We aim at the determination of the absolute, but temporally changing ocean circulation flow field and of associated mass and heat transports. The study is based on a state‐of‐the‐art circulation model assimilating the dynamic ocean topography (DOT) derived geodetically by subtracting the geoid from sea surface heights observed by satellite altimetry. Our geoid model is based on a satellite‐only combination of GRACE and GOCE. A prerequisite for the generation of the DOT and its assimilation is a spectral consistency between altimetric data and gravity field. Two different filter strategies were investigated, a global approach performed in the spectral domain and a track‐wise approach partly realized in the space domain. Further, error propagation needs to be performed to ensure optimal information content of the measured data. Our analysis focuses on the Southern Ocean and especially the Weddell Gyre, a region of high variability but also of poor data quality due to the presence of seasonal sea ice cover. Results are presented for different spatial resolutions and the impact of assimilating the geodetic DOT on the shape of the modelled Weddell Gyre, oceanic fronts and deeper ocean is discussed.