**3.2 Simulation of the "cauliflower effect" with the RuiCells© model**

To address the "cauliflower effect," we used a specific cellular automaton so-called RuiCells, that has been already described before [26, 27]. For this specific simulation, we simulate the sum of surfaces flowing within networks. Cells at the beginning of the simulations are initialized with their surface (defined by the TIN and depending on the DEM resolution, here 50 m as previous studies have been calibrated on this). RuiCells© handles the advection operator in moving surfaces between each cell, so a formal property defined in classical CA is maintained [48], as transition rules operate on cells based on local neighborhood. Surface flow is routed via each cell until the downstream boundary is reached [48]. At the end of the simulation, a graph presents sum of surfaces registered at each interaction to present the morphological signature of the basins, defined as a function of distance *n* from the outlet (**Figure 3**). Steps are length steps since the surface flow diffusion depends on the spatial lattice size. These surface flow graphs give the 2D theoretical spatial behavior of a catchment. This improves older methods, that only informed on the number of links in the network at a flow distance x to the outlet [46], as areas flowing in RuiCells© follow hydrological rules (differences between surface, linear, or node transition are accounted), and are based on a triangular lattice.

#### **Figure 3.**

*Sum of surfaces per iteration, simulated by RuiCells©.*

#### **Figure 4.**

*The concentration index (CI) estimated by the RuiCells© model.*

**Figure 5.**

*Line of SMax in catchments where runoff concentrate in a short distance (according to Douvinet, 2008): the so-called "cauliflower effect."*

In addition, to track the "cauliflower effect," the highest sum of surfaces (*Smax*) is divided by the square root of the catchment area (A') located upstream (**Figure 3**), to define a Concentration Index (CI). *Smax* equals to the highest line of cells located at a distance n from the point of measurement. As *Smax* is related to a length (since the square root equals to the average diameter of the upstream area), CI is dimensionless (**Figure 4**). Values are automatically calculated during the simulation process and are mapped. Strong values (colored in red) identify the neuralgic points inside the basin where the network is very effective with respect to the shape in which it is inserted. Values have the same significance regardless of the basin area if the TIN resolution never changes. In this approach, we always use a DEM of 50-m long. If CI equals to 50, it indicates a medium flow concentration: the peak of surfaces (*Smax*) corresponds to half of the average diameter. But if CI values exceed 55, networks and surfaces appear highly well-structured [25]. If strong values are observed, the efficient line of cells *Smax* is mapped, and a perfect form (so-called the "cauliflower effect") appears. Examples (**Figure 5**) illustrate this in previously studied catchments: red stars located the efficient points, blue lines some of the branches of the networks, and black lines the surfaces. Points

and linear with IC > 55 concentrate high surface flows in a short distance, with a minimum energy expenditure [27, 47].

#### **3.3 Prospects and limitations**

Simulating the influence of morphological conditions on hydrological responses is limited for a few reasons: (1) this theoretical approach cannot be compared with real simulation results obtained with more pervasive models; (2) the efficient points can be located within catchments where no violent floods occurred (probably due to the lack of intense rains); (3) sediment production is not combined with water production, while these processes could complexify the real hydrological response.

Estimating the "cauliflower effect" in the five catchments located at the apex of the Montecito may, however, allow: (1) to check if the erosive areas are related to sudden debris flows and important damage; (2) to compare information supported by the "cauliflower" effect to other results. If the model identifies real sensitive areas, it could extend the model's usefulness and the scope of the model. If the model identifies sensitive areas that have not experienced severe flooding, the rainfall can have not been sufficient to cause them to respond, and the lack of correlation could raise concerns about a future event. If the model does not identify sensitivity in areas that have been affected, the relevance of this model may be excluded, and the morphometric factors should be excluded as efficient, to look for the origin of the susceptibility in the other variables (soil, burned areas, rain, exposure...). This validation process finally allows us to know if RuiCells© can be useful for the decision-makers in the era of extremes, to whom we could say: then, "if you observe a cauliflower effect in a burned catchment, be very careful in case of rains!"
