Soil pH, as one of the important indices of soil quality, is generally the acidity and alkalinity of soil systems and ranges from 0 to 14 (Ji et al., 2014). Acidic, neutral and alkaline soils generally refer to soils with pH < 7, = 7 and > 7, respectively. Soil pH can regulate the mineralization of soil organic carbon (Dlamini et al., 2016), soil microbial community structure (e.g. α-diversity, community composition) (Zhang et al., 2020; Zhang and Fu, 2021), plant community structure (e.g. β-diversity) (Sun et al., 2021; Wang et al., 2021b), plant growth (Veresoglou et al., 2011; Wang et al., 2021a; Zhang et al., 2021), herbage nutritional quality and storage (Fu et al., 2021; Zha et al., 2022). Soil pH is also closely correlated with base cations (K, Ca and Mg) (Baumann et al., 2009), soil nitrogen and phosphorus availability (Paul et al., 2001; Fu and Shen, 2017). Thus, estimating soil pH variation at manifold spatio-temporal scales is critical for examining the impacts of globe change on soil quality and other related scientific studies in terrestrial ecosystems (Odhiambo et al., 2020). Under such background, a great deal of scientific studies explored the influence and feedback of environmental factors on soil pH (Fernandez-Calvino et al., 2011; Sikora et al., 2011; Hong et al., 2018; Puissant et al., 2019; Huang et al., 2022). These earlier studies can be benefit for improving soil quality and facilitating soil high-quality management. However, most of these earlier studies are mainly performed at fine spatial scales (i.e., single points or transect scale), because well documented data on observed soil pH are relatively sparse due to the high time and financial cost of observed soil pH (Wuest, 2015; Chen et al., 2019). In order to obtain soil pH with larger spatial scales and longer time series, spatiotemporal interpolation or model development of soil pH is a good solution. Current soil pH models can be divided into two types depending on whether or not they depend on other variables (Mao et al., 2014; Odhiambo et al., 2020). The soil pH models independent of other variables (e.g., Kriging and inverse distance weighted spatial interpolation) can obtain the soil pH during the sampling period of the whole region, but cannot obtain the soil pH during the non-sampling period. In other words, this method can only be used for spatial interpolation of soil pH, but not for temporal interpolation of soil pH. This limits the scope of application of this method (e.g., the temporal change of soil pH cannot be studied). In contrast, the soil pH models dependent of other variables can be used for spatio-temporal interpolation of soil pH. The current soil pH models use different independent variables, and the model accuracies of soil pH do not increase with increasing the number of independent variables, but even decrease (Chen et al., 2019; Jia et al., 2021; Wang et al., 2022). Moreover, the widespread popularization and application of such soil pH models are limited due to the availability or relatively low accuracy of some independent variables (Odhiambo et al., 2020). The development of machine learning techniques (e.g., RF: random-forest) can provide new ideas on the studies related to soil pH at manifold spatio-temporal scales (Chen et al., 2019; Jia et al., 2021; Wang et al., 2022). However, it is not clear on which one of machine learning techniques are better in estimating soil pH than the other machine learning technologies. Consequently, further studies are needed to better serve for the management of soil pH and quality at manifold spatio-temporal scales under impacts of humankind activities and climate change.

Various grassland systems are the main land cover in the Tibet, and they are the important foundation of high-quality development of livestock in Tibet Autonomous Region (Fu et al., 2022; Zha et al., 2022). Soil pH is closely correlated with grassland production and in turn high-quality development of livestock in the Tibet (Zhang et al., 2021). For example, soil pH was positively correlated with aboveground net primary production along an elevation gradient in alpine grassland of Nyenchen Tanglha (Wang et al., 2021a). However, soil pH was negatively correlated with the content of crude protein and water-soluble carbohydrate (Fu et al., 2022). Under such background, many studies have investigated the impacts of soil pH on ecosystem structure and function, and the driving factors of soil pH in grassland regions (Ji et al., 2014; Yu et al., 2019; Sun et al., 2021). However, these previous studies are not performed over the whole grassland areas of the Tibet due to the lack of large-scale soil pH datasets (Chen et al., 2019). In order to resolve such issue, it is necessary to develop an optimal model of soil pH in grassland areas of the Tibet.

