# A Novel Index for Detecting Bare Coal in Open-Pit Mining Areas Based on Landsat Imagery
## 3 Methods
### BCI Thresholds  
To apply the proposed BCI to satellite data, it is crucial to determine the lower and upper thresholds of the index. This study utilized a pixel-based simulation program for this purpose [38]. The simulation assumes that the mixed pixel comprises three components, namely, soil, man-made surfaces, and bare coal, following a linear spectral mixing model [39]. The spectral model of the mixed pixel is created by varying the proportions of these three components, as shown in Equation (3). \[ \begin{array}{l}R_{1}(\lambda)=f_{s}\times R_{s}(\lambda)+f_{m}\times R_{m} (\lambda)\quad\quad f_{s}+f_{m}=1,\ f_{s}=0,\ 0.1,\ \cdots,\ 0,\ 0.9,\ 1\\ R_{mix}(\lambda)=f_{1}\times R_{1}(\lambda)+f_{2}\times R_{BC}(\lambda)\quad \quad f_{1}+f_{2}=1,\ f_{1}=0,\ 0.1,\ \cdots,\ 0.9,\ 1\end{array}  \tag{3}\]  
In this equation, \(R_{1}\) is the combined reflectance of soil and man-made surfaces, where \(f_{s}\) and \(f_{m}\) are the proportions of the soil (\(R_{s}\)) and man-made surfaces (\(R_{m}\)). \(R_{BC}\) is the reflectance of the BC component. \(\lambda\) is the wavelength. \(f_{1}\) and \(f_{2}\) are the proportions of \(R_{1}\) and \(R_{BC}\) in a mixed land cover scenario, respectively. (\(R_{mix}\)), \(R_{s}(\lambda)\), \(R_{m}(\lambda)\), and \(R_{BC}(\lambda)\)  
Figure 6: Separability test with different Landsat OLI band or band combinations. are obtained from the average reflectance of each component in Figure 4a. Specifically, \(R_{1}\) was first simulated by adopting the two-component linear spectral mixture model and then \(R_{mix}\) was obtained from simulating the combination of \(R_{1}\) and \(R_{BC}\). The BCI of different land cover scenarios is shown in Figure 7. It is evident that the BCI rises with an increase in the BC fraction across all scenarios. Notably, the BCI remains relatively stable until the bare coal fraction reaches 80%, beyond which it experiences a sharp ascent. This observation leads to the conclusion that the optimal range for recognizing the bare coal fraction lies between 80% and 100%, with a corresponding BCI threshold of 0-3.776. Theoretically, precise bare coal detection only necessitates setting a lower threshold. In practical application, omitting an upper threshold does enhance the accuracy of bare coal identification while concurrently reducing the omission rate. This point arises because, when constructing the BCI, the unique spectral reflectance of bare coal in the SWIR1-SWIR2 band combination was taken into account. Specifically, only BCI values with a bare coal fraction greater than 80% will exceed 0. However, in practice, certain buildings with gray roofs and Gobi Desert areas can also exhibit BCI values greater than 0, which are close to those with an 80% bare coal fraction. Therefore, for more accurate detection of bare coal information, we ultimately set the recognizable bare coal fraction at 90%. This means that pixels with a bare coal fraction greater than or equal to 90% are considered to be bare coal, corresponding to a BCI threshold of 0.8. However, setting a higher threshold for bare coal identification may indeed result in missing some bare coal areas, as confirmed by the results in Figure 8. Nonetheless, given that the objective of this study was to further automate the identification of open-pit mining areas and temporary coal piles based on bare coal areas, we limited the identifiable range to ensure the most accurate identification of bare coal areas. We believe that this threshold can be adjusted flexibly to accommodate different research objectives and achieve optimal results. Figure 7: BCI values in simulated scenarios with different BC fractions. Additionally, we found that some water areas could not be removed using the threshold when detecting bare coal with the BCI. These water areas typically have high sediment or chlorophyll content, altering their reflectance and causing confusion with bare coal detection results. To mitigate this issue, water bodies should be removed before applying the BCI for bare coal detection.