The underlying uncertainties in the prediction of freshwater evolutions in some regions can be induced by several unmitigated human actions, multi-scale climatic drivers, and dynamic physical processes. These factors have enduring hydro-ecological effects on the environments and combine to limit our understanding of large scale hydrological processes and impacts of climate on water availability. Considering the fact that several hydrogeological perturbations and disturbances have been reported during the last decade in South America (SA), a further assessment of continental land water storage is therefore warranted. In this study, a two-step regularization approach that combined the JADE (Joint Approximate Diagonalisation of Eigen matrices) algorithm and PLSR (partial least squares regression) was employed to assess GRACE (Gravity Recovery and Climate Experiment)-terrestrial water storage (TWS) over SA. Based on the Bartlett's statistics, significant independent patterns of SST (Sea Surface Temperature) anomalies from the Pacific and Atlantic oceans were used in the PLSR scheme to model the temporal evolutions of TWS (2002 - 2017) over twelve prominent river basins in SA. From the JADE rotation of TWS over SA, strong inter-annual changes in TWS observed over the Amazon basin and within its floodplain corridors were identified. The unabated mass loss in Patagonia ice-field caused by warming of the climate and other GRACE-hydrological signals were also retrieved from the JADE scheme. The rainfall TWS relationship is considerably strong (r = 0.80 at 0 - 2 months lag) in much of tropical SA, including the Amazon basin and highlights the influence of climate variability in the region. Medium (r = 0.40) and moderately strong (r = 0.60) rainfall-TWS relationship were also found to be significant (a = 0.05) but with up to 4 months lag and more in some basins. During the 2010 - 2017 period, estimated TWS trends (a = 0.05) showed a considerable fall in Orinoco (- 38.48 +/- 7.90 mm/yr) and Sao Francisco (- 30.84 +/- 4.17) while the strongest rise was found in Uruguay (28.28 +/- 3.49 mm/yr). As the rainfall-TWS relationship is not statistically significant (a = 0.05) in some areas, the spatial distribution of trends in TWS and rainfall, especially in some arid regions, which are inconsistent confirm possible impacts resulting from complex hydrogeological processes and/or anthropogenic influence. Further, in the modelling of TWS time series using the JADE-PLSR scheme, several validation skill metrics (e.g., R-2 , Nash-Sutcliffe Efficiency) confirm the considerable agreements between predicted and observed TWS in the Amazon (R-2 = 0.95), Orinoco (R-2 = 0.94), Tocantins (R-2 = 0.91), and Chobut (R-2 = 0.88). However, GRACE-hydrological signals in some regions are somewhat complex given the relatively higher uncertainties in the multivariate models employed in this study.