## 3 Results
### Assessment of Model Performance  
According to the 10-fold cross-validation of the two ALR-transformed PSFs in the BQ region (Table S2), the RF (random forest) predictions based on AR (all-relevant variable) sets were better than the AV (exhaustive covariate) sets, and the best prediction of the two ALR-transformed PSFs were both based on the HC (hill climbing) sets. Meanwhile, for the predictions by Cubist, the AR sets performed better than AV sets for the prediction of silt\({}_{\text{iIr}}\) and worse for the prediction of clay\({}_{\text{iIr}}\). As for the predictions with minimal-optimal variable sets, SA (simulated annealing) set had the best prediction on clay\({}_{\text{alr}}\), and GB (greedy backward) set had the best prediction on silt\({}_{\text{alr}}\). Both of them were better than the prediction based on AV and AR sets. As for the back-transformed PSFs, the ALR-RF model performed better than ALR-Cubist. According to the predictions by ILR-RF, the AR sets performed better than the AV sets. Among the minimal-optimal variable sets, SA and HC sets performed best on the prediction of clay\({}_{\text{iIr}}\) and silt\({}_{\text{iIr}}\), respectively. As for the predictions by Cubist, AR set performed better than AV set on clay\({}_{\text{iIr}}\) and worse on silt\({}_{\text{iIr}}\). Among the minimal-optimal variable sets, SA sets had the best predictions of both components. The ILR-RF model exhibited superior prediction compared to all the other predictions in the BQ region. In the WQ region, AR sets outperformed AV sets by ALR-RF. Among the minimal-optimal variable sets, SA and HC sets had the best prediction on clay\({}_{\text{alr}}\) and silt\({}_{\text{alr}}\), respectively, which were better than AR sets. As for the predictions by ALR-Cubist, AV sets outperformed AR sets. GB and HC sets had the best prediction on clay\({}_{\text{alr}}\) and silt\({}_{\text{alr}}\), respectively, which were better than AV sets. According to the back-transformed PSFs, ALR-Cubist outperformed ALR-RF. According to the prediction of transformed PSFs by ILR-RF, AR sets performed better than AV sets. Among the minimal-optimal variable sets, GB and GF sets had the best prediction on clay\({}_{\text{iIr}}\) and silt\({}_{\text{iIr}}\), respectively, better than AR sets. When using ILR-Cubist, AR sets performed better than AV set. Among the minimal-optimal sets, GF and SA sets had the best prediction on clay\({}_{\text{iIr}}\) and silt\({}_{\text{iIr}}\), respectively, better than the AR sets, and outperformed all the other predicted soil PSFs in the WQ region (Table S2). The model assessment on back-transformed PSFs was presented in Table 3. In terms of RMSE, RF (random forest) performed better than Cubist, and ILR transformation performed better than ALR in general. The prediction by ILR-RF was best in both study areas. For the prediction of clay\({}_{\text{irl}}\) at the BQ region, SA retained vegetation (i.e., evi_1, evi_9, ndvi_1, and gpp_9), terrain (i.e., SWI and VRM), and LST (i.e., yr_n_i_9) covariates. In terms of the silt\({}_{\text{irl}}\) prediction, HC retained terrain (i.e., s1_d_a_1, s2_df_a_9, s2_df_a_1 and s3_d_a_9) and climatic (i.e., pre_s1_9) factors. The SA and HC set covered all categories of covariates contained in AR sets of ILR-transformed PSFs. In the WQ region, GB retained vegetation (i.e., evi_1, evi_9, ndvi_1 and gpp_9) and LST (i.e., s1_d_i_9, s1_n_i_9, s2_df_e_1 and s4_df_e_9) covariates for clay\({}_{\text{irl}}\) prediction. Furthermore, GF only retained LST covariates (i.e., s2_df_a_1, s3_df_i_9, s4_d_e_9, s4_n_e_1, s4_n_i_9 and yr_n_i_9) for silt\({}_{\text{irl}}\) modeling. The GB and GF sets contained all types of all-relevant covariates as well. Predictions based on five covariate sets were different, even using the same prediction model. In general, all-relevant models had comparable performance to exhaustive models across all four prediction methods, indicating that the AR sets contained almost equivalent predictive power to exhaustive variables.