Estimating the Stage-Discharge Relationship at the Confluence of Ungauged Streams: A Hydrological Modeling Approach

Abstract

Abstract Understanding flow patterns and developing a stage-discharge relationship is essential for effectively managing and protecting water resources in watersheds. Evidence of streambank erosion at confluences due to high peak flows further highlights the urgency of implementing sustainable management strategies. However, the unavailability of discharge data for sub-watersheds necessitates the use of modeling techniques. This study employed a three-layered Hydrological model VIC to estimate the stage-discharge relationship and analyze flow dynamics. Beaver Creek, a tributary of the Clinch River, and Cox Creek, situated in Knox County, Tennessee, experience seasonal flow fluctuations and sedimentation, which pose significant challenges to stream sustainability. To validate the VIC model, downstream USGS stations were selected to compare model output flow. The VIC model incorporated vegetation, soil, and climate inputs and was calibrated using the efficient Shuffled Complex Evolution Algorithm. The final model outputs demonstrated high performance, with a Nash Sutcliffe efficiency of 0.90 and a linear correlation exceeding 0.87 compared to the USGS downstream stations. The daily fluxes accurately captured flow peaks, demonstrating the model's efficacy. Additionally, the derived stage-discharge relationship provided a power equation with a correlation of 0.76, facilitating further research and analysis. The outcomes of this study hold significant implications for future hydrodynamic modeling efforts, allowing for the observation of flood inundation and wall shear stress at the confluence of Beaver-Cox Creeks.