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According to General Relativity Theory (GRT), by comparing the frequencies between two precise clocks at two different stations, the gravity potential (geopotential) difference between the two stations can be determined due to the gravity frequency shift effect. Here, we conduct a clock-transportation experiment for measuring geopotential differences based on frequency comparisons via satellite links between two remote hydrogen atomic clocks. Based on the net frequency shift between the two clocks in two different periods, the geopotential difference between stations of the Beijing 203 Institute Laboratory (BIL) and Luojiashan Time-frequency Station (LTS) is determined. Comparisons show that the experimental result deviated from the reference of Earth gravity model EGM2008 result by (38.5[Formula: see text]45.9) m in Orthometric Height (OH). The results are consistent with the frequency stabilities of the hydrogen clocks (at the level of [Formula: see text]) used in the experiment. With the rapid development of time and frequency science and technology, the approach discussed in this study for measuring the geopotential is prospective and thus, could have broad applications.

Orthometric height datum systems are critical in the geodetic community. Nonetheless, individual nations or local regions maintain their distinct height systems. These systems, primarily determined by conventional spirit leveling, exhibit inhomogeneity, as the mean sea level does not represent an equi-geopotential surface. As such, accurately unifying global height systems is a persistent challenge. The gravity frequency shift equation provides a promising approach to this issue, offering a means to unify global height systems by comparing the frequencies of two distant clocks via optical fibers. In this study, we develop a model based on the Optical Fiber Frequency Transfer (OFFT) method, recognized for its unparalleled precision. We simulated a network of optical clocks interconnected by optical fibers to unify the height system across Southeast Asia. Our study suggests that the optical fiber clock network can realize height propagation between any two height datums at the centimeter level, providing a favorable opportunity for achieving regional height system unification.

Abstract In this paper, the surface texture parameters and distribution patterns are studied by numerical simulation and experiment. First, a three-dimensional micro-textured CFD fluid lubrication model with cavitation effect is established, and different texture arrays are designed to study the influence of different distribution modes on bearing capacity, friction coefficient and pressure distribution of the oil film. Then, the simulation results are further analyzed and verified by the visualized plane slider experimental platform, and the formation rules of cavitation bubbles in the micro-textured array, as well as the influences of the surface shape and different distribution modes of the micro-textured array on the cavitation bubbles are discussed. The results show that the existence of cavitation is one of the main reasons for the microtexture to increase the bearing capacity of the oil film, which cannot be ignored in the simulation study. The texture array with single symmetric orientation is the best to improve the oil film bearing capacity, and the bearing performance is the best when the texture inclination angle is 26.6°.The friction coefficient of the asymmetrically oriented textured array is 29.4% lower than that of the non-textured sample.The results in the experiment are consistent with the simulation.

The development of remote frequency transfer techniques, especially the appearance of optical clocks with unprecedented stability, has prompted geoscientists to study their applications in geodesy. Using remote frequency transfer technique, by frequency comparison of two optical clocks at two points P and Q connected by optical fibers, one can measure the signal's frequency shift between them, and the geopotential difference between them can be determined based on the gravity frequency shift equation. Given the orthometric height of P, the orthometric height of Q can be determined. Since the present stability of the optical clock has achieved 1 × 10−18 or better and comparing the frequency transfer via optical fiber provides stability at 10−19 level, the optical clock network enables determining the orthometric height at centimeter-level. This study provides a formulation to determine the height difference at one-centimeter level between two points on the ground based on the optical fiber frequency transfer technique.

The time window from stroke onset is critical for the treatment decision. However, in unknown onset stroke, it is often difficult to determine the exact onset time because of the lack of assessment methods, which can result in controversial and random treatment decisions. Previous studies have shown that serum biomarkers, in addition to imaging assessment, are useful for determining the stroke onset time. However, as yet there are no specific biomarkers or corresponding methodologies that are accurate and effective for determining the onset time of unknown onset stroke. Herein, we describe our novel advanced metabolites-based machine learning method (termed extreme gradient boost [XGBoost]) combined with recursive feature elimination, which accurately screened five metabolites from 1124 metabolites detected in serum. These metabolites were capable of both detecting acute ischemic stroke and backtracking the acute ischemic stroke onset time. To further investigate the pathological mechanisms of acute ischemic stroke, we also examined characteristic metabolites in different brain regions, and found two metabolites that could distinguish the core infarct area from the ischemic penumbra. Although this study is based on animal experiments, our machine learning framework and selected metabolites may provide a basis for clinical stroke evaluation and treatment.

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.

