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In this study, we develop a model that allows to combine gravimetric and geometric data. By the combination, we improve the spatial resolution of the resulting mass balance estimate compared to a purely gravimetric one. The equivalent ice or firn density of the changing ice volume is estimated within a mathematical inversion model, which includes geometric information about the volumetric change of the ice sheet and the resulting gravity change. This gravity change is computed from monthly GRACE gravity fields. They have a limited spatial resolution of a few 100 km, but allow direct conclusions about the true mass changes over Greenland. The ice-volume changes are described by a product by the Climate Change Initiative of European Space Agency, which is based on altimetry data. They have a very fine spatial resolution (down to a few km), but are not directly sensitive to mass changes. By combining both data sets in a common mathematical model, the advantages of both data types (direct sensitivity to mass versus high spatial resolution) are made use of. In this way, we improve the spatial resolution of mass balance estimates over Greenland. This leads to a map of mass trends, which has the same spatial resolution as the input map of geometric changes, but which is consistent with the input gravity fields. It will enable improving the localization of mass change signals of ice sheets and glaciers, which are usually rather small-scale. We compare our estimates to the results of complementary studies regarding the total mass loss of the Greenland ice sheet and its surrounding land surface. Our study leads to a value of |$-213\pm 37\, \text{Gt}\,\text{a}^{-1}$| in the time span from 2011 to 2015. We also discuss the problem of separating the mass contribution of the Greenland ice sheet itself and its surrounding region. [ABSTRACT FROM AUTHOR]