# Spatial Prediction of Soil Contaminants Using a Hybrid Random Forest-Ordinary Kriging Model
## 4 Discussion  
To evaluate the quantified predictive performance of the machine learning-geostatistics combination model proposed in this study, a search was conducted on the existing studies. However, due to the lack of research in the same application category, comparisons were made with the combination models from other applications analyzed in the Introduction (Table 4). For both metrics, relative comparisons were made rather than direct comparisons, and in the case of the RMSE, the values showed a large difference, because it is the relevant error of the predicted data value. However, compared to other studies, the RMSE for the combined machine learning and geostatistics model is significantly lower than for the single techniques. Similarly, the R\({}^{2}\) shows that the hybrid model performs markedly better than other cases. However, note that the three cases compared were based on large amounts of data and separated the training and validation data. In contrast, this study was conducted with a small amount of data (40 points), learning 40 points and predicting 40 points with auxiliary variables (RF) or interpolating based on sampling data (OK). Therefore, further research should be conducted with a larger amount of sampling data.  
Figure 11: Comparison of the performance metrics calculated by the RF, OK, and RF–OK models. (**a**) RMSE and R\({}^{2}\), and (**b**) True values versus predicted values.  
In this study, the anisotropy option was not used when applying a method based on heavy metal concentration data. The PyKrige library allows the configuration of this feature with anisotropy scaling and anisotropy angles; however, it is only valid when the coordinate type is set to Euclidean and is not applicable to geographic coordinates. Consequently, in areas where anisotropy is prominent only in specific regions, differentiating between regions with and without significant anisotropy is necessary to conduct a thorough analysis. In addition, the model performance can be further improved by using additional auxiliary data. The auxiliary variables employed in this study are only those that can be obtained from elevation, but it is expected that higher prediction performance can be improved by obtaining and utilizing in-soil influencing factors. Finally, there are numerous other machine learning models and geostatistical techniques that were not used, so several combined models should be created to evaluate the performance of each model.  
The results of this study are expected to provide a more accurate assessment of the level of contamination in areas where environmental monitoring is required, which will be important for effective remediation and prevention strategies. When monitoring and remediation activities are determined by the concentration of heavy metals in the soil in abandoned mine areas, soil contamination maps generated from the results of single and combined models may have different scope, area, and remediation costs. Therefore, using the combined model is expected to produce soil contamination maps with lower interpolation errors, which may have an impact on soil contamination monitoring, remediation planning, and decision making.