# Investigating Effects of Landfill Soil Gases on Landfill Elevated Subsurface Temperature
## 5 Results
### Effect of Variable Combinations on Temperature
There might be other missing variables that are triggering the SET with the same gas combinations. Therefore, insignificant impacts on temperature were observed in events with gas combinations such as: (\(<\) 45% and \(>\)60% CH\({}_{4}\), (CH\({}_{4}\):CO\({}_{2}\)) ratio \(<\) 1, RN\({}_{2}\) \(<\) 20%, O\({}_{2}\) \(<\) 5%); (\(<\) 45% and \(>\)60% CH\({}_{4}\), (CH\({}_{4}\):CO\({}_{2}\)) ratio \(<\) 1, RN\({}_{2}\) \(>\) 20%, O\({}_{2}\) \(<\) 5%); (\(<\) 45% and \(>\)60% CH\({}_{4}\), (CH\({}_{4}\):CO\({}_{2}\)) ratio \(<\) 1, RN\({}_{2}\)\(<\) 20%, O\({}_{2}\)\(>\) 5%). In their landfill study, [PERSON] et al. (2017a, b) reported a trend among numerous gas-extraction wells in which a decreasing CH\({}_{4}\)-to-CO\({}_{2}\) ratio occurred prior to an increase in the wellhead temperature. A decreasing CH\({}_{4}\)-to-CO\({}_{2}\) ratio and a CH\({}_{4}\) level above the recommended range were noticed in these three combination pairs, which indicates that the conditions of RN\({}_{2}\) and O\({}_{2}\) do not govern the increase in temperature. Rather, other possible gases such as H\({}_{2}\) or CO may control the situation. * Moreover, no boxplot was created for seventeen other combinations due to the absence of these combinations in the sample datapoints, which implies that these events do not occur or are extremely rare. Increasing the volume of sample data from recent years could firmly establish the truth of this statement. Figure 6: Temperature datapoints categorized in different event conditions. We used a group histogram to plot the variance and frequency of temperature in different combinations. Figure 7 presents the temperature distribution in each of the above cases, including their spread, peaks, and symmetry. The histogram shows temperature data with different frequencies, peaks, frequently non-normal values, and outliers. Histograms include multiple peaks in some cases that indicate multimodal distributions. The question remains whether the mean temperature range statistically varies with respect to the combinations. The Wilcoxon rank-sum test [57], a nonparametric test method, is able to interpret the interpretation of the difference between these events. The test is robust against the presence of outliers and the non-normality of a sample distribution. Tests for a null hypothesis test (H\({}_{\text{o}}\)) of equal means in two independent samples were performed. All pairs of the combinations were tested with the null hypothesis of no difference between any two events. Figure 8 shows the median values of the difference between a pair of events that resulted from the Wilcoxon rank-sum tests shown in a matrix of events. Each event is represented in a sequence of the safe and unsafe condition of temperature, CH\({}_{4}\), CH\({}_{4}\)CO\({}_{2}\) ratio, and residual N\({}_{2}\) and O\({}_{2}\). The color ranges from green, white, and red in the figure represent a high negative difference, no difference and high positive difference between two events, respectively. For example, a pair of events (temperature = 1, CH\({}_{4}\) = 1, CH\({}_{4}\)CO\({}_{2}\) = 1, RN\({}_{2}\) = 1, O\({}_{2}\) = 0) and (temperature = 0, CH\({}_{4}\) = 1, CH\({}_{4}\)CO\({}_{2}\) = 1, RN\({}_{2}\) = 1, O\({}_{2}\) = 1) have the highest positive difference, while the (temperature = 0, CH\({}_{4}\) = 0, CH\({}_{4}\):CO\({}_{2}\) = 0, RN\({}_{2}\) = 0, O\({}_{2}\) = 1) events and (temperature = 1, CH\({}_{4}\):CO\({}_{2}\) = 1, RN\({}_{2}\) = 1, O\({}_{2}\) = 0) events have the highest negative difference. In the figure, (***) represents an insignificant \(p\)-value \(<\)0.05 for that pair of events. The nondirectional two-sided test resulted in a significant \(p\)-value \(<\) 0.05 for all pairs except three pairs which indicates that the means for the three pairs of events share a significant similarity in their means and variance spreads.