## 3 Results
### Spatial Variability of DOC and DTN  
Since our data on DOC and DTN have no trend in any direction over the study area, an isotropic semi-variogram was created for DOC or DTN (Figure A2). The experimental semi-variograms showed that the best fit for the spatial variability of DOC and DTN was an exponential model (Figure A2). Table 3 lists all the essential parameters for the semi-variogram models. The nugget ratio of DOC (0.09) was similar to that of DTN (0.10). The nugget effects of DOC (740.00) and DTN (84.00) were relatively small compared to the respective silt values of 8140.00 and 812.10. The ranges of DOC and DTN were 34.2 and 35.1, respectively, and were rather similar.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Variables** & \(n\) & **Mean** & **SD** & **CV** & **Skewness** & **Kurtosis** & **Minimum** & **Maximum** & \(p\) **of Shapiro–Wilk Test** \\ \hline DOC (mg C kg\({}^{-1}\) soil) & 111 & 288.14 & 89.31 & 31.00 & 0.00 & \(-\)0.39 & 73.15 & 490.74 & 0.8395 \\ DTN (mg N kg\({}^{-1}\) soil) & 111 & 97.26 & 27.97 & 28.76 & 0.09 & \(-\)0.24 & 36.43 & 173.14 & 0.4147 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Descriptive statistics of dissolved organic carbon (DOC) and dissolved total nitrogen (DTN). SD: standard deviation; CV: coefficient of variation.  
Spatial Distribution Characteristics of DOC and DTN and Their Correlation with Environmental Factors  
Figure 3 shows a comparison between the distribution maps of DOC and DTN generalized by ordinary kriging and those generalized by cokriging. Both methods generated similar spatial patterns of DOC and DTN, although most of the parameters (ME, RMSE, RMSSE) had smaller values using cokriging than those for ordinary kriging (Figure A4). Both DOC and DTN concentrations decreased from southeast to northwest across the study area. DOC and DTN were strongly correlated (Figure A3), with a correlation coefficient of 0.69 (\(p<0.0001\)). However, it should be noted that there were still over 30% of DOC and DTN values that were not matched exactly, and this is why the spatial distribution maps for DOC and DTN were slightly different, but with a similar trend. The DOC and DTN densities were 23.92 and 8.07 g m\({}^{-2}\), respectively.  
Figure 4 shows the correlation analyses of the relationships between environmental factors and DOM concentration, with DOC and DTN having similar patterns. Both DOC and DTN showed no significant correlations with environmental factors. However, elevation and soil temperature had a weak correlation (with \(p\) values falling between 0.05 and 0.1) with DOC and DTN, which indicates that the higher the elevation, the smaller the DOC and DTN concentrations, and the higher the soil temperature, the larger the DOC and DTN concentrations.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Variable** & **Model** & **Nugget C\({}_{\text{o}}\)** & **Sill (C\({}_{\text{o}}\) + C)** & **C\({}_{\text{o}}\)/(C\({}_{\text{o}}\) + C)** & **Range (m)** & **R\({}^{2}\)** & **RSS** \\ \hline DOC & Exponential & 740.00 & 8140.00 & 0.09 & 34.20 & 0.53 & 488333 \\ DTN & Exponential & 84.00 & 812.10 & 0.10 & 35.10 & 0.56 & 5008 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of semi-variogram models for DOC and DTN. Nugget: the undetectable measurement error, inherent variability, or variation within the minimum sampling distance. Sill: total variation. Nugget sill ratio: the degree of spatial variability. RSS: residual sum of squares.  
Figure 2: Relationship between the CV of DOC and DTN with increasing sampling area. Error bars represent the standard error of the mean.  
Figure 4: Correlation matrix (with individual \(p\) values shown in the upper left of the panel) of DOC and DTN with environmental factors. VW: soil moisture; T: soil temperature.  
Figure 3: Spatial distribution of DOC and DTN estimated by ordinary kriging (**a,b**) and cokriging (**c,d**) across the study area.