A measure of the Earth's gravity contains contributions from solid Earth as well as climate-related phenomena, that cannot be easily distinguished both in time and space. Aftermore than 7 years, the GRACE gravity data available now support more elaborate analysis on the time series. We propose an explorative approach based on a suitable time series decomposition, which does not rely on predefined time signatures. The comparison and validation against the fitting approach commonly used in GRACE literature shows a very good agreement for what concerns trends and periodic signals on one side, and on the other it reveals where other behaviours can occur. Variations over frequency lower than the usual semi-annual or annual ones and variations in the rates of the secular trends indeed occur, related to geophysical phenomena, climate and even to human activities. A careful analysis of the residues allows to design a screening algorithmto identify regionswhere anomalous gravity variations deserve further investigations. It also allows to raise the amount of information one can obtain exclusively from gravity data, prior and preliminary to any subsequent specifically targeted study. This approach has been used to assess the possibility of finding evidence ofmeaningful geophysical signals different from hydrology over Africa in GRACE data. In this casewe conclude that hydrological phenomena are dominant and so time variable gravity data in Africa can be directly used to calibrate hydrological models.