Purpose: Particle size distribution (PSD) assessment, which affects all physical, chemical, biological, mineralogical, and geological properties of soil, is crucial for maintaining soil sustainability. It plays a vital role in ensuring appropriate land use, fertilizer management, crop selection, and conservation practices, especially in fragile soils such as those of the North-Western Himalayas. Materials and methods: In this study, the performance of eleven mathematical and three Machine Learning (ML) models used in the past was compared to investigate PSD modeling of different soils from the North-Western Himalayan region, considering that an appropriate model must fit all PSD data. Results and discussion: Our study focuses on the significance of evaluating the goodness of fit in particle size distribution modeling using the coefficient of determination (R²_adj = 0.79 to 0.45), the Akaike information criterion (AIC = 67 to 184), and the root mean square error (RMSE = 0.01 to 0.09). The Fredlund, Weibull, and Rosin Rammler models exhibited the best fit for all samples, while the performance of the Gompertz, S-Curve, and Van Genutchen models was poor. Of the three ML models tested, the Random Forest model performed the best (R² = 0.99), and the SVM model was the lowest (R² = 0.95). Thus, the PSD of the soil can be best predicted by ML approaches, especially by the Random Forest model. Conclusion: The Fredlund model exhibited the best fit among mathematical models while random forest performed best among the machine learning models. As the number of parameters in the model increased better was the accuracy.

The evaluation of soil bulk density (BD) is essential for studying soil processes like water retention, air circulation, and carbon sequestration. Conventional direct BD measurement methods are often time-consuming, costly, and laborious. In contrast, the use of pedotransfer functions (PTFs) based on readily available soil properties offers a cost-effective alternative approach that can provide indirect quick estimates of soil BD. Although several region-specific PTFs are available, none is tailored for use in the hilly North-Western Himalayas (NWH) area. Thus, this work developed a novel PTF to estimate the soil BD of 300 soil samples collected from the NWH area and analyzed by stepwise regression (SR), partial least-squares regression (PLSR), multiple linear regression (MLR), linear regression (LR), and advanced machine-learning algorithms, including artificial neural networks (ANN) and decision tree (DT). The site-specific SR-based equation performed better than the PLSR model by explaining up to 72.2% variability of BD and achieving a coefficient of determination (R²) of 0.73, a mean absolute error (MAE) of 0.0379 g cm⁻³, and a root mean square error (RMSE) of 0.0487 g cm⁻³ for the BD prediction. Soil organic matter and clay contents were the most significant contributors, showing the highest importance in the projection. Furthermore, the performance of the SR-based PTF was validated by comparison with 63 PTFs currently in use, which showed to perform poorly and vary widely in BD estimation (R²: 0.006–0.71, RMSE: 0.0649–0.405 gcm^− 3, MAE: 0.0512–0.395 g cm^− 3). The promising SR equation and PTF developed in this work showed high accuracy and excellent suitability for stakeholders and professionals in the study area and the scientific community as a reliable BD estimator for hilly soils. This study introduces proposed the first-ever site-specific PTF for BD estimation in hilly soils, contributing to scientific challenge by enhancing soil database and improving BD predictions in complex terrains worldwide. In terms of global significance, the outcomes of this study are essential for soil quality and vulnerability studies, resilience indicators estimates carbon sequestration initiatives, and digital soil mapping, and can also be used to construct a BD database for hilly soils across the globe. Graphical Abstract The evaluation of soil bulk density (BD) is essential for studying soil processes like water retention, air circulation and carbon sequestration, and soil quality, vulnerability and resilience. Conventional direct methods to measure soil BD are often time-consuming, costly and laborious, whereas pedotransfer functions (PTFs) based on readily available soil properties offer an efficient alternative approach that provides indirect quick estimates of soil BD. However, none of the several region-specific PTFs currently available, is tailored for use in the hilly North-Western Himalayas (NWH) area. A novel PTF was developed in this work to evaluate the BD of 300 soil samples collected from agriculture, horticulture, forest and fallow hilly soils in the North West Himalaya area. Stepwise regression (SR), partial least-squares regression (PLSR), multiple linear regression (MLR), linear regression (LR), and advanced machine-learning algorithms, including artificial neural networks (ANN) and decision tree (DT) were tentatively applied for BD estimation of the studied soils, showing that the site-specific SR-based equation performed the best. Various soil properties were evaluated in the models, with soil organic matter and clay contents being the most significant contributors to the projection. Furthermore, the performance of the SR-based PTF was validated by comparison with 63 PTFs currently in use, which showed to perform poorly and vary widely in BD estimation for the hilly soils studied in this work. In conclusion, the SR equation and PTF developed in this work show excellent and promising suitability for stakeholders and professionals in the study area and for the global scientific community as a reliable BD estimator for hilly soils. Furthermore, the results of this work can be used for soil management, land use planning, and climate change mitigation in fragile ecosystems like the Himalayas.