## 3 Experiment Setup  
We conducted simulation experiments to verify the SFST method of connecting two VHSs. The main idea of the experiment is to compare a set of true values to a set of simulated observation values, as depicted in Figure 4.  
We chose two datum stations for the experiment. The first was the Qingdao Datum Station (QDDS, located at Qingdao Guanxiangshan mountain, which serves as a height reference datum for China's VHS). The second was the San Francisco Datum Station (SFDS, located at the California Academy of Science, which is supposed to be the height datum station of the US's VHS). The two datum stations are connected via a GNSS-type satellite, as shown in Figure 5. The experiment period was 1.5 h, from 6:00 a.m. to 7:30 a.m. on 1 March 2023. The satellite needed to be intervisible to both ground datum stations during the experiment period; thus, we chose the GPS navigation satellite SVN-56, which satisfies this requirement. It should be noted that the SFST method requires the satellite to be equipped with a frequency signal transponder, which is not applicable in current GPS satellites. However, in our simulated experiments, we assumed that the GPS satellite was equipped with two transponders. Therefore, the satellite could simultaneously connect with the two ground stations with the SFST method. The trace of SVN-56 obtained during our experiment period is depicted in Figure 5.  
Figure 4: The scheme of the simulation experiment.  
We obtained the orbit information of the GPS navigation satellite SVN-56 from the precise ephemeris provided by IGS (www.igs.org/products (accessed on 20 March 2023)), which are regarded as true values. We sampled the frequency comparison result between the two stations every 5 s. Hence, we obtained a set of observation values for every 5 s. Since the time interval of the precise ephemeris was 15 min, we used polynomial interpolation [46] to acquire the data set in 5 s intervals (true values). Then, we used the EGM2008 model [12] to calculate the gravitational potentials of the satellite and the two ground sites corresponding to the \"observation\" time points. These gravitational potentials are regarded as true values, because we do not consider the errors caused by EGM2008 (the accuracy of EGM2008 is about 10-20 cm at the ground and better than 1 cm at the GNSS satellite altitude). Then, the true value of the geopotential difference between QDDS and SFDS, \(\Delta W_{QD-SF}\), could be obtained.  
Microwave signal frequencies are affected by the ionosphere and troposphere medium. We used the International Reference Ionosphere Model [47; 48] to obtain the electron density values and the Global Pressure and Temperature (GPT) [49] to obtain the temperature and pressure values. Then, we were able to estimate the ionospheric and tropospheric influences on the signal frequencies [50; 51]. The heights and geopotentials of the two ground sites will also be influenced by the periodical tidal effect, which has been well-modeled [52] and can be removed by various software. We used a Python Library Tidal Potential ([[https://github.com/joernc/tidal-potential](https://github.com/joernc/tidal-potential)]([https://github.com/joernc/tidal-potential](https://github.com/joernc/tidal-potential)) (accessed on 10 March 2023)) to calculate the tidal effect.  
In our experiment, the two datum stations were connected to SVN-56 simultaneously via SFST links. Relevant input parameters are listed in Table 1. It should be noted that the Chinese government releases the OH of QDDS as China's height datum origin, but the US has no corresponding height datum origin. Therefore, the OH of SFDS was deduced from EGM2008. We assumed the height difference between China's VHS and the US's VHS to be 1.000 m (as true value), and China's VHS was higher than the US's VHS.  
Figure 5: Experiments were conducted for the time duration during which the satellite SVN-56 moved from position \(S\) to position \(S^{\prime}\) (from 6:00 a.m. to 7:30 a.m., 1 March 2023).