The directional unit hydrograph model: Connecting streamflow response to storm dynamics

Storm velocity (i.e., direction and speed) and structure (i.e., shape and intensity) play a critical role in streamflow response. These characteristics determine the timing and magnitude of precipitation fluxes across the watershed that drive runoff generation and conveyance along the river network. While previous efforts have used spatially explicit hydrologic models to assess the role of storm properties in streamflow magnitude, their computational demand significantly limits the range of scenarios that can be explored, hindering our ability to systematically identify critical conditions leading to extreme events. To address this technical gap, we introduce the Directional Unit Hydrograph (Directional-UH) model, a parsimonious approach based on the classic theory of the Unit Hydrograph. The Directional-UH extends the original theory by relaxing the assumption of spatial uniform rainfall and incorporating storm direction and speed into the unit hydrograph function. The model conceptualizes storms as rectangular structures with constant intensity moving along a linear trajectory with constant speed. We verify and validate our conceptualization by comparing with simulations, based on observations of extreme rainfall events, of the distributed hydrological model Hillslope-Link-Model (HLM) in the Turkey River basin in Iowa, USA. Then, the Turkey River basin is used as a testbed to illustrate three practical applications of the Directional-UH model. First, we identify the storm trajectory that produces the highest peak flow response. Second, we determine the storm characteristics that maximize the peak flow response by synchronizing storm motion and flood wave; we refer to this as the resonance condition. Third, we systematically explore the compounding effects of consecutive storm events with different trajectories to identify critical combinations that exacerbate the peak flow magnitude. The results on our testbed demonstrate that storm velocity has the potential to increase by a factor of two the peak flow magnitude when compared to stationary storm events. Overall, the parsimonious nature of the Directional-UH model offers a unique and valuable tool for modeling, predicting, and interpreting rainfall-runoff dynamics through the lens of storm direction, speed, and structure.