To comprehensively evaluate model performance, we applied two complementary validation strategies: 10-fold cross-validation on the training dataset (80 %) and independent validation using a held-out test set (20 %). These schemes were implemented across the entire study region to assess the predictive accuracy of forest soil BD and pH.

In 10-fold cross-validation, the training set was randomly partitioned into ten equal subsets. In each iteration, nine subsets were used to train the model, and the remaining one was used for validation. This procedure was repeated ten times, ensuring each subset served as validation data exactly once. Model accuracy was assessed by averaging performance metrics across folds, including mean error (ME), root mean square error (RMSE), and the model efficiency coefficient (MEC).

For independent validation, the reserved test set was excluded entirely from model training and hyperparameter tuning, thereby providing an unbiased evaluation of generalizability. The formulas used for calculating the evaluation metrics are as follows: 3ME=1n∑i=1n(y^i-yi)4RMSE=1n∑i=1n(yi-y^i)25MEC=1-∑i=1n(yi-y^i)2∑i=1n(yi-y¯)2 where yi is the observed soil property value, y^i is the predicted value, and y¯ is the mean of observed values. ME, also referred to as bias, measures average deviation. RMSE reflects the overall prediction error, with lower values indicating higher accuracy. MEC, equivalent to the coefficient of determination (R2), ranges from 0 to 1, with higher values indicating better predictive performance.

To enhance model interpretability and quantify the contribution of each environmental covariate to the predictions of soil BD and pH across the five soil layers, we utilized SHAP (SHapley Additive exPlanations) (Lundberg and Lee, 2017), a game-theoretic approach that assigns each feature a Shapley value representing its contribution to model output. SHAP provides a unified framework for evaluating feature importance and the directionality of each feature's effect on model predictions. This allows us to determine not only how each environmental factor influences the model's predictions for soil BD and pH but also revealing the direction (positive or negative) and magnitude of the feature's impact on that specific prediction. SHAP values were computed using TreeSHAP based on the training dataset.

Quantifying spatial uncertainty is essential in DSM, as prediction errors may arise from input data variability, model structure, and environmental heterogeneity (Arrouays et al., 2014; Poggio et al., 2021; Liu et al., 2022a; Shi et al., 2025). To visualize the spatial distribution of prediction uncertainty, we calculated the Prediction Interval Ratio (PIR), defined as the ratio between the 90 % prediction interval width and the median estimate: 6PIR=q0.95-q0.05q0.50 where q0.95 and q0.05 represent the upper and lower bounds of the 90 % prediction interval, respectively, and q0.50 denotes the median prediction. PIR is a dimensionless metric that quantifies the relative spread of prediction uncertainty around the central estimate. Higher PIR values indicate greater dispersion and, therefore, higher predictive uncertainty.

To evaluate the calibration of these uncertainty estimates, we used the Prediction Interval Coverage Probability (PICP), computed from the independent validation dataset (Goovaerts, 2001). PICP measures the proportion of observed values that fall within their corresponding prediction intervals at a specified confidence level (e.g., 90 %). A well-calibrated model should yield a PICP value close to the nominal coverage. For example, a 90 % prediction interval is considered reliable if the empirical PICP also approximates 90 %. Systematic deviation from this benchmark can indicate miscalibration: a PICP above the target level suggests that intervals are too narrow (underestimated uncertainty), while a PICP below the target indicates overly wide intervals (overestimated uncertainty) (Poggio et al., 2021; Liang et al., 2019). This diagnostic approach supports the robust interpretation of uncertainty in DSM outputs.

As shown in Fig. 3 and Table S7 in the Supplement, the dataset comprises 4356 forest soil profiles distributed nationwide. Soil properties were standardized to fixed depth intervals (0–5, 5–15, 15–30, 30–60, and 60–100 cm) using the equal-area spline method, resulting in 15 845 horizons for BD and 15 978 horizons for pH, which were visualized using violin plots to illustrate their distribution across soil depths. Differences among soil depth intervals were assessed using the Kruskal–Wallis test, followed by Dunn's post hoc pairwise comparisons with Bonferroni correction. Statistical significance was determined at p<0.05 based on adjusted p-values.

