## 3 Results and Discussion
### Discussion  
#### 3.4.1 Conceptualization and Development of the MAS Model  
In this multiagent model, the transition rules were developed to be simple and easy to implement, with various simplifying assumptions. Like most multiagent models, this makes it a tool that can be transposed and used in various problems. The comments of [53] have emphasized this simplicity of CA/MAS models compared to approaches based on physical equations. However, this point of view needs to be discussed. Certainly, the behavioural rules used to represent water and its path are often simple, but practice shows that the implementation of the model can introduce unexpected complexity into its overall behaviour. This is what makes these approaches so valuable. The complexity results mainly from the interactions between runoff generation, water flow, and infiltration.  
The instantaneous rainfall (Assumption 1) and short concentration time (Assumption 3) seem to be sufficient for the work on our small watershed, provided that we keep about the same surface size, given the fine resolution of the DTM. These assumptions are also adapted to our region where most rainfall events are short and intense, such as thunderstorms, generating fast and sudden floods. This confirms the fact that the model presented in this paper is particularly adapted to the study of flash floods.  
From the moment we want to free ourselves from these hypotheses, which can be limiting, the main obstacle to overcome is the memory capacity of computers. Indeed, a point that must be considered in cellular automaton or multiagent system type models is the computing time and the hardware requirements necessary to run the simulations. The simplifying assumptions that have been adopted allow us to run a simulation by creating only one (and only one) hydrological agent on each field cell during the rainfall simulation. Considering the resolution of our DTM, the model creates about 110,000 hydrological agents at the same time. With this, the simulation time needed with a good computer is already very long. With the ever-increasing evolution of computer memory, it will be possible to eliminate these assumptions with more powerful machines.  
The choice aimed at not using the unit of flow measurement (m\({}^{3}\)/s) because our model is not intended to plot a flood hydrograph. Rather, its objective is to quantify  
Figure 12: Evolution of the gap between the connectivity for a 40 mm rainfall and for a 5 mm rainfall (**left**). Evolution of the gap between the connectivity for a 40 mm rainfall and for a 5 mm rainfall (**right**).  
connectivity based on synthetic spatial indicators. However, it is technically possible to calculate the discharge (m\({}^{3}\)/s) even with the \"ticks\" of the model. This has already been performed for the SMA model of [38], in which the authors were able to correctly reconstruct flood hydrographs and compare them to actual measurements. To this purpose, we considered the time step \"ticks\" as being a time step with a classical unit of time (the second, for example--in practice, however, it can be the time step corresponding to the hydrometric data that we have). We name this time step dt. Then, we assigned a displacement speed to the hydrological agent (by giving it a certain value or by using a hydrological formula--Manning's equation, for example). We can then calculate, at each time step, the distance that is covered by the hydrological agent in one tick. Each agent then moves over this distance carrying its volume of water. Finally, to determine the discharge (in m\({}^{3}\)/s) at the outlet (or at any point where we wish to calculate it), we divided the sum of the volumes of water brought by all the agents on this point by the simulation time step dt. Although this goes beyond the objective of this paper, it would be interesting in other circumstances to consider using this technique.