## 4 Discussion
To reduce the complexity of the IMDP and to study comprehensive underlying patterns, the 13 IMDP were combined using PCA, resulting in three multi-metal distribution patterns. PCA was used in other studies and was an adequate tool to describe the underlying complexity of soil metal concentrations and their factors [77, 78]. However, the explicit interpretation of PCA rotated values as spatial patterns indicative of soil metal concentrations, as achieved in our study, appears to be a novel approach. Three MMDPs were found to describe a large proportion of the variation in the IMDP. Two models (those for MMDP1 and MMDP3) performed reasonably well, with OOB R\({}^{2}\) values of 0.87 and 0.72, respectively, while the model for MMDP2 had an R\({}^{2}\) of 0.36. The high portion of the distribution variance explained by the three MMDP shows that these multi-metal distribution patterns may hold information that exceeds that of individual distribution patterns. One of the study's main goals was to identify the environmental factors that determine the distribution of metals in floodplain soils. The most important variables of the respective models showed that the spatial patterns of MMDP1, MMDP2, and MMDP3 depend on different environmental factors. In the MMDP1 model, the proximity to the streams west-1 and east-3 was the most important, i.e., changes in these variables affected the model result the most strongly. The rock and soil chemistry in the western mountain ranges is affected by volcanic activity, and the metal-rich matter is transported into the floodplain [39, 40]. The results of our study support the idea that this transportation of matter from the mountains has this effect on the floodplain soils. Other important variables came from the group of soil parameters, especially soil hydraulic conductivity, and rock, and sand content. These soil features have been found to affect the metal concentrations in soils in other studies [79, 80]. The effects of the different groups in the MMDP2 model were not as distinctive. Most of the variables were of similar importance. In the MMDP3 model, the most important variables were the distance to the Sacramento River and the density of the main river network. As another route by which metals are input and transported into the floodplain, the Sacramento River may play a major role in metal accumulation [81, 82]. The proximity to the west and east streams played a role, while soil properties were the least important for the variance of MMDP3. Vegetation, in the form of NDVI and EVI, did not play a major role in the RF models, even though it has been found to affect metal concentrations in other studies [83, 84]. This is probably caused by the relative homogeneity of the vegetation in the research area. Most of the Sacramento Valley is covered by agriculture. The results showed that each metal had a relationship with each of the MMDPs, therefore, a relationship with spatially varying factors. The importance of the MMDP RF model features, in combination with the correlation results in Figure 6, revealed further interesting connections. MMDP1 was negatively correlated with 8 of the 13 IMDP, i.e., Al, Ca, Ce, Ga, K, La, Rb, and Sr. This result highlights that the distribution of these metals is negatively affected by the specific environmental features that affect the distribution of MMDP1. These environmental features are attributes belonging to the groups Input streams and Soil. The five other IMDP, Cs, Li, Ni, Sc, and V, were positively correlated with the distribution of MMDP1. This means that the relationship with the same factors of Input streams and Soil affecting MMDP1 is inverted for these metals, when compared to the metals with a negative correlation. MMDP2 was positively correlated to almost all IMDP, except Sr, which had a weak negative correlation. MMDP3 was positively correlated with five IMDPs and negatively correlated with four IMDPs. Of the aforementioned, less commonly studied metals, Ga, Sc, and V were significantly negatively correlated with MMDP3.