Grid digital elevation model based algorithms for determination of hillslope width functions through flow distance transforms

Recently developed hillslope storage dynamics theory can represent the essential physical behavior of a natural system by accounting explicitly for the plan shape of a hillslope in an elegant and simple way. As a result, this theory is promising for improving catchment-scale hydrologic modeling. In this study, grid digital elevation model (DEM) based algorithms for determination of hillslope geometric characteristics (e.g., hillslope units and width functions in hillslope storage dynamics models) are presented. This study further develops a method for hillslope partitioning, established by Fan and Bras (1998), by applying it on a grid network. On the basis of hillslope unit derivation, a flow distance transforms method (TD infinity) is suggested in order to decrease the systematic error of grid DEM-based flow distance calculation caused by flow direction approximation to streamlines. Hillslope width transfer functions are then derived to convert the probability density functions of flow distance into hillslope width functions. These algorithms are applied and evaluated on five abstract hillslopes, and detailed tests and analyses are carried out by comparing the derivation results with theoretical width functions. The results demonstrate that the TD infinity improves estimations of the flow distance and thus hillslope width function. As the proposed procedures are further applied in a natural catchment, we find that the natural hillslope width function can be well fitted by the Gaussian function. This finding is very important for applying the newly developed hillslope storage dynamics models in a real catchment.