## 4 Experiments and Results
### Evaluation of the Flash Flood Forecasting Method  
In the case of the experiments related to flood forecasting, data were used from the sensor displayed in Figure 7. Furthermore, assuming the current time is \(t\) for instance, cases of floods were included to forecast when the average river level from \(t+1\) to \(t+5\) (5 min in advance) or the average from \(t+6\) to \(t+10\) (5 min in advance after \(t+5\)) was higher than 2 m. The average from \(t+1\) to \(t+5\) was considered to be enough to cause alerts with a high risk of flooding (classified as red alerts). The average from \(t+6\) to \(t+10\) was considered to be enough to trigger alerts (classified as yellow), when there is the risk of flooding. The average value of 2 m was defined for the location because of the local features of the environment. It was noticed that in a 5-min interval there is the possibility that the river will rise by 3 m, which represents the occurrence of a flood in the region. This means that, if the river level reaches 2 m, there might be a flood in the following 5 min. It is worth remembering that in this critical case only local data of the cluster is taken into account. In an analysis using data from other nodes, as in the case of the system fully operational, the accuracy of the forecasts can be refined. To determine the input and output parameters of the forecast models, created by the MLP, we used the procedure described in [25]. In this approach, the river level time series (Figure 7) is analysed using Chaos Theory, more specifically the Takens' Immersion Theorem [27], where the time series is unfolded to better extract its behavior and facilitating its analysis. However, unlike [25], we used only the peaks of the river level to make this study and thus, extending the previous work. According to [PERSON] [27], a time series \(x_{0},x_{1},...,x_{n-1}\) can be reconstructed in a multidimensional space \(x_{n}(m,\tau)=(x_{n},x_{n+\tau},...,x_{n+(m-1)\tau})\), also called time-delay coordinate space, where \(m\) is the embedded dimension and \(\tau\) represents the time delay (or separation dimension). To estimate the separation dimension (\(\tau\)), [PERSON] and [PERSON] [28] propose the use of the Auto-Mutual Information technique (AMI), where the first minimum is the main candidate for \(\tau\). After estimating the separation dimension, the embedded dimension (\(m\)) can be estimated using the False Nearest Neighbors method (FNN), as proposed by [PERSON] [29], where \(m\) is selected when the fraction of false neighbors is equal to zero. Applying this procedure, the AMI for the river level time series is shown in Figure 8. \begin{table}
\begin{tabular}{l r r r} \hline \hline \(\alpha\) & **Round 18** & **Round 19** & **Round 20** \\ \hline
0.0 & 100 & 5 & 0 \\
0.1 & 100 & 7 & 0 \\
0.2 & 100 & 4 & 0 \\
0.3 & 100 & 6 & 0 \\
0.4 & 100 & 8 & 0 \\
0.5 & 100 & 12 & 0 \\
0.6 & 100 & 6 & 0 \\
0.7 & 100 & 6 & 0 \\
0.8 & 100 & 10 & 0 \\
0.9 & 100 & 10 & 0 \\
1 & 100 & 7 & 0 \\
0.5 (500 modes) & 500 & 464 & 36 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Number of active nodes per round. The first minimum obtained makes \(\tau=17\) but when AMI slightly reduces as the separation dimension increases, another good option for the separation dimension is \(\tau=1\), as described in [25; 29]. These two values for \(\tau\) were used to estimate the embedded dimension (\(m\)) as shown in Figure 9.  
Real-world time series, as the ones obtained in natural environments, may contain noises making it difficult to obtain a value for \(m\), where the fraction of false neighbors is equal to zero. In such cases, we can select the number of dimensions in which the fraction of false neighbors becomes less than 30%, as presented in [25; 30]. Thus, we selected \(m=3\) when \(\tau=1\) and \(m=4\) when \(\tau=17\) for  
Figure 8: Auto-Mutual Information for the river level. Figure 9: Percentage of false neighbors for the river level, considering (a) \(\tau=1\) and (b) \(\tau=17\). the unfolding process.