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Evaluation of Time of Concentration Estimation Equations in Selected Watersheds of Ardabil Province
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Saeed Safari *   , Ali Reza Vaezi , Hossein Shahab Arkhazloo |
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Abstract: (51 Views) |
Extended Abstract
Introduction: Time of concentration is one of the key hydrological parameters in rainfall–runoff analysis. It is widely used for estimating peak flood discharge, designing hydrographs, and determining the dimensions of hydraulic structures. Inaccurate estimation of the time of concentration may lead to erroneous peak discharge calculations, which can result in uneconomical or unsafe hydraulic designs. Since most empirical equations for estimating time of concentration have been developed based on data from specific regions, their direct application to watersheds with different climatic and geomorphological conditions especially in semi-arid and mountainous regions may involve considerable errors. Therefore, evaluating and comparing the performance of these equations under the local conditions of Ardabil Province is essential. The steep slopes of the Ardabil Province’s semi-arid region combined with the high intensity of rain can produce large amounts of runoff very fast. This means it is essential to select a proper time of concentration equation in order to estimate floods accurately and design hydraulic infrastructure correctly. Although many empirical equations are commonly used, few of them have been evaluated systematically in order to determine their applicability in the unique physiographic characteristics of northwestern Iran.
Materials and Methods: This study was conducted in 15 watersheds located in the central part of Ardabil Province, including Aladizgeh, Iyril, Barough, Balighloo Chay, Samian, Soola, Shams-Abad, Amooghin, Anbaran, Kozeh-Topraghi, Namin, Naneh-Karan, Nooran, Nair, and Hir. Morphometric characteristics of the watersheds—including area, basin length, main channel length, mean slope, shape coefficients, and drainage network indices—were extracted using ArcGIS software and topographic maps. Observed time of concentration values were obtained from hydrometric data over the statistical period 2009–2019 (1389–1398 in the Iranian calendar). The time of concentration was then estimated using eight empirical equations: Bransby–Williams, Giandotti, Chow, Federal Aviation Administration (FAA), California, Kerby, Kirpich, and Ventura. Model performance was evaluated using statistical indices including coefficient of determination (R²), root mean square error (RMSE), mean error (ME), mean absolute error (MAE), and Nash–Sutcliffe efficiency coefficient (NSE).
Results and Discussion: The observed time of concentration in the studied watersheds varied between 1.07 and 10.41 hours and showed a very strong and significant correlation with basin area (r = 0.97, p < 0.01), basin length (r = 0.97, p < 0.01), and main channel length (r = 0.91, p < 0.01). The model evaluation results indicated that the Federal Aviation Administration (FAA) method achieved the best overall performance, with an NSE of 0.92, the lowest RMSE (0.67 hours), and the lowest MAE (0.53 hours). The superiority of this method can be attributed to the consistency of its equation structure with the most important controlling factors of time of concentration in the region, namely basin area and flow path length. The observed time of concentration exhibited a very strong and significant correlation with area (r = 0.97, p < 0.01) and basin length (r = 0.97, p < 0.01). The reliance of the FAA equation on key geometric parameters and its balanced consideration of length and slope effects reduced bias and enhanced its accuracy in the semi-arid and mountainous watersheds under study. The California (NSE = 0.88) and Bransby–Williams (NSE = 0.78) methods also demonstrated acceptable accuracy. In contrast, the Ventura method, with a negative NSE (–0.14) and the highest error values, showed the weakest performance. Some relationships, such as the Chow and Kirpich equations, tended to systematically underestimate the time of concentration, which may lead to overestimation of peak discharge. Equations that were mainly based on slope and basin length parameters showed more stability across various watershed scales, according to the comparative statistical analysis. Furthermore, as a result of the scale sensitivity of empirical formulations, model performance tended to improve in medium-to-large watersheds while small and steep catchments showed higher variability and estimation errors. The results also indicated that the accuracy of empirical equations depends on watershed morphometric characteristics, and no single equation performs uniformly under all conditions
Conclusion: Based on the findings of this study, the Federal Aviation Administration (FAA) method is recommended as the most suitable equation for estimating the time of concentration in semi-arid and mountainous watersheds of Ardabil Province. However, due to the strong dependence of model performance on watershed physical characteristics, it is recommended that selected equations be locally calibrated before practical application in hydraulic and watershed structure design, or that a combination of superior equations be used to reduce uncertainty and improve design safety and accuracy. The results highlight how using empirical formulas created in various geomorphological and climatic settings without conducting a regional evaluation could greatly raise the uncertainty in estimating peak discharge. Thus, in similar semi-arid mountainous environments, combining local calibration techniques with morphometric analysis can significantly increase the safety and sustainability of watershed and hydraulic structure design as well as the dependability of hydrological modelling.
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Article number: 7 |
| Keywords: Watershed management, Mountainous watershed, Peak flood discharge, Hydrological models, Semi-arid region. |
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Type of Study: Research |
Subject:
Special
Received: 2026/02/25 | Revised: 2026/05/23 | Accepted: 2026/05/19 | Published: 2026/05/23 | ePublished: 2026/05/23
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safari S, Vaezi A R, Shahab Arkhazloo H. Evaluation of Time of Concentration Estimation Equations in Selected Watersheds of Ardabil Province. jwmseir 2025; 19 (71) : 7 URL: http://jwmsei.ir/article-1-1226-en.html
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