Laboratory demonstration of geopotential measurement using transportable optical clocks

We report an experimental demonstration of geopotential difference measurement using a pair of transportable ^(40)Ca^(+) optical clocks(TOC-729-1 and TOC-729-3)in the laboratory,each of them has an uncertainty of 1.3×10^(−17) and an instability of 4.8×10^(−15)/√τ.Referenced to a stationary clock of TOC-729-1,the geopotential difference measurements are realized by moving TOC-729-3 to three different locations and the relevant altitude differences are measured with uncertainties at the level of 20 cm.After correcting the systematic shifts(including gravitational red shift),the two-clock frequency difference is measured to be–0.7(2.2)×10^(−17),considering both the statistic(1.0×10^(−17))and the systematic(1.9×10^(−17))uncertainties.The frequency difference between these two clocks is within their respective uncertainties,verifying the reliability of transportable ^(40)Ca^(+) optical clocks at the low level of 10^(−17).

Determination of Geopotential of Local Vertical Datum Surface

This paper first develops the approaches to determine the geopotential of the local mean sea level,and then investigates the offset of the 1985 vertical datum surface defined by the mean sea level of Yellow Sea at the Dagang Tide Gauge in Qingdao city using the developed approaches and GPS/leveling data.It shows that the geopotential of the local mean sea level at the tide gauge is equal to 62 636 853.5±0.2 m2·s -2 and that the 1985 vertical datum surface is 24.6±5.4 cm above the geoid realized by the geopotential W 0= 62 636 856.0±0.5 m2·s -2.

Determination of the geopotential and orthometric height based on frequency shift equation

The orthometric height (OH) system plays a key role in geodesy, and it has broad applications in various fields and activities. Based on general relativity theory (GRT), on an arbitrary equi-geo- potential surface, there does not exist the gravity frequency shift of an electromagnetic wave signal. However, between arbitrary two different equi-geopotential surfaces, there exists the gra- vity frequency shift of the signal. The relationship between the geopotential difference and the gravity frequency shift between arbitrary two points P and Q is referred to as the gravity frequency shift equation. Based on this equation, one can determine the geopotential difference as well as the OH difference between two separated points P and Q either by using electromagnetic wave signals propagated between P and Q, or by using the Global Positioning System (GPS) satellite signals received simultaneously by receivers at P and Q. Suppose an emitter at P emits a signal with frequency f towards a receiver at Q, and the received frequency of the signal at Q is , or suppose an emitter on board a flying GPS satellite emits signals with frequency f towards two receivers at P and Q on ground, and the received frequencies of the signals at P and Q are and , respectively, then, the geopoten-tial dif- ference between these two points can be determined based on the geopotential frequen- cy shift equation, using either the gravity frequency shift ? f or ? , and the corresponding OH difference is further determined based on the Bruns’ formula. Besides, using this approach a unified world height datum system might be realized, because P and Q could be chosen quite arbitrarily, e.g., they are located on two separated continents or islands.

A preliminary experiment of determining the geopotential difference using two hydrogen atomic clocks and TWSTFT technique

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 of10-15/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).

Geopotential difference determination using optic-atomic clocks via coaxial cable time transfer technique and a synthetic test

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 is 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 τis 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 fourhour period of observation.

THE CCA BETWEEN 500 hPa GEOPOTENTIAL HEIGHT FIELDS OVER NORTHERN HEMISPHERE AND RAINFALL OF CHINA IN MAY

Based on the theory of Canonical Correlation Analysis (CCA), the correlation between 500 hPa geopotential height (H) fields over the Northern Hemisphere (NH) and a 15-region rainfall (R) field of China in May is studied. The results indicate that: (1) there is a strong relationship between the H fields in January / May and the R field in China, (2) the variation of the general circulation over the whole NH (especially the 500 hPa H field over Europe and Asia) can affect the R in China, (3) in January and February the atmospheric general circulation can affect the R mainly by means of planetary waves, while in April and May the main control mechanism can be due to some teleconnections, and (4) the characteristic vectors for R in May and H from January to May have wave train structure, alternating sign from south to north.

Recent Study of Anomaly of Global Annual Geopotential Height and Global Warming

This paper studies the anomaly of global annual 500 hpa geopotential anomaly and global warming through the period (1950-2011). Anomaly method, linear trend and linear correlation coefficient techniques are referred to identify and describe the correlation between anomaly of global geopotential height field and global surface air temperature, North Atlantic Oscillation (NAO), Southern Oscillation Index (SOI), El-Nino3.4. The results revealed that, the anomaly of global annual geopotential height is completely controlled by global warming and NAO, SOI, El-Nino3.4 during the study period. However, the trend of the global surface air temperature anomaly completely coincides with the trend of 500 hpa geopotential height anomaly. This result uncovers the exist of abnormal weather phenomena through the last decades.

