Applying non-tidal atmosphere and ocean loading corrections on the observation, normal equation, and parameter levels in GNSS data analysis

To achieve the 1 mm accuracy and 0.1 mm/year stability of Terrestrial Reference Frame (TRF) required by Global Geodetic Observing System (GGOS), various surface displacements have to be precisely modeled. Non-tidal atmosphere, ocean, and hydrology loading displacements are major sources causing stochastic and systematic effects in station coordinates estimated by space geodetic techniques such as Global Navigation Satellite Systems (GNSS). Studies show that the correction of non-tidal loading displacements in GNSS station coordinate time series reduces coordinate repeatability and thereby improves stability. Currently, non-tidal loading displacements are corrected on the observation level in Very Long Baseline Interferometry (VLBI) data analysis for standard IVS (International VLBI Service for Geodesy and Astrometry) products, but not in GNSS data analysis. We applied the ESMGFZ non-tidal atmosphere and ocean loading displacements (NTAOL) on the observation, normal equation, and parameter levels for global GNSS network solutions in 2005-2019. We demonstrate that the station coordinate repeatability can be significantly improved when correcting NTAOL displacements, especially in the up component where a reduction of 20-30% can be observed at middle and high latitudes. Whereas for other geodetic parameters, such as satellite orbits, Earth Rotation Parameters (ERP), and geocenter motion, however, the impact of NTAOL displacements is insignificant. The difference between applying NTAOL displacements on the observation to that on the normal equation level is on sub-daily scales and we show that most of these differences are absorbed by receiver clocks. As for the differences of applying NTAOL on the observation and on the parameter levels, small but systematic effects on the horizontal components of station coordinates appear, which are mainly due to network alignment. We also demonstrate that the a priori tropospheric delay modeling affects the non-tidal atmosphere loading signals in station coordinates, i.e., when applying empirical tropospheric delay models, e.g., GPT3, NTAL correction introduces a significantly smaller improvement of station coordinate repeatabilities (below 5% in up component). Hence, we recommend always using discrete tropospheric delay products from Numerical Weather Model (NWM) as a priori values when NTAL corrections are applied.