## Materials and Methods  
### Caesar-Lisflood LEM: Model Description and Calibration  
Caesar-Lisflood is a second-generation LEM that can be used to model short- and long-term topographic changes and sediment flux of complex natural landscapes. In the last decade, the model was extensively used for the analysis at different temporal and spatial scales of issues of applied geomorphology and hydrology. As a matter of fact, there are at least 60 published papers dealing with model applications [40]. A rigorous and complete description is beyond the scope of this paper and is reported in [41]. The Caesar-Lisflood LEM uses a hydrological model to generate spatially distributed runoff, which is generated on a DEM to estimate flow depths and velocities [41]. Such data are used to model topographic changes and to assess topographic modification (i.e., erosion and deposition) within an active layer with a pre-defined grain-size of deposits. The modified DEM becomes the starting point for the next time step of the simulation. The user can select a catchment mode with no internal influxes other than rainfall or a reach mode, where the flow enters through the main river. Input data of the model are: DEM, grain-size features, rainfall, depth of bedrock and Manning coefficient values [24; 41]. Rainfall precipitation represents the input to derivate catchment runoff, which in turn drives topographic changes (i.e., erosion and deposition) and controls fluvial and slope processes for the modeled time step [28]. Depths and velocities of the flow are estimated from flow discharges between raster cells using the Manning's equation and are then used to model both the sediment transport and erosion/deposition processes. Caesar-Lisflood estimates sediment transport in relation to nine grain-size fractions, which are selected by use. Sediment can be transported as bed load or as suspended load. Soil creep and landslide processes can be also included in the simulation [41; 42] using a critical slope angle threshold. This condition allows the re-distribution of landslide and soil creep deposits from slopes to the fluvial system. Elevations and grain size features of the cells are updated according to the estimation of erosion/deposition and slope process. Model outputs are: (i) elevation changes; (ii) flow discharges; (iii) sediment fluxes at the outlet over time [24; 28; 41; 42; 43]. The model is able to reconstruct topographic changes at a sub-metric scale. Input data and model parameters represent the key to derive a robust predictive model, although a recent work by [44] demonstrated that results of the Caesar-Lisflood LEM are influenced only by a limited number of parameters. More specifically, the authors suggest that spatial distribution of Manning coefficient and the selection of the sediment transport formula are the main sensitive parameters of the model results. For this reason, we have carefully selected these parameters: for example, [PERSON]'s sediment transport formula [45] was reconstructed using laboratory tests on (predominantly) sand-based channels and we have here chosen this equation according to the prevalent grain-size deposits of the study area. A 5-m DEM was used for the simulation. Moreover, the other input parameters were accurately derived from lithological, climate, and land-use features of the study area. To introduce a representative framework of the study area, we have preliminarily reconstructed the bedrock depth through a field-based analysis of the lithological units. To this aim, a detailed lithological map has been drawn by review of previous works and new geological surveys. Moreover, field surveys of the soil depth have been performed for the different lithological units of the study area (Figure 2, [34]). This approach allowed us to infer the soil thickness and bedrock depth for each lithological. This kind of information was summarized in a map showing the isopachs of the mean soil thickness (Figure 2c).