## 3 Results
### Effect of Different Sampling-Point Numbers on the Prediction Accuracy of SOM Content  
The closer the ME approaches 0, the higher the spatial prediction accuracy of SOM. As can be seen from Figure 3, when the number of sampling points was greater than 150, the value of ME were almost all close to 0 and varied little. The ME of the predicted value reached a minimum of \(-0.12\) when the number of samples was 150. The value of the ME increased significantly when the number of samples was less than 150, and the ME of the predicted values at both 100 and 75 was approximately close to 1. This showed that when the number of sample points was greater than or equal to 150, Kriging interpolation method could better preserve the accuracy on the spatial prediction.  
The smaller the value of RMSE, the higher the spatial prediction accuracy of the SOM. There was no obvious change trend in RMSE with the increase in sampling numbers, and all values fluctuated between 3.60 and 4.65. The value of RMSE reached the maximum when the number of sample points was 50; when the number of sample points changed from 75 to 400, the value of RMSE was relatively stable and essentially maintained at around 3.7; but when the number of sample points was greater than 400, the value of RMSE showed a certain degree of volatility. However, it did not directly explain the relationship between the  
Figure 3: The spatial prediction error of SOM in different number of sampling points.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number of** **Samples** & **Model Type** & **Nugget (Co)** & **Sill** & **Nugget Ratio** (Co/sill)** & **Range/(m)** & **R\({}^{2}\)** & **RS** \\ \hline
800 & Spherical & 9.09 & 13.02 & 69.81\% & 2780.00 & 0.22 & 14.60 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The semivariance model of SOM content at 800 sample points and its fitting parameters.  
increase or decrease in sample points and the spatial-prediction error of SOM. This showed that the single verification index of RMSE did not indicate the result of spatial-prediction accuracy.  
ASE is an indicator used to evaluate the variability of a predicted value. If the value of ASE is equal to the value of RMSE, it means that the Kriging interpolation correctly estimates the spatial variation of SOM. The variability of spatial prediction is overestimated if ASE is greater than RMSE, and underestimated if ASE is less than RMSE. As can be seen from Figure 3, when the number of sampling points was less than 150, the values of ASE were mostly greater than 4, which were much higher than the value of RMSE. The large difference between the ASE and RMSE indicated that the variability of SOM spatial prediction was overestimated at this time, and the spatial prediction results had great uncertainty. When the number of sampling points was between 150 and 800, the value of ASE dropped to around 4.0 and remained relatively stable, and the difference between ASE and RMSE was relatively small in general. It reflected that the spatial prediction of the Kriging interpolation method was relatively stable and the prediction results were relatively accurate when the number of samples was more than or equal to 150.  
Based on the above three verification indexes of spatial-prediction accuracy, it can be inferred that collecting at least 150 soil samples could meet the demand of spatial-variation expression for SOM within the Kenli County of the Yellow River Delta. It was equivalent to at least 107 sample points to be set on every 1000 km\({}^{2}\) area.