## 6 Conclusions  
The PLS-MARS method was proposed to construct a nonlinear model for SOM content prediction, in which the MVARC-R-KS method was adopted to select the optimal calibration set. Several commonly used calibration set selection methods were applied to calibrate the PLS-MARS model, and their influences on the prediction precision of the established model were investigated. The implementation procedure for the proposed method was described in detail. The proposed approach was illustrated and validated through a simulated data set and practical application in the Jianghan Plain. A comparative study with conventional prediction methods indicated that the proposed PLS-MARS method presents the following advantages: (1) the proposed method can efficiently estimate the nonlinear relationship underlying data with numerous variables; (2) the proposed method can accurately construct the highly nonlinear relationship of the SOM content with VNIR spectra, with consideration of the spatial heterogeneity of the relationship; (3) the proposed method can automatically construct a prediction model without substantial prior knowledge of the data set.  
The following new findings were obtained based on the application of the PLS-MARS method to estimate SOM content in the Jianghan Plain in China: (1) the accuracy of prediction models, including the PLS-MARS model, depends significantly on the selected calibration sets; (2) the combined PLS-MARS and MVARC-R-KS methods have immense stability and prediction capabilities when estimating the relation of SOM content with VNIR spectra in the study area.  
In general, the proposed PLS-MARS method can accurately estimate the nonlinear relationship with local differences. The PLS-MARS method calibrated by the samples obtained utilizing the MVARC-R-KS method has considerable potential for estimating SOM. Furthermore, the PLS-MARS method is conceptually simple and easily executed via a programming language, thereby ensuring easy application.  
Future studies will focus on further practical applications of the PLS-MARS method. For example, a PLS-MARS model calibrated by the calibration set selected utilizingMVARC-R-KS method can serve as a potential prediction model to estimate other soil properties (e.g., iron content, copper content, and soil organic C) based on the VNIR spectra in the study area or other areas. The proposed PLS-MARS method can also be used to characterize the nonlinear relationships of other geographic phenomena.  
[PERSON] and [PERSON] conceived and designed the experiments; [PERSON] and [PERSON] performed the experiments; all the authors analyzed the data; [PERSON] wrote the paper; all authors contributed to the revision of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research was funded by [the Scientific Research Program of the Hunan Education Department] grant number [19C1113], [the Natural Science Foundation of Hunan Province] grant number [2020]J5363], and the National Natural Science Foundation of China grant number [41901314].  
Not applicable.  
Data Availability Statement: Data available on request due to restrictions privacy. The data presented in this study are available on request from the corresponding author. The data are not publicly available because the data is the result of the whole research group's hard work.  
The authors declare no conflict of interest.