Fig 14 provides a useful example Fig 14b shows the morphology

Fig. 14 provides a useful example. Fig. 14b shows the morphology captured by a 5 m DTM, and in Fig. 14c, the derived drainage upslope area is displayed. Fig. 14d and e depict the airborne lidar 1 m DTM and the derived drainage upslope area, respectively. We used the D∞ flow direction algorithm (Tarboton, 1997) for the calculation of

the drainage area because of its advantages over the methods that restrict flow to eight possible directions (D8, introducing grid bias) or proportion flow according to slope (introducing unrealistic dispersion). It is clear from the figure that it is possible to correctly detect the terraces only with high-resolution topography (∼1 m DTM, Fig. 14d), thus providing a tool to identify the terrace-induced flow direction changes with more detail. Another interesting result can be extracted from this picture. Significant parts of the surveyed terrace failures mapped in the field through DGPS (red points) are located exactly (yellow arrows) where there is an evident flow direction change due to terrace feature (Fig. 14e). However, this approach (purely topographically based), while providing a first useful overview of the problem needs to be improved with other specific and physically based analyses because some of the surveyed wall failures are not located on

flow direction changes (Fig. 14e). To automatically identify the location of terraces, we applied a feature extraction technique based Nutlin-3 ic50 on a statistical threshold. Recent studies underlined how physical processes and anthropic features leave topographic signatures that can be derived from the lidar DTMs (Tarolli, 2014). Statistics can be used to automatically detect or extract particular features (e.g., Cazorzi et al., 2013 and Sofia et al., 2014). To automatically detect terraces, we represented surface morphology with a quadratic approximation of the original surface (Eq. (1)) as proposed by Evans (1979).

equation(1) Z=ax2+by2+cxy+dx+ey+fZ=ax2+by2+cxy+dx+ey+fwhere x, y, and Z are local coordinates, filipin and a through f are quadratic coefficients. The same quadratic approach has been successfully applied by Sofia et al. (2013), and Sofia et al. (2014). Giving that terraces can be considered as ridges on the side of the hill, we then computed the maximum curvature (C  max, Eq. (2)) by solving and differentiating Eq. (1) considering a local moving window, as proposed by Wood (1996). equation(2) Cmax=k⋅g⋅(−a−b+(a−b)2+C2)where C  max is the value of maximum curvature, the coefficients a  , b, and c   are computed by solving Eq. (1) within the moving window, k   is the size of the moving window and g   is the DTM resolution. The moving window used in this study is 5 m because it was demonstrated in recent studies (e.g., Tarolli et al., 2012) that the moving window size has to be related to the feature width under investigation.

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