## 3 Results and Discussion  
### The CARS-SCA Characteristic Band Selection Algorithm  
The CARS algorithm was used to perform rough selection of the original soil spectra, and the number of Monte Carlo samples was set at 100. Figures 5 and 6 show the selection process of spectral variables for the CARS method. In Figures 5a and 6a, the number of variables gradually decreases, and the downward trend is slower and slower; the RMSECV value in Figures 5b and 6b indicates the prediction effect of the PLS model based on the characteristic wavelength of the adaptive reweighted sampling selection; In Figures 5c and 6c, each line represents the change trend of the coefficient of reversion of each wavelength, and the * marks the position with the smallest RMSECV value. After the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Study** & **Sample** & **Sample** & **Minimum** & **Maximum** & **Mean** & **CSV** & **Skewness** & **Kurtosis** \\ \hline \multirow{2}{*}{Honghu} & Calibration & 19 & 27.33 & 39.21 & 33.44 & 3.34 & 9.98\% & 0.03 & \(-\)0.49 \\  & Validation & 10 & 26.54 & 37.09 & 31.7 & 3.72 & 11.7\% & 0.05 & \(-\)1.17 \\ \multirow{2}{*}{Daye} & Calibration & 41 & 7.19 & 12.84 & 9.37 & 1.17 & 12.5\% & 0.61 & 0.37 \\  & Validation & 22 & 7.04 & 11.24 & 9.12 & 0.99 & 10.8\% & 0.31 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical characteristics of the soil As content. Figure 4: The spectra of the soil samples from the different regions. (**a**) Honghu. (**b**) Daye. *, the RMSECV value starts to increase because the valid variable is deleted. For the Daye area, the trend of the RMSECV obtained by 10-fold cross-validation (CV) is shown in Figure 5b, where it can be seen that the RMSECV value changes significantly. When the number of samples is 62, the RMSECV value is the smallest, which indicates that the model has the highest accuracy. As the sampling runs increase, the RMSECV increases and the model effect deteriorates. Therefore, when the number of samples is 62, the selected spectral band subset is the optimal one, and the RMSECV value is the smallest. In total, 28 characteristic bands (401 nm, 402 nm, 420 nm, 566 nm, 577 nm, 676 nm, 677 nm, 688 nm, 689 nm, 690 nm, 697 nm, 705 nm, 706 nm, 707 nm, 822 nm, 826 nm, 827 nm, 871 nm, 957 nm, 984 nm, 1826 nm, 1906 nm, 2242 nm, 2232 nm, 2344 nm, 2382 nm, 2393 nm, 2394 nm) were obtained. For the Honghu area, the variation trend of the RMSECV obtained by 10-fold CV is shown in Figure 6b. When the number of sampling runs is 60, the RMSECV value is the smallest. This shows that the model has the highest accuracy at this point, and as the sampling runs increase, the increase of the RMSECV indicates that some important variables related to the prediction of As in soil have been eliminated. Therefore, when the sampling frequency is 60 times, the selected spectral band subset is the optimal one, and the RMSECV value is the smallest. In total, 23 characteristic bands (401.9 nm, 405 nm, 408.1 nm, 437.3 nm, 813.6 nm, 818.6 nm, 822.3 nm, 823.5 nm, 827.2 nm, 978.9 nm, 997.6 nm, 998.5 nm, 999.4 nm, 1000.3 nm, 1896.8 nm, 1929.2 nm, 1942.9 nm, 2303 nm, 2357.7 nm, 2362.4 nm, 2376.4 nm, 2385.7 nm) were obtained. Figure 5: (**a**) Change in the number of selected variables with the change in the number of samples runs for the CARS algorithm in Daye. (**b**) Change in the 10-fold root-mean-square error of cross-validation value with the change in the number of sample runs for the CARS algorithm in Daye. (**c**) Change in the regression coefficient variable with the change in the number of samples runs for the CARS algorithm in Daye. Figure 6: (**a**) Change in the number of selected variables with the change in the number of samples runs for the CARS algorithm in Honghu. (**b**) Change in the 10-fold root-mean-square error of cross-validation value with the change in the number of sample runs for the CARS algorithm in Honghu. (**c**) Change in the regression coefficient variable with the change in the number of samples runs for the CARS algorithm in Honghu.