## 3 Results and Discussion
### PLS-DA Analysis  
The first PLS-DA model was developed using the full spectral region of the excitation of the QCL. Reflectance spectra from 1000 to 1600 cm\({}^{-1}\) from the various soil types, with and without petroleum, were used, and a PLS-DA model with a relatively poor ability to discriminate sea sand was obtained (results not shown; see Supplementary Material). The ability of this model to detect pollutants in sea sand samples was so poor because of the low intensity of the signals between 1300 and 1600 cm\({}^{-1}\) due to the low reflectance of the sand samples in this spectral region. Thus, a second PLS-DA model was generated using only the spectral region between 1300 and 1600 cm\({}^{-1}\) and an improved differentiation was achieved. Figure 4 shows the differentiation between different soil types, with and without petroleum traces, for the improved PLS-DA model. Above the red dotted line (discrimination threshold), the classification of petroleum concentrations ranging from 0.2% to 10% _w/w_ in the soil samples was nearly perfect. The PLS-DA model had sensitivity and selectivity values of 0.936 and 0.976 for CV and 0.942 and 0.964 for test validation (TV), respectively. These values are indicative that the model can predict samples correctly in the soils studied. It also indicates that the model is robust, and the technique is robust enough for the detection of petroleum in soil. The classification of some samples was not entirely correct, and there were some failures in discrimination. As shown in Figure 4, most of the discrimination failures were observed in samples of brown soil with low petroleum concentrations (\(\leq\)0.2%). This was because this type of soil contains high amounts of organic matter. Therefore, brown soils show spectral peaks near 1413 cm\({}^{-1}\), typical of organic matter carboxylate species that can mislead the discrimination model. PLS-DA models based on reflectance spectra of the solid matrices and the pollutant concentrations were constructed separately. Models developed based on the solid forms for soils (brown and red soils), and a separate PLS-DA model was developed for sea sand only (models not shown; see Supplementary Material). A statistical analysis using the parameters of sensitivity, selectivity, and area under the ROC plot was developed to represent the changes in probability for sensing contaminated soils when the petroleum concentrations in soil and sea sand varied, as shown in Figure 5. The sensitivity parameters for Cal., CV., and Pred. ; and the area ROC for each PLS-DA model was developed given the petroleum concentrations and types of solid matrices;  
Figure 3: Reflectance spectra of soils with and without the pollutant. (**a**) Sea sand + 8% _w/w_ petroleum (sand + P8%); (**b**) brown soil + 10% _w/w_ petroleum (brown soil + P10%); and (**c**) red soil + 10% _w/w_ petroleum (red soil + P10%). these values are listed in Table 1. Additionally, a PLS-DA model using all data was developed for the optimized spectral region between 1300 to 1600 cm\({}^{-1}\), the area ROC, parameters such as sensitivity and specificity for Cal., CV., and Pred. were also calculated. The areas under the ROC plots represent the probabilities that a randomly selected positive case will receive a higher score than a randomly selected negative case. To determine the detection and decision limits, fitting was carried out for each probability, and the best fit was obtained with a double reverse fit, according to Equation (4):  
\[\text{p}=1/(\text{a}+[\text{ b}/\text{\% of P}]) \tag{4}\]  
The petroleum concentrations necessary to accurately measure contamination at probability levels of 50% and 93% for samples were determined from the fit (Equation (4)). These values correspond to the limit of decision (LD) and the limit of detection (LOD), respectively [62]. Table 2 shows the fitting parameters and the prediction % of petroleum for each probability value (50% and 93%). The LD and LOD values for the sand and soil samples were 0.02% and 0.2%, respectively (bold numbers).