## 5 Conclusions  
Due to the lack of field observations, the datasets focused on the spatial distribution of soil PSFs in permafrost regions of the Qinghai-Tibet Plateau are still scarce. We carried out the mapping of soil PSFs at two typical permafrost distributed regions by integrating two log-ratio transformation methods, five variable selection techniques, and two learning approaches. The Boruta all-relevant technique retained vegetation and LST covariates, and excluded air temperature in both regions. The difference in variable selection in the two regions is that precipitation and topographic covariates were retained at BQ but excluded at WQ. In general, the AR models had comparable accuracy with the exhaustive models, and the parsimonious models exhibited superior prediction compared to the exhaustive \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Region** & **PSF** & \(\mathbf{R^{2}}\) & **RMSE** & **Bias** \\ \hline \multirow{4}{*}{SG250} & \multirow{4}{*}{BQ} & clay & 0.028 & 0.102 & 0.098 \\  & & silt & 0.008 & 0.142 & \(-\)0.048 \\  & & sand & 0.000 & 0.157 & \(-\)0.051 \\ \cline{2-6}  & \multirow{4}{*}{WQ} & clay & 0.017 & 0.082 & 0.058 \\  & & silt & 0.014 & 0.322 & 0.320 \\  & & sand & 0.049 & 0.387 & \(-\)0.378 \\ \hline \multirow{4}{*}{CDSL} & \multirow{4}{*}{BQ} & clay & 0.027 & 0.069 & 0.059 \\  & & silt & 0.205 & 0.121 & \(-\)0.023 \\  & & sand & 0.087 & 0.145 & \(-\)0.035 \\ \cline{2-6}  & \multirow{4}{*}{WQ} & clay & 0.230 & 0.067 & 0.004 \\  & & silt & 0.117 & 0.293 & 0.291 \\  & & sand & 0.000 & 0.308 & \(-\)0.295 \\ \hline \multirow{4}{*}{CSCD} & \multirow{4}{*}{BQ} & clay & 0.001 & 0.062 & 0.042 \\  & & silt & 0.004 & 0.151 & \(-\)0.007 \\ \cline{1-1}  & & sand & 0.008 & 0.176 & \(-\)0.035 \\ \cline{1-1} \cline{2-6}  & \multirow{4}{*}{WQ} & clay & 0.012 & 0.064 & 0.016 \\ \cline{1-1}  & & silt & 0.113 & 0.305 & 0.297 \\ \cline{1-1}  & & sand & 0.074 & 0.328 & \(-\)0.313 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Assessment of soil PSFs extracted from SoilGrids250m (SG250), China dataset of soil properties for land surface modeling (CDSL), and China soil characteristic dataset (CSCD). Figure 7: Spatial distribution of soil particle size fractions (PSFs) at the WQ region using ILR-RF and extracted from three soil datasets. covariates. It confirms the necessity of variable selection prior to model fitting. However, we did not find a universal method for covariate selection. In addition, we prefer to compare multiple variable selection techniques than recommend a specific one. The ILR-RF model outperformed all the other models in both study areas. These results suggest that the combination of log-ratio transformation, covariate selection, and machine learning approaches are feasible in mapping soil PSFs in both study areas. The following are available online at [[https://www.mdpi.com/article/10.3390/rs13071392/s1](https://www.mdpi.com/article/10.3390/rs13071392/s1)]([https://www.mdpi.com/article/10.3390/rs13071392/s1](https://www.mdpi.com/article/10.3390/rs13071392/s1)), Figures S1 and S2: Importance of the all-relevant covariates of ALR- and ILR-transformed PSFs in the BQ and WQ regions. Figures S3 and S4: Spatial distribution of soil particle size fractions in the BQ and WQ regions predicted by four log-ratio models. Figures S5 and S6: Fitted variable importance plots for \(\text{clay}_{\text{ir}}\) and \(\text{sil}_{\text{ir}}\) by the ILR-RF model in the BQ and WQ regions. Figures S7 and S8: Comparison between the distribution of sand and the predictors in the BQ and WQ regions. Table S1: Selected covariates identified by Boruta, GF, GB, HC and SA techniques in the two study areas. Table S2: Assessment on the predictions of two transformed fractions by the exhaustive, all-relevant and parsimonious models. Conceptualization, C.W. and L.Z. ; methodology, C.W. and L.Z. ; software, C.W., L.W., and Z.X. ; validation, C.W. and D.Z. ; formal analysis, H.F. and C.W. ; investigation, H.F., G.H., X.W., Y.Z., Y.S., Q.P., E.D., and G.L. ; resources, L.Z.