Two methods for predicting direct runoff from rainfall data were applied to several basins and the resulting hydrographs compared to measured values. The first method uses a geomorphology-based unit hydrograph to predict direct runoff through its convolution with the excess rainfall hyetograph. The second method shows how the resulting hydraulic routing flow equation from a kinematic wave approximation is solved using a spectral method based on the matrix representation of the spatial derivative with Chebyshev collocation and a fourth-order Runge-Kutta time discretization scheme. The calibrated Green-Ampt (GA) infiltration parameters are obtained by minimizing the sum, over several rainfall events, of absolute differences between the total excess rainfall volume computed from the GA equations and the total direct runoff volume computed from a hydrograph separation technique. The improvement made in predicting direct runoff using a geomorphology-based unit hydrograph with the ephemeral and perennial stream network instead of the strictly perennial stream network is negligible. The hydraulic routing scheme presented here is highly accurate in predicting the magnitude and time of the hydrograph peak although the much faster unit hydrograph method also yields reasonable results.