## 3 Results  
A correlation between all 38 metals was performed to understand the relationships between the different metals. As shown in Figure 3, of the 722 possible unique correlations, 484 (67%) were significant (\(p<0.05\)), consisting of 364 positive correlations and 120 negative correlations. Tungsten (W), Ga, and thallium (TI) had more than 28 positive correlations each, while 21 metals had 20 or more positive correlations (Figure 3). The least positive correlations were found for sodium (Na) and tin (Sn), which had eight positive correlations, and Cd, which only had seven. Na had the most significant negative correlations, totalling 20. Ni, strontium (Sr), Cr, calcium (Ca), Co, Mg, niobium (Nb), potassium (K), and lithium (Li) had more than ten negative correlations. Three metals, i.e., Ba, Cd, and Sn, had no significant negative correlations. Additionally, these three metals also had relatively few positive correlations. The results of the correlation study showed that there are moderate to strong relationships between the individual metals in the Sacramento River floodplain. Figure 2: Overview of the research process, detailing the different steps and input data. Due to a large number of significant correlations, we next aimed to find a more condensed representation of the relationships between the metals and describe more generalized distribution patterns. In this first step of complexity reduction, the RF model analysis for each of the 38 metals resulted in 13 IMDPs, each named after the individual metal best describing the distribution pattern (Table 2). Model results were only considered when the OOB R\({}^{2}\) reached 0.7, and 22 models remained. The IMDP \"Ni\", defined by the distribution pattern of nickel, best described the distribution of four metals (Ni, Co, Cr, and Mg). V was IMDP for three other metals, while Ga, La, Li, rubidium (Rb), and Sc were IMDP for two metals each. Aluminium (Al), Ca, cerium (Ce), caesium (Cs), K, and Sr were each IMDP for a single other metal. The correlation values between the IMDP and the metals were all medium to very strong (correlation coefficients 0.61 to 0.98) and positive. The only negative IMDP relationship with metal was between the IMDP V and the metal Na. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**IMDP** & **Al** & **Ca** & **Ce** & **Cs** & **Ga** & **K** & **La** & & **Li** \\
**Described Metal** & **Ga** & **Sr** & **La** & **Li** & **Al** & **Be** & **Rb** & **Ce** & **Nb** & **Cs** & **Ni** \\ \hline RF R\({}^{2}\) & 0.89 & 0.83 & 0.92 & 0.93 & 0.86 & 0.76 & 0.81 & 0.91 & 0.84 & 0.92 & 0.90 \\ Correlation & 0.86 & 0.89 & 0.98 & 0.90 & 0.86 & 0.70 & 0.73 & 0.98 & 0.84 & 0.90 & 0.78 \\ \hline
**IMDP** & **Ni** & **Rb** & **Sc** & **Sr** & **Sr** & **V** & **V** \\
**Described Metal** & **Co** & **Cr** & **Mg** & **K** & **T1** & **V** & **Y** & **Ca** & **Fe** & **Na** & **Sc** \\ \hline RF R\({}^{2}\) & 0.88 & 0.77 & 0.83 & 0.85 & 0.72 & 0.90 & 0.80 & 0.77 & 0.88 & 0.87 & 0.94 \\ Correlation & 0.69 & 0.73 & 0.74 & 0.73 & 0.73 & 0.92 & 0.61 & 0.89 & 0.86 & \(-\)0.70 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The 22 metals for which the RF model performance exceeded an R\({}^{2}\) of 0.7. Figure 3: Correlation matrix of the 38 metals studied in the soil samples of the research area. The size and colour of the circles indicate the direction and strength of the correlation (larger indicating stronger correlations, red indicating negative, and green indicating positive correlations). Non-significant correlations are marked with an \(\times\). The IMDP showed clear spatial patterns, as shown in the kriging maps in Figure 4. The IMDP Ca, Ce, K, La, and Sr showed similar patterns, with the highest concentrations in the southeast of the floodplain. Al, Ga, and Rb had similarly high concentrations in the south and central region and differing higher concentrations in the north. Cs, Li, Ni, Sc, and V had very low concentrations in the southeast.