Developing a generalized dimensionless unit hydrograph based on a hybrid Haan-Fréchet model for enhanced flood forecasting in the data-scarce arid environment of Saudi Arabia

Accurate flood forecasting in arid regions is challenging due to limited hydrological data, complex rainfall patterns, and rapid runoff. This study presents a generalized Dimensionless Unit Hydrograph (DUH) developed using field-measured streamflow data from 28 single-peaked storm events across four sub catchments in the Yiba basin, southwestern Saudi Arabia. Unit Hydrographs (UHs) were derived using the Φ-index loss method, S-curve transformation, and ensemble averaging. The ensemble average UH was normalized to obtain DUH, which was modeled using various fitting equations. The optimal DUH was achieved by combining the Haan equation (rising limb) with the Fréchet model (falling limb), outperforming conventional models like NRCS and SGS. Validation showed excellent agreement in hydrograph shape, with high accuracy in runoff volume ( r = 1, RMSE = 12,102 m 3 ) and peak flow estimation ( r = 0.87, RMSE = 48.75 m 3 /sec). However, time parameters exhibited relatively weak performance: time to peak, T P , ( r = 0.07, RMSE = 0.25 hr) and base time, T B , ( r = 0.54, RMSE = 22.4 hr); Therefore, they should be used cautiously in time-sensitive forecasting. Despite this, the proposed DUH offers a robust and scalable tool for flood forecasting in arid and ungauged basins, although further refinement is needed for the time parameters of the hydrograph.