Vertical load is the power flow between electrical transmission and distribution networks. In the past, large-scale generators connected to transmission systems supplied consumers connected to lower voltage levels across distribution grids. Thus, vertical loads tended to be downward-oriented. This paper presents a spatiotemporal distributed energy resources (DER) diffusion model to analyze vertical load uncertainty resulting from different DER diffusion process representations currently used in the industry and academia. Network planners and operators can use such model to understand the long-term evolution of load at the T/D boundary. The proposal is applied to the Portuguese power system, combining, as first of its kind, highly granulated population census with georeferenced transmission and distribution network datasets. This application analyzes the 20-year evolution of such vertical load flows at the transmission-distribution boundary under a strong uptake of DER embodied in lower voltage levels in Portugal.