Empirical Formulation for Time of Concentration Based on Watershed Morphometry Using the Diffusion Wave Equation (DWE) Model

Time of concentration (Tc) is a crucial parameter in flood design analysis, impacting water structure dimensions and infrastructure planning. Inaccuracies in Tc can lead to potential errors in peak discharge (Qp) estimations of approximately 75%. Therefore, this study aimed to investigate Tc empirical formulation based on morphometric characteristics using the Diffusion Wave Equation (DWE) model. Tc formulation model was developed by considering the morphometry characteristics of the watershed related to drainage density. The development process was conducted by numerical modeling using the HEC-RAS 2D 6.4 version to model the precipitation and infiltration data. Subsequently, a rainfall simulator for laboratory experiments was used to test the hydrological performance in the physical model, enabling calibration of Tc. The results showed that Tc equation was based on morphometric parameters, specifically with the addition of the influence of drainage density (D). Through trial and error as well as HEC-RAS 2D modeling using DWE method, the equation was obtained by modifying the Kerby-Hathaway equation with Tc = 1.95. . Validation using 35 numerical model data showed an RMSE value of 12.65, NSE of 0.84, and PBIAS of 5.91, indicating excellent model performance in predicting Tc. The verification formula in four measured watersheds including Bangga, Baholomeo, Upper Ciliwung, and Wiroko, showed an average error of 13.48%. The value was better than the Kerby-Hathaway, Kirpich, and Nakayasu SUH equations, with errors of 18.70%, 27%, and 20.37%, respectively. These results showed that the developed equation performed optimally for predicting Tc in the observed watersheds.