The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in \(10^{18}\) level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about \(0.1\,\hbox {m}^{2}\,\hbox {s}^{-2}\), equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about \(2 \times 10^{-18}\).

The latest generation of optical atomic clocks is approaching the level of one part in 10 ¹⁸ in terms of frequency stability and uncertainty. For clock comparisons and the definition of international time scales, a relativistic redshift effect of the clock frequencies has to be taken into account at a corresponding uncertainty level of about 0.1 m ² s ⁻² and 0.01 m in terms of gravity potential and height, respectively. Besides the predominant static part of the gravity potential, temporal variations must be considered in order to avoid systematic frequency shifts. Time-variable gravity potential components induced by tides and non-tidal mass redistributions are investigated with regard to the level of one part in 10 ¹⁸ . The magnitudes and dominant time periods of the individual gravity potential contributions are investigated globally and for specific laboratory sites together with the related uncertainty estimates. The basics of the computation methods are presented along with the applied models, data sets and software. Solid Earth tides contribute by far the most dominant signal with a global maximum amplitude of 4.2 m ² s ⁻² for the potential and a range (maximum-to-minimum) of up to 1.3 and 10.0 m ² s ⁻² in terms of potential differences between specific laboratories over continental and intercontinental scales, respectively. Amplitudes of the ocean tidal loading potential can amount up to 1.25 m ² s ⁻² , while the range of the potential between specific laboratories is 0.3 and 1.1 m ² s ⁻² over continental and intercontinental scales, respectively. These are the only two contributors being relevant at a 10 ⁻¹⁷ level. However, several other time-variable potential effects can particularly affect clock comparisons at the 10 ⁻¹⁸ level. Besides solid Earth pole tides, these are non-tidal mass redistributions in the atmosphere, the oceans and the continental water storage.

We carried out a 26-day comparison of five simultaneously operated optical clocks and six atomic fountain clocks located at INRIM, LNE-SYRTE, NPL and PTB by using two satellite-based frequency comparison techniques: broadband Two-Way Satellite Time and Frequency Transfer (TWSTFT) and Global Positioning System Precise Point Positioning (GPS PPP). With an enhanced statistical analysis procedure taking into account correlations and gaps in the measurement data, combined overall uncertainties in the range of 1.8 × 10 ⁻¹⁶ to 3.5 × 10 ⁻¹⁶ for the optical clock comparisons were found. The comparison of the fountain clocks yields results with a maximum relative frequency difference of 6.9 × 10 ⁻¹⁶ , and combined overall uncertainties in the range of 4.8 × 10 ⁻¹⁶ to 7.7 × 10 ⁻¹⁶ .

GFZ (German Research Centre for Geosciences) set up the Zugspitze Geodynamic Observatory Germany with a worldwide unique installation of a superconducting gravimeter at the summit of Mount Zugspitze on top of the Partnach spring catchment. This high alpine catchment is well instrumented, acts as natural lysimeter and has significant importance for water supply to its forelands, with a large mean annual precipitation of 2080 mm and a long seasonal snow cover period of 9 months, while showing a high sensitivity to climate change. However, regarding the majority of alpine regions worldwide, there is only limited knowledge on temporal water storage variations due to sparsely distributed hydrological and meteorological sensors and the large variability and complexity of signals in alpine terrain. This underlines the importance of well-equipped areas such as Mount Zugspitze serving as natural test laboratories for improved monitoring, understanding and prediction of alpine hydrological processes. The observatory superconducting gravimeter, OSG 052, supplements the existing sensor network as a novel hydrological sensor system for the direct observation of the integral gravity effect of total water storage variations in the alpine research catchment at Zugspitze. Besides the experimental set-up and the available data sets, the gravimetric methods and gravity residuals are presented based on the first 27 months of observations from 29 December 2018 to 31 March 2021. The snowpack is identified as being a primary contributor to seasonal water storage variations and, thus, to the gravity residuals with a signal range of up to 750 nm s⁻² corresponding to 1957 mm snow water equivalent measured with a snow scale at an altitude of 2420 m at the end of May 2019. Hydro-gravimetric sensitivity analysis reveal a snow–gravimetric footprint of up to 4 km distance around the gravimeter, with a dominant gravity contribution from the snowpack in the Partnach spring catchment. This shows that the hydro-gravimetric approach delivers representative integral insights into the water balance of this high alpine site.

We present the activities and improvements of the International Geodynamics and Earth Tide Service (IGETS) over the last four years. IGETS collects, archives and distributes long time series from geodynamic sensor, in particular superconducting gravimeter data currently from more than 40 stations and 60 different sensors. In addition to the raw 1-s and 1-min gravity and atmospheric pressure data (Level 1), IGETS produces end-user products on different levels. These include gravity and atmospheric pressure data corrected for major instrumental perturbations and ready for tidal analysis (Level 2). Since 2019, IGETS provides gravity residuals corrected for most geophysical contributions (Level 3) which can be used directly for geophysical applications without any expert knowledge in the processing of gravimetric time series.