Abstract Over the decades, testing gravitational red-shift (GRS) based on microwave links has made great process, including the GPA experiment, the planned Atomic Clock Ensemble in Space mission, and the China Space Station (CSS). Until now, the formulations of microwave links are almost all based on the time comparison. However, there are advantages of using frequency comparison instead of time comparison to test GRS. Here we develop a tri-frequency combination method based on the measurements of the frequency shifts of three independent microwave links between a space station and a ground station. Aiming at the frequency links’ accuracy of $$3\times 10^{-16}$$ 3 × 10 - 16 , we should consider various effects, including the Doppler effect, second-order Doppler effect, atmospheric frequency shift, tidal effects, refraction caused by the atmosphere, and Shapiro effect, with accuracy levels of tens of centimeters. The CSS will complete construction in 2022, and the formulation proposed in this study will enable us to test GRS at an accuracy level of at least $$2\times 10^{-6}$$ 2 × 10 - 6 , which is one order higher than the present accuracy level of $$7\times 10^{-5}$$ 7 × 10 - 5 .

General relativity theory (GRT) concludes that a precise clock ticks at different running rates if it is under the influence of different geopotentials. Therefore, by comparing the running rates of clocks at arbitrary two stations, the geopotential difference between them can be determined. In this study, with the help of two hydrogen atomic clocks (noted as H-masers), using the two-way satellite time and frequency transfer (TWSTFT) technique, we carried out experiments of the geopotential difference determination at the China Aerospace Science & Industry Corporation (CASIC), Beijing. Here the ensemble empirical mode decomposition (EEMD) method is adopted to remove periodic signals included in the original observations. Finally, the clock-comparison-determined geopotential difference in the experiments is determined. Results show that the difference between the geopotential difference determined by GRT and that determined by measuring tape is about 1316.1 ± 931.0 m2s-2, which is equivalent to 134.3 ± 95.0 m in height, and in consistence with the stability of the H-masers applied in the experiments (at the level of 10−15/day). With the rapid improvement of atomic clocks' accuracy, the geopotential determination by accurate clocks is prospective, and it is promising to realize the unification of the world vertical height system (WVHS).

Based on the general relativity theory, the geopotential difference can be determined by comparing the change in time difference between precise clocks using the precise point positioning (PPP) time transfer technique, referred to as the relativistic PPP time comparison approach. We focused on high-precision time comparison between two high-performance clocks for determining the geopotential difference using this approach, and conducted the simulation experiments to validate this approach. In the experiment, we consider three cases for evaluating the performance of this approach with different types of atomic clocks, namely, the fractional frequency stabilities of the clocks equipped at three selected ground stations (BRUX, OPMT, and PTBB) are $4.0 \times 10^{-13} / \sqrt {\tau }$ (Case 1), $2.3 \times 10^{-14} / \sqrt {\tau }$ (Case 2), and $2.8 \times 10^{-15} / \sqrt {\tau }$ (Case 3) at averaging time ${\tau }$ , respectively, and the accuracy of these clock have been evaluated to be $5.3 \times 10^{-16}$ , $7.8 \times 10^{-17}$ , and $8.6 \times 10^{-18}$ . Two main conclusions can be drawn from the experimental results. First, high-performance clocks can significantly improve the precision for GNSS PPP time transfer. Compared to Case 1, the long-term stabilities of the time link OPMT-BRUX as well as PTBB-BRUX are improved in Cases 2 and 3. Second, the geopotential difference between any two stations can be determined at the decimeter level, and the accuracy of geopotential difference is consistent with the stabilities of the time links in Cases 1-3. In Case 3, the determined geopotential differences between OPMT and BRUX deviate from the EIGEN-6C4 model values by -0.64, m2/2 with an uncertainty of 1.11 m2/s2, whereas the deviation error between PTBB and BRUX is 0.76 m2/s2 with an uncertainty of 1.79 m2/s2. The results of this study suggest that a one decimeter-level geopotential difference between two arbitrary stations can be determined based on this approach.

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.

According to Einstein’s general relativity theory, a precise (atomic) clock runs faster at a position with higher gravitational potential than a clock at a position with lower potential. Here, we provide a direct clock comparison using a fixed hydrogen clock and a portable hydrogen clock for geopotential determination based on the two-way satellite time and frequency transfer (TWSTFT) technique. After synchronizing the two hydrogen clocks at positions at the same height, the clocks were compared for a height difference of 22 m over a period of 14 days using the TWSTFT technique. Interpretation of the observed time elapse implies a height difference of 175 m +/- 59 m, which matches the frequency stability of our instruments. This study and relevant experiments provide a way of determining the geopotential using ultra-high precise clocks based on the TWSTFT technique in the near future.

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 long distance and tight construction period of the earth pressure balance shield tunneling in Beijing sandy cobble ground have a very positive impact on grasping the construction progress and improving the organization efficiency. Based on the real-time monitoring data of on-site earth pressure, cutter head speed, total thrust, screw conveyor speed, and cutter head torque, this study investigated the correlation between the shield advancement rate and the above parameters based on multiple nonlinear regression analysis method, which lay down the foundation of shield advancement rate prediction. The prediction model achieved satisfactory results and was further applied to an airport project. The results show that it is of guiding significance to use multiple regression method to establish shield prediction model and put forward the best advancement parameters to ensure the construction progress. The order in which the four operational parameters affect the advancement rate is total thrust, cutter head torque, screw conveyor speed, and cutter head speed. When the advancement time is greater than 57 min, the average advancement rate and daily progress are highly positively correlated. The research provides a reliable basis for the advancement rate prediction, safety control, and parameter optimization of shield advancement in similar ground.