Evaluation of the geopotential value W_0^(LVD) of China

Estimation of the zero-height geopotential value W_0^（LVD） for the CVD（China Vertical Datum） plays a fundamental role in the connection of traditional height reference systems into a global height system.Estimation the W_0^（LVD） of China is based on the computation of the mean geopotential offset between the value W_0= 62636856.0 m^2 s^（-2）, selected as reference in this study, and the unknown geopotential value W_0^（LVD）. This estimation is based on the combination of ellipsoidal heights, levelled heights（referring to the CVD）, and some physical parameters, such as geopotential values, gravity values, and geoid undulations.The geoid undulations derived from the GGM（Global Geopotential Models）. This combination is performed through three approaches： The first one is based on the theory of Molodensky, and the second one compares levelled heights and geopotential values derived from the GGMs, while the third one analyses the differences between GPS/Levelling and GGMs geoid undulations. The approaches are evaluated at 65 benchmarks（BMs） covered around Qingdao where the tide gauge is used to observe the local mean sea level of China. The results from three approaches are very similar. Furthermore, the W_0^（LVD）determined for the China local vertical datum was 62636852.9462 m^2 s^（-2）, indicates a bias of about3.0538 m^2/s^（-2） compared to the conventional value of 62636856.0 m^2 s^（-2）.

THE MECHANISM OF THICKNESS OF GEOPOTENTIAL HEIGHT DIPOLE AND ITS RELATION WITH CLIMATE VARIABILITY IN ASIA-AUSTRALIA IN BOREAL WINTER

With the EOF of reanalysis data being analyzed, a northern-southern dipole is found in the upper troposphere geopotential height field of over the Asian-Australian monsoon region in the winter of the Northern Hemisphere(NH),which is defined as Asian-Australian dipole(AAD) in this study. Its intensity index is defined as AADI. Correlation and synthetic analysis illustrate that AADI is closely related to the weather and climate of Asian-Australian region in boreal winter. The index can reflect the simultaneous anomalies of temperature and precipitation on interannual and decadal scales in the boreal winter of Asian-Australian region. The superposition of the decadal and interannual signals is significant for the relationship between the AADI and climate change. The index can be used as an indicator of intensity of the Asian-Australian monsoon. In the years of strong AADI, the East Asia major deep trough is stronger,the Subtropical High is weaker and the Alaska ridge and the westerly jet are stronger than those in normal years.Enhanced meridional circulation between high and low latitudes exists in the years of strong AADI. These relationships reflect the intrinsic link between the anomalies in the upper troposphere geopotential height and climate in the Asian-Australian region.

ON THE KEY REGIONS OF 500 hPa GEOPOTENTIAL HEIGHTS OVER NORTHERN HEMISPHERE IN WINTER

Variance analysis, correlation analysis and regression analysis methods are applied to analyze the variation of circulation at 500 hPa. In winter, there are three regions (180°E – 150°W, 45°N – 60°N, 70°W – 100 °W,45°N – 75°N, 60°E – 100°E, 65°N – 80°N) whose variations are strong. Those regions are the key regions in which atmospheric circulation can change. Those regions are correlated to some teleconnections and can present a part of variations of 500 hPa to some degree. The linear contemporary correlation between those regions and the height at 500 hPa is significant. Those regions can account for 88 % of variations of concurrent height at 500 hPa. Those regions can present and forecast some variations to some degree in March and April. The longer the time interval, the worse the forecast effect will be. The interannual variations of Q1, Q2 and the SST are weak in the western Pacific.

THE CHARACTERISTICS OF 500 hPa GEOPOTENTIAL AND SST FIELD OF EXTREMELY SEVERE COLD MONTHS IN SOUTH CHINA WINTER

The region of south China is sometimes subject to major climatic catastrophes in winter. To have a clear understanding, the time in which extremely severe cold months occur in the south China wintertime over the past 45 years are determined and characteristics of the 500-hPa geopotential fields and SST fields are studied for the simultaneous and preceding 6-month periods. Similarity exists in the 500-hPa geopotential fields between each current severely cold month, with the geopotential pattern of being high in the north, but low in the south, of Asian-Pacific region and meridional circulation developing. The work presents anomalies of the months with significant differences in the 500-hPa geopotential field of the previous periods. The SSTA is continuous in the distribution from each extremely severe cold winter month back to the 6 months leading up to it for the region of south China while the SST pattern is of El Ni?o in January and the preceding 1 ~ 6 months for equatorial eastern Pacific but of La Ni?a in February and December. It is concluded that the prediction of severely cold winter months are possible with the use of the geopotential field at 500 hPa and the SST fields for the months ahead of the target time.

