Extended Abstract
Introduction
Time of concentration (Tc) is one of the most critical hydrological parameters in rainfall-runoff analysis, widely used for estimating peak flood discharge, designing hydrographs, and determining the dimensions of hydraulic structures. Inaccurate estimation of Tc may lead to erroneous peak discharge calculations, resulting in uneconomical or unsafe hydraulic designs. Since most empirical equations for estimating Tc 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 these equations under the local conditions of Ardabil Province is essential. The steep slopes of the region, combined with high-intensity rainfall, can generate large amounts of runoff very rapidly, making the selection of an appropriate Tc equation crucial for accurate flood estimation and proper design of hydraulic infrastructure. Although many empirical equations are commonly used, few have been systematically evaluated to determine their applicability to the unique physiographic characteristics of northwestern Iran. This study aims to evaluate eight empirical Tc estimation methods against observed data from 15 watersheds in Ardabil Province, identify the most accurate equation for local conditions, and assess the influence of morphometric characteristics on model performance. The findings are expected to improve hydrological modeling and support safer watershed management decisions in semi-arid mountainous environments.
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—including area, basin length, main channel length, mean slope, shape coefficients (Horton, elongation ratio, circularity ratio, Gravelius), drainage density, and bifurcation ratio—were extracted using ArcGIS software, topographic maps, and Google Earth, followed by field verification. Observed Tc values were derived from hourly hydrometric data over the period 2009–2019. For six watersheds equipped with limnigraphs, flood hydrographs were directly recorded. For the remaining nine watersheds with only stage data, reliable stage-discharge rating curves were used to convert water levels into hourly discharge, and direct runoff hydrographs were reconstructed. Following NRCS and Chow (1988) standard procedures, Tc was determined as the time interval from the end of effective rainfall to the inflection point on the recession limb of the hydrograph after separating base flow using numerical or semi-logarithmic methods. Tc was then estimated using eight empirical equations: Bransby–Williams (1980), Giandotti (1934), Chow (1962), FAA (1970), California (1942), Kerby (1959), Kirpich (1940), and Ventura (2007). Model performance was evaluated using R², RMSE, ME, MAE, and Nash–Sutcliffe efficiency (NSE). Pearson correlation analysis examined relationships between Tc and morphometric parameters. All analyses were performed using SPSS 22, Excel 2021, and ArcGIS 10.8.2.
Results and Discussion
Observed Tc in the studied watersheds ranged from 1.07 to 10.41 hours and exhibited very strong, significant correlations 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), indicating that geometric dimensions are the dominant controlling factors. The 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). Its superiority is attributed to the consistency of its equation structure with the key controlling factors—basin area and flow path length. The California (NSE = 0.88) and Bransby–Williams (NSE = 0.78) methods also demonstrated acceptable accuracy. In contrast, the Ventura method showed the weakest performance, with a negative NSE (–0.14) and the highest error values (RMSE = 2.44, MAE = 1.67). Several equations, including Chow and Kirpich, tended to systematically underestimate Tc, which could lead to overestimation of peak discharge. Model performance improved in medium-to-large watersheds, while small, steep catchments showed higher variability and estimation errors. No single equation performed uniformly across all conditions, highlighting the scale sensitivity of empirical formulations and the need for local evaluation.
Conclusion
Based on the findings of this study, the Federal Aviation Administration (FAA) method is recommended as the most suitable equation for estimating Tc in the semi-arid and mountainous watersheds of Ardabil Province. The FAA method demonstrated balanced performance with minimal bias and high efficiency. The California and Bransby–Williams methods may be used as alternatives but require more caution due to systematic underestimation or overestimation. In contrast, the Ventura and Chow methods are not recommended for application in this region. Due to the strong dependence of model performance on watershed physical characteristics, it is strongly recommended that any selected equation be locally calibrated using hydrometric data before practical application in hydraulic and watershed structure design. Where sufficient data are unavailable, combining results from superior equations (e.g., FAA and Bransby–Williams) is advised to reduce uncertainty and improve design safety and accuracy. The results highlight that applying empirical formulas developed in different geomorphological and climatic settings without regional evaluation can greatly increase uncertainty in peak discharge estimation. Therefore, in similar semi-arid mountainous environments, integrating local calibration techniques with morphometric analysis can significantly enhance the reliability of hydrological modeling, the safety and sustainability of watershed and hydraulic structure design, and ultimately contribute to more effective flood risk management. |
