<p>Time of concentration (Tc) is a crucial parameter in flood design analysis; inaccuracies in Tc estimation can lead to potential errors in peak discharge (Qp) of up to 75%. This study aims to develop a new empirical Tc formulation based on morphometric characteristics using the Diffusion Wave Equation (DWE) model. Addressing the spatial limitations of conventional equations, the core novelty of this research lies in the integration of drainage density (D) to better capture the spatial complexity of watersheds. 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 parameter optimization (curve fitting) of DWE method, the equation was obtained by modifying the Kerby-Hathaway equation with Tc = 1.95.(L. n)<sup>0.467</sup>. s<sup>− 0.235</sup>. D<sup>− 0.1</sup>. Validation using 35 numerical model data showed an RMSE value of 12.65&#xa0;min, 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 equations, with errors of 18.70%, and 27%, respectively. These results showed that the developed equation performed optimally for predicting Tc in the observed watersheds.</p>

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

  • Mohamad Bagus Ansori,
  • Umboro Lasminto,
  • Anak Agung Gde Kartika,
  • Satria Damarnegara

摘要

Time of concentration (Tc) is a crucial parameter in flood design analysis; inaccuracies in Tc estimation can lead to potential errors in peak discharge (Qp) of up to 75%. This study aims to develop a new empirical Tc formulation based on morphometric characteristics using the Diffusion Wave Equation (DWE) model. Addressing the spatial limitations of conventional equations, the core novelty of this research lies in the integration of drainage density (D) to better capture the spatial complexity of watersheds. 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 parameter optimization (curve fitting) of DWE method, the equation was obtained by modifying the Kerby-Hathaway equation with Tc = 1.95.(L. n)0.467. s− 0.235. D− 0.1. Validation using 35 numerical model data showed an RMSE value of 12.65 min, 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 equations, with errors of 18.70%, and 27%, respectively. These results showed that the developed equation performed optimally for predicting Tc in the observed watersheds.