Representing elevation uncertainty in runoff modelling and flowpath mapping

Vertical inaccuracies in terrain data propagate through dispersal area subroutines to create uncertainties in runoff flowpath predictions. This study documented how terrain error sensitivities in the D8, Multiple Flow (MF), DEMON, D-Infinity and two hybrid dispersal area algorithms, responded to changes in terrain slope and error magnitude. Runoff dispersal areas were generated from convergent and divergent sections of flow, medium, and high gradient 64-ha parcels using a 30 m pixel scale control digital elevation model (DEM) and an ensemble of alternative realizations of the control DEM. The ensemble of alternative DEM realizations was generated randomly to represent root mean square error (RMSE) values ranging from 0·5 to 6 m and spatial correlations of 0 to 0·999 across 180 m lag distances. Dispersal area residuals, derived by differencing output from control and ensemble simulations, were used to quantify the spatial consistency of algorithm dispersal area predictions. A maximum average algorithm consistency of 85% was obtained in steep sloping convergent terrain, and two map analysis techniques are recommended in maintaining high spatial consistencies under less optimum terrain conditions. A stochastic procedure was developed to translate DEM error into dispersal area probability maps, and thereby better represent uncertainties in runoff modelling and management. Two uses for these runoff probability maps include watershed management indices that identify the optimal areas for intercepting polluted runoff as well as Monte-Carlo-ready probability distributions that report the cumulative pollution impact of each pixel's downslope dispersal area.