## Appendix A Clustering the Landfill Based on Its Temperature  
The original landfill configuration, shown in Figure 5, used shapefiles with following number of pixels:  
Number of cells for whole landfill = 306  
Number of cells South quarry (lower region) = 180  
Number of cells Neck area (middle region) = 72  
Number of cells North quarry (upper region) = 54  
To apply this methodology for any landfill, landfills can be clustered based on their temperature profile. This will help in focusing on regions that have higher temperature or substantial temperature differences in the same landfill. The temperature profile can be built from the satellite observations for any number of years or months. Doing so, we bear in mind that subsurface heat elevation or smoldering events will last long (persistent for some time) if it is not treated by the landfill operators and its effect will be shown in all subsequent satellite images. For Bridgeton landfill, we collected 115 satellite observations from year 2000 to 2016 as shown in Table 1. These observations construct a temperature time series; therefore; to create new clusters we need to consider observation time from image 1 at t\({}_{\text{i}}\) = 1 until t\({}_{\text{e}}\) = 115 for all the image pixels (i, j). Clustering can be done using any of the clustering techniques such as k-means or PCA. However, we clustered the landfill based on the deviation from the mean as follows:  
\[\text{t}_{\text{i}} =\text{initial time }(\text{ image }1)\] \[\text{t}_{\text{e}} =\text{end time }(\text{ image }115)\]  
n = number of observations  
\[\text{T}_{\text{ij}}(\text{t})=\text{Temperature at cell i,j and time t}\]  
\(\text{T}_{\text{avg,LF(t)}}\) = mean landfill temperature at time t  
\(\Delta_{\text{ij}}(\text{t})=\left(\text{T}_{\text{ij(t)}}-\text{ T}_{\text{avg,LF(t)}}\right)\) for cells, i,j are the pixel coordinates  
\(\text{mean}=(\frac{\text{t}_{\text{e}}}{\text{t}_{\text{i}}}\Delta_{\text{ ij}}(\text{t}))\)/n  
\[\text{STD }=\text{Standard deviation}\left(\sum\
olimits_{\text{t}_{\text{i}}} ^{\text{t}_{\text{e}}}\Delta_{\text{ij}}(\text{t})\right)\]  
Then calculating:  
\[\text{mean}-\text{STD }\overset{\text{yields}}{\longrightarrow}\text{ Cluster }1(\text{yellow})\] \[\overline{\text{mean}}+\text{STD }\overset{\text{yields}}{\longrightarrow}\text{ Cluster }2(\text{green})\]  
Cluster 3 is all the rest (blue). The resultant cluster is shown in Figure 11.  
Cluster 3 (blue) is equivalent to lower part or South quarry where the highest temperature is recorded most of the time, cluster 2 (green) similar to middle region where moderate temperature is recorded and the cluster 1 (yellow) is the upper region where the lowest temperature is recorded most of the time. The shapefiles and the number of cells for each region has been changed to:  
Number of cells for whole landfill = 306  
Number of cells South quarry (lower region) = 52 Number of cells Neck area (middle region) = 190  
Number of cells North quarry (upper region) = 64  
This analysis is simple and helps to identify the regions of concern and the percentage of landfill going under different heat elevation levels; for instance, about 17% of the landfill is under subsurface heat elevation (blue), about 62% is under moderate heat elevation (green) and 21% of the landfill is under normal heat conditions. Reproducing spatial temperature profiles was previously obtained in Figures 3 and 4, based on new clusters that show similar heat trends. In addition, using k-means clustering resulted in a similar classification.