## 4 Discussion  
Spatial variation of soil properties is controlled by various structural and random factors. The larger the ratio of Nugget to Sill, the more obvious the influence of human activities, such as irrigation, fertilization and cultivation. On the contrary, structural factors such as soil parent material, climate, biology, topography and other natural factors play a major role [35,36]. The ratio of Nugget to Sill of almost all sample sets in this study was less than 25% and showed strong spatial autocorrelation, indicating that the spatial variation of soil pH in the study area was mainly affected by structural components such as topography, climate and soil parent material. When the sampling point was less than 150, the ratio of Nugget to Sill reached 40%, indicating that the spatial autocorrelation of these sample sets was weakened, and was influenced by structural components and random factors. With the decreased of the number of sampling points, the small-scale structural factors and random factors gradually increased, while the influence of large-scale structural factors such as parent material, topography and soil type on soil pH gradually weakened, which caused the soil pH to change strongly with the small number of sampling points. Figure 4: Expression diagram of soil pH spatial variation of different point sets. The letters (**a**–**l**) represent the spatial variation expression of soil pH at 908, 797, 700, 594, 499, 398, 299, 200, 149, 100, 75 and 50 sampling points respectively. Note: The eastern of Kenli County was not sampled because the area is in the Yellow River Delta National Nature Reserve. However, for the continuity and completeness of maps, the result of the unsampled area was deduced and extended by the Kriging interpolation based on the near sampled soils. According to the analysis of spatial prediction accuracy of soil pH with different sampling sets, the ME of predicted values gradually increased when the number of sampling points was too small. The RMSE could basically be maintained at a certain value with a decrease of sampling numbers, except for being slightly larger at 50 sample points. Interpolation prediction error and interpolation of the distribution map had a certain synergistic relationship with the change of sample numbers. When there were less than 150 samples, the difference between ASE and RMSE was large. Correspondingly, the spatial distribution maps of soil pH with less than 150 sampling points were too smooth to show the spatial distribution of soil pH accurately. However, when the number of samples was increased to 150 or more, details of the spatial variation expression diagram of soil pH were more obvious, and could show the spatial variation expression of soil pH more accurately. In addition, at 150 or more sampling points, the prediction error maps of RMSE, ME and ASE of soil pH and the expression maps of spatial variation of soil pH in different point sets could better predict the spatial variation of soil pH. Therefore, it was shown that the prediction error of soil pH was consistent with the spatial distribution of soil pH. In this paper, the influence of the number of different sampling points on the spatial distribution of soil pH in the Yellow River Delta region was investigated by using the ordinary Kriging method. It was concluded that the number of sampling points most suitable for Kenli County in the Yellow River Delta region should be no less than 150; that is, at least 107 sampling points should be taken every 1000 km\({}^{2}\). This paper also compared the existing literature investigating reasonable sampling numbers of soil pH. Study [37] showed that the rational sampling number at the county scale was about 4900 samples per 1000 km\({}^{2}\), which was inconsistent with our findings. This may be because in that study the area was located in a more undulating mountainous and hilly region resulting in a reduced spatial autocorrelation of soil pH.