Comparison of Single and Multiple Flow Direction Algorithms for Computing Topographic Parameters in TOPMODEL

Abstract

Single flow direction (sfd) and multiple flow direction (mfd) algorithms were used to compute the spatial and statistical distributions of the topographic index used in the watershed model TOPMODEL. An sfd algorithm assumes that subsurface flow occurs only in the steepest downslope direction from any given point; an mfd algorithm assumes that subsurface flow occurs in all downslope directions from any given point. The topographic index in TOPMODEL is ln (a/tan β), where In is the Napierian logarithm, a is the upslope area per unit contour length, and tan β is the slope gradient. The ln (a/tan β) distributions were computed from digital elevation model (DEM) data for locations with diverse topography in Arizona, Colorado, Louisiana, Nebraska, North Carolina, Oregon, Pennsylvania, Tennessee, Vermont, and Virginia. The means of the ln (a/tan β) distributions were higher when the mfd algorithm was used for computation compared to when the sfd algorithm was used. The variances and skews of the distributions were lower for the mfd algorithm compared to the sfd algorithm. The differences between the mfd and sfd algorithms in the mean, variance, and skew of the ln (a/tan β) distribution were almost identical for the various DEMs and were not affected by DEM resolution or watershed size. TOPMODEL model efficiency and simulated flow paths were affected only slightly when the ln (a/tan β) distribution was computed with the sfd algorithm instead of the mfd algorithm. Any difference in the model efficiency and simulated flow paths between the sfd and mfd algorithms essentially disappeared when the model was calibrated by adjusting subsurface hydraulic parameters.