Evaluation of flow direction methods against field observations of overland flow dispersion

Despite the broad effort made in grid-based distributed catchment modeling to account for planar overland flow dispersion, actual dispersion experienced by overland flow along a natural slope has not been measured so far, and the ability of terrain analysis methods to reproduce this dispersion has not been evaluated. In the present study, the D8, D8-LTD, D$infty$-LTD, D$infty$, MD$infty$, and MD8 flow direction methods are evaluated against field observations of overland flow dispersion obtained from novel experimental methods. Thin flows of cold (2--10$^circ$C) water were released at selected points on a warmer (15--30$^circ$C) slope and individual overland flow patterns originating from each of these points were observed using a terrestrial laser scanner and a thermal imaging camera. Prior to each experimental water release, a ScanStation C10 terrestrial laser scanner by Leica Geosystems was used to acquire a point cloud having average density of 25~points/cm$^2$. This point cloud was used to generate alternative grid-based digital elevation models having resolution $h$ ranging from 1~cm to 2~m. During the experiments, an Avio Advanced Thermo TVS-500EX camera by Nippon Avionics was used to monitor land surface temperature with resolution better than $0.05^circ$C. The overland flow patterns were also found to be discernible in terrestrial laser scanner reflectance signal acquired immediately following the flow experiments. Overland flow patterns were determined by considering contrasted temperature and reflectance of the dry and wetted land surface portions. Predicted propagation patterns and observed flow patterns were compared by considering the fractions of flow released at the point source that propagates through the grid cells. Predictions of these quantities were directly provided by flow direction methods and by related flow accumulation algorithms. Suitable data for the comparison were derived from observed overland flow patterns by assuming a uniform distribution of flow along each cross section. Planar overland flow dispersion is found to play an important role in the region lying immediately downslope of the point source, but attenuates rapidly as flow propagates downslope displaying a nearly constant width of about 50~cm. In contrast, existing dispersive flow direction methods are found to provide a continued dispersion with distance downslope. Predicted propagation patterns, for all methods considered here, depend critically on $h$. All methods are found to be poorly sensitive in extremely fine grids ($h leq 2$~cm), and to be poorly specific in coarse grids ($h = 2$~m). Satisfactory results are, however, obtained when $h$ approaches the average flow width, with the best performances in terms of Pearson correlation coefficient displayed by the MD8 method in the finest grids ($5~{ m cm} leq h leq 20~{ m cm}$), and by the MD$infty$, D$infty$, and D$infty$-LTD methods in the coarsest grids ($20~{ m cm} < h leq 1~{ m m}$). The results obtained in this study suggest further testing of terrain analysis methods with longer flow patterns and coarser grids. Scale issues affecting the relation between land surface microtopography, dispersion, and size of grid cells involved need then to be addressed to provide a hydrologic model of flow partitioning along the slope directions identified by terrain analysis methods.