Estimating time of concentration on low-slope planes using diffusion hydrodynamic model

The time of concentration (T _c) is an important parameter for hydrologic design, analysis, and modeling. Error in the estimation of T _c will cause error in prediction of peak discharge (Q _p), resulting in an incorrect design. Overland flow T _c depends on several factors, such as rainfall intensity (i), length (L), topographic slope (S ₀), and flow resistance (n). Generally, T _c has an inverse relation to S ₀. For the areas with very small or zero S ₀, use of such small values for S ₀ in traditional methods (empirical equations) for estimating T _c can produce very large values of T _c that seem to be unrealistic and incorrect. This study was conducted to identify a lower slope bound (SLB) for the use of traditional equations in determination of T _c and to propose the use of an alternate method for the determination of T _c on low-slope planes. The diffusion hydrodynamic model (DHM) was validated using data collected from published studies and field data collected in this study, including observed rainfall hyetographs and runoff hydrographs for 27 rainfall events for watersheds with relatively low-slope. After model validation, DHM was used to generate parametric relations between T _c and its explanatory variables (rainfall intensity, length, slope and resistance to flow) and extend the regression model to low-slope planes.