Objectives This study employs different methods to predict farmland soil organic matter (SOM) in the typical geomorphic areas of the Loess Plateau. We examined the applicability and uncertainty of the prediction methods in different regions for the estimation of spatial distribution of SOM more accurately, which was of great significance for the efficient use and refined management of soil resources.

Methods This study was conducted in the three geomorphological regions of the Loess Plateau -the hill and gully area (HGA, in Zhuanglang County), high plateau area (Ning County), and the plain area (Wugong County). We collected 3788, 4048, and 3860 soil samples, respectively, from the study areas to determine SOM content. The spatial distribution characteristics of SOM in the study areas were analyzed using geostatistics theory. 75% of the original data was extracted for modeling, and the remaining 25% were used for validation using ordinary Kriging (OK), random forest (RF), and random forest + ordinary Kriging (RF+OK) methods. The modeling techniques considered soil multi-source influencing factors such as soil type, terrain, climate, vegetation, human activities, etc. We clarified the uncertainty of each prediction method through error analysis and spatial structure inspection.

Results The average SOM content in the hill and gully area, high plateau area, and the plain area were 14.29, 13.15, and 14.48 g/kg. The study areas’ SOM content fell into a low level, and the coefficients of variation were 18.96%, 19.54%, and 26.71%, showing medium variation. Nugget effects were 8.60%, 17.41%, and 10.01% as affected by the combination of randomness and structural factors, with the latter having a higher significant effect. The SOM content in the hilly and gully area and plain area were 0.26 and 0.14, while ZI were 26.56 and 13.51, showing a significant spatial autocorrelation. In the high plateau area, Moran’s I of SOM content was 0.02, and ZI was 1.55, indicating a lack of spatial autocorrelation. The spatial distribution of SOM content in the hilly and gully areas, high plateau area, and the plain area was most affected by temperature, altitude, and precipitation, respectively. The RF+OK method had the smallest error (MSE, RMSE, MAE, etc) in the plain area compared with the RF and OK method. The correlation coefficient (r) between the observed and predicted values was the highest, and the spatial structure of the predicted value was closer to the observed value in plain area. The spatial distribution of SOM in the high plateau area was irregular, and the OK method was not applicable in this area. There was no significant difference between the errors of the RF and RF+OK method. Still, the r-value of the RF method was higher, and the predicted value’s spatial structure was close to the actual characteristics of the high plateau area. In the hill and gully area, the uncertainty of the OK method’s prediction results was relatively large. There was no significant difference between the errors and r of the RF and RF+OK methods, but the spatial structure of the RF method’s predicted values was closer to the observed values. Compared with the other two regions, the SOM variability and modeling and validation errors in the plain area were the largest.

Conclusions In different geomorphic areas, environmental factors and spatial structures are different, and the prediction accuracy of different methods vary. Compared with the hill and gully area and high plateau area, the spatial prediction results’ uncertainty in the plain area is higher. We found differences in the results of the three prediction methods within the same geomorphic area. The RF+OK method in the hilly and gully area is better at predicting the spatial distribution of SOM, while the RF method is better in the high plateau and plain areas. When regional SOM has a significant spatial correlation, a high fit of the semi-variance function, and a small residual, the RF+OK method can significantly improve the model's prediction accuracy.