## 4 Method
### Selecting the Main Initial Variables for Prediction  
In order to apply prediction methods, we have to select the appropriate variables on which the performance of the prediction depends [61]. In the literature, we can find various approaches for selecting variables as follows: filtering techniques [62], which are \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rank** & **Variables, Units** & **Min.** & **Max.** &
\begin{tabular}{c} **Importance** \\ **(Gini Impurity)** \\ \end{tabular} \\ \hline
1 & Spilled oil volume, m\({}^{3}\) & 10 & 1000 & 10.69 \\
2 & Surface spreading coefficient, m\({}^{-1}\) & 5 & 30 & 6.51 \\
3 & Ground type & 4 possible values: sand, sandy loam, loam, clay & 6.17 \\
4 & Ground thickness, m & 3 & 5 & 5.41 \\
5 & Time after the spill, days & 1 & 10 & 4.63 \\
6 & Oil density, kg/m\({}^{3}\) & 750 & 930 & 4.54 \\
7 & Depth of groundwater, m & 3.15 & 5.35 & 4.32 \\
8 & Ground temperature, \({}^{\circ}\)C & 3 & 11 & 4.15 \\
9 & Soil moisture & 0.08 & 0.2 & 3.92 \\
10 & Terrain relief, m & 130 & 170 & 3.9 \\
11 & Air temperature, \({}^{\circ}\)C & 5 & 25 & 3.68 \\
12 & Ground moisture & 0.18 & 0.46 & 3.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: An initial set of variables for predicting the impact of an oil spill on the ground environment. Figure 2: The visualization of the mathematical model for predicting the impact of an oil spill on the ground environment. applied before model training [62]; questionnaires [63], which are based on human expert judgments as to whether a variable is relevant; visual analysis, such as the removal of a feature that has only one value or where most of the values are missing; and the assessment of features using some statistical criteria (variance, correlation, \(X^{2}\), etc.) [64]. Compared to the other variable selection approaches, questionnaires are subjective and difficult to collect [65]. Therefore, we use the statistical selection of variables as presented below. To refine an initial set of variables derived from the mathematical model, we use the impurity of the tree applying the R software environment, a Random Forest [25; 26; 27] (Section 4.2) (Equation (19)), and a set of correlations (i.e., Spearman and Kendall correlation coefficients). The ranking of variables for prediction based on their importance is presented in Figure 3.  
Consequently, we selected the four most important initial variables for the prediction of the consequences of oil spills as the following: spilled oil volume, oil density, surface spreading coefficient, and ground thickness. The choice of more variables increases the level of training of ML and ANFIS in terms of time and resources, and the complexity of the prediction model increases with the increase of input parameters. The correlation analysis between the selected four variables is presented as follows. The Pearson correlation coefficient [66; 67] measures the linear relationship among two variables as the ratio of the covariance of the two variables to the product of their standard deviations (Equation (6)). It ranges in the interval from \(-1\) to \(1\), where \(1\) shows a very strong positive correlation and \(-1\) a very strong negative correlation. The closer the value to \(0\), the weaker the relationship between the two variables. \[r_{xy}=\frac{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})(y_{i}-\overline{y})}}{ \sqrt{\sum\limits_{i=1}^{n}{(x_{i}-\overline{x})^{2}\sum\limits_{i=1}^{n}{(y_ {i}-\overline{y})^{2}}}}} \tag{5}\]  
Figure 3: The ranking of variables for prediction (#1, #2,..., #12 is a number of a variable). In order to determine the statistical significance of a correlation, a \(p\)-value can be calculated as presented in Equation (6). A \(p\)-value less than 0.05 typically shows a statistically significant correlation.