## 3 Results
### Geostatistical Analysis  
According to the Kolmogorov--Simirnov normal distribution test, the indexes of sand content, clay content and saturated hydraulic conductivity in the study area do not conform to the normal distribution, but all the six indexes follow a lognormal distribution (Table S2). To facilitate comparison, all six indexes were transformed into logarithms, which were imported into the software GS\({}^{+}\)9.0 for geostatistical analysis. GS9.0\({}^{+}\) software allocates point pairs by establishing the lag class. When the active lag distance and lag distance interval were determined, the number of pairs was equal to the number of lag classes. Generally, the active lag distance was 80% of the maximum interval distance, 3120.86 m. Considering the distribution of sampling points, the minimum interval of 361.31 m was taken as the lag interval, and uniform distribution was selected for lag class. According to the parameter setting, there were eight pairs of points in this study. The results of isotropic analysis are shown in Table 3.  
The nugget is caused by random factors such as sample experimental error [38], which reflects the variation of regional variables on a small sampling scale; the sill is the half square difference of the variation function when the variable is stationary, which is the overall characteristic of the variable. The larger the sill, the stronger the spatial heterogeneity; the smaller the nugget coefficient, the stronger the spatial autocorrelation of the system; otherwise, the change between samples is closely related to random factors. The range reflects the maximum autocorrelation distance of the variable. Table 3 reveals that there are four kinds of statistical models for the six soil properties: Gaussian, exponential, linear and spherical. The small nugget coefficient of the silt content indicates that the silt content in the study area has a strong spatial autocorrelation. Additionally, its range is the smallest, which shows that the scale range of its spatial continuity is the smallest [18]. The nugget coefficients of the other five soil properties were between 0.4 and 0.5, which can be considered to have moderate spatial autocorrelation. The order from the largest to the smallest is: \(\mathrm{K_{s}}>\mathrm{sand}>\gamma>\mathrm{clay}>\theta_{\mathrm{s}}\). The range values of the other five soil properties range from 1913.92 m to 5097.43 m. The sequence of the range values from the largest to the smallest is: \(\mathrm{clay}>\mathrm{sand}>\theta_{\mathrm{s}}>\mathrm{K_{s}}>\gamma\). Based on the model fitted in Table 3, simple Kriging interpolation maps of soil properties (logarithm) were drawn (Figure 3), which can directly reflect the spatial distribution of soil properties. The spatial distribution of the six soil properties is varied, and there is no obvious regularity in the spatial distribution of bulk density, saturated water content and saturated hydraulic conductivity. However, two conclusions can be drawn from Figure 3: One is that the sand content gradually increases from north to south, while the clay content shows the opposite. Secondly, the colour of the silt content changes slightly, which is consistent with the extremely weak nugget coefficient of silt content, although in classical statistics, the coefficient of variation of silt content is not the lowest. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Soil Property**} & \multicolumn{6}{c}{**Geostatistical Analysis (Isotropy)**} \\ \cline{2-7}  & **Model** & \(\mathbf{C_{0}}\)1 ** & **Range(m)** & \(\mathbf{R^{2}}\) \\ \hline Sand & Gaussian & 0.24450 & 0.49500 & 0.494 & 4094.57 & 0.886 \\ Silt & Exponential & 0.00001 & 0.00401 & 0.002 & 1119.00 & 0.713 \\ Clay & Gaussian & 0.10870 & 0.24340 & 0.447 & 5097.43 & 0.969 \\ \(\gamma\) & Gaussian & 0.00045 & 0.00095 & 0.468 & 1913.92 & 0.759 \\ \(\theta_{\mathrm{s}}\) & Linear & 0.00119 & 0.00185 & 0.402 & 3051.46 & 0.661 \\ \(\mathrm{K_{s}}\) & Spherical & 0.27110 & 0.54320 & 0.499 & 2173.00 & 0.504 \\ \hline \end{tabular}
\end{table}