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Since the beginning of the 1990s, absolute gravity has been observed at several locations in Norway with FG5-type instruments to investigate the temporal gravity changes due to glacial isostatic adjustment (GIA). Previous work suggests that some of the estimated secular gravity trends may be affected by remaining unmodelled geophysical effects, such as the effect of local hydrology. In this work, we compute hydrological gravity effects from global hydrological models for the far zone and a combination of regional run-off models and modelling of residual hydrological effects for the near zone. The method developed in this paper is first tested at the geodetic observatory in Wettzell, Germany, where both high-resolution superconducting gravimeter data as well as a regional hydrological model are available. Next, the method is transferred to two Norwegian gravity sites (NMBU and TRYC), with long time-series of frequent absolute gravity observations using FG5-226. At these sites, we investigate the impact of the hydrological gravity correction on data variability as well as estimated secular gravity trends. We find that the data variability is reduced by up to 40 per cent when applying the modelled hydrological gravity effect at TRYC. The reduction is less at NMBU where the amplitude of the hydrological signal and in consequence also the signal-to-noise ratio are smaller. We also note that it is challenging to determine the near zone residual hydrological effects without carefully taking into account the hydrogeological setting of the area for modelling such effects. When utilizing the long corrected absolute gravity series to determine the gravity trends, we find that the estimated trends are not significantly different from the uncorrected observations. However, the uncertainty of the estimated trends is reduced significantly for a limited corrected gravity series. We further suggest repeatability analysis of the absolute gravimeter. From the long time-series at NMBU we find a significant step coinciding with hardware replacement. We find that the fit between observed and modelled secular trends improves when introducing the step. Further analysis of gravity rates at other stations is needed to verify the existence of a real instrumental offset. [ABSTRACT FROM AUTHOR]