## 3 Results
### Prediction of SOC Using Different Predictive Models  
The NDVI time series data of 12 months were used as predictors in the SLR model. After variables that caused multicollinearity or nonsignificant were filtered and removed, the NDVI datasets in January, February, April, June, July, August, and September were used as the auxiliary variables in creating the SLR model. Table 3 shows the detailed parameters of SLR. The unstandardized coefficients showed the influence of NDVI variables on SOC with dimension, and the normalized coefficient showed the influence without dimension. All independent variables showed the influence degrees of NDVI to SOC in different months because they had the same unit. The coefficients of NDVI showed that NDVIs in February, September, January, and April and July, August, and June had negative and positive relationships with SOC. The NDVI in September exhibited the highest coefficient (\(-11.22\)) among all months, whereas that in April presented the lowest coefficient (\(-4.78\)). Thus, these predictors explained most of the spatial variations of SOC, which showed relatively strong correlation with SOC. Conversely, the absolute values of beta in the rest of months were slightly lower than suggested in these months, with NDVI demonstrating a weak effect on SOC. Thus, the influences of NDVIs to SOC varied with months and revealed the relationships between vegetation and SOC. Meanwhile, the significance of all independent variables used in calculation was less than 0.05. This result was credible from the perspective of statistics. Figure 8: Pearson correlation coefficient between SOC (soil organic carbon) and NDVI (normalized difference vegetation index) from January to December. NDVI\({}_{\text{Feb}}\) is the NDVI data in February, and NDVI\({}_{\text{Jul}}\) is the NDVI data in July, etc. Figure 9 shows the experimental variogram of the OK model. The best fit variogram model was a spherical one with a range of 308.97 m, nugget value of 21.67, and partial sill of 17.60. The range size reflects the scope of influence of the variables. Thus, the SOC of neighboring soil samples exhibits strong spatial autocorrelation when the distance is less than 308.97 m. The nugget value can reflect the randomness of regionalized variables, whereas sill size represents the amplitude of variation for regionalized variables. The ratio of nugget variance (C\({}_{0}\), 21.67) to the total sill (C\({}_{0}\) + C, 39.27) was 55.18%. The ratio of nugget variance to the sill variance of variables was usually considered a norm to classify the spatial dependence of environmental factors [75]. Ratios of <25%, between 25% and 75%, and 75% indicate strong, moderate, and weak spatial dependence, respectively [76]. Thus, the moderate spatial dependence in this area indicated that extrinsic factors, such as sampling methods or other anthropogenic activities, weakened the spatial dependence caused by intrinsic factors, such as parent material and other geological characteristics [77]. The intrinsic factors strengthened the spatial dependence, whereas extrinsic ones accounted for weak spatial dependence [78]. The PLSR algorithm selects successive orthogonal factors that maximize the covariance between predictors (X, e.g., NDVI time series data) and response variables (Y, e.g., SOC). In this research, highly suitable auxiliary predictor data were extracted from the NDVI series data using PLSR. The suitable number of LVs was three, which was selected through cross-validation, to evaluate the SOC content. Table 4 shows the detailed information. The percentages of variance of the three LVs of NDVI were 93.69%, 1.52%, and 1.45%, and those of SOC were 55.48%, 10.64%, and 1.71%, respectively. The cumulative percent of variance of the three LVs (of NDVI) was 96.66%, indicating that these LVs