Vertical land motion and the redistribution of masses within and on the surface of the Earth affect the Earth’s gravity field. Hence, studying the ratio between temporal changes of the surface gravity g˙ and height (h˙) is important in geoscience, e.g., for reduction of gravity observations, assessing satellite gravimetry missions, and tuning vertical land motion models. Sjöberg and Bagherbandi (2020) estimated a combined ratio of g˙/h˙ in Fennoscandia based on relative gravity observations along the 63 degree gravity line running from Vågstranda in Norway to Joensuu in Finland, 688 absolute gravity observations observed at 59 stations over Fennoscandia, monthly gravity data derived from the GRACE satellite mission between January 2003 and August 2016, as well as a land uplift model. The weighted least-squares solution of all these data was g˙/h˙ = − 0.166 ± 0.011 μGal/mm, which corresponds to an upper mantle density of about 3402 ± 95 kg/m3. The present note includes additional GRACE data to June 2017 and GRACE Follow-on data from June 2018 to November 2023. The resulting weighted least-squares solution for all data is g˙/h˙ = − 0.160 ± 0.011 μGal/mm, yielding an upper mantle density of about 3546 ± 71 kg/m3. The outcomes show the importance of satellite gravimetry data in Glacial Isostatic Adjustment (GIA) modeling and other parameters such as land uplift rate. Utilizing a longer time span of GRACE and GRACE Follow-on data allows us to capture fine variations and trends in the gravity-to-height ratio with better precision. This will be useful for constraining and adjusting GIA models and refining gravity observations.

The utilization of remote sensing observations to monitor essential climate variables (ECVs) has become increasingly important in studying their regional and global impacts, as defined by the Global Climate Observing System (GCOS). Understanding the Earth's surface conditions, including soil moisture runoff, snow, temperature, precipitation, water vapour, radiation, groundwater and sea surface height (SSH), can positively impact the environment and ecosystems. Here, the authors present an overview of how global navigation satellite systems (GNSS) can be employed for environmental monitoring, with a particular focus on sea surface height monitoring. This includes examination of the advantages and disadvantages of utilizing a network of permanent GNSS stations for monitoring sea level rise along shorelines.

Airborne mobile mapping systems are crucial in various geodetic applications. A key aspect of these systems is the accurate estimation of exterior orientation parameters (EOPs), which is achieved through the integration of global navigation satellite systems (GNSSs) and inertial measurement unit (IMU) technologies. One critical component in this integration is the lever arm (LA), the vector that connects the GNSS antenna and the IMU center. The uncertainty (standard deviation) in LA measurements can introduce errors in the EOP estimation, thereby affecting the overall system performance. However, how much the EOP estimation is affected by LA measurement uncertainty is examined in this study based on calibration data (test flight) using the TerrainMapper 2 system collected by Lantmäteriet in Sweden. The findings reveal that LA uncertainties have minimal influence on attitude and negligible impacts on position in terms of standard deviation (SD) if the LA is measured with an accuracy of less than 2-3 cm. Additionally, the research explores the combined effects of virtual reference station-rover baseline length and dilution of precision on positioning accuracy and their correlation with LA uncertainty, providing further insights into the complexities of EOP estimation. By advancing GNSS/IMU integration techniques, this study contributes to the enhancement of geodetic technologies customized for airborne mobile mapping applications.

The high-resolution Moho depth model is required in various geophysical studies. However, the available models' resolutions could be improved for this purpose. Large parts of the world still need to be sufficiently covered by seismic data, but existing global Moho models do not fit the present-day requirements for accuracy and resolution. The isostatic models can relatively reproduce a Moho geometry in regions where the crustal structure is in an isostatic equilibrium, but large segments of the tectonic plates are not isostatically compensated, especially along active convergent and divergent tectonic margins. Isostatic models require a relatively good knowledge of the crustal density to correct observed gravity data. To overcome the lack of seismic data and non-uniqueness of gravity inversion, seismic and gravity data should be combined to estimate Moho geometry more accurately. In this study, we investigate the performance of two techniques for combining long- and short-wavelength Moho geometry from seismic and gravity data. Our results demonstrate that both Butterworth and spectral combination techniques can be used to model the Moho geometry. The results show the RMS of Moho depth differences between our model and the reference models are between 1.7 and 4.7 km for the Butterworth filter and between 0.4 and 4.1 km for the spectral combination.

Coastal global navigation satellite system (GNSS) stations equipped with a standard geodetic receiver and antenna enable water level measurement using the GNSS interferometry reflectometry (GNSS-IR) technique. By using GNSS-IR, the vertical distance between the antenna and the reflector surface (e.g., water surface) can be obtained in the vertical (height) reference frame. In this study, the signal-to-noise ratio (SNR) data from four selected stations over three months are used for this purpose. We determined the predominant multipath frequency in SNR data that is obtained using Lomb-Scargle periodogram (LSP) method. The obtained sea surface heights (SSH) are assessed using tide gauge observations regarding accuracy and correlation coefficients. In this study, we investigated daily and hourly GNSS observations and used single frequencies of GPS (L1, L2 and L5), GLONASS (L1 and L2), Galileo (L1, L5, L6, L7 and L8), and BeiDou (L2 and L7) signals to estimate the SSH. The results show that the optimal signals for extracting the SSH are the L1 signal for the GPS, Galileo, and GLONASS systems and the L2 signal for the BeiDou system. The accuracy and correlation parameters for the optimal GPS signal in the daily mode are 2 cm and 0.87, respectively. The same parameters for the optimal GLONASS signal are 4 cm and 0.91. However, the obtained accuracy and correlation coefficients using the best Galileo and BeiDou signals are reduced, i.e., 4 cm and 0.88 using Galileo and 12 cm and 0.52 by employing the Galileo signals, respectively. Our results also show that the GPS L1 signal is more consistent with the tide gauge data. In the following, using the time series derived from the L1 signal and tide gauge readings, the tidal frequencies are extracted and compared using the Least Square Harmonic Estimation (LS-HE) approach. The findings demonstrate that 145 significant tidal frequencies can be extracted using the GNSS-IR time series. The existence of an acceptable correlation between the tidal frequencies of the GNSS-IR and the tide gauge time series indicates the usefulness of the GNSS-IR time series for tide studies. From our results, we can conclude that the GNSS-IR technique can be applied in coastal locations alongside tide gauge measurements for a variety of purposes.