On the Couplings between Chebyshev Coefficients as Derived from the Monthly Mean Geopotential Fields at 500 hPa over East Asia and the Southern Oscillation

The first six Chebyshev polynomial coefficients (i.e., A00, A01, A10, A11, A02, A20) were derived from monthly mean geopotential height over East Asia for the period 1951-1983. Spectral analysis of these coefficients reveals relative maxima of power in the frequency bands of 200 months (- 16.7 years), 25 months (the quasi-biennial oscillation), 5-6 months, and 2-3 months. Cross-spectral characteristics between Chebyshev coefficients and the Southern Oscillation Index (SOI) were also explored. Coherence spectrum for the zonal and meridional circulation index (A01 and A 10) with the SOI was significant near 4 years, the QBO, and 2-3 months. Some physical explanations were offered for the spatial linkages (i.e., teleconnections) between the SO and atmospheric circulation anomalies overEast Asia.

The Response of Geopotential Height Anomalies to El Niño and La Niña Conditions and Their Implications to Seasonal Rainfall Variability over the Horn of Africa

In this study, we unveil atmospheric circulation anomalies associated with the large-scale tropical teleconnections using National Center for Environmental Prediction (NCEP) reanalysis dataset. Composite analyses have been performed to know the impact of large-scale tropical circulations on the Horn of Africa. The composite analysis performed at the geopotential height of 850 Mb and 200 Mb, and precipitation rate (mm/day) during six strong El Niño and La Niña episodes revealed that the large-scale tropical variability induced climate anomalies in space and time. A substantial decrease in upper-level height (200 Mb) has been observed in the study area during El Niño composite years as compared to the La Niña years. During El Niño conditions, the upper-level divergence initiates low-level vertical motion, thereby enhancing convection, however, during La Niña composite years, nearly contrasting situations are noticed in Belg (February to May) season in Ethiopia. However, geopotential height anomalies at 850 Mb are above-normal during the strong El Niño years, suggesting suppressed convection due to vertical shrinking and enhancement of divergence at the lower level. Compared to the Belg (February to May), geopotential anomalies were generally positive during the Kiremt (June to September) season, thereby suppressing the rainfall, particularly in Southern Ethiopia and Northern Part of Kenya. In contrast, an increase in rainfall was observed during the Belg season (February to May).

Future Changes in Various Cold Surges over China in CMIP6 Projections

Cold surges(CSs)often occur in the mid-latitude regions of the Northern Hemisphere and have enormous effects on socioeconomic development.We report that the occurrences of CSs and persistent CSs(PCSs)have rebounded since the 1990s,but the trends related to the frequencies of strong CSs(SCSs)and extreme CSs(ECSs)changed from increasing to decreasing after 2000.The highest-ranked model ensemble approach was used to project the occurrences of various CSs under the SSP1-2.6,SSP2-4.5,and SSP5-8.5 scenarios.The frequencies of the total CSs show overall decreasing trends.However,under the SSP1-2.6 scenario,slight increasing trends are noted for SCSs and ECSs in China.Atmospheric circulations that are characterized by an anomalous anticyclonic circulation with a significantly positive 500-hPa geopotential height(Z500)anomaly at high latitudes along with significant negative anomalies in China were favorable for cold air intrusions into China.In addition,the frequencies of all CS types under the SPP5-8.5 scenario greatly decreased in the long term(2071-2100),a finding which is thought to be related to negative SST anomalies in the central and western North Pacific,differences in sea level pressure(SLP)between high-and mid-latitude regions,and a weaker East Asian trough.In terms of ECSs,the decreasing trends observed during the historical period were maintained until 2024 under the SSP1-2.6 scenario.Compared to the SSP1-2.6 scenario,the Z500 pattern showed a trend of strengthened ridges over the Ural region and northern East Asia and weakened troughs over Siberia(60°-90°E)under the SSP2-4.5 and SSP5-8.5 scenarios,contributing to the shift to increasing trends of ECSs after 2014.

