## 4 Discussion
The important bands of SOM are 400-500, 1350-1400, and 1900-2400 nm [10; 32; 47; 48; 49], while the effective bands of Fe are 400-750, 1520-1680, and 1800-2400 nm [50]. In this study, the effective bands of Cd and SOM primarily overlapped at 450-460, 1310-1330 nm and 2140-2150 nm, while the characteristic wavelengths of SOM and Pb mostly overlapped at 560-680, 1330-1340 nm, 1900-1980 and 2320-2390 nm. The important wavelengths of Cr and SOM and Fe mostly overlapped in the ranges of 400-500, 510-670, and 2000-2020 nm. In summary, these preliminary analyses of spectral reflectance provided the basis for a reference for the selection of characteristic bands. In this study, we employed the PLSR, BPNN, and MEA-BPNN models to estimate heavy metal concentrations in the soils from VNIR spectra. Many previous studies have analyzed models for the estimation of heavy metal concentrations from VNIR spectra and reported R\({}^{2}\) values of 0.102-0.95 for Cd, 0.010-0.990 for Cr, and 0.200-0.820 for Pb [10; 17; 20; 45; 46; 47; 51; 52; 53]. We have also summarized some studies on heavy metal estimation using limited samples (less than 50), which reported R\({}^{2}\) values of 0.102-0.880 for Cd, 0.460-0.860 for Cr, and 0.940 for Pb [17; 26; 42]. In this study, the optimal R\({}^{2}\) of the PLSR model for Cd, Cr and Pb contents were 0.759, 0.664 and 0.853, the BPNN model yielded corresponding optimal R\({}^{2}\) values of 0.728, 0.737, and 0.675, and the MEA-BPNN model yielded corresponding optimal R\({}^{2}\) values of 0.873, 0.884, and 0.857. These results were consistent with those of previous studies. In this study, the MEA-BPNN model usually produced better results. Compared with the BPNN model, the MEA can optimize the initial weights and thresholds of the BP neural network and it is easier to get the optimal result. For remediated soil, since there may be a nonlinear relationship between heavy metal content and spectral reflectance, the BPNN model would be superior to PLSR. In general, the generalization ability of MEA-BPNN model is better, and the MEA-BPNN model can be better applied to remediated soil with heavy metal content changes. Thus, VNIR spectroscopy coupled with the MEA-BPNN model is a promising method for estimating the concentration of some heavy metals (e.g., Cd, Cr, and Pb) in soils. The RMSE values in this study were relatively large compared to those of previous investigations [37; 46; 52], mainly because the accuracy of the estimated model is related to the average of the measured values of soil heavy metal content (Table 3). Due to the concentration gradient setting in the heavy-metal pollution remediation soil experiments of this study, the heavy metal contents of the collected soils were too large during the early stages of plant growth. The arithmetic average of various heavy metal contents was thus higher than the measured values in other investigations, and therefore the predicted root mean square error also increased. However, one of the purposes of this study was to test the feasibility of the VNIR model for estimating heavy metals in soil samples that are undergoing pollution remediation. Therefore, samples with extreme values of soil heavy metal content were not excluded from the original dataset. In addition, these models also had certain limitations in the study. The small number of soil samples under each heavy metal stress in the study will cause model instability and uncertainty in calibration, which will affect the accuracy and precision of model estimation. Furthermore, the composition and structure of the soil in the field is more complex, and correlations between different heavy metal contents will interfere with the accuracy of the model. Therefore, in future experimental research, optimization of the calibration dataset can be examined and a sufficient number of soil samples will be collected in the field to verify the feasibility of the model.