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We introduce an approach for the direct measurement of the gravitational potential (GP) along the trajectory of a satellite, with a specific focus on Low-Earth Orbit (LEO) satellites. A LEO satellite communicates with several Geosynchronous Equatorial Orbit (GEO) satellites via frequency signal links. The GP difference can be measured in real-time using the gravitational frequency shift approach by equipping both LEO and GEO satellites with precise atomic clocks. Since the GP at the high orbits of the GEO satellites can be precisely determined by the present gravitational field model EGM2008, the GP along the LEO satellite’s trajectory can be determined. In this study, simulation experiments were conducted, featuring a GRACE-type satellite as the LEO satellite in communication with three equidistant GEO satellites. The results indicated that the accuracy of the GP measurements along the LEO satellite’s trajectory primarily depends on the precision of the onboard atomic clocks. Supposing optical atomic clocks attain an instability level of 1×10−17τ−1/2 (τ in seconds), we determined the GP distribution covered by the LEO satellite’s trajectories with 30-day observations. Then, we determined a gravitational field at the centimeter level based on the GP distribution. The GP data derived from the trajectory of a LEO satellite can be utilized to establish temporal gravitational fields, which have broad applications in different disciplines.

The International Association of Geodesy (IAG) aims to establish the International Height Reference System (IHRS) as one of its primary scientific objectives. Central to the realization of the IHRS is global vertical datum unification, which requires the connection of existing local vertical height reference systems (VHS) robustly and consistently. However, conventional methods are not suitable for estimating the offsets between two distant local height systems. In this paper, we propose a framework for connecting two local VHSs using ultraprecise clock frequency signal links between satellites and ground stations, referred to as the satellite frequency signal transmission (SFST) approach. The SFST approach allows for the direct determination of the geopotential and height differences between two ground datum stations without any location restrictions between the two VHSs. The simulation results show that the VHSs of China and the US can be unified with an accuracy of several centimeters, provided that the stability of atomic clocks used on-board the satellite and at on-ground datum locations reaches 4.8×10−17τ−1/2 for an averaging time τ (in seconds). We conclude that the SFST approach shows promise for achieving centimeter-level accuracy in unifying the global vertical height datum and represents a new paradigm for the realization of the IHRS.

Applications of optical clocks in physical geodesy for determining geopotential are of increasing interest to scientists as the accuracy of optical clocks improves and the clock size becomes more and more compact. In this study, we propose a data processing method using the ensemble empirical mode decomposition technique to determine the geopotential difference between two sites in Wuhan based on the frequency comparison of two optical clocks. We use the frequency comparison record data of two Ca+ optical clocks based on the optical fiber frequency transfer method, provided by the Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences (Wuhan, China). By optical clock comparisons we obtained a geopotential difference of 42.50 ± 1.03 m2∙s−2 (equivalent to height difference of 4.33 ± 0.11 m) between the two sites, which is excellent compared to the geopotential difference of 42.56 ± 0.29 m2∙s−2 (equivalent to height difference of 4.34 ± 0.03 m) measured by a spirit leveling. The results show that the optical fiber frequency transfer method is promising in determining the geopotential and potential for unifying the world height system.

NeQuick2 is a three-dimensional ionospheric electron density empirical model that uses numerical integration to calculate the total electron content along any line-of-sight (LOS). As one of the most commonly used three-dimensional ionospheric models, it is necessary to objectively evaluate the accuracy and stability of NeQuick2 over a long period, especially over the mid-latitudes of the northern hemisphere where most of the ground-based GNSS stations are distributed. Therefore, different methods are used in this study to evaluate the accuracy of the NeQuick2 model from 2008 to 2021, including comparison with the International Global Navigation Satellite System Global Ionosphere Maps (IGSG), Jason2 Vertical Electron content (VTEC), and self-consistent evaluation. The comparison with IGSG shows that the standard deviation (STD) value is about 2.59 TECU. The accuracy of the IGSG and NeQuick2 model over ocean regions shows that the bias of IGSG is more significant than that of the NeQuick2 model. The mean STD value is 2.09 TECU for IGSG, and the corresponding value is 3.18 TECU for the NeQuick2 model, which is about 50% worse than IGSG. The dSTEC assessment results indicate that the variation in bias for IGSG is more stable than that of the NeQuick2 model. The mean STD value is 0.86 and 1.52 TECU for IGSG and NeQuick2 model, respectively. The conclusion could be made that NeQuick2 model represents the average ionosphere electron content and its accuracy fluctuates with solar conditions. Compared with the IGSG, the NeQuick2 model always underestimates TEC value, especially in low solar activity periods and compared with Jason2, the TEC values obtained by NeQuick2 model are overestimated, but the degree of overestimation is smaller than that of IGSG.