The absence of a reliable Global Navigation Satellite System (GNSS) signal leads to degraded position robustness in standalone receivers. To address this issue, integrating GNSS with inertial measurement units (IMUs) can improve positioning accuracy. This article analyzes the performance of tightly coupled GNSS/IMU integration, specifically the forward Kalman filter and smoothing algorithm, using both single and network GNSS stations and the post-processed kinematic (PPK) method. Additionally, the impact of simulated GNSS signal outage on exterior orientation parameters (EOPs) solutions is investigated. Results demonstrate that the smoothing algorithm enhances positioning uncertainty (RMSE) for north, east, and heading by approximately 17-43% (e.g., it improves north RMSE from 51 mm to a range of 42 mm, representing a 17% improvement). Orientation uncertainty is reduced by about 60% for roll, pitch, and heading. Moreover, the algorithm mitigates the effects of GNSS signal outage, improving position uncertainty by up to 95% and orientation uncertainty by up to 60% using the smoothing algorithm instead of the forward Kalman filter for signal outages up to 180 s.

In classical two-dimensional (2D) geodetic networks, reducing slope distances to horizontal ones is an important task for engineers. These horizontal distances along with horizontal directions are used in 2D geodetic adjustment. The common practice for this reduction is the use of vertical angles to reduce distances using trigonometric rules. However, one faces systematic effects when using vertical angles. These effects are mainly due to refraction, deflection of the vertical (DOV), and the geometric effect of the reference surface (sphere or ellipsoid). To mitigate refraction and DOV effects, one can choose to observe the vertical angles reciprocally if the baseline points' elevation difference is small. This paper quantifies these effects and proposes a proper solution to eliminate the effects in small-scale geodetic networks (where the longest distances are less than 5 km). The goal is to calculate slope distances into horizontal ones appropriately. For this purpose, we used the SWEN17_RH2000 quasigeoid model (in Sweden) to study the impact of the DOV applying different baseline lengths, azimuths, and vertical angles. Finally, we propose an approach to study the impact of the geometric effect on vertical angles. We illustrate that the DOV and the geometric effects on vertical angles measured reciprocally are significant if the height difference of the start point and endpoint in the baseline is large. Geometric correction should be considered for the measured vertical angles to calculate horizontal distances correctly if the network points are not on the same elevation, even if the vertical angles are measured reciprocally.

Determination of the Earth’s gravity field and geopotential value is one of the fundamental topics in physical geodesy. Traditional terrestrial gravity and precise leveling measurements can be used to determine the geopotential values at a local or regional scale. However, recent developments in optical atomic clocks have not only rapidly improved fundamental science but also contributed to applied research. The latest generation of optical clocks is approaching the accuracy level of 10−18 when facilitating atomic clock networks. These systems allow examining fundamental theories and many research applications, such as atomic clocks applications in relativistic geodesy, to precisely determine the Earth’s gravity field parameters (e.g., geopotential values). According to the theory of relativistic geodesy, the frequency difference measured by an optical clock network is related to the gravity potential anomaly, provided that the effects of disturbing signals (i.e., tidal and non-tidal contributions) are filtered out. The relativistic geodesy principle could be used for a practical realization of global geodetic infrastructure, most importantly, a vertical datum unification or realization of height systems. This paper aims to review the background of relativistic (clock-based) geodesy and study the variations of optical atomic clock measurements (e.g., due to hydrology loading and land motion).

In this study, three different procedures: checkpoint RMS of residuals, statistical evaluation of AT results using t-test, and comparison of a photogrammetric digital surface model (DSM) and LiDAR data are used to analyse the effect of IMU and GNSS uncertainties on the final adjusted results. The outcome suggests that the method of block-wise GNSS shift correction is the better method for aerial triangulation and one should use appropriate observable weights in AT. The comparison of checkpoint RMS residuals between the two methods shows that the block-wise solution is on average 6cm more accurate than the strip-wise solution. 

GNSS/INS applications are being developed, especially for direct georeferencing in airborne photogrammetry. Achieving accurately georeferenced products from the integration of GNSS and INS requires removing systematic errors in the mobile mapping systems. The INS sensor's uncertainty is decreasing; therefore, the influence of the deflection of verticals (DOV, the angle between the plumb line and normal to the ellipsoid) should be considered in the direct georeferencing. Otherwise, an error is imposed for calculating the exterior orientation parameters of the aerial images and aerial laser scanning. This study determines the DOV using the EGM2008 model and gravity data in Sweden. The impact of the DOVs on horizontal and vertical coordinates, considering different flight altitudes and camera field of view, is assessed. The results confirm that the calculated DOV components using the EGM2008 model are sufficiently accurate for aerial mapping system purposes except for mountainous areas because the topographic signal is not modelled correctly.