Storm direction and storm velocity play a critical role in streamflow response; and despite evidence of ongoing changes in storm tracks around the world, there is no practical approach to efficiently assess and quantify the role of these storm properties in streamflow magnitude. We address this technical gap by introducing the Directional Unit Hydrograph (Directional-UH) model to systematically evaluate the storm hydrograph as a function of storm direction and storm velocity. The Directional-UH is based on the well-known theory of the unit hydrograph, which has served as a foundational block of multiple rainfall-runoff models for streamflow prediction. The Directional-UH relaxes the assumption of spatial uniform rainfall prescribed in the original concept of the unit hydrograph, by incorporating storm direction and storm velocity into the unit hydrograph function. The storm structure within the Directional-UH is represented by rectangular storms moving with constant velocity over a linear trajectory. We demonstrated, based on observations of extreme rainfall events, that rectangular storm representations can reproduce streamflow responses similar to those expected from actual radar rainfall observations. The Turkey River basin located in Iowa, USA, is used as a testbed to illustrate three practical applications of the Directional-UH model. First, the storm trajectory that produces the highest peak flow response is identified. Second, the conditions that lead to the rainfall-runoff resonance are determined, which occurs when the storm motion and the flood wave are in sync to maximize the peak flow response. Third, streamflow responses from consecutive storm events are quantified, allowing exploration and identification of critical combinations of storm events that exacerbate the magnitude of flood events. Overall, the simple hydrological inference offered by the Directional-UH makes this model a unique and essential hydrological tool that provides new perspectives to expand our understanding of rainfall-runoff dynamics through the lenses of storm direction and storm velocity.