Simulation and Analysis about the Effects of Geopotential Height Anomaly in Tropical and Subtropical Region on Droughts or Floods in the Yangtze River Valley and North China

Previous study comes to the conclusion： based on the anomalies of the South Asian high （SAH）, 100-hPa geopotential height, and 100-hPa circulation over tropical and subtropical regions, we can predict precipitation anomaly in the Yangtze River Valley and North China. To test its validity, a series of experiments have been designed and operated, which include controlled experiment, sensitivity experiment （which has added anomalies into 100-hPa geopotential height and wind field）, and four-composite experiments. Experiments based on the composed initial field such as EPR-CF, EPR-CD, EPR-HF, and EPR-HD, can reproduce the floods or droughts in the Yangtze River Valley and North China. It suggests that anomalies of the SAH, 100- hPa geopotential height, and circulation over tropical and subtropical regions may probably imply summer precipitation anomalies in the two regions. Sensitivity experiment results show that anomalies of the SAH, 100-hPa geopotential height, and southwest flow in the previous period is a signal of droughts or floods for the following summer in the Yangtze River Valley and North China. And it is also one of the factors that have impact on summer precipitation anomaly in the two regions. Positive anomaly of 100-hPa geopotential height and the anomalous intensifying of the SAH and southwest flow will induce floods in the Yangtze River Valley and droughts in North China; while negative anomaly of 100-hPa geopotential height and anomalous weakening of the SAH and southwest flow will induce droughts in the Yangtze River Valley and floods in North China.

Evaluating the weekly changes in terrestrial water storage estimated by two different inversion strategies in the Amazon River Basin

In this study,we estimated the weekly Gravity Recovery and Climate Experiment(GRACE)spherical harmonic(SH)solutions and regional mascon solutions using GRACE-based Geopotential Difference(GPD)data and investigated their abilities in retrieving terrestrial water storage(TWS)changes over the Amazon River Basin(ARB)from January 2003 to February 2013.The performance of the weekly GPD-SH and GPDmascon solutions was evaluated by comparing them with the weekly GFZ-SH solutions,Global Land Data Assimilation Systems(GLDAS)-NOAH hydrological model outputs,and monthly GFZ-SH,GPD-SH,and CSRmascon solutions in the spatio-temporal and spectral domains.The results demonstrate that the weekly GPD-SH and GPD-mascon present good consistency with the weekly GFZ-SH solutions and GLDAS-NOAH estimates in the spatio-temporal domains,but GPD-mascon presents stronger signal amplitudes and more spatial details.The comparison of the monthly average of weekly estimates and monthly solutions demonstrates that the weekly GPD-mascon and GFZ-SH with DDK1 filtering are close to the monthly CSRmascon and GFZ-SH solutions,respectively.However,the signal amplitudes of TWS changes from GPD-SH and GFZ-SH with 650 km Gaussian filtering are smaller than the monthly solutions,and the corresponding Root Mean Square Errors between the TWS change time series from the monthly average of weekly solutions and monthly estimates are 18.12 mm(GPD-mascon),18.81 mm(GFZ-SH-DDK1),24.93 mm(GPDSH-G650km),and 33.07 mm(GFZ-SH-G650km),respectively.Additionally,the TWS change time series derived from weekly solutions present more high-frequency time-varying information than monthly solutions.Furthermore,the 300 km Gaussian filtering can improve the signal amplitudes of TWS changes from the weekly GPD-SH solutions more than those with 650 km Gaussian filtering,but the corresponding noise level is higher.The weekly GPD-SH and GPD-mascon solutions can extend the application scopes of GRACE and provide good complements to the current GRACE monthly solutions.

Height connection across sea by using satellite altimetry data sets,ellipsoidal heights,astrogeodetic deflections of the vertical,and an Earth Gravity Model

Islands and the mainland are separated by seas,and the distances between them might be so long that the height on the mainland cannot be exactly translated to the islands,resulting in different height systems on the mainland and the islands.In this study,we used astrogeodetic deflections of the vertical and ellipsoidal heights of points on the mainland and island near their coastlines to implement height connection across sea areas.First,the modeled gravity and modeled astrogeodetic vertical deflections of segmentation points along connecting routes over the sea between the mainland and the island were determined by Earth Gravity Model(EGM),and the ellipsoidal heights of segmentation points were determined by the satellite altimetry data sets.Second,we used a linear interpolation model to increase the precision of the vertical deflections of segmentation points.Third,we computed the geopotential difference of points between the mainland and the island using a method derived from geopotential theory and the astronomical leveling principle.Finally,we estimated the normal height of the point on the island using the geopotential-difference iterative computation approach.Using observed data of normal heights,ellipsoidal heights,and astrogeodetic vertical deflections referring to height sites in Qingdao,Shandong Province,we conducted a numerical experiment involving the normal height connection across sea regions.We determined the data of the ellipsoidal heights and gravity of segmentation points along the connecting route across the water in the numerical experiment using DTU10.The distance of the height connection across the sea was approximately 10.5 km.According to China's official leveling specifications,the experimental results met the criterion of third-class leveling precision.

