## 4 Discussion
### The Metric Analysis Grid in the Two-Dimensional Euclidean Space  
The analysis of river segments using the metric analysis grid allows us to properly quantify the river dynamics in space-time. Figure 13 shows the superior quality of the results obtained with the metric analysis grid, compared to what we would have obtained using cross-sections. As shown by the classical approach, in the case of the Clamoux River, cross-sections could not allow us to properly quantify bank dynamics because (i) mean active-channel width (\(W\)) variations are very weakly negative (\(W=-0.33\) m), which does not at all reflect the bank dynamics (i.e., right bank accretion and left bank retreat) perceived by the metric grid analysis, and (ii) the critical sites for bank management are not captured. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Lateral Mobility Rate (LMR)**} \\ \hline \hline \multirow{2}{*}{Number of cells with morphological change (\(n_{\mathrm{gc}}\))} & Left bank & Right bank \\  & 190 & 201 \\  & 206 & 206 \\  _LMR_ (in \%) & 92 & 98 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Application of the _LMR_ indicator from the study case (Clamoux River). This metric analysis grid is a dashboard that is useful not only for scientists but also for river managers. In fact, in a river-restoration context, we need fairly detailed monitoring of the geomorphological readjustments produced by the river subjected to new boundaries conditions (removal of lateral constraints, increase in the energy slope, the channel width and braided index, decrease of sinuosity index, reactivation of sediment transport and alluvial forest development). We strongly recommend annual monitoring in the case of a dynamic river (\(\omega>30\) W/m\({}^{2}\)) in addition to a survey after a significant flood event. It is therefore necessary to plan one to several overflights of the studied area (drone, plane) to obtain images (photos, LIDAR). Monitoring campaigns should not be held during the growing season in order to limit vegetation hold on images. This metric analysis grid constitutes a simplified approach to the geomorphological reality. A grid with a metric resolution (i.e., the resolution chosen here) indeed makes it possible to perceive geomorphological changes (e.g., bank retreat, bar accretion) within the active channel greater than 1 m. As part of a braided, active channel without strong human and/or material stakes, we are not within a meter. If this is the case, we must move to an engineering-type approach. Anyway, the analysis resolution can be adjusted by the operator depending on the precision desired. The grid does not prevent finer measurements on erosion processes, but the advantage is to bring geographical (systemic) dimensions of the active-channel functioning here. This systemic vision is what managers expect from researchers. This method based on the metric grid also has the advantage of being able to survey the river banks without using images. In fact, the bank lines can be first surveyed with a GPS and then subsequently transferred to the metric grid. It can even be considered to transfer all types of field observations (geomorphology, sediment, vegetation, structures) directly to the grid. This method assumes a good knowledge of the field and geomorphological processes because rivers are systemic, and it is not enough to observe erosion or deposition in such sites rather than others: we have to know how to interpret and predict the future of the river segments at +5 or +10 years at least (ideally +50 years). Only the understanding of geomorphological processes makes it possible to interpret our metric analytical grid and its use in the future. About the braided index, the work can be improved concerning the quantification of the number of alluvial bars. However, for river restoration, this may be enough to identify sediment storage areas.