Forest soil BD exhibited a non-linear vertical distribution pattern, characterized by an increase from surface soils to mid-depth layers followed by a decrease in deeper layers (Fig. 3a; Table S7). Specifically, mean BD values were similar in the two surface layers (1.206 gcm-3 at 0–5 cm and 1.209 gcm-3 at 5–15 cm), increased in the 15–30 cm layer (1.287 gcm-3), and reached the maximum value in the 30–60 cm layer (1.340 gcm-3). In the deepest layer (60–100 cm), mean BD declined to 1.242 gcm-3. The violin plots revealed a relatively compact distribution of BD across all soil layers, with no pronounced extreme outliers (Fig. 3a). The left and right contours of the violin plots were well balanced, corresponding to low skewness values (0.16–0.42), indicating nearly symmetrical distributions. BD differed significantly among soil depth intervals (Fig. 3a), with statistically significant differences observed between layers (p<0.05).

Forest soil pH exhibited a monotonic vertical distribution pattern, with values increasing progressively with soil depth (Fig. 3b; Table S7). Mean pH increased from 6.066 in the 0–5 cm layer to 6.131 at 5–15 cm and 6.172 at 15–30 cm, followed by a more pronounced increase in deeper layers, reaching 6.458 at 30–60 cm and 6.466 at 60–100 cm. The violin plots for the upper layers (0–5, 5–15, and 15–30 cm) showed more extended contours, whereas the deeper layers (30–60 and 60–100 cm) exhibited wider upper contours, indicating a higher density of pH values toward the higher end of the scale (Fig. 3b). The violin plot profiles for pH were nearly symmetric, with low skewness values (0.05–0.19), indicating a distribution close to normal. Pairwise comparison results revealed that soil pH formed two distinct depth-related levels, with no significant differences within the 0–30 and 30–100 cm intervals, but significant differences between these two groups (Fig. 3b).

Table 1 presents the evaluation results of model predictive performance based on 10-fold cross-validation (CV) and independent validation (IV). Overall, model performance varied between soil properties and validation strategies, yet consistently indicated reliable predictive capability across all depth intervals.

For soil BD, the MEC values obtained from 10-fold CV range from 0.782 to 0.889, with RMSE values between 0.079 and 0.090 gcm-3, while the mean error (ME) remains close to zero. Under the independent validation scheme, MEC values are slightly lower (0.598–0.657), accompanied by higher RMSE values (0.155–0.181 gcm-3); however, the predictive performance remains acceptable, and ME values are likewise close to zero, indicating the absence of systematic bias.

Model performance for soil pH is consistently higher. This result is consistent with previous studies indicating pH as a more stable and predictable property at regional scales (Abdullah et al., 2025). The MEC values derived from 10-fold CV range from 0.834 to 0.868, with RMSE values of 0.214–0.256, whereas the independent validation yields MEC values of 0.705–0.812 and RMSE values of 0.432–0.515. Across all soil depths, ME values are consistently close to zero, further confirming the unbiased nature of the predictions. The comparable performance between the CV and IV results suggests good model generalizability across soil depths.

We applied the QRF model to generate spatially explicit maps of soil BD and pH across five depth intervals in forested regions of China. To characterize their spatial patterns, we calculated depth-specific mean values of BD and pH along both latitudinal and longitudinal gradients. In addition, the prediction results were statistically summarized and visualized using boxplots to illustrate regional differences (Figs. 4 and 5).

