Runoff Prediction for Dam Safety Evaluations Based on Variable Time of Concentration

This paper describes a method for estimating runoff hydrographs for dam safety evaluations in which the time of concentration is considered dependent on the magnitude of the excess rainfall intensity. Current practice for hydrologic routing assumes the time of concentration to be invariant and a function of basin characteristics. The proposed method addresses the limitations arising from the assumed linearity in the unit hydrograph by showing that the time of concentration is dependent on the excess rainfall intensity through a power relationship. The proposed method uses a variable flow velocity approach to compute travel time and construct time-area curves for a range of excess rainfall intensities. From the derived relationships between time of concentration, flow, and excess rainfall intensity, an explicit nonlinear convolution is performed to compute runoff hydrographs. In its current implementation, the method assumes a uniform distribution of rainfall over the entire watershed. This method is applied to a 282-km2 gauged watershed in Northern California and computed hydrographs are compared with measured runoff hydrographs for six large storms. The proposed method is then compared with constant time of concentration predictions. It is shown that using the traditional invariant time of concentration would require different times of concentration for different storms to match measured discharges. By incorporating a variable flow velocity field and a variable time of concentration, surface hydrologic predictions would reproduce more closely measured discharge. The time of concentration is not a property of the physical characteristics of a watershed alone but a variable that depends also on the intensity and temporal distribution of precipitation. Because the method explicitly accounts for the nonlinear effects arising from variations in rainfall intensity, it is best suited for the evaluation of extreme events, which are characterized by large precipitation intensity pulses. It is shown that current hydrologic models based on a constant time of concentration may underestimate peak discharge associated with the extreme events used in dam safety evaluations.