Weekly ocean bottom pressure anomalies (OBP) are modeled using the Finite Element Sea-ice Ocean Model (FESOM). The model's OBP error, mostly unknown so far, is assessed by comparing two model simulations, each forced by different atmospheric forcing data sets. The mean estimated error of modeled OBP is found to be 0.04 m per 1.5 × 1.5 grid cell. The error varies strongly from 0.003 m in the equatorial region to 0.31 m in the Weddell and Ross Seas. We believe that the spatial variations of the errors are an important improvement over previous error models. The new error estimates are implemented in a joint inversion of Gravity Recovery and Climate Experiment (GRACE) gravity measurements, GPS site displacements and modeled OBP, resulting in a larger overall OBP weight in the inversion, most notably in the Polar Regions. Additionally, the inversion provides a global mass correction term to adjust the ocean mass budget of the model. The estimated term is used to correct the model's fresh water balance, making it consistent with GRACE and GPS on seasonal and longer timescales. All model results, weekly GRACE estimates and the inverse solutions are compared with measurements from in situ bottom pressure recorders. The newly estimated error model of the combination solution results in higher correlations than the previously used constant error model of the combination solution.