Chronometric Levelling to Establish a Global Height System

Projekt: Chronometric Levelling to Establish a Global Height System

Forschende: M.Sc. Asha Vincent & Prof. Dr.-Ing. habil. Jürgen Müller

Projektidee: Height system unification using atomic clocks.

Advances in optical atomic clocks have opened a new path in geodesy by allowing the direct measurement of gravitational potential differences through clock frequency comparisons. According to general relativity, a clock ticks more slowly in a stronger gravitational field. This makes it possible to determine the physical height differences from changes in the ticking rate. A clock with a relative frequency stability of 10⁻¹⁸ can measure a height change of 1 cm. Traditional height systems, based on levelling and gravity measurements, are tied to local tide gauges and often suffer from inconsistencies across national borders. With growing demands for a unified global height system, driven by international infrastructure, sea-level monitoring, and climate-related applications, the International Association of Geodesy (IAG) has proposed the International Height Reference System (IHRS). In IHRS, the vertical coordinate is defined by the geopotential number, a physically meaningful quantity that clocks can measure directly.

The unification is approached through a joint adjustment procedure with simulated clock observations, aligning all local height systems (LHS) to a common reference datum. For the simulation, an a priori height system is selected, and levelling points are grouped into LHS based on their location and association with tide gauges. The success of the unification is assessed by comparing the estimated heights to the original a priori values.

In this study, Brazil serves as a test region for evaluating the potential of chronometric levelling in unifying local height systems. Using a levelling dataset provided by the SIRGAS working group, a simulation framework was developed to unify 10 LHS, each associated with nearby tide gauges. The Imbituba tide gauge defines the unifying reference datum. Systematic offsets and tilts were introduced into the remaining LHS to simulate real-world inconsistencies. A network of four clocks, positioned at the extreme locations of each LHS, was used to generate simulated clock observations incorporating tidal corrections and link uncertainties.

Results show that, with optical clocks operating at the 10⁻¹⁸ level and a well-distributed network, height unification with an accuracy of 1 cm is achievable. The dominant limitations arise from clock noise and error correlations, which must be carefully modelled to avoid loss of information and degradation in accuracy. While fibre links can support high-precision comparisons, extending clock networks globally will require satellite-based links, where further advancements are needed to reach comparable accuracy.

Importantly, the approach is flexible, allowing transportable clocks to be deployed in campaign mode, requiring only a single measurement between the sites. As clocks uniquely provide direct measurements of geopotential differences, chronometric levelling stands out as a promising technique for establishing a unified global height system.

For further reading, see, https://doi.org/10.48550/arXiv.2411.07888.