Soil pH was estimated from measured meteorological data and normalized difference vegetation index (NDVI) on the basis of the RF, generalized-linear-regression (GLR), generalized-boosted-regression (GBR), multiple-linear-regression (MLR), artificial-neural-network (ANN), conditional-inference-tree (CIT), support-vector-machine (SVM), eXtreme-gradient-boosting (eXGB), and recursive-regression-tree (RRT) in grassland areas of Tibet. Three previous studies have explained the reasons why some of the nine methods (e.g., RF and SVM) were adopted to model plant species α-diversity (Tian and Fu, 2022), herbage nutritional quality and production (Han et al., 2022), soil moisture (Wang and Fu, 2023) in grassland areas of Tibet. Besides the causes mentioned above, it is still not clear on which one of the nine methods is best in quantifying soil pH of grassland area in Tibet. Thus, the nine methods were used to estimate soil pH. This study focused on comparing the accuracies of the nine methods in estimating soil pH. Several studies have confirmed that the performance of the RF approach was better than other approaches in predicting some important plant variables in grassland systems of Tibet (Han et al., 2022; Tian and Fu, 2022). Therefore, we assumed that the RF approach had the best performance in estimating soil pH amongst the nine approaches in grassland areas of the Tibet.

Compared to the MLR and RRT methods, meteorological data and NDVI_max on the basis of the RF method had greater explanation abilities of soil pH. This phenomenon was similar to some previous studies conducted in grassland areas of Tibet (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023). Moreover, the developed RF and RRT models had the greater explanation abilities of soil pH than previous studies, but the developed MLR models had nearly equal explanatory abilities of soil pH than previous studies (Ji et al., 2014). Therefore, compared with the MLR and RRT methods, the RF method can have greater explanation abilities of environmental variables (at least for soil pH and moisture, plant α-diversity, herbage nutritional quality and production) in grassland areas of the Tibet (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023).

The support vector numbers of the developed SVM models were lower than the tree numbers of the developed RF models ( Table 1 ). This finding was in consistent with two earlier studies (Han et al., 2022; Wang and Fu, 2023), but quite contrast with another one previous study (Tian and Fu, 2022). The tree numbers of the developed GBR models were higher than those of the developed RF models ( Table 1 ), which was in line with two earlier studies (Tian and Fu, 2022; Wang and Fu, 2023). Moreover, the tree numbers of the developed RF and GBR models were not equal to the default value (i.e., 500 of the randomForest package and 100 of the gbm package in 4.2.1, respectively). This phenomenon was similar to earlier studies (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023). Therefore, default values of tree numbers were not the best choice, at least for soil pH and moisture, plant α-diversity, herbage nutritional quality and production in grassland areas of the Tibet (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023). The computational speed and model complexity varied with environmental variables and methods (Tian and Fu, 2022).

The developed RF models of soil pH had the highest accuracy, but the developed eXGB models of soil pH had the lowest accuracy amongst the nine methods ( Table 3 , Figures 1 – 6 ). The phenomenon was similar to earlier studies which revealed that the developed RF models of plant α-diversity, herbage nutritional quality and production and soil moisture had the better performance than the other approaches in grassland areas of Tibet (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023). This finding was supported by the following facts/causes. First, similar to earlier research (Han et al., 2022; Tian and Fu, 2022; Wang and Fu, 2023), slopes between the modelled soil pH on the basis of the RF models and measured soil pH were the nearest to 1 amongst the nine methods ( Figures 1 – 6 ). Second, similar to earlier studies (Han et al., 2022; Tian and Fu, 2022), RMSE values and absolute values of relative deviation between modelled soil pH on the basis of RF models and measured soil pH were generally the lowest for most cases ( Table 3 ). Third, similar to earlier research (Han et al., 2022; Tian and Fu, 2022), the situation where one model value correspond to multiple measurements was relative lower for the developed RF models of soil pH ( Figures 1 – 6 ). Fourth, similar to earlier research (Han et al., 2022; Tian and Fu, 2022), the scatter was relatively and closely around the 1:1 line for the developed RF models of soil pH ( Figures 1 – 6 ). Fifth, the RF models did not assume that the relationships between soil pH and independent variables (AT, AP, ARad, NDVI_max) were linear. The relative optimum mixture of parameters ntree and mtry, and randomness character of the RF method may further ensure the relatively higher accuracies of the developed RF models in estimating soil pH. Therefore, the developed RF models can be used to estimate soil pH from AT, AP, ARad and/or NDVI_max, at least for grassland areas of the Tibet.

