## 4 Discussion
It is not guaranteed that this is a sufficient enough sample size to obtain highly accurate soil mapping results. In the future, the influence of the sample size on soil mapping accuracy using the proposed method will be further explored. In the proposed method, the diversity index (DI) was critical in determining the number of sampling points. Undoubtedly, different environmental covariates should have different weights when calculating the DI, since they have different relationships with the target variable. However, we do not have a priori knowledge of the relationship between the environmental covariates and the target variable. Thus, this paper gave the same weight to different environmental covariates when computing the DI. To further improve the proposed method, the correlation coefficients between these environmental covariates and the target variable were calculated based on the soil samples that were collected in that year and then regarded as the weights of the environmental covariates when calculating the DI. Then, the improved method was used to form the sampling design for the next year, and the results were compared to the results of the original method to validate the effectiveness. The experimental results (Figures 7 and 8) demonstrated that the proposed method had more potential for selecting representative soil samples that produce more precise soil mapping results compared to regular grid sampling and k-means sampling at limited sample sizes. The former of the two competitive methods considers good spatial coverage, and the latter considers good feature space coverage. These results demonstrated the superiority of the balance of good spatial coverage and good feature space coverage in good sampling design. In addition, Figure 8 shows that the regular grid sampling method resulted in better soil mapping accuracy than the k-means sampling method. A possible reason may be that the OK method was used for soil mapping in this paper. The OK is a regression algorithm for spatial modeling and prediction (interpolation) of stochastic processes/fields based on a covariance function. Thus, the sampling design resulting in good spatial coverage may generate more precise soil maps compared to that with only good feature space coverage when using the OK method as the mapping method. An interesting phenomenon was observed in Figure 5, in which the MAE and RMSE did not show a trend as the super-grid size increased. As shown in Figure 5, the \(400\times 400\) m\({}^{2}\) and \(600\times 600\) m\({}^{2}\) super-grids generated lower average MAE values and wider-ranging RMSE values compared to other different sized super-grids. A possible reason may be that only one sampling point was recognizedwithin certain super-grids and this did not occur in the sampling design results that were generated by these two super-grids (Table 3). As described in Section 2.2.3, the rules for determining one sampling point location and multiple sampling point locations within one super-grid are different. The results of that the \(400\times 400\) m\({}^{2}\) and \(600\times 600\) m\({}^{2}\) super-grid generated lower average MAE values indicated that the rule for recognizing multiple sample locations is superior to that for recognizing one sample location in producing reliable SOM content mapping results. However, the more ranges of RMSE values in the \(400\times 400\) m\({}^{2}\) and \(600\times 600\) m\({}^{2}\) super-grids indicated the instability of the rule in recognizing multiple sample locations to obtain reliable SOM mapping results. In addition, the \(500\times 500\) m\({}^{2}\) super-grid resulted in the largest prediction error, as indicated by the highest MAE and RMSE values. This result revealed the poor robustness of the rule in determining representative sample locations. Nevertheless, the proposed method was significantly better compared to the other two sampling design methods (Figure 8). In the future, the rule for determining sample locations will be further improved to obtain more reliable SOM content mapping results.