Spatial modeling of soil particle size distribution based on log-ratio transformation and random forest optimization

Three log-ratio transformations—additive log-ratio (ALR), centered log-ratio (CLR), and isometric log-ratio (ILR)—were taken to map the soil particle-size fractions in the Yarkant River Plain oasis. The interpolation and machine learning were combined to identify the most suitable log-ratio transformation for the closed compositional data. The performance gains were also quantified using inverse distance weighting (IDW) as an auxiliary variable in co-Kriging (CK) followed by Random Forest (RF) optimization. Surface soil samples were collected for comparison. Laboratory measurements were used to obtain the three particle-size fractions. Compositional data was transformed in the training set using ALR, CLR, and ILR; All interpolation and variogram fitting were conducted in the transformed Euclidean space. The obtained datasets were then back-transformed and normalized for evaluation. Preliminary interpolation was performed with the inverse distance weighting, ordinary Kriging, and co-Kriging with IDW outputs as auxiliary covariates. Cross-validation and independent hold-out tests were used to assess performance by root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient. Finally, IDW+CK predictions were used as the inputs into Random Forest (RF), trained against measured values for nonlinear correction and final soil mapping. The highest accuracy of interpolation was achieved to reconstruct the distributional shape (skewness, kurtosis, and mean) with ILR after validation. The ILR interpolation was achieved in the lowest mean RMSE of 0.027 and the highest average correlation coefficient of 0.915 after cross-validation. Since the IDW was introduced as an auxiliary covariate in the CK, the interpolation error was reduced substantially: mean RMSE over the three fractions decreased, and correlations increased markedly. In independent hold-out (extrapolation) tests, the IDW contribution was variable and spatially dependent: marked improvement was observed for clay fraction, while silt fraction performance deteriorated in some hold-out samples—indicating context-sensitive benefits. Subsequently, RF correction with IDW+CK outputs further improved the generalization: RMSE and MAE of test-set and whole-sample were reduced, whereas the overall correlation increased. Spatial maps preserved the local extrema after RF correction, indicating the more realistic texture patterns. The class proportions were adjusted significantly, compared with the uncorrected predictions. The isometric log-ratio (ILR) transformation with IDW-assisted co-Kriging and Random Forest correction also provided superior accuracy and spatial patterns for the closed compositional soil data in the study area. The larger gains were observed in the higher density of the sample and strongly correlation between auxiliary and primary variables. Conversely, the limited or negative benefits were found in the regions with sparse sampling or weakly correlated settings. The workflow therefore offered a practical, empirically support to map the soil particle-size fraction. While its transferability can be tested under different sampling and auxiliary data sources.