Quantifying and predicting soil buffering capacity in the African context: a multidimensional titration-based framework using chemical signatures and MIR spectroscopy

Abstract

Soil acidity is a major constraint to agricultural productivity across sub-Saharan Africa, where highly weathered soils exhibit strong spatial heterogeneity in chemical reactivity. While soil pH identifies acidity status, it does not indicate how a soil will respond to corrective liming how strongly it resists pH change or how much amendment it ultimately requires. Soil buffering capacity fills this gap, yet current practice typically reduces this multidimensional behavior to a single metric that cannot simultaneously capture instantaneous reactivity, average resistance, and cumulative lime demand. This study proposes a structured framework for quantifying and predicting short-term soil buffering capacity defined here as the immediate chemical response measured during controlled calcium hydroxide titration with 25-minute equilibration intervals using three complementary indices derived from titration curves: punctual buffering capacity (BCP), quantifying instantaneous pH sensitivity at a defined titration stage; linear buffering capacity (BCL), reflecting average resistance across the liming correction interval; and integral buffering capacity (BCI), integrating the full titration response to express cumulative neutralization demand. Together, these indices characterize distinct dimensions of soil behavior under liming, providing actionable information for lime-rate calibration and acidity-management planning. A total of 543 soil samples from six African countries (Ivory Coast, Ghana, Malawi, Zimbabwe, Zambia, and Mozambique) were analyzed. Random Forest and Extreme Gradient Boosting (XGBoost) ensemble algorithms were trained to predict the three buffering indices from routine soil chemical properties (organic matter, pH, cation exchange capacity, and texture). Random Forest achieved the strongest cross-validated agreement between measured and predicted buffering values (R² = 0.70–0.73, RMSE = 0.26–2.99, RPIQ = 2.51–2.60), with consistent performance on independent test sets (R² = 0.69–0.71, RMSE = 0.24–3.20, RPIQ = 2.34–2.44). Predictor importance analysis revealed that the soil properties governing each index shifted systematically: organic matter and clay dominated BCP, reserve acidity indicators controlled BCL, and pH-related variables governed BCI. In parallel, mid-infrared (MIR) spectroscopy was evaluated as a rapid, reagent-free alternative. Absorbance spectra collected and used as inputs to Partial Least Squares Regression (PLSR) models, which relate the spectral signature of soil mineral and organic components directly to buffering behavior. PLSR models achieved R² up to 0.81 (RMSE = 0.23, RPIQ = 2.73) for BCP under cross-validation and R² = 0.78 (RMSE = 0.32, RPIQ = 2.50) on independent test sets, enabling rapid buffering assessment at scale. Classification into low, medium, and high buffering classes revealed that most soils exhibited limited short-term resistance under BCP and BCL, while BCI showed a more balanced distribution indicating that soils with modest immediate reactivity may carry substantial cumulative lime demand. This contrast underscores the agronomic value of the multidimensional approach: knowing both how quickly a soil responds and how much amendment it ultimately requires enables more precise liming, reduces over- or under-application risk, and supports cost-effective acidity management in heterogeneous smallholder systems across Africa.

