Evaluating the area and position accuracy of surface water paths obtained by flow direction algorithms

•Area and position indicators are created to assess extracted surface water path (SWP).•Theoretical SWP is deduced based on the formula of synthetic surfaces.•Artificial dispersion occurs in SWPs extracted by multiple flow direction algorithms.•Upscaling DEM resolution can decrease the value and position precisions.•Cross compensation decreases value precision but increases position precision. The surface water path (SWP) extracted from digital elevation model (DEM) by flow direction algorithms is widely employed to obtain a variety of topographic variables used in hydrological modeling. Accurate SWPs can facilitate understanding the underlying mechanisms of water movement on Earth’s surface. However, the accuracy of extracted SWPs by different flow direction algorithms has not been systematically studied. In this work, two indicators are developed to measure the area and position errors of extracted SWPs relative to theoretical SWPs on four synthetic surfaces representing typical terrains of natural watersheds. Based on the formulas of the synthetic surfaces, theoretical true SWP can be derived for any grid cell on the DEM discretized from the synthetic surfaces. Several widely used flow direction algorithms including three single flow direction (SFD) algorithms (i.e. D8, Rho8 and D8-LTD approaches) and three multiple flow direction (MFD) algorithms (i.e. FDFM, MFD-md and D∞ approaches) are implemented to extract SWPs. Results suggest that significant distinctions can be detected in SWPs extracted by different flow direction algorithms. The SWPs extracted by SFD algorithms are always one-dimensional non-dispersive lines because SFD algorithms allow only one flow direction at each grid cell. In contrast, the SWPs extracted by MFD algorithms show excessive artificial dispersion. The average area error of extracted SWPs ranges from 16.3% to 75.2% on different synthetic surfaces and the minimum is obtained by FDFM approach for all synthetic surfaces. The average position error falls in the range of 46.0% to 161.4%. The maximum is gained by D8 or FDFM approach, and the minimum by D8-LTD or D∞ approach. The cross compensation of SWP area induced by artificial dispersion leads to relatively high area accuracy but relatively low position accuracy of MFD algorithms. In addition, increasing DEM resolution without capturing more topographic variability can decrease the area and position accuracy due to error accumulation from more steps of flow direction calculation