Variation of Dynamical Parameters with Upper Tropospheric Potential Vorticity in Tropical Cyclone over the North Indian Ocean Using WRF Model

Meteorologists are experiencing many challenges in the reliable forecasting of the track and intensity of tropical cyclones(TC).Uses of the potential vorticity(PV)technique will enrich the current forecasting system.The use of PV analysis of TC intensification over the North Indian Ocean(NIO)is rare.In this study,the authors analyze the behaviour of upper-level PV with dynamic parameters of TCs over NIO.The authors used NCEP FNL reanalysis 1×1 degree data as input in WRF model version 4.0.3 with one-way nesting between the parent and child domains.The authors used a coupling of the Kain-Fritsch(new Eta)scheme and the WSM 6-class graupel scheme as cumulus and microphysics options to run the model.The authors found that at least one potential vorticity unit(PVU)(1 PVU=10^(-6) m^(2)s^(-1)KKg^(-1))upper PV is required to maintain the intensification of TC.Larger upper PV accelerates the fall of central pressure.The high value of upper PV yields the intensification of TC.The wind shear and upper PV exhibited almost identical temporal evolution.Upper PV cannot intensify the TCs at negative wind shear and shear above the threshold value of 12 ms^(-1).The upper PV and geopotential heights of 500 hPa change mutually in opposite trends.The upper PV calculated by the model is comparable to that of ECMWF results.Therefore,the findings of this study are admissible.

Analysis of the Simulated Climatic Characters of the South Asia High with a Flexible Coupled Ocean-Atmosphere GCM

The ability of a climate model to reproduce the climatic characters of the South Asia High （SAH） is assessed by analyzing the 110-yr output of a Flexible Coupled GCM, version 0 （FGCM-0）. Comparing the results of FGCM-0 with the NCEP/NCAR reanalysis data, the major findings show that FGCM-0 has better results in simulation of the geopotential height field at 100 hPa, and reproduces fairly the main atmospheric circulation centers. However, there are still some differences in the simulated results compared with the reanalysis data. The coupled model also successfully reproduces the mean seasonal variation of the SAH, that is, it moves from the Pacific Ocean to the Asian continent, remaining over the Tibetan Plateau from winter to summer, and then withdraws from the Tibetan Plateau to the Pacific Ocean from summer to winter. However, such observed relationships between the SAH positions and the summer precipitation patterns cannot be fairly reproduced in the FGCM-0.

Simulation analysis of regional surface mass anomalies inversion based on different types of constraints

Surface mass anomalies estimated by mass concentration(mascon)approach using Gravity Recovery and Climate Experiment(GRACE)observations with regularization constraints generally present higher spatial resolution than the spheric harmonic(SH)solutions.To analyze the influence of different types of constraints on the estimation of mascon solutions,we carried out a closed-loop simulation experiment to estimate surface mass anomalies over South America based on simulated GRACE intersatellite geopotential differences.Tikhonov regularization with spatial constraint(SC),uniform weighting constraint(UWC),and a prior information constraint(APC)were employed to stabilize the mascon solutions,and the corresponding optimal regularization parameters were determined based on the minimum residual root-mean-square(RMS)criterion.The results show that mascon solutions estimated under different types of constraints are consistent and equivalent when the optimal regularization parameters are selected.The spatial distributions and main characteristics of regional surface mass anomalies estimated by the three types of constraints agree well,and the values of residual RMS with different constraints are very close.But due to the smoothing effect of regularization,the signal strength of mascon solutions is a bit weaker than that of original true signal,especially in the regions with strong signals.In addition,due to the ill-conditioned problem is more serious for higher grid resolution,the relative contribution of the three types of constraints to the final mascon solutions would be stronger.The results show that the averages of relative contribution percentages of these constraints for 2°×2° mascon grids are 80%-90%,while the corresponding values for 4°×4° mascon grids are 30%-60%.However,based on the minimum residual RMS criterion,the accuracy of estimation results is not affected by the type of constraints and their relative contribution to the final mascon solutions.