Visualization of prediction uncertainty using the PIR highlighted clear regional variations in uncertainty for BD and pH across China. Higher uncertainty for BD was concentrated in the northeastern and southwestern regions, while lower uncertainty characterized the southeastern coastal areas (Fig. S3 in the Supplement). Conversely, pH uncertainty was more pronounced in northern China and parts of the southwest, with relatively lower levels observed in the northeast and the central-eastern coastal zone (Fig. S4 in the Supplement). Overall, areas of elevated uncertainty predominantly coincided with southwestern China, where complex soil-landscape interactions likely contribute to increased model uncertainty. Additionally, regions with sparse data coverage, such as high-altitude areas, exhibited amplified extrapolation uncertainty due to limited representation in the training dataset, further challenging model reliability in these environments. For both BD and pH, prediction uncertainty generally increased with soil depth, a pattern potentially attributable to the reduced availability of soil observations at deeper intervals.

To ensure that biased uncertainty estimates do not compromise practical applications of the model, we further employed the PICP to perform this critical validation step. Five predictive accuracy plots were generated to evaluate the alignment of predicted intervals with actual observations for BD and pH (Fig. 6). The QRF-based digital soil mapping model showed close adherence to the 1:1 reference line across both properties, indicating strong consistency in local uncertainty estimation. However, for pH, a slight overestimation of uncertainty was detected at intermediate probability levels (60 %–90 %) within subsurface layers (0–60 cm), suggesting minor deviations from optimal calibration. In contrast, uncertainty quantification for BD remained well-calibrated across all depth intervals and probability thresholds.

SHAP analysis revealed that climate-related covariates accounted for most of the model-attributed spatial variation in forest soil BD and pH across China. The relative importance of individual predictors differed markedly between BD and pH, as well as among soil depths. For BD, annual precipitation (PRE_A), annual potential evapotranspiration (PET_A), and growing-season solar radiation (SR_GS) consistently ranked among the most influential predictors. In contrast, PRE_A dominated pH predictions across most soil layers, whereas the importance of the normalized difference water index (NDWI_A) increased with soil depth. These depth-stratified patterns are evident in both the SHAP importance rankings and the summary plots (Figs. 7 and 8).

While national datasets such as CSDLv2 (Shi et al., 2025) and ChinaSoilInfoGrids (Liu et al., 2022a) provide extensive information on soil properties, and global products such as SoilGrids 2.0 (Poggio et al., 2021) offer valuable worldwide references, their application to forest ecosystem studies remains constrained by the limited representation of forest-specific soil-forming environments. To address this data gap, our study developed a comprehensive nationwide forest soil dataset for China and integrated it with the FRFS-QRF model to simulate the spatial distribution of BD and pH in Chinese forests. By comparing our results with existing national and global products, we aim to quantify the potential enhancements achievable through the use of a forest ecosystem data foundation and the FRFS-QRF methodology we propose for DSM in forest ecosystems.

The proposed model exhibits enhanced predictive accuracy and reliability for forest soil BD and pH when compared to existing datasets, as illustrated in Table 2. The model achieved reductions in RMSE of 27.41 %, 37.26 %, and 49.46 % relative to CSDLv2, ChinaSoilInfoGrids, and SoilGrids 2.0, respectively. For pH, RMSE reductions were 65.98 %, 68.43 %, and 73.69 % against the same benchmarks. The model was calibrated exclusively on forest soils, thereby reducing the environmental and sampling heterogeneity introduced when cropland, grassland, and forest observations are combined in a single training dataset. Although mixed land use datasets remain valuable for broad scale mapping, the relationships they capture may be influenced by anthropogenic processes that are less prevalent in forests, including soil compaction associated with tillage and traffic and pH modification caused by fertilization or liming (Hamza and Anderson, 2005; Guo et al., 2022).

