2.2.3 Weighting factor - HydrogeomorphologyTools/SedInConnect_2.3 GitHub Wiki

The weighting factor W, which appears in upslope and downslope components of IC (Eqs. 2 and 3), was introduced by Borselli et al. (2008) to model the impedance to runoff and sediment fluxes due to properties of the local land use and soil surface. Borselli et al. (2008) used the C-factor of USLE-RUSLE models (Wischmeier and Smith 1978; Renard et al. 1997) as weighting factor W. The C-factor, related to vegetation cover and management, attains its maximum value when the soil is more at risk of erosion and approaches zero when the soil is more protected. However, the same authors stressed that W should be derived from the surface characteristics that influence runoff processes and sediment fluxes within a watershed or on a hillslope. Manning’s n roughness coefficient meets these requirements; it could be especially suitable, as an alternative to the C-factor, in areas with a great heterogeneity of land use or in the case of a study aiming at evaluating the role of different vegetation covers on sediment dynamic). LiDAR-derived HR-DTMs permit the computation of geomorphometric indices able to represent fine-scale topographic variability, thus furnishing valuable information on the surface roughness. Accordingly, we decided to propose a local measure of topographic surface roughness, i.e. a roughness index (RI), as the weighting factor W. The roughness index is calculated as the standard deviation of the residual topography at a scale of few meters (Cavalli et al. 2008; Cavalli and Marchi 2008). The residual topography is computed as the difference between the original DTM and a smoothed version derived by averaging DTM values on an nxn cells moving window. The averaged DTM is necessary to avoid the effect of large scale topography (i.e. slope gradient). Finally, the standard deviations of residual topography values are computed in an nxn cells moving window over the residual topography grid. The roughness index is then defined as:

Eq. 4

where n^2 is the number of the processing cells within the nxn cells moving window, xi is the value of one specific cell of the residual topography within the moving window, and x_m is the mean of the n^2 cells values. The weighting factor is expressed as follow:

Eq. 5

where RI_MAX is the maximum value of RI in the study area. To avoid infinites or close-to-infinite ratios in Eq. 3, all the values in W that fall in the range 0-0.001 are trimmed to 0.001. This standardization of roughness value, which causes W to range from 0.001 to 1, is introduced for three reasons: (i) to have the same range of variation as for S factor in order to weight them equally in the model; (ii) to remove the bias due to high RI values, and (iii) to provide comparable values with USLE C-factor and therefore with the original model by Borselli et al. (2008). The use of a roughness index as weighting factor in the IC has several advantages: i) the weight is estimated objectively; ii) it avoids the use of tabled data such as those used for the C-factor of USLE, which are essentially devised for agricultural environments; iii) it allows the model to be applied straightforwardly, requiring only the DTM as an input. Furthermore, the model by Borselli et al. (2008) focuses on environments that justify the use of the USLE C-factor. Vegetation cover and land use management data used to determine the C-factor are suitable to describe impedance to runoff and sediment fluxes process in agricultural and forest environments. In Alpine catchments, large unvegetated areas are present with different surface roughness depending on the characteristics of outcropping rock and debris cover. In these bare areas, the C-factor would not provide differences in the impedance to sediment transport, which can be better represented by a proxy based on topographic roughness. Moreover, a roughness-based index is more suited for modeling sediment transfer by debris flows, which have a major role in sediment-related processes in Alpine basins. In such a context, we argue that the characterization of surface roughness represents a better proxy for sediment transport impedance compared to the C-factor. It is important to emphasize that the choice of the weighting factor W related to the impedance to sediment fluxes is free. This means that, according to the objective of the study, the user can use different parameters expressing the impedance to sediment fluxes (e.g., C-factor of the USLE as in the Borselli et al., 2008, Manning’s n, or topographic roughness computed on a high-resolution DTM). A basic requirement to be met is that the weighting factor varies on the range 0 < x < 1.