1 Introduction

Soil acidity is a major constraint on agricultural productivity worldwide, particularly in tropical and subtropical regions with highly weathered soils (1). Across sub-Saharan Africa, intense rainfall promotes leaching of base cations and accelerates soil acidification, resulting in extensive areas of strongly acidic soils (2). These soils frequently exhibit substantial spatial heterogeneity in chemical reactivity, rendering uniform liming strategies inefficient and, at times, counterproductive. Applying identical amendment rates across contrasting soils may lead to overliming in weakly buffered systems, causing nutrient imbalance, or underliming in strongly buffered soils, leaving acidity constraints unresolved (2). Effective acidity management therefore requires not only measuring soil pH, which identifies the current acidity status, but also understanding how soils will respond when corrective lime is applied. Soil buffering capacity refers to the soil’s resistance to changes in pH following the addition of base amendments. From a liming management perspective, buffering behavior determines both the rate and extent of soil pH response to applied lime and the total amendment quantity required to reach agronomic targets (3). Soils with identical pH values may exhibit markedly different responses to liming, depending on their mineral composition, organic matter content, and reserve acidity (4). Buffering capacity thus constitutes a strategic tool for soil acidity management: it does not merely identify that a soil is acidic but provides the decision-support information needed to determine how much lime to apply, how quickly the soil will respond, and what correction trajectory to expect. In this sense, buffering capacity functions as the operational bridge between diagnosis (pH measurement) and prescription (lime rate calibration). Several buffer-based methods have been developed to estimate the lime requirement of acidic soils, including the SMP buffer (5), the Adams–Evans buffer (6), the Mehlich buffer (7), and the Sikora buffer (8). These methods rely on measuring the pH depression of a buffered solution after equilibration with a soil sample, using the resulting pH value to estimate the amount of lime needed to raise soil pH to a target value. The SMP buffer method, which is used in this study, measures the equilibrium pH of a soil–buffer suspension (pH_smp) prepared according to the Shoemaker–McLean–Pratt procedure; a lower pH_smp value indicates greater reserve acidity and, consequently, a higher lime requirement. While these buffer methods provide practical, single-point estimates of lime requirement and remain the most widely accepted tools for liming recommendations in routine soil testing laboratories, they reduce the complexity of the buffering response to a single value and do not differentiate between instantaneous reactivity, average resistance, and cumulative neutralization demand the three dimensions addressed by the present framework. Cation exchange capacity (CEC) is often used as a primary indicator of a soil’s ability to retain and supply nutrients, and it is closely related to buffering capacity through shared controlling factors. Both CEC and buffering capacity are governed by the abundance and reactivity of negatively charged surfaces provided by clay minerals and organic matter (9). Soils with high CEC generally exhibit greater buffering capacity because the same exchange sites that retain base cations also participate in proton-exchange reactions that resist pH change (10). However, CEC and buffering capacity are not interchangeable: CEC quantifies the total charge available for cation retention at a given pH, whereas buffering capacity describes how the soil resists changes in pH when acid or base is added. Two soils with identical CEC values may exhibit different buffering behaviors depending on the nature and distribution of their exchange sites, the composition of the exchange complex, and the pools of reserve acidity mobilized during liming (4). In the context of nutrient management, CEC is the more direct parameter for assessing nutrient retention and availability, while buffering capacity is the more relevant parameter for predicting pH response to amendment inputs. Beyond acidity correction, buffering capacity informs sensitivity to acidifying inputs such as ammonium-based fertilizers, ecosystem resilience to acid deposition, and site-specific nutrient management where pH stability governs nutrient availability and microbial activity (11). In heterogeneous African agroecosystems with limited site-specific information, a reliable buffering assessment framework supports both corrective and preventive soil management decisions. Despite its importance, soil buffering capacity is commonly estimated using a single operational formulation, most often expressed as the ratio of added base to the resulting change in pH (e.g., β = ΔB/ΔpH or its differential form, dB/dpH) (11). Such slope-based expressions provide a practical measure of resistance to pH change but cannot adequately represent the full complexity of soil buffering behavior. Buffering processes involve both rapid surface reactions and progressively mobilized acidity pools, meaning that resistance to pH change is inherently scale-dependent (12). Instantaneous reactivity, average resistance across a correction interval, and cumulative neutralization demand are three distinct dimensions that a single index cannot capture simultaneously. Collapsing these into one parameter risks misrepresenting how a soil will behave at different stages of a liming program and can lead to systematic errors in amendment estimation. To address this limitation, this study structures buffering capacity into three complementary indices derived from calcium hydroxide titration curves: punctual buffering capacity (BCP), which quantifies instantaneous pH sensitivity at a defined stage of the titration; linear buffering capacity (BCL), which reflects average resistance across the correction interval; and integral buffering capacity (BCI), which integrates the full titration response to express cumulative neutralization demand (13). Together, these indices provide a multidimensional decision-support framework: BCP informs short-term reactivity and fine-tuning of lime rates, BCL supports planning of standard liming programs, and BCI determines total amendment requirements and long-term correction strategy. A key question is whether these indices can be predicted from measurable soil attributes. In this study, buffering capacity is first modeled using a reduced chemical signature based on routinely measured laboratory variables including organic matter, pH_w, pH_smp, cation exchange capacity, and texture. These properties directly influence exchangeable acidity, surface charge, and proton-buffering reactions (14). In parallel, mid-infrared (MIR) spectroscopy is evaluated as a rapid and scalable alternative (15) for predicting the three buffering indices across diverse African soils. MIR spectroscopy captures mineralogical and organic spectral features that directly control buffering processes and has been widely applied to predict soil properties such as organic carbon, texture, and cation exchange capacity (16–19). Recent large-scale applications have further demonstrated MIR’s capacity to predict functional soil attributes including plant-available nutrients and water-holding characteristics across diverse tropical soils (20). However, despite this broad predictive scope, its application to soil buffering capacity a dynamic functional property reflecting liming response rather than a static compositional attribute has not previously been explored within a multidimensional framework. Existing MIR studies of soil acidity have focused predominantly on pH prediction or on single-index buffering metrics, leaving the combined prediction of punctual, linear, and integral buffering indices unaddressed. No prior work, to the best of our current understanding, has evaluated MIR-based prediction of a three-dimensional buffering framework across heterogeneous tropical soils, which represents the central methodological contribution of the present study. Beyond this methodological gap, practical constraints further justify the need for a spectroscopic alternative. Conventional titration procedures are labor-intensive and time-consuming, limiting their practicality for large-scale monitoring. Predictive modeling based on routine laboratory variables reduces analytical complexity, whereas MIR spectroscopy requires minimal sample preparation, generates no chemical waste, and enables rapid processing at low marginal cost. In regions with limited laboratory infrastructure and financial resources, efficient estimation of multidimensional buffering behavior supports more accurate lime recommendations, minimizes the risk of overapplication, and contributes to long-term soil sustainability. We hypothesize that the three buffering capacity indices BCP, BCL, and BCI capture statistically independent dimensions of soil liming response that are governed by distinct but measurable physicochemical drivers, and that these indices can be reliably predicted both from routine chemical soil properties and from mid-infrared spectral signatures across pedologically diverse African soils. The objectives of this study are to: (i) quantify soil buffering capacity using calcium hydroxide titration and derive three complementary indices BCP, BCL, and BCI each capturing a distinct dimension of liming response; (ii) evaluate the predictive performance of a reduced laboratory chemical signature for estimating these indices and identify the key soil properties governing each; (iii) assess the potential of mid-infrared spectroscopy to predict the multidimensional buffering framework across heterogeneous African soils, an application not previously reported in the literature; and (iv) develop a classification system that translates buffering indices into agronomically meaningful categories to support lime rate calibration and amendment planning.

