Terrestrial water storage (TWS) can be defined as the storage of water on and below the land surface, and includes snow, ice, surface water, soil moisture, and ground water. TWS is a key component of the terrestrial and global hydrological cycles, which have important control over the water, energy and biogeochemical fluxes, and plays a major role in the Earth’s climate. An accurate estimation of terrestrial water storage is thus important for improved water management. However, direct determination of TWS is difficult due to insufficient in-situ data. TWS estimation can be obtained through hydrological modelling, although models are not free from uncertainties due to inaccurate forcing data and weak modelling assumptions. However, the launch of the Gravity Recovery and Climate Experiment (GRACE) twin satellite mission has provided the first space based dataset for TWS estimates, although with coarse resolution and limited accuracy. It is expected that combining GRACE observations and estimates from a model could improve TWS estimates, and one way to this through data assimilation. In this thesis, the ensemble Kalman filter (EnKF) and the ensemble Kalman smoother (EnKS) have been applied to assimilate the GRACE TWS variation data into the HBV-96 model, a conceptual rainfall-runoff model over the Rhine river basin, for the study period of February 1st 2003 to January 31st 2004. Two TWS variation estimates were inferred from two sets of GRACE solutions, one from DEOS – TU Delft, and another from CSR - University of Texas. Both solutions use different filtering methods which yield different estimates, and therefore can be expected to have different effect on the data assimilation. The EnKF and EnKS have been successfully applied, fulfilling the expectation of having a new estimate with lower variance than both the prior model estimate and the GRACE observation estimate. The model estimated discharge after the data assimilation was compared with measured discharge at several stations. The discharge estimates were improved at the beginning of the experiment, but the degree of improvement decreased with time. Both of the GRACE data sets gave comparable results. Longer experiment period and comparison with other validation data could lead to a more definitive conclusion.