Abstract: A new matrix operator framework is developed to analyze results from climate modeling studies that employ numerical water tracers (WTs), which track the movement of water in the aerial hydrological cycle from evaporation to precipitation. Model WT output is related to the fundamental equation of hydrology, and the moisture flux divergence is subdivided into the divergence of locally evaporated moisture and the convergence of remotely evaporated moisture. The formulation also separates locally and remotely sourced precipitation. The remote contribution (also the remote moisture convergence) may be further subdivided into zonal, meridional, intrabasin, and interbasin parts. This framework is applied to the preindustrial climate as simulated by a global climate model in which water has been tagged in 108 latitude bands in each of the major ocean basins, and in which each major land mass has been tagged separately. New insights from the method reveal fundamental differences between the major ocean basins in locally sourced precipitation, remotely sourced precipitation, and their relative partitioning. Per unit area, the subtropical Atlantic is the largest global moisture source, providing precipitable water to adjacent land areas and to the eastern Pacific tropics while retaining the least for in situ precipitation. Subtropical moisture is least divergent over the Pacific, which is the smallest moisture source (per unit area) for global land areas. Basins also differ in how subtropical moisture is partitioned between tropical, midlatitude, and land regions. Part II will apply this framework to hydrological cycle perturbations due to CO2 doubling.