2 Methodology

2.1 Soil sampling and preparation

A total of 543 soil samples were collected across six sub-Saharan African countries: the Ivory Coast (n = 65), Ghana (n = 127), Malawi (n = 60), Zimbabwe (n = 60), Zambia (n = 131), and Mozambique (n = 100), within the framework of the DAQARA Africa project (Figure 1). The sampling sites covered a broad range of agroecological zones, including humid, sub-humid, and semi-arid environments, representative of the diversity of soil types, land-use histories, and management practices typical of smallholder farming systems in the region. Soil samples were collected from the cultivated topsoil layer (0–20 cm), corresponding to the agronomically active horizon most directly affected by fertilization, liming, and other soil management practices. The same sampling depth was applied consistently across all countries to ensure comparability of soil chemical and buffering-related measurements. Sampling campaigns were conducted between 2023 and 2024, predominantly during the dry season in each country, to minimize short-term variability associated with soil moisture conditions and recent field operations. The sampling sites encompassed a range of soil types representative of the weathered landscapes of sub-Saharan Africa. According to the World Reference Base for Soil Resources (WRB) classification (21), the dominant soil groups across the six countries included Ferralsols and Acrisols, which are deeply weathered, low-activity clay soils characteristic of humid and sub-humid tropical environments; Lixisols and Plinthosols, found in transitional zones with seasonal moisture contrasts; Cambisols, indicating moderately developed soils with some horizon differentiation; and, in specific areas of Malawi and Zimbabwe, Vertisols and Luvisols, reflecting higher clay activity and base status. These soil groups span a broad range of mineralogical composition, exchange capacity, and weathering intensity, ensuring that the buffering capacity analyses capture the pedological diversity relevant to liming management across the region. After collection, all soil samples were air-dried at room temperature, gently crushed with a rubber mallet, and sieved through a 2 mm mesh, in accordance with standard soil preparation procedures. The<2 mm fraction was thoroughly homogenized and stored under controlled laboratory conditions prior to chemical, physical, spectroscopic, and titration analyses. Soil pH was measured in a 1:1 soil-to-water suspension (10 g soil: 10 mL deionized water) after a 30-minute equilibration period using a calibrated pH meter. The instrument was calibrated with standard buffer solutions (pH 4.00, 7.00, and 10.00) before each analytical session and was verified periodically to ensure measurement stability, and pH in SMP buffer was measured following the Shoemaker–McLean–Pratt procedure (5) to characterize soil buffering behavior. The cation exchange capacity (CEC) was determined using the ammonium acetate (NH₄) extraction method at pH 7.0, and CEC is expressed in cmol(+) kg⁻¹ soil (CEAEQ (22)). Total carbon was measured by dry combustion using a CHNS elemental analyzer following standard procedures (23), and values were converted to organic matter using the conventional 1.724 conversion factor (Van Bemmelen factor), which assumes that soil organic matter contains 58% carbon. Particle-size distribution was determined using the hydrometer method, enabling quantification of the sand, silt, and clay fractions (22). All results are presented in Table 1.

