# Contrails and Their Dependence on Meteorological Situations
## 3 Results
### Advanced Statistical Methods for the Evaluation of Data
#### 3.2.3 Random Forests  
The most successful classification method that was programmed in Knime was Random Forests. The same continuous input variables x(\({}_{1-12}\)) were used for modeling, and the discrete y was divided according to contrail lifetime into short-lived ones up to 1 min (y\({}_{1}\)) and long-lived ones above 1 min (y\({}_{2}\)). This method gave the best results among all models based on all performance characteristics; the F1 score was almost 100%. Table 5 shows the outputs of measured y and predicted \(\gamma_{\text{p}}\). The confusion matrix reflects the general performance of the classifier and is the result of iterative training and testing, performance characteristics of this model are given in Table 6.  
The model correctly identifies 239 short-lived contrails up to 1 min and 82 long-lived contrails longer than 1 min. The accuracy of the model reached 97%. The performance shows that in terms of precision (indicating what proportion of positive \(\gamma_{\text{p}}\) predictions are  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**S** & **P** & **R** & **F1** \\ \hline
0.9727 & 0.9757 & 0.9938 & 0.9847 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance characteristics of the Discrete categorical model with a 5 min division of contrail lifetime.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measured y** & **Predicted y\({}_{1}\)** & **Predicted y\({}_{2}\)** & \(\Sigma\) \\ \hline \(\gamma_{1}\) & 310 & 2 & 342 \\ \(\gamma_{2}\) & 31 & 2 & 33 \\ \(\Sigma\) & 341 & 4 & 345 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion matrix of outputs y, \(y_{\text{p}}\) for the Discrete categorical model with a 5 min division of contrail lifetime.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**S** & **P** & **R** & **F1** \\ \hline
0.9043 & 0.9091 & 0.9935 & 0.9494 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Confusion matrix of outputs y and \(y_{\text{p}}\) for Random Forests with 1 min division of contrail lifetime.  
correct) and sensitivity (how many true y were classified correctly), this model is the best of all. F1 demonstrates the fact that the model can handle the imbalance of the data in the ensemble well.  
For this method, the modeling was tested for a finer distribution of the contrail lifetime, where y was divided into four intervals as follows: 1 = (up to 0.5 min), 2 = (0.5-1 min), 3 = (1-2 min), and 4 = (over 2 min). The results of the measured y and predicted y\({}_{\rm p}\) outputs are shown in Table 7. The performance characteristics of this model are listed in Table 8.  
The model correctly identifies 195 short-lived contrails up to 0.5 min, 34 short-lived contrails in the interval 0.5-1 min, 51 long-lived contrails in the interval 1-2 min, and 27 long-lived contrails over 2 min. The accuracy of the model again reached a high value of 93%. The only slight limitation was the achieved sensitivity. Its value is quite high, but it was one of the weakest of the observed models. This model could be used to predict the average contrail lifetime, which is 122 s.