A Re-Evaluation of the Relativistic Redshift on Frequency Standards at NIST, Boulder, Colorado, USA

Primary frequency standards that realize the definition of the second based on the Caesium (Cs) atom are used to steer International Atomic Time. According to the theory of relativity, their frequency should be adjusted to that at which these would operate, if located on the geoid. Current best standards for the current definition of the second are approaching uncertainties of one part in 10¹⁶. Optical frequency standards however are now reaching uncertainties of few parts in 10¹⁸ and are expected to lead to a new definition of the second. Their performance requires centimetre-level geoid accuracy, in order to calculate accurately the redshift frequency offset necessary for their inter-comparison.

We re-evaluated the relativistic redshift of the frequency standards at NIST in Boulder, Colorado, USA, based on a recent precise GPS survey of several benchmarks on the roof of the building where these are housed, and on global and local geoid models supported by data from the GRACE and GOCE missions, including EGM2008, USGG2009, and USGG2012. We also evaluated the redshift offset based on the published NAVD88 geopotential number of the levelling benchmark Q407, after estimating the bias of the NAVD88 datum at our specific location. We present and discuss the results that we obtained using different methods, and provide our current estimate of the redshift offset and of its accuracy, considering the main error sources contributing to the total error budget. We compare our current estimates to those published by Pavlis and Weiss in 2003, using the data and models that were available at that time. We also discuss the prospects of using inter-connected ultra-precise frequency standards for the direct determination of geoid height differences, which may provide in the not-too-distant future an alternative approach for the establishment of vertical datums and the independent verification of the accuracy of global and local geoid models.