Unification of height systems using chronometric geodesy – A more realistic scenario

The high accuracy of optical atomic clocks can be well utilized in geodetic applications. When clocks are placed on the ground, their position and mass distribution decide their ticking rates due to the relativistic phenomena of gravitational redshift. Hence, the fractional frequency difference between two terrestrial atomic clocks provides the gravitational potential difference or the corresponding height difference between them. This novel method of relative height measurement can be used in estimating the discrepancies between local and regional height systems to an accuracy of 1 cm with high-performance clocks achieving a fractional frequency uncertainty of about 10^-18. In our simulation, more realistic errors in the local height values are assumed by considering different scenarios like systematic tilts that can accumulate with the distance from the tide gauges, effects due to the elevation of the leveling points, the presence of noisy leveling lines, etc. As a test case, a known a priori height system was split into local systems affected by various errors, and the reunification was carried out using simulated clock measurements. External tidal effects at each clock site have also been considered for a more realistic comparison. The accuracy in the estimation of specific height errors in the involved systems highly depends upon the number of clocks and their spatial distribution in each local system and hence, they have to be optimized in each test case. The error accumulation during height measurements over long distances does not play a role for clock measurements, in contrast to classical spirit leveling. Thus, chronometric leveling proved to be a promising technique that can complement and partly replace the traditional methods in geodesy.