In many river basins around the world, inaccessibility of flow data is a major obstacle to water resource studies and operational monitoring. This paper describes a geospatial streamflow modeling system which is parameterized with global terrain, soils and land cover data and run operationally with satellite‐derived precipitation and evapotranspiration datasets. Simple linear methods transfer water through the subsurface, overland and river flow phases, and the resulting flows are expressed in terms of standard deviations from mean annual flow. In sample applications, the modeling system was used to simulate flow variations in the Congo, Niger, Nile, Zambezi, Orange and Lake Chad basins between 1998 and 2005, and the resulting flows were compared with mean monthly values from the open‐access Global River Discharge Database. While the uncalibrated model cannot predict the absolute magnitude of flow, it can quantify flow anomalies in terms of relative departures from mean flow. Most of the severe flood events identified in the flow anomalies were independently verified by the Dartmouth Flood Observatory (DFO) and the Emergency Disaster Database (EM‐DAT). Despite its limitations, the modeling system is valuable for rapid characterization of the relative magnitude of flood hazards and seasonal flow changes in data sparse settings.