## 3 Results
### The Influence of Different Sampling Points on the Spatial Prediction Accuracy of Soil pH  
For each sample set, Kriging interpolation was used to carry out the spatial prediction of soil pH. Root mean square error (RMSE), mean error (ME) and average standard error (ASE) were used to measure the prediction accuracy of soil pH under different sampling points.  
It can be seen from Figure 3 that ME of 75, 100, 150, 200 and 300 was greater than 0, and that of other sampling points was less than 0. The ME value varies with the number of sampling points, but the variation does not follow the law that the ME decreases with the increase of sample number. When the sampling points were 50 and 300, the ME values were close to 0. In theory, the closer the ME to 0, the higher the accuracy of spatial prediction. In this case, the value of ME is generally calculated from statistical methods. It is possible that the independent verification results of each sample point were poor, but the residual errors after addition and averaging were smaller. When ME is close to 0, the prediction has low accuracy. Therefore, the ME index cannot indicate the accuracy very well at this point. On the other hand, a single index cannot indicate the interpolation accuracy well, and multiple indexes may be more accurate to judge the interpolation accuracy. With the decreased of sample size, the distance of ME deviating from X axis first increased, then decreased and then slightly increased. It basically surrounded the X axis except for 75 and 100 sample points. Therefore, when the number of sample points was too small (75, 100), the ME of predicted values would become larger.  
The RMSE was slightly larger with 50 samples. There was no obvious change trend with the decreased sample size, and it could remained at a certain value. This shows that the RMSE had no obvious difference in the spatial prediction accuracy of different  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sampling Point** & **Model** & **Nugget (C0)** & **Sill (C0 + C)** & **C0/Sill (\%)** & **Range** (km)** & **Determination** & **Residual** \\ \hline
926 & exponential model & 0.0350 & 0.1786 & 19.60 & 4.80 & 0.68 & 0.00 \\
801 & exponential model & 0.0360 & 0.1778 & 20.25 & 5.13 & 0.72 & 0.00 \\
704 & exponential model & 0.0360 & 0.1752 & 20.55 & 4.77 & 0.68 & 0.  
sample subsets, i.e., the accuracy of Kriging interpolation had no significant difference with decreased sample size.  
The uncertainty of Kriging prediction was measured by the ASE. The closer the ASE the RMSE, the more accurate the prediction of attribute value. In this study, when there were 150, 200 and 900 samples, ASE and RMSE were basically equal, indicating that the spatial variability of the earth was properly estimated. When the number of sampling points was 300-800, the ASE was smaller than the RMSE, and the difference between them was very small, indicating that these sampling points overestimated the spatial variability. However, when the number of sampling points was less than 150, the ASE was obviously less than the RMSE, so these sample sets could not reasonably predict the variability.  
Considering the ME, RMSE and ASE, 107 sampling points per 1000 km\({}^{2}\) could meet the needs of spatial variation expression of soil pH in the Yellow River Delta. According to the above analysis, we also determined that it was not enough to evaluate Kriging prediction accuracy only by a single evaluation index. Therefore, it was necessary to use a variety of evaluation indexes and combine them to accurately evaluate the prediction results.