## 3 Results
### Analysis of Spectral Characteristics of Heavy metal Soil  
Differences in soil spectra are mainly indicated by differences in reflectance. The characteristic absorption bands exhibited by the different soil types differed in location and strength. In the experiment, the spectral intensity of soil under heavy metal Cr stress was lower than that of the other two heavy metal stress soils. This may be due to the dark soil color, with the reflectance absorbing additional light energy [46]. Figure 5 shows the reflectance for the soil with different heavy metal contents in the experiment. Generally speaking, the original spectral curves of the three heavy metal soils were relatively smooth. As shown in Figure 5, the spectral reflectance increased gently with wavelength from 400-760 nm (the visible wavelength band). The upward trend of reflectance was obvious between 850-900 nm. The reflectance reached the first reflection peak between 1350 nm and 1400 nm. Three more significant absorption peaks appeared at 1440 nm, 1900 nm, and 2200 nm, which were due to soil moisture. At 1400, 1800, 2000, and 2250 nm, prominent reflection peaks formed, while the rest of the bands were steady. The spectral reflectance range of Cd and Pb increased with the change of their heavy metal content, while the spectral reflectance of Cr exhibited a smaller response to the change of its content. In addition, we can also find the spectral reflectance of Cd- and Pb-contaminated soil generally decreases with time, and the spectral reflectance of Cr increased with time. Combining with Figure 4, heavy metal content in soil decreased over time, so, we could roughly judge that the spectral \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & **Number of Samples** & **Maximum** & **Minimum** & **Standard** & **Skewness** & **Kurtosis** & **Coefficient of Variation** \\  & **Samples** & **(mg/kg)** & **(mg/kg)** & **(mg/kg)** & & & **Variation** \\ \hline Cd & 36 & 29.30 & 0.13 & 5.20 & 4.32 & 20.49 & 2.16 \\ Cr & 36 & 813.00 & 6.90 & 202.02 & 2.45 & 5.83 & 1.65 \\ Pb & 36 & 397.20 & 0.84 & 112.75 & 1.72 & 2.19 & 1.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical results of heavy metal concentrations in soil samples. Figure 4: Changes in soil heavy metal concentration with time. (**a**) The change in Cd concentration; (**b**) the change in Cr concentration; (**c**) the change in Pb concentration. reflectance of soil was positively correlated with the content of Cd and Pb, and inversely correlated with the content of Cr. After the differential transformation, the spectral characteristics of the three heavy metals were similar (Figure 6). Several absorption features were highlighted across all heavy metal classes, such as the significant absorption peaks and valleys at approximately 950 nm, 1300 nm and 1900 nm. The spectral reflectance after the second derivative transform was closer to 0, indicating that the baseline drift and mixed overlapping peaks had been gradually removed, and the spectral intensity had also been reduced. The reciprocal logarithmic transformation can stretch and enhance the reflectance of the original spectrum, but the information enhancement effect was less significant than that of the derivative transformation. In this study, the Spearman correlation analysis was carried out with the soil heavy-metal contents and the spectral reflectance after the first-order differential transformation, second-order differential transformation and logarithmic transformation of the reciprocal. Compared with the original reflectance spectra, the correlation values of the derivative transformed reflectance spectra were significantly improved. As shown in Table 4, the first derivative effect on the reflection spectrum is best, followed by the second derivative. The correlation between the original spectral reflectance with Cd and Pb content was weak, and the correlation with Cr was more significant.