A levelling network was readjusted and a new geoid model compiled within the framework of geodetic vertical datum modernization at the Hong Kong territories. To accomplish all project objectives, the quasigeoid model has to be determinedtoo. A quasigeoid model can be obtained from existing geoid model by applying the geoid-to-quasigeoid separation. Thegeoid-to-quasigeoid separation was traditionally computed as a function of the simple planar Bouguer gravity anomaly, whiledisregarding terrain geometry, topographic density variations, and vertical gravity changes due to mass density heterogeneities below the geoid surface. We applied this approximate method because orthometric heights of levelling benchmarksin Hong Kong were determined only approximately according to Helmert’s theory of orthometric heights. Considering afurther improvement of the accuracy of orthometric heights by applying advanced numerical procedures, we determinedthe geoid-to-quasigeoid separation by applying an accurate method. The comparison of the accurately and approximatelycomputed values of the geoid-to-quasigeoid separation revealed signifcant diferences between them. The approximatevalues are all negative and reach -2.8 cm, whereas values from the accurate method vary between -4.1 and+0.2 cm. In addition, we assessed the efect of anomalous topographic density on the geoid-to-quasigeoid separation by employing a newlydeveloped digital rock density model. According to our estimates the efect of anomalous topographic density reaches amaximum value of 1.6 cm, refecting a predominant presence of light volcanic rocks and sedimentary deposits at the HongKong territories. Our numerical fndings indicate that the conversion between geoid and quasigeoid models should be doneaccurately, even in regions with a moderately elevated topography

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.

Human-made infrastructure, such as dams, bridges, tunnels, and high towers, requires highly precise geodetic control networks and continuous monitoring to detect potential failure risks and plan civil engineering maintenance works. In classical 2D geodetic networks, reducing slope distances to horizontal ones is an important task for engineers. The common practice for this reduction involves using vertical angles and applying trigonometric rules. However, using vertical angles introduces systematic errors, primarily due to air refraction, deflections of the vertical (DOV), and the geometric effects of the reference surface, whether it is a sphere or an ellipsoid. Therefore, employing vertical angles in establishing geodetic control networks in 2D is challenging due to these systematic errors. To mitigate the refraction and DOV effects, reciprocal observations of vertical angles can be considered, especially if the elevation differences are small. In this study, we quantify these effects and propose an innovative solution to eliminate these systematic errors in small-scale geodetic networks. Specifically, we propose a new technique that does not rely on vertical angles for the reduction of distances, which is called the network-aided method. Thus, the geometric, physical, and refraction effects cancel out in this method. The results of this study hold significant importance for surveying guidelines. The main advantage of the proposed method is less fieldwork and, hence cost reduction since there is no need for different OFF-construction (reference) and ON-construction (monitoring) networks. Consequently, the number of network points will be less than in traditional networks. There is no need for reciprocal observations since vertical angles are not utilized, while the precision remains equal or even superior (in terms of quality factors i.e., higher redundancy numbers and smaller error ellipses).

Most human-made infrastructures require regular deformation monitoring to detect failure risks and plan maintenance works. Continuous health monitoring is crucial for assessing infrastructure stability and plays a key role in mitigating damages and disasters within various environmental and engineering contexts. Structural deformation monitoring methods can be divided into two methods: geodetic and non-geodetic. Geodetic techniques enable the detection of displacements with respect to an external geodetic reference system, while non-geodetic methods can detect relative, internal changes within the monitored object. Both methods will be covered in this lecture note. In addition, after presenting the theoretical background and principle of the least-squares approach in Chapter 1, the necessary recommendations and guidelines for deformation monitoring using geodetic and non-geodetic methods will be provided.

The aim of this lecture note is to provide a theoretical background in the field of deformation monitoring, specifically using geodetic methods, for engineers, students, and researchers. One of the motivations behind this effort is the lack of references that adequately present the methods and recommendations for this purpose.

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 better 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.