The monthly global land water storage (GLWS) data set provides the total water storage anomaly (TWSA), root-zone soil moisture, groundwater and surface water (i.e. local lakes, global lakes, local wetlands, global wetlands, reservoirs and rivers per WaterGAP definition) on 0.5° grids.GLWS is produced by assimilating (Gerdener et al., 2023) gridded GRACE and GRACE-FO-derived TWSA into the WaterGAP global hydrological model. The resulting data set represents thus an optimal synthesis of GRACE data and all data sets that went into the hydrological model. This synthesis seeks to fit GRACE (-FO) TWSA grids within error bars, and at the same time it solves the horizontal and vertical water balances as represented in the hydrological model, again within error bars. To this end, the uncertainty of the hydrological model simulation is represented via an n-member ensemble, where we take into account the uncertainty of forcing (precipitation and radiation) data as well as the uncertainty of some model calibration parameters.As a result, when no GRACE (-FO) data is available, the GLWS data set represents the mean of an ensemble where each member is dynamically consistent with the model. It is important to understand that this mean depends on the ensemble creation and thus will differ from published WaterGAP standard runs, even if there is no GRACE data within a particular month. It is also important to understand the assimilation-derived GLWS data set does not represent a simple downscaling of the GRACE data, i.e. spatial smoothing of GLWS does not necessarily correspond to GRACE (-FO) TWSA.The data is provided for 01/2003 to 12/2019. Additionally, the standard deviations are provided (computed from the ensemble).The main updates of RL004 (and RL003) with respect to the published release 002 (Gerdener et al., 2023a) were a new assimilation filter algorithm and GRACE/-FO settings as described in Gerdener (2024). The main updates of RL004 with respect to the unpublished release 003 were a new setup to derive initial values in a joint spin up and open loop phase.