The predicted accuracies of soil pH based on the developed RF models in this study were greater than those reported by earlier studies (Shi et al., 2009; Holmberg et al., 2018; Hong et al., 2019; Odhiambo et al., 2020; Carrillo et al., 2022). For example, the simulated soil pH based on random forest or XGBoost can only explain about 70–72% variation with RMSE of 0.71–0.73 in observed soil pH in China (Chen et al., 2019). The simulated soil pH based on artificial neural network can only explain about 92% variation in observed soil pH in Chinese vegetable fields (Wang et al., 2022). The simulated soil pH based on artificial neural network, support vector machine, ridge regression and geographic weighted regression explained about 12.04–97.33% variation in observed soil pH in the Yinbei area of Ningxia, China (Jia et al., 2021). Compared to this study, the numbers of model parameters in some previous studies are much larger (Chen et al., 2019; Wang et al., 2022). Moreover, the model accuracies of soil pH simulated from three parameters were not always lower than those simulated from four parameters. Therefore, more model parameters do not always lead to higher accuracy of soil pH. It is better to elevate simulation accuracy of soil pH by screening methods than to increase the simulation accuracy of soil pH by introducing more variables.

In general, this study was the first study which estimated soil pH_p and pH_a at three soil depths (i.e., 0–10, 10–20, and 20–30 cm) on the basis of nine methods in grasslands of the Tibet. Three independent variables (i.e., AT, AP, ARad) were used to estimate the pH_p. Four independent variables (i.e., AT, AP, ARad and NDVI_max) were used to estimate the pH_a. The nine methods had different performances in estimating soil pH, and the developed RF models had the better performance than the other eight methods. Measured soil pH can be nearly 100% explained by modelled soil pH on the basis of the RF, GBR, SVM and RRT models, and about 99% explained by modelled soil pH on the basis of the MLR, ANN, GLR and eXGB models. Modelled soil pH on the basis of the CIT models explained about 99–100% variation of measured soil pH. The slopes between modelled and measured soil pH were 0.96–1.03 for all the nine methods. The slopes (i.e., 0.99–1.01) between modelled soil pH on the basis of the RF models and measured soil pH were the nearest to 1 amongst the nine methods. The RMSE values (i.e., ≤ 0.28) between modelled soil pH on the basis of the RF models and measured soil pH were the lowest. In contrast, the RMSE values (i.e., ≤ 3.94) between modelled soil pH on the basis of the eXGB models and measured soil pH were the highest. The absolute values of relative deviation between measured soil pH and modelled soil pH on the basis of eXGB, GLR, RF and GBR models were ≤ 47.87%, ≤ 3.87%, ≤ 1.26% and ≤ 1.72%, respectively, and those on the basis of the other methods were ≤ 2.74%. Accordingly, climate data and NDVI cannot always quantify the variation of observed pH, which were relied on the algorithm chosen. The suggested RF models of soil pH can be used to obtain soil pH of the whole Qinghai-Tibet Plateau grassland in the past decades or even the next hundred years, which can be benefit for soil pH management. For example, soil acidification and salinization under global change can be helped by the suggested RF models of soil pH. The suggested RF models of potential and actual soil pH can be also used to quantify the relative influences of climatic change and humankind activities on soil pH.

The original contributions presented in the study are included in the article/ Supplementary Material . Further inquiries can be directed to the corresponding author.

Conceptualization, GF and ED. Methodology, GF. Software, ED. Validation, GF. Formal analysis, GF and ED. Investigation, GZ. Resources, ED. Data curation, GF. Writing—original draft preparation, GF and ED. Writing—review and editing, GF and ED. Visualization, ED. Supervision, ED. Project administration, ED. Funding acquisition, ED. All authors contributed to the article and approved the submitted version.