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.

In previous studies, the northern hemisphere of the Earth is considered to be in compression while the southern one is in expansion. In this study, based on three different methods, we calculate average vertical variations of the two hemispheres from velocity field data under the ITRF2008 (International Terrestrial Reference Frame 2008) solution. Results show that the northern hemisphere is in expansion at the rate about 1 mm/yr, while the compression rate of the southern hemisphere is one order smaller than the expansion rate of the northern one. After the post glacial rebound effect is subtracted, results show that the expansion and compression rates of the northern and southern hemispheres are 0.46 mm/yr and –0.19 mm/yr, respectively. Transformation between the velocity fields under ITRF2008 and ITRF2000 can explain why different authors have different conclusions about the expan­sion/compression pattern of one hemisphere or the other. Anyway, the entire Earth is expanding at a rate about 0.2 mm/yr, and this estimation coincides with results of our previous studies. The mean variation rates of the radii at different latitudes have been calculated.

According to the general theory of relativity, two clocks placed at two different positions with different geopotentials run at different rates. Thus one can determine the geopotential difference between these two points by comparing the running rates of the two clocks. Using the most precise optic-atomic clocks whose stability achieves 10−18 level and the time transfer technique with comparison accuracy higher than 10ps level by 100 m coaxial cable, the relativistic geodesy method for determining the geopotential may be realizable in the near future. In this paper, we propose, design and describe in detail an approach for determining the geopotential difference between two points based upon a simulation experiment. We select two stations A and B whose ground distance is within 100 m, height difference being about 30 m. Each station is equipped with an atomic clock whose instability is 3.2×10−16/τ (where τ is time in second). And the two stations are connected with a coaxial cable for time transfer. Our simulation experiment results show that the accuracy could reach 0.16 m2/s2 (equivalent to 1.6 cm in height) level after a four-hour period of observation.

According to the space-geodetic data recorded at globally distributed stations over solid land spanning a period of more than 20-years under the International Terrestrial Reference Frame 2008, our previous estimate of the average-weighted vertical variation of the Earth's solid surface suggests that the Earth's solid part is expanding at a rate of 0.24 ± 0.05 mm/a in recent two decades. In another aspect, the satellite altimetry observations spanning recent two decades demonstrate the sea level rise (SLR) rate 3.2 ± 0.4 mm/a, of which 1.8 ± 0.5 mm/a is contributed by the ice melting over land. This study shows that the oceanic thermal expansion is 1.0 ± 0.1 mm/a due to the temperature increase in recent half century, which coincides with the estimate provided by previous authors. The SLR observation by altimetry is not balanced by the ice melting and thermal expansion, which is an open problem before this study. However, in this study we infer that the oceanic part of the Earth is expanding at a rate about 0.4 mm/a. Combining the expansion rates of land part and oceanic part, we conclude that the Earth is expanding at a rate of 0.35 ± 0.47 mm/a in recent two decades. If the Earth expands at this rate, then the altimetry-observed SLR can be well explained. Keywords: ITRF2008 coordinates, Ice melting, Thermal expansion, Earth expansion, Sea level rise (SLR), Space-geodetic data, Velocities altimetry, Earth's solid surface

Reliable prediction of traffic accidents is crucial for the identification of potential hazards in advance, formulation of effective preventative measures, and reduction of accident incidence. Existing neural network-based models generally suffer from a limited field of perception and poor long-term dependency capturing abilities, which severely restrict their performance. To address the inherent shortcomings of current traffic prediction models, we propose the Traffic Transformer for multidimensional, multi-step traffic accident prediction. Initially, raw datasets chronicling sporadic traffic accidents are transformed into multivariate, regularly sampled sequences that are amenable to sequential modeling through a temporal discretization process. Subsequently, Traffic Transformer captures and learns the hidden relationships between any elements of the input sequence, constructing accurate prediction for multiple forthcoming intervals of traffic accidents. Our proposed Traffic Transformer employs the sophisticated multi-head attention mechanism in lieu of the widely used recurrent architecture. This significant shift enhances the model's ability to capture long-range dependencies within time series data. Moreover, it facilitates a more flexible and comprehensive learning of diverse hidden patterns within the sequences. It also offers the versatility of convenient extension and transference to other diverse time series forecasting tasks, demonstrating robust potential for further development in this field. Extensive comparative experiments conducted on a real-world dataset from Qatar demonstrate that our proposed Traffic Transformer model significantly outperforms existing mainstream time series forecasting models across all evaluation metrics and forecast horizons. Notably, its Mean Absolute Percentage Error reaches a minimal value of only 4.43%, which is substantially lower than the error rates observed in other models. This remarkable performance underscores the Traffic Transformer's state-of-the-art level of in predictive accuracy.