## 3 Results
Sc and V had an almost identical distribution along the north-south axis of the research area. Cs, Li, and Ni had higher concentrations in the areas along the floodplain's western side. Next, using PCA, multi-metal distribution patterns were created to extract comprehensive spatial patterns that describe most of the metal distributions in the Sacramento River floodplain. After performing the PCA, three principal components (PC) with an eigenvalue (the square of the standard deviation) over 1.0 were considered for further study (Table 3). PC1 described 41% of the variation in the input data, PC2 described 31%, and PC3 described 13%. Together, all three PC reflected 86.9% of the variation in the data. The relationship between the respective IMDP and the three PC is shown in the Supplementary Figures S4-S16. The respective spatial distribution patterns of the rotated values of the PC, i.e., the multi-metal distribution patterns (MMDP), are shown in Figure 5. The higher values of MMDP1 were concentrated in the western regions of the floodplain, while the eastern side showed very low values. MMDP2 showed a northern region of high values and a southern region of higher values focused on the floodplain's central areas. MMDP3 was similar to  
Figure 4: The 13 individual metal distribution patterns are named after the respective metal concentrations in the topsoil of the Sacramento River floodplain. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **PC1** & **PC2** & **PC3** \\ \hline Standard deviation & 2.3225 & 2.0286 & 1.3387 \\ Proportion of variance & 0.4149 & 0.3165 & 0.1379 \\ Cumulative proportion & 0.4149 & 0.7315 & 0.8693 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the principal component analysis with information about the three utilized principal components. the distribution of MMDP1, but the band of low values in the east was broader, the western region with high values did not stretch south as far, and there was a patch of high values in the southeast of the floodplain. Another correlation was performed to identify the relationship between the three MMPD and the respective metal distributions in the soil. Figure 6 shows the correlation coefficients between the three MMDP and the 13 IMDP. MMPD1 showed strong negative correlations with the IMDP Ca, Ce, La, and Sr, and relatively strong positive correlations with Ni, Li, and Cs. MMDP2 had positive correlations with the metal concentrations, except for a very weak negative correlation with Sr. The correlations with Al and Ga were very strong, followed by Cs, Rb, Sc, and V. The correlations between MMDP3 and the IMDP were generally weaker than those of MMDP1 and MMDP2; the strongest positive correlation was with K, and the strongest negative correlations were with Sc and V.  
After defining the multi-metal spatial patterns of soil metal concentrations in the Sacramento River floodplain, the goal was to identify the environmental factors of these patterns. To achieve this, three RF models were used. Where necessary, spatial predictors were included to overcome the effects of spatial autocorrelation (Supplementary Figure S17). The R\({}^{2}\) values of the RF model for MMDP1, MMDP2, and MMDP3 were 0.87, 0.36,  
Figure 5: The three resulting multi-metal distribution patterns describe the generalized metal accumulation in the Sacramento River floodplain. Figure 6: Correlation of the three MMDP with the 13 IMDP. Non-significant correlations are displayed in white. and 0.72, respectively. Figure 7 shows the respective six most important variables of the three RF models. Changes in these variables had the highest effect on the prediction power of the model. The most important feature in the MMDP1 RF model was the proximity to stream west-1, followed by the proximity to stream east-3. The next most important variables all belonged to the Soil category, especially soil hydraulic conductivity and soil rock and sand percentages. Three categories, Input streams, Sacramento River, and Soil, were present in the most important features in the MMDP2 model.