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The Gravity Recovery and Climate Experiment (GRACE) mission ended its operation in October 2017, and the GRACE Follow-On mission was launched only in May 2018, leading to approximately 1 year of data gap. Given that GRACE-type observations are exclusively providing direct estimates of total water storage change (TWSC), it would be very important to bridge the gap between these two missions. Furthermore, for many climate-related applications, it is also desirable to reconstruct TWSC prior to the GRACE period. In this study, we aim at comparing different data-driven methods and identifying the more robust alternatives for predicting GRACE-like gridded TWSC during the gap and reconstructing them to 1992 using climate inputs. To this end, we first develop a methodological framework to compare different methods such as the multiple linear regression (MLR), artificial neural network (ANN), and autoregressive exogenous (ARX) approaches. Second, metrics are developed to measure the robustness of the predictions. Finally, gridded TWSC within 26 regions are predicted and reconstructed using the identified methods. Test computations suggest that the correlation of predicted TWSC maps with observed ones is more than 0.3 higher than TWSC simulated by hydrological models, at the grid scale of 1 degrees resolution. Furthermore, the reconstructed TWSC correctly reproduce the El Nino-Southern Oscillation (ENSO) signals. In general, while MLR does not perform best in the training process, it is more robust and could thus be a viable approach both for filling the GRACE gap and for reconstructing long-period TWSC fields globally when combined with statistical decomposition techniques.