Both options continue to treat NRTK observations as point-based position solutions, resulting in poor correlation with surrounding survey control marks. The third option overcomes this issue by utilising the automatically computed GNSS baselines between NRTK observations and their Virtual Reference Station (VRS) to create a connected network that can be adjusted like a static GNSS network. Using a typical urban NRTK survey in Sydney as an example, it is shown that this method offers a rigorous computation of PU, while maintaining the quick and easy nature of NRTK positioning.

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.

One of the major challenges of satellite altimetry (SA) is to produce accurate sea surface heights data up to the shoreline, especially in geomorphologically complex sea areas. New advanced re-tracking methods are expected to deliver better results. This study examines the achievable accuracy of Sentinel-3A (S3A) and Jason-3 (JA3) standard retrackers (Ocean and MLE4) with that of improved retrackers adapted for coastal and sea ice conditions (ALES+ SAR for S3A and ALES+ for JA3). The validation of SA data was performed by the integration of tide gauges, hydrodynamic model and high-resolution geoid model. The geoid being a key component that links the vertical reference datum of the SA with other utilized sources. The method is tested in the eastern section of Baltic Sea. The results indicate that on average reliable sea surface height (SSH) data can be obtained 2–3 km from the coastline for S3A (for both Ocean and ALES+SAR) whilst an average distance of 7–10 km for JA3 (MLE4 and ALES+) with a minimum distance of 3–4 km. In terms of accuracy, the RMSE (with respect to a corrected hydrodynamic model) of S3A ALES+ SAR and Ocean retrackers based SSH were 4–5 cm respectively, whereas with the JA3 ALES+ and MLE4 associated SSH RMSE of 6–7 cm can be achieved. The ALES+ and ALES+ SAR retrackers show SSH improvement within a range of 0.5–1 cm compared to the standard retrackers. This assessment showed that the adaptation of localized retrackers for the Baltic Sea (ALES+ and ALES+SAR) produced more valid observation closer to the coast than the standard retrackers and also improved the accuracy of SSH data.

Because oceans cover 71% of Earth’s surface, ocean warming, consequential for thermal expansion of sea water, has been the largest contributor to the global mean sea level rise averaged over the 20 th and the early 21 st century. This study first generates quasi-observed monthly globally averaged thermosteric sea level time series by removing the contributions of global mean sea level budget components, namely, Glaciers, Greenland, Antarctica, and Terrestrial Water Storage from satellite altimetry measured global sea level changes during 1993–2019. A baseline kinematic model with global mean thermosteric sea level trend and a uniform acceleration is solved to evaluate the performance of a rigorous mixed kinematic model. The model also includes coefficients of monthly lagged 60 yearlong cumulative global mean sea surface temperature gradients and control variables of lunisolar origins and representations for first order autoregressive disturbances. The mixed kinematic model explains 94% ( Adjusted R 2 ) 1 of the total variability in quasi-observed monthly and globally averaged thermosteric time series compared to the 46% of the baseline kinematic model’s Adjusted R 2 . The estimated trend, 1.19±0.03 mm/yr., is attributed to the long-term ocean warming. Whereas eleven statistically significant (α = 0.05) monthly lagged cumulative global mean sea surface temperature gradients each having a memory of 60 years explain the remainder transient global mean thermosteric sea level changes due to the episodic ocean surface warming and cooling during this period. The series also exhibit signatures of a statistically significant contingent uniform global sea level acceleration and periodic lunisolar forcings.

GNSS satellite signals are affected by the media when traversing Earth’s atmosphere, and the performance of GNSS based positioning and navigation is correlated with these effects. In the ionosphere, the signals are affected by the number of electrons along the signal path which can be quantified by the total electron content. The focus of this article is scintillation effects caused by electrons in the Arctic ionosphere, and the rate of the total electron content index, the ROTI, is used as a measure of the scintillation. Data from permanent GNSS reference stations in Greenland is used to generate maps of the ROTI in Greenland, and the novelty of the work in this paper is the application of the ordinary kriging method as the basis for ROTI maps in the Arctic. Further, the choice of satellite constellations as well as the elevation mask used in the data analyses are analyzed and discussed. Also, the performance of using ordinary kriging for ROTI maps during times with both a low and a very high geomagnetic activity are discussed. The results show that ordinary kriging performs well during high geomagnetic activity, while during low activity the natural neighbor interpolation method is a better choice for the Arctic.

The tide gauge record at Brest, France, along Eastern part of Atlantic coast is one of the longest records in Europe spanning 212 years (1807–2019). Analyzing these records has important ramifications in assessing anthropogenic impact of climate change at local and regional scales during this period. All the previous studies that analyzed Brest’s tide gauge record have used vaguely defined quadratics models and did not incorporate the effect of sea level variations at various frequencies, which confounded the presence or absence of a plausible uniform acceleration. Here, we entertained two competing kinematic models; one with a uniform acceleration representing 212 years of monthly averaged tide gauge data, the other is a two-phase trend model (Phase I is 93 years long and Phase II is 119 years long). Both models include statistically significant (α = 0.05) common periodic effects, and sub and super harmonics of luni-solar origin for representing monthly averaged sea level anomalies observed at Brest. The least squares statistics for both models’ solutions cannot distinguish one model over the other, like earlier studies. However, the assessment of Phase I segment of the records disclosed the absence of a statistically significant trend and a uniform acceleration during this period. This outcome eliminates conclusively the occurrence of a uniform acceleration during the entire 212-year data span of the tide gauge record at Brest, favoring the two-phase trend model as a sound alternative.

This paper is concerned with the study of new turbulent method technique for the determining of vertical refraction when total stations are used. Required measurement accuracy of vertical refraction by conventional methods is extremely difficult due to rapid random changes in the angle of refraction. Geodetic observations are recommended to performing only during periods of indifferent temperature stratification, while the refraction is close to zero and practically unvaried. However, this period is extremely short and its boundaries are not defined, so the inefficiency of all known methods for determining refraction must be attention. The complete liberation of geodetic observations from the influence of turbulent and fluctuation processes in the atmosphere is possible only by directly measuring the angle of refraction at the time of observation. The creation of electronic total stations with automatic guidance to the target allows to successfully solving the problem of determining refraction by a turbulent method. The aim of this work is to study the new method for determining refraction in a turbulent atmosphere. The measurements are performed with a Trimble total station. The obtained results confirm that the accuracy for determining refraction is ~2″, which almost corresponds to the instrumental accuracy of the device used.

In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates.

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.