Evaluation of the topologic instantaneous unit hydrography on rural watersheds in Southeast Arizona

Abstract

Discharge hydrographs computed from the theory of linear flow through topologically random channel networks are compared to observed hydrographs on nine arid-region watersheds, with drainage areas ranging from 0.33 hectares to 1363 hectares, at the Walnut Gulch Experimental Watershed in southeast Arizona. Over 90 rainfall-runoff events are tested, with extremes ranging from 12.5 mm to 71 5 mm for rainfall depth, 0.4 mm to 50 mm for runoff volume, and 0.031 ems to 73.5 ems for peak discharge. Topologic Instantaneous Unit Hydrographs (TIUH's) are estimated from topologic and link-length parameters, and a scaling parameter. The topologic information is parameterized as the number of first-order links (magnitude) and the link-length distribution is parameterized by the mean. Both can be measured in the field or from topographic mapping and aerial photography. The scaling parameter is the "effective" kinematic celerity, which is a single-valued estimate of the kinematic celerity of the flow through the channel network for the duration of the event. The TIUH's lead to unit hydrographs, which are convolved with temporally distributed rainfall excess patterns computed using both the 0 index and the curve number, to give composite watershed hydrographs. Effective kinematic celerities are varied until the composite hydrographs match the observed hydrographs in terms of peak discharge and hydrograph efficiency. Results indicate that the TIUH approximately reproduces observed hydrographs, with calibrated effective kinematic celerities that fall within a reasonable range of magnitudes. Agreement between simulated and observed hydrographs is improved by introducing a lag to account for overland travel times to the channel network. The magnitude of the calibrated effective kinematic celerity is significantly related to watershed characteristics, including area, length, and slope. Regression equations are developed and the resulting predicted celerities are combined with map measured topologic and link-length parameters to give simulated hydrographs that approximately match the observed. Magnitude and link-length combine into a single parameter that is consistent across map scales and has the potential to be a watershed descriptor. Calibrated values of effective kinematic celerity vary little across map scales, suggesting that adequate results are obtained without additional expense for highly detailed mapping.