Height System Unification Of Africa Using Relativistic Approach

Establishing an International Height Reference Frame（IHRF）has really been a consid-erable goal of the International Association of Geodesy（IAG）for a very long time.One obstacle is to obtain the vertical coordinates,i.e.,geopotential numbers,of the recom-mendation stations with high accuracy and likewise global harmony.The International Association of Geodesy began a massive job to concentrate on and service this concern to set up a global reference height system.Africa struggles with bad gravity data and gen-eral practitioner benchmarks.This research aims to utilize the benefits of atomic clocks to develop and specify a unified height system for Africa AFRUHS.An appealing approach to establishing and defining a unified height system is using clock networks,which are effective in specifically obtaining geopotential or elevation differ-ences between far-off stations by determining the gravitational redshift result by con-trasting clocks frequencies.Our research will be simulation research to make use of the ACES atomic clock set precede with microwave signals communication to figure out the geopotential difference between the ACES and the selected ground stations in Africa.In the beginning,we choose three stations in Africa with a good distribution,the first station at Alexandria Egypt（northeast）,the second was at Dakar,Senegal（west）and the third station was at Windhoek,Namibia（south）[These Stations have been se-lected before by the IAG community to Establish a global height reference system,see https://ggos.org/item/height-reference-frame/].The gravitational potential variations between these ground stations are then calculated using the tri-frequencies combination method.The ACES（Atomic Clock Ensemble in Space）has been used to conduct simu-lation experiments.In contrast to the time and frequency transmission on the ground,the transfer between the ground and likewise a satellite supplied a lot more issues in addition to challenges.The atmosphere as well as the ionosphere,for example,will trigger signal hold-up in addition to the frequency change,and likewise,the Earth’s turning and likewise tidal activity will also have an impact on time and also frequency transmission.When the frequency transfer accuracy requirement surpasses 10^-18or better,methodical mistakes may be the significant error triggers instead of clock security.The ESA-CNES Atomic Clock Ensemble in Space（ACES）experiment（Cacciapuoti and Salomon,2011.a;Meynadier et al,2018）,which was deployed onboard the International Space Station（ISS）,is primarily designed to examine gravitational redshift.It attempts to test the gravitational redshift to a level of(2×10^-6),which is one and a half orders higher than the GPA experiment,using atomic clocks with fractional frequency instability and error of 1-3×10¹⁶.An active hydrogen maser（SHM）and a cold caesium atom are the principal onboard instrumentation（PHARAO）.The fractional frequency stability of the PHARAO clock is 1.1×10^13√τ,whereτis the integration time in seconds and accuracy of a few parts in 10¹⁶.Meanwhile,after 10000 s of integration time,SHM shows a fractional frequency instability of 1.5×10¹⁵.Two clocks will produce an onboard time scale by combining the H-short-term maser’s stability with the caesium clock’s long-term stability and precision.ACES uses two in-dependent time and frequency transfer connections（Microwave Hyper-links（MWL）and European Laser Timing（ELT）optical link）to investigate general relativity and develop applications in geodesy（relativistic geodesy）and time and frequency metrology（Caccia-puoti et al,2017.a;Meynadier et al,2018）.These science goals are closely linked to the MWL efficiency Meynadier et al（2018）,and theireffectiveness is critical in this study.To transfer time/frequency,MWL employs an uplink of provider frequency 13.475 GHz（Ku-band）and downlinks of carrier frequencies 14.70333 GHz（Ku-band）and 2248 M Hz（S-band）.MWL will outperform 0.3 ps at 300 s,7 ps at 1 day,and 23 ps at 10 daysin terms of time discrepancy Hess et al（2011.）.After a few days of integration,these results,which are 12 orders of magnitude better than current approaches（TWSTFT and GPS）,will allow comparisons（common view and uncommon view）of ground clocks with 10^-17frequency resolution Hess et al（2011.）.Regarding the ACES goal,some research studies have highlighted the test of gravitational redshift regarding the time comparing（Cacciapuoti and Salomon,2009.a;Duchayne et al,2009.a;Blanchet et al,2001.）,however,there are very fewarticles referring to frequency comparison.When compared to time comparison,frequency comparison provides the following advantages:（1）It can reduce the impact of phase ambiguity because frequency monitoring is insignificant with ranging and is a result of measuring over a short period of time;（2）it can evaluate the immediate gravitational potential,whereas,for time com-parison,we must collect information in order to solve the time-shiftingrate in order to indicate the gravitational redshift value.However,because the precision of measuring the immediate frequency is largely confined,we must