The SHAP analysis suggests that BD and pH in forest soils are controlled primarily by climatic and hydrological factors. For BD, the dominant predictors were annual precipitation, annual potential evapotranspiration, and growing-season solar radiation, with surface layers showing stronger sensitivity to litter input, organic matter dynamics, drying–rewetting, and root activity, and deeper layers reflecting longer-term water redistribution and profile differentiation (Jenny, 1941; Brady and Weil, 2016). For pH, climatic and hydrological controls also dominated, consistent with sustained leaching of base cations and continuous acid inputs from litter decomposition and root processes in forest ecosystems (Abdullah et al., 2025; Huang et al., 2022b; Liu et al., 2024b). Compared with broader mixed-land-use studies, this pattern suggests a stronger role of climate- and vegetation-related controls in forest ecosystems. In forests, soil properties are more tightly coupled to canopy-mediated water balance, litter inputs, root activity, and biologically mediated acidification, so climate, hydrology, and vegetation can become more influential than the broader cross-ecosystem relationships captured in general-purpose products (Augusto et al., 2022; Huang et al., 2022b). Visual comparison of Figs. 6 and S5 in the Supplement further suggests that divergence from existing datasets may be more pronounced in humid southern forests and mountainous regions of southwestern China, where strong precipitation gradients, steep terrain, and heterogeneous vegetation structure intensify local soil variability.

Our results indicate a non-linear vertical pattern of forest soil BD, with BD peaking in the 30–60 cm layer and declining in the 60–100 cm layer (Fig. 9). This profile differs from the commonly reported monotonic increase in BD with depth in many ecosystems, including forest systems where BD generally increases with soil depth (Shen et al., 2022). However, non-monotonic vertical BD distributions have also been documented in forest soils, particularly in relation to long-term stand development and soil profile differentiation (Tang et al., 2025), suggesting that forest soil BD may not universally follow a simple monotonic depth trend. This depth profile is plausibly linked to clay illuviation and deep-root processes. Downward translocation and mid-profile accumulation of fine clay can promote denser packing and reduce pore space, leading to higher BD in intermediate layers, as commonly observed in soils affected by argilluviation (Jenny, 1941; Brady and Weil, 2016). In deeper horizons, lower clay contents together with more pronounced root activity may enhance biopore formation and maintain a looser structure, thereby contributing to lower BD (Jobbágy and Jackson, 2000; Angers et al., 2011). Comparison with existing datasets further suggests that currently available products do not fully represent this complex depth-dependent variation in forest BD. In particular, for the 60–100 cm layer, our model predicts a mean BD of 1.25 gcm-3, lower than the 1.37–1.38 gcm-3 reported by existing datasets (Fig. S5). This discrepancy implies that extrapolations based solely on those datasets may overestimate forest soil organic carbon stocks at this depth.

Assuming other terms remain constant, using the SoilGrids estimate (1.37 gcm-3) instead of our forest-specific estimate (1.25 gcm-3) would increase the estimated soil mass, and thus the SOC stock, of the standard 60–100 cm layer by approximately 9.6 %. However, the magnitude and ecological meaning of this bias should be interpreted cautiously because the standardized 60–100 cm interval does not always correspond to a fully developed and ecologically equivalent soil body in forest ecosystems. In this study, all profiles were harmonized to the GlobalSoilMap standard depth intervals to improve comparability among heterogeneous datasets (Bishop et al., 1999; Arrouays et al., 2014). Yet in many forested landscapes, especially mountainous regions, effective soil depth is constrained by topography, parent material, erosion, and shallow bedrock. Under such conditions, the nominal 60–100 cm layer may partly approach saprolite or the bedrock interface, and in some cases may reflect the standardized extension of limited deep-horizon information rather than a complete and ecologically uniform mineral-soil unit. Consequently, uncertainty in deep-soil carbon estimates arises from both BD and the actual soil volume represented by the standard layer. Generalized products may therefore overestimate subsoil carbon storage not only by assigning a higher BD, but also by implicitly assuming a uniformly developed 40 cm soil layer where the effective soil depth is smaller. Although DTB was included as a predictor in this study, future work should more explicitly couple standard-depth soil products with effective soil thickness or depth-to-bedrock constraints to improve the ecological realism and reliability of national-scale deep-soil carbon assessments (Adhikari et al., 2013; Chen et al., 2019).

