Online Resource 1: Details of DEM pre-processing and interpolation
To produce the DEMs, the input data were the contour lines with 5 m intervals from the 1:5,000 topographic maps of Gobierno de Canarias (GRAFCAN, 2009). The DEMs for each studied edifice were obtained by lineal interpolation implemented into the ILWIS software package (Gorte and Koolhoven, 1990). This interpolation starts with rasterization of the input contour data with the elevation values. Once all contour lines are rasterized, a linear interpolation is made between the grid cells with elevation values. To obtain the undefined elevation values, the shortest distances are measured between neighbouring contour lines, based on the Borgefors distance method (Borgefors, 1984; Gorte and Koolhoven, 1990). Thus, the undefined elevation values, Zgrid cell, are calculated as (ILWIS, 2001):
Zgrid cell = (1)
where Z1 and Z2 are the elevation values of the lower and higher contour lines, respectively. Thus the Z2–Z1 is the contour interval of the input data (i.e. 5 min the present study). The terms d1 and d2 are the shortest distances between Zgrid cell and the lower and higher contour lines. Due to the rasterization of the original input data as a first step of data processing, the user-defined grid cell size is crucial. If the user-defined grid cell size is less than the minimum distance between the contour lines, some contour lines will share the same grid cell, leading to inappropriate rasterized representation of the original data. Thus, in the present study, the grid cell size was determined on the basis of contour line properties, such as distance between neighbouring contour lines, i.e. complexity of the terrain modelled(e.g. Hengl, 2006). On a try and error-basis, input vector lines were rasterized into 0.5 m and 1 m horizontal resolutions, respectively (Fig. 4). Neighbouring contour lines were detected after rasterization by a 33 moving window. Based on the number of neighbouring rasterized contour lines, a 0.50.5 m grid cell size was chosen as itis small enough to resolve the topography captured by the original contour data. The elevation value for each grid cellwas established with a precision of 4 decimals, to avoid artificially generated flat cells (i.e. neighbouring cells with the same elevation value). Note thatthe DEM’s generated in this study with 0.5 m horizontal resolution does not imply a better accuracy of topography than a high-resolution (1–2 m), Light Detection and Ranging (LiDAR) survey-based Digital Surface Model (DSM). This0.5 m grid cell size is, however, needed to avoid information loss during interpolation. Therefore, the scale and accuracy of the topographic and geometric information extracted from our DEMs here isof 1:5 000, i.e. the scale of the input topographic maps.
On the interpolated DEMs, flat analysis (Fig. 4) was performed in order to detect interpolation errors derived from, for example, the inadequate determination of resolutions (Martz and Garbrecht, 1998). The real flat cells (i.e. ‘no flow’), are those cells that have at least onecell in its 33neighbourhood with the same elevation value (Martz and Garbrecht, 1998; Jordan, 2007). There are two additional types of flat cells: inflow and outflow cells(Garbrecht and Martz, 1997). An inflow cell is characterized by neighbouringcells in the 33 matrix with higher or equal elevation values. Thus, the cell can receive inflow from the higher neighbours, but the flow cannot leave the cell. For outflow cells, all neighbours have lower or equal elevations. The importance of flat cell detection is that in a grid-based environment, the first-order derivate of a surface (e.g. slope angle or aspect) of a given location of a DEM is calculated ‘indirectly’ from the values of the surrounding cells in a 33 grid kernel. Thus, the existence of any kind of flat cells may cause errors in the calculations of the derivates. For example, the slope and aspect value of a real flat cell is zero (e.g. Jordan, 2007). On the DEMs of the Bandas del Sur, small and mostly scattered distributions of flat cells are located at (1) landslides scarps, (2) anthropogenic pits and walls, as well as, (3) on the bottom of gullies and valleys. These errors were systematically removed with a 55 (i.e. 2.52.5 m) average moving window. The real flat cells on topographic peaks and depressions were discardedfrom gradient vector calculations. Detailed properties of the produced DEM can be found in the Online Resource 2.
References
Borgefors, G., 1984. Distance transformations in arbitrary dimensions. Computer Vision, Graphic, and Image Processing, 27(3): 321-345.
Garbrecht, J. and Martz, L.W., 1997. The Assignment of Drainage Direction over Flat Surfaces in Raster Digital Elevation Models. Journal of Hydrology, 193: 204-213.
Gorte, B.G.H. and Koolhoven, W., 1990. Interpolation between isolines based on the Borgefors distance transform. ITC Journals, 1990-3: 245-247.
GRAFCAN, 2009. Mapa Topográfico de las Islas Canarias (1:5.000). Cartográfica de Canarias.
Hengl, T., 2006. Finding the right pixel size. Computers & Geosciences, 32: 1283-1298.
ILWIS, 2001. ILWIS 3.0 Academic - User's Guide. Unit Geo Software Development, Sector Remote Sensing & GIS, IT Department, International Institute for Aerospace Survey and Earth Sciences (ITC), Enschede, The Netherlands.
Jordan, G., 2007. Digital Terrain Analysis in a GIS Environment. Concepts and Development. In: R.J. Peckham and G. Jordan (Editors), Digital Terrain Modelling. Development and Applications in a Policy Support Environment. Springer, Berlin, pp. 1-43.
Martz, L.W. and Garbrecht, J., 1998. The Treatment of Flat Areas and Depressions in Automated Drainage Analysis of Raster Digital Elevation Models. Hydrologic processing, 12: 843-855.