additionally accumulate data in order to obtain more accurate results.The tri-frequency combination（TFC）approach will be employed in our research project to get the gravitational potential difference by combining three frequency measurements.For the one-way frequency transfer model with a precision requirement of 10^-16,we use Blanchet et al（2001.）formulation in free space with medium,which is precise to c^-3order.We made contributions to theory by extending the Blanchet et al（2001.）model from free space to real space with media and formulating a method to eliminate the Doppler frequency shift（the term Doppler effect or Doppler frequency shift used in this study refers to the first Frontier Doppler effect）while considering the time balance out among three links.Our final TFC model is capable of effectively eliminating all types of shifts ranging in value from 10^-16.We performed simulation tests that took into account the actual orbit,realistic clock noises,real atmosphere,and real gravity in order to evaluate our model and identify the magnitude of conditions that were required to be met.To achieve the objective of our research,initially,we need a gravity field model to deter-mine the gravitational potential at the ground station（in the simulation process）,so we begin our study by identifying a precise geoid model for Africa using the shallow-layer technique.Then we use this geoid as a gravity model in the simulation process.The shallow-layer method is different from the traditional Stokes and Molodenesky geoid de-termination methods as it comes from the definition of the geoid itself.In our work,we apply the shallow-layer method to determine a 5^′×5^′geoid model for Egypt which ranges from（21°≤?≤32°;24°≤λ≤37°）.The global digital topographic model DTM2006.0,the Danish National Space Center DNSC08 model,the EGM2008 gravity field model,and the CRUST2.0 crust model were used to distinguish boundaries for the shallow-layer and determine its interior structure.The computed shallow-layer geoid model for Africa has been validated using the recently developed AFRgeo2019 gravimetric geoid model（Abd-Elmotaal et al,2020b）determined in the framework of the activities of the IAG Sub-Commission on the Gravity and Geoid in Africa.Differences between these geoids reveal the important impact of using local gravity data.These differences are significantly small（below 0.5 m）in most areas of the African continent.Another study has been per-formed comparing the geoid produced using several global geopotential models and the computed shallow-layer geoid.This study reveals that they all give comparable geoid results.The precision of the computed shallow-layer geoid depends upon the precision of the used input models.Blunders in EGM2008,DTM2006.0 and CRUST1.0 models have impacted the precision of the output geoid.Errors in the DTM2006.0 elevations,which is a supplement to EGM2008,may introduce large errors in the geoidal heights（Merry,2003.;Kiamehr and Sj¨oberg,2005.）.A simulation study has been done to determine the gravitational potential between the ACES and the three stations in Africa,and then the gravitational potential of these stations has been determined.the results show that using the clock networks in the near future after the lunch of ACES and the CSS will help and give an accurate technique to Establish the International height reference system IHRS.By building a global Atomic clocks networks,it will be easy to adapt and validate all the geodetic work,also it will be helpful in studying,understanding and modelling global change.Likewise offers a reliable frame for constant analysis and modelling of global phenomena and procedures affecting the Earth’s gravity field,the Earth’s surface geometry and the Earth’s rotation.The simulation study shows that the Doppler frequency shift is the most important part,the Shapiro frequency shift is the smallest part,and the relativistic frequency shift includes the gravitational redshift and the lateral Doppler effect.The refraction effect cannot be ignored,it is much larger than the ionospheric frequency shift and the tropospheric frequency shift.In the experiment,although the residuals of some errors（especially the high-order terms of the ionosphere）are larger than 10^-16,due to the randomness of the errors,simulation experiments show that after long-term averaging,it can be less than10^-16.Finally,after the average of all the data,the value of the gravity level for Alex.station can be obtained as 62636440.270m²s^-2,which is 3.894 m²s^-2compared to the standard gravity level value of 62636444.164 m²s^-2,and the corresponding elevation difference near the ground is 0.4±1.1 m.The value of the gravity level for Dakar station can be obtained as 62636652.310m²s^-2,which is 5.240 m²s^-2compared to the standard gravity level value of 62636657.550m²s^-2,and the corresponding elevation difference near the ground is 0.2±1.2 m.The value of the gravity level for Windhoek station can be obtained as 62620192.794m²s^-2,which is 8.706 m²s^-2compared to the standard gravity level value of 62620201.500 m²s^-2,and the corresponding elevation difference near the ground is 0.6±0.9 m.