Forest soil pH profiles are primarily governed by chemical processes and generally exhibit an increasing trend with depth. Model comparison results indicate that forest soil pH in China displays a consistent spatial pattern characterized by lower values in southern regions and higher values in northern regions, while vertically increasing with soil depth (Yu et al., 2020). This depth-dependent pattern is in line with the commonly observed pH profiles of forest soils (Fig. 10). However, spatial statistical analyses reveal that, across all soil layers, the mean forest soil pH predicted in this study (5.70–6.01) is consistently lower than the corresponding values reported by existing datasets (5.93–6.23) (Fig. S6 in the Supplement). This systematic difference likely reflects ecosystem-specific acidification processes in forest soils. Long-term leaching under relatively high precipitation regimes promotes the removal of base cations, while the continuous accumulation of acidic inputs derived from organic matter decomposition and root exudation further contributes to soil acidification (Farooq et al., 2022a; Abdullah et al., 2025). As a result, forest soils typically exhibit lower pH values than soils in other ecosystems. These findings suggest that existing datasets may underestimate the degree of soil acidification in Chinese forests, particularly when generalized across ecosystems or derived from limited forest-specific observations.

Overall, our results indicate that the use of forest-specific datasets and modeling strategies can substantially improve the representation of soil BD and pH in forest ecosystems. The discrepancies identified relative to existing products suggest that generalized soil datasets may overestimate forest soil carbon stocks and underestimate soil acidification, underscoring the necessity of ecosystem-specific digital soil mapping for reliable soil assessments and forest management.

The high-resolution spatial dataset of forest soil BD and pH developed in this study represents a national-scale digital soil mapping product that captures the spatial variability of key soil physical and chemical properties across forested regions in China. Accurate knowledge of BD and pH is fundamental for estimating soil carbon stocks (Batjes, 2016), and monitoring forest ecosystem responses to land-use and climate change (Pan et al., 2011). Bulk density is critical for accurate estimation of soil carbon stocks, while pH governs nutrient availability, microbial activity, and forest productivity (Liu et al., 2024b), and is significant for understanding forest soil acidification (Farooq et al., 2022b). The dataset fills longstanding gaps in forest soil data coverage in China, and supports applications in ecosystem assessment and long-term soil monitoring. Beyond its scientific value, this product contributes to national strategies on carbon neutrality and ecological restoration and aligns with international environmental commitments including the UN Decade on Ecosystem Restoration and the Sustainable Development Goals (UNEP, 2021; IPCC, 2022).

Our study advances high-resolution DSM in forest ecosystems; however, several methodological limitations remain and merit further investigation, particularly regarding the predictive reliability of machine learning approaches. Machine learning techniques, while significantly enhancing DSM by capturing nonlinear soil–environment relationships, are constrained by limitations in spatial coverage and feature-space representativeness (Yang et al., 2013; Chen et al., 2019). Forest ecosystems exhibit pronounced landscape heterogeneity, complicating sampling design and frequently resulting in imbalanced training datasets (Huang et al., 2022a; Liu et al., 2022b; Shao et al., 2022). As demonstrated by Westhuizen et al. (2024), models trained on such datasets may yield biased predictions in undersampled regions. Although ensemble methods can manage uncertainty in sparse data settings, they may prioritize statistical regularities over mechanistic soil formation processes (Sylvain et al., 2021; Liu et al., 2022b). Consistent with these broader concerns, the discrepancy observed between cross-validation and independent validation in our study suggests that random cross-validation may have benefited from residual spatial autocorrelation among nearby samples, whereas the independent validation results likely offer a more realistic assessment of model transferability.

