## 2 Materials and Methods
### Analysis and Validation Methods  
Partial least squares regression (PLSR) was reported by [PERSON] et al. (1985) [34] and has become a widely used modeling technique in soil physical and chemical composition prediction and highly collinear spectral analysis [35; 36]. PLSR specifies the linear relationship between the independent (X) and dependent variables (Y) by extracting several linear combinations (T). The original spectrum matrix (X) could be computed as eigenvectors. After estimating the model parameters, the final predictive model is presented Formulas (3)-(5). PLSR analysis specifies the linear relationship between X and Y by reducing the data from the covariance matrix X to generate new components composed of linear combinations of the original covariates. Throughout this process, the aim is to capture the variability in predictor variables and maximize the covariance between all the linear combinations of the covariance matrix X and the response variable Y. PLSR allows for modeling multiple response variables by effectively handling the strongly correlated variables and noisy independent variables. \[\text{T}=\text{XV} \tag{3}\]  
where V represents the weights. \[\text{Y}=T_{q}+f \tag{4}\]  
Figure 3: Examples of preprocessing of wet soil spectrum: (**a**) original spectrum, (**b**) absorbance conversion, (**c**) absorbance using Savitzky–Golay smoothing, and (**d**) absorbance using the Standard Normal Variate. where \(T\) represents the relationship between variables X and Y, while \(f\) denotes the residuals, indicating the noise and unrelated variability between X and Y.  
\[\mathrm{y}=b_{0}+x_{i}\widetilde{b_{i}} \tag{5}\]  
where \(b_{0}\) represents the intercept, and \(\widetilde{b_{i}}\) represents the regression vector. Unscrambler (ver. 10.4, CAMO, Inc., Oslo, Norway) was used to develop predictive regression models of the soil properties and spectra using PLSR. The collected spectra were divided into two spectral bands--(1) VIS at 400-700 nm, and (2) NIR at 700-2500 nm--and the chemical composition of the collected soil samples was analyzed using PLSR. A total of 120 samples were randomly selected and divided into data sets for regression and validation using the PLSR regression model at a ratio of 8:2. To increase the predictive capability and decrease the potential for overfitting, a cross-validation procedure was used to select the number of PLS factors to use for regression. To evaluate the performance of the soil property prediction regression model, we utilized the coefficient of determination (R\({}^{2}\)), root-mean-square error of prediction (RMSE), and relative reproducibility deviation (RPD), which is the ratio of the standard deviation to the RMSE [37]. Of these values, R\({}^{2}\) is a measure of the goodness of fit of a regression equation, indicating how well the regression line estimated using the sample data fits the actual measured data; the RMSE represents the ratio between the means of the measured data, indicating the relative estimation error; and RPD denotes the ratio of the standard deviation of the entire data set to the RMSE [38]. RPD is calculated as the standard deviation of the measured value, divided by the RMSE of the validation data Formulas (6)-(8). \[R^{2}=1-\frac{\sum_{i=1}^{n}\left(Y_{measure}-Y_{pred}\right)^{2}}{\sum_{i=1}^{ n}\left(Y_{i}-Y_{mean}\right)^{2}} \tag{6}\]  
where \(Y_{measure}\) represents the measured value, \(Y_{pred}\) denotes the predicted value, \(Y_{mean}\) reflects the average of the measured values, and n represents the number of measurements and predictions, where \(i=1\) to \(n\). \[RMSE=\sqrt{\frac{1}{n}{\sum_{i=1}^{n}\left(Y_{pred}-Y_{measure}\right)^{2}}} \tag{7}\]  
where \(SD\) represents the standard deviation of the measured values. \[RPD=\frac{SD}{RMSE} \tag{8}\]  
where \(RMSE\) represents the root-mean-square error of the verification data. [PERSON] et al. (2017) [39] proposed the RPD as an alternative to the RMSE when comparing the results from highly variable data.