The continuing impact between the Eurasia Plate and India results in the thickening and shortening of the N-S Tibetan Plateau. There has been strong tectonic movement along the boundary of the zones of deformation of the NE corner of the Tibetan plateau (NET) since the new tectonic period, with its dynamic mechanisms remaining controversial. Here, we use observations of 39 Continuous Global Positioning System (CGPS) gauges and 451 Crustal Movement Observation Network of China (CMONOC) campaign-mode stations to detect the three-dimensional deformation of the crust in the NET. Improved processing procedures are implemented to strengthen the patterns of strain throughout the NET. The principal component analysis (PCA) technique is introduced to decompose the time series into spatial eigenvectors and principal components (PCs), and the first three PCs are used to estimate and rectify common mode errors (CMEs). In addition, GRACE observations are used to detect deformation changes that account for non-tidal oceanic mass loading, hydrological loading, and surface pressure. The rectified deformation of the crust indicates the anisotropic nature of both the subsidence and uplift, and that the highest uplift rate of the Longmen Shan fault uplift reaches 7.13 ± 0.53 mm/yr. Finally, the horizontal velocity is further used to enumerate the strain rates throughout the NET. The results show that the shear band retained property in line with the strike-slip fault along the Altyn Tagh fault, the Qilian Shan faults, the Haiyuan fault, the West Qinling fault, the East Kunlun fault, and the Longmen Shan fault. In addition, the results further indicate that the whole NET shows a strong relationship with the mean principal rates of horizontal shortening strain. Extension and compression of the crust reasonably describe its sinking and uplifting.

The conversion factor is a key parameter for converting zenith wet delays (ZWD) into precipitable water vapour (PWV) with a mean value of 0.15, and the traditional method of calculating it is to model the weighted average temperature in the process of conversion factor calculation. Here, we overcome the dependence on high-precision atmospheric weighted average temperature for mapping ZWD onto PWV and build a global non-meteorological parametric model for conversion factor GΠ model by using the gridded data of global conversion factor time series from 2006 to 2013 provided by the Global Geodetic Observing System (GGOS) Atmosphere. Internal and external accuracy tests were performed using data from four times (UTC 00:00, 06:00, 12:00, and 18:00) per day throughout 2012 and 2014 as provided by the GGOS Atmosphere, and the statistical average root-mean-square (RMS) and mean absolute errors (MAE) on a global scale are 0.0031/0.0026 and 0.0030/0.0026, respectively, which only account for 1.5–2% of the conversion factor value. In addition, the observed GPS data are also used to validate the established GΠ model, and the RMS of the PWV differences between the established model and the observed meteorological data was less than 3.2 mm. The results show that the established GΠ model has a high accuracy, which can be used to calculate the PWV value where no observed meteorological parameters are available.

According to general relativity theory (GRT), the clock at a position with lower geopotential ticks slower than an identical one at a position with higher geopotential. Here, we provide a geopotential comparison using a non-transportable hydrogen clock and a transportable hydrogen clock for altitude transmission based on the two-way satellite time and frequency transfer (TWSTFT) technique. First, we set one hydrogen clock on the fifth floor and another hydrogen clock on the ground floor, with their height difference of 22.8 m measured by tape, and compared the time difference between these two clocks by TWSTFT for 13 days. Then, we set both clocks on the ground floor and compared the time difference between the two clocks for seven days for zero-baseline calibration (synchronization). Based on the measured time difference between the two clocks at different floors, we obtained the height difference 28.0 ± 5.4 m, which coincides well with the tape-measured result. This experiment provides a method of height propagation using precise clocks based on the TWSTFT technique.

Potential evapotranspiration (PET) can reflect the characteristics of drought change in different time scales and is the key parameter for calculating the standardized precipitation evapotranspiration index (SPEI). The Thornthwaite (TH) and Penman–Monteith (PM) models are generally used to calculate PET, but the precision of PET derived from the TH model is poor, and a large number of meteorological parameters are required to evaluate the PM model. To obtain high-precision PET with fewer meteorological parameters, a high-precision PET (HPET) model is proposed to calculate PET by introducing precipitable water vapor (PWV) from Global Navigation Satellite System (GNSS) observation. The PET difference (DPET) between TH- and PM-derived PET was calculated first. Then, the relationship between the DPET and GNSS-derived PWV/temperature was analysed, and a piecewise linear regression model was calculated to fit the DPET. Finally, the HPET model was established by adding the fitted DPET to the initial PET derived from the TH model. The Loess Plateau (LP) was selected as the experiment area, and the statistical results show the satisfactory performance of the proposed HPET model. The averaged root mean square (RMS) of the HPET model over the whole LP area is 8.00 mm, whereas the values for the TH and revised TH (RTH) models are 34.25 and 12.55 mm, respectively, when the PM-derived PET is regarded as the reference. Compared with the TH and RTH models, the average improvement rates of the HPET model over the whole LP area are 77.5 and 40.5%, respectively. In addition, the HPET-derived SPEI is better than that of the TH and RTH models at different month scales, with average improvement rates of 49.8 and 23.1%, respectively, over the whole LP area. Such results show the superiority of the proposed HPET model to the existing PET models.