# A Novel Index for Detecting Bare Coal in Open-Pit Mining Areas Based on Landsat Imagery
## 3 Methods
### Spectral Feature of Bare Coal  
Determining the spectral characteristics of bare coal and other land cover types is crucial for developing a robust bare coal index. In this study, we obtained a total of 860 samples based on the Landsat imagery. These samples included 660 bare coal (BC) pixels--220 pixels from each of the Chenqi, Shengli, and Dongsheng coalfields. In each study area, 20 pixels were sampled for each bare coal fraction ranging from 0% to 100%, as determined from the bare coal fraction maps (Figure 1). A bare coal fraction of 0% indicates that there is no bare coal within the mixed-cover pixel, while a bare coal fraction of 100% means the pixel contains only bare coal. Additionally, we sampled four non-BC categories (soil, man-made structures, vegetation, and water), with 50 pixels each, determined from high-resolution imagery.  
Given the varying coal types and natural background conditions in the study area, we first plotted the mean spectral curves of different coal types using pixels with a 100% bare coal fraction from the three coalfields. As shown in Figure 3, the spectral reflectance of lignite is generally higher than that of bituminous coal. However, notable regional variations in lignite reflectance are observed. These differences may stem from the fact that lignite types were not further classified in this study, and distinct lignite types exhibit varying spectral characteristics, contributing to the observed regional disparities in reflectance. Additionally, variations in natural environmental conditions may further contribute to the observed differences in coal reflectance between these regions. Although there are differences in the reflectance levels of different coal types in Landsat imagery, the spectral curves are similar across these types. This indicates that constructing a bare coal index can effectively identify all coal types, as the differences among them have minimal impact on the index. Consequently, the bare coal spectral values used in the subsequent experiments are the average spectral values of three different coalfields.  
Figure 2: Methodology flowchart in this study.  
It is noteworthy that this study did not further differentiate secondary categories of crop types, soil types, and man-made surfaces due to the difficulty of acquiring such details from Landsat images. Based on the obtained average spectral curves (Figure 4a) and the correlation coefficient (Figure 4b) of different land cover types, it is evident that soil, man-made structures, and water have a high correlation with BC, making them the primary interference factors in identifying BC. Additionally, as shown in Table 2, only bare coal exhibits a higher reflectance in the SWIR2 band than in the SWIR1 band. As the bare coal fraction decreases, the difference between SWIR2 and SWIR1 diminishes, and SWIR2 reflectance becomes lower than SWIR1 when the bare coal fraction is 70%. This distinctive characteristic of bare coal allows for the use of SWIR2 and SWIR1 as the primary bands to differentiate bare coal from other features. By conducting a comprehensive analysis of additional bands or band combinations, a new index can be constructed to accurately identify bare coal pixels.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**BC**} & \multicolumn{3}{c}{**BC (90\%)**} & \multicolumn{3}{c}{**BC (80\%)**} & \multicolumn{3}{c}{**BC (70\%)**} & \multicolumn{3}{c}{**Soil**} & \multicolumn{3}{c}{**Man-Made**} & \multicolumn{3}{c}{**Vegetation**} & \multicolumn{3}{c}{**Water**} \\ \cline{2-13}  & \(\mu\) & \(\sigma\) & \(\mu\