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).

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.

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.