Large-scale covariations of freshwater fluxes and storages on land can critically regulate the balance of green (evapotranspiration) and blue (runoff) water fluxes, and related land-atmosphere interactions and hydroclimatic hazards. Such large-scale covariation patterns are not evident from smaller-scale hydrological studies that have been most common so far, and remain largely unknown for various regions and climates around the world. To contribute to bridging the large-scale knowledge gaps, we synthesize and decipher hydroclimatic data time series over the period 1980-2010 for 6,405 catchments around the world. From observation-based data, we identify dominant large-scale linear covariation patterns between monthly freshwater fluxes and soil moisture (SM) for different world parts and climates. These covariation patterns are also compared with those obtained from reanalysis products and Earth System Models (ESMs). The observation-based data sets robustly show the strongest large-scale hydrological relationship to be that between SM and runoff (R), consistently across the study catchments and their different climate characteristics. This predominantly strongest covariation between monthly SM and R is also the most misrepresented by ESMs and reanalysis products, followed by that between monthly precipitation and R. Comparison of observation-based and ESM results also shows that an ESM may perform well for individual monthly variables, but fail in representing the patterns of large-scale linear covariations between them. Observation-based quantification of these patterns, and ESM and reanalysis improvements for their representation are essential for fundamental understanding, and more accurate and reliable modeling and projection of large-scale hydrological conditions and changes under ongoing global and regional change.