In addition to data-related limitations, uncertainty may also arise from harmonizing environmental covariates originating from heterogeneous native spatial resolutions into a common fine grid. The integration of multi-resolution covariates through resampling is a standard practice in national-scale digital soil mapping to ensure spatially consistent modeling (Shi et al., 2025). However, this process inherently introduces scale-related uncertainty and potential smoothing effects in the resulting predictions, particularly for covariates derived from coarser-resolution sources (Cavazzi et al., 2013; Piedallu et al., 2022). The influence of covariate resolution on prediction accuracy is a recognized challenge in DSM, as the representativeness of environmental predictors can vary substantially with spatial scale (Guo et al., 2019; Adhikari et al., 2020). Importantly, this limitation is not unique to the present study but is widely acknowledged in large-scale mapping initiatives, including established global products such as SoilGrids (Poggio et al., 2021). While predictive models can quantify uncertainty associated with sampling density and algorithmic structure, explicit quantification of uncertainty arising solely from the resampling of multi-resolution covariates remains methodologically challenging and is rarely addressed in existing studies (Wadoux et al., 2020; Sylvain et al., 2021). Consequently, the resulting soil property maps should be interpreted as conditional estimates, representing the most probable spatial patterns given the selected covariates and their effective spatial resolution, rather than exact representations of fine-scale soil heterogeneity (Robb et al., 2025).

Finally, incomplete environmental data coverage restricted soil property prediction to areas where all covariates were consistently available. This decision reflects a fundamental trade-off in DSM between spatial completeness and predictive reliability. Omission-based approaches, such as those used in SoLIM (Nussbaum et al., 2018; Zhu et al., 2018), prioritize accuracy by excluding data-deficient regions but result in spatial gaps that limit practical applications. In contrast, imputation techniques such as 3×3 window smoothing (Padarian et al., 2019; Fan et al., 2020) preserve continuity but may introduce significant errors, particularly in ecotones where environmental gradients are steep and covariate relationships become unstable (Hengl et al., 2015). In our study, such limitations were most evident along elevational boundaries and remote sensing index thresholds, where fragmented gaps produced compounding spatial uncertainty. To mitigate these effects, predictions were restricted to the maximal common spatial domain defined by all covariates. This conservative approach was based on three considerations: (1) the statistical instability of edge extrapolations, (2) elevated error propagation risks in transitional environments (Dong et al., 2023), and (3) a practical emphasis on accuracy over exhaustive coverage. While this approach slightly reduced the total mappable forest area, it improved the overall reliability of spatial outputs by minimizing uncertainty in marginal regions (Smith, 2001; Huettmann and Gottschalk, 2011). The resulting trade-off underscores the persistent tension between spatial coverage and predictive confidence in large-scale DSM. Future advances should explore adaptive frameworks that integrate uncertainty-aware imputation with hybrid models, using localized gap geometry to guide prediction boundaries (Arrouays et al., 2014). Such innovations may help reconcile spatial completeness with predictive precision in next-generation soil mapping.

Looking forward, emerging hybrid frameworks that integrate environmental similarity metrics with pedological expertise show promise for addressing both data imbalance and scale-related challenges (Zhao et al., 2024), although their scalability and operational feasibility at national extents require further validation (Miranda et al., 2023; Potash et al., 2023; Rodrigues et al., 2025). Specifically, strategic sampling designs incorporating stratified and adaptive approaches across diverse forest landscapes and soil types are crucial for mitigating dataset imbalance and capturing underlying heterogeneity (Brus et al., 2011). Concurrently, exploring novel covariates derived from multi-source remote sensing (e.g., hyperspectral, LiDAR, and radar) and proximal sensing (Xue et al., 2025), alongside improved representations of depth-dependent properties and long-term environmental legacies. These data could enrich the feature space, improve the characterization of deep-soil processes, and partly alleviate the current over-reliance on climatic predictors in deeper soil layers (Vaysse and Lagacherie, 2017; Wadoux et al., 2020). Integrating such refined datasets within hybrid modeling frameworks holds considerable potential for improving the accuracy and reliability of forest DSM predictions.