Figure 1

2.2 Soil titration procedure

Soil buffering behavior was characterized using an acid–base titration procedure based on incremental additions of calcium hydroxide [Ca(OH)₂], following the general soil titration framework commonly used to quantify lime requirement and buffering capacity (25, 26), with adaptations to the present experimental conditions. For each soil, 30 g of air-dried soil (< 2 mm) was weighed and transferred to a polypropylene beaker, then mixed with 30 mL of distilled water to obtain a soil–solution suspension (1:2.5 w/v). The suspension was mechanically stirred for 30 min at room temperature (25 ± 2 °C) to ensure adequate equilibration between the soil solid phase and the solution prior to the initial pH measurement. Soil pH (pH₀) was measured using a calibrated glass electrode pH meter standardized with pH 4.00, 7.00, and 10.00 buffer solutions. A standardized 0.022 mol L⁻¹ Ca(OH)₂ solution was prepared from analytical-grade reagents and standardized prior to use. The titration was performed by adding Ca(OH)₂ in increments to the soil suspension. After each addition, the mixture was stirred for 25 min, then equilibrated for 5 min; the pH was recorded. Successive additions were continued until the soil pH exceeded 7.0, which represents the agronomic target for liming correction. For each soil, the titration typically yielded 7 to 8 points: approximately five points in the acidic range (pH< 7) to characterize the buffering response during the correction interval, and two to three additional points above pH 7 to capture the post-correction behavior and confirm that the agronomic target had been reached. A quality control was ensured by including a Reference soil at the beginning of each titration series, allowing verification of measurement consistency and analytical stability across sessions. At each step, the cumulative amount of Ca(OH)₂ added and the corresponding pH were recorded. The titration procedure generated soil-specific pH response curves describing the evolution of soil pH as a function of cumulative Ca(OH)₂ input. These curves constituted the experimental basis for calculating buffering capacity indices.

2.3 Buffering capacity framework derived from titration iterations

Soil buffering capacity was quantified using mathematical expressions derived from iterative soil titration curves obtained through successive additions of calcium hydroxide. Each buffering capacity index was calculated from the same set of pH measurements, corresponding to multiple titration points collected for each soil. The different buffering-capacity expressions were designed to capture soil resistance to pH change at complementary analytical scales while remaining fully derived from the same titration iterations. Three buffering capacity indices were computed: punctual buffering capacity (BCP), linear buffering capacity (BCL), and integral buffering capacity (BCI). These indices differ in their mathematical formulation and in the portion of the titration curve they exploit, but they are all based exclusively on experimental titration data.

2.3.1 Punctual buffering capacity

The punctual buffering capacity (BCP) was calculated to quantify soil resistance to pH change at a specific stage of the titration process. BCP was defined as the amount of calcium hydroxide required to induce a unit change in pH between two successive titration points. For each soil, BCP was calculated by interpolating between two consecutive points on the titration curve spanning a 1-unit pH interval (13). The buffering capacity was expressed as the ratio of the incremental Ca(OH)₂ input to the corresponding pH change and is reported in units of cmol H⁺ kg⁻¹ pH⁻¹. This approach provides a localized estimate of buffering behavior, directly derived from the iterative titration measurements.

2.3.2 Linear buffering capacity

The linear buffering capacity (BCL) was derived from the portion of the titration curve where the relationship between cumulative Ca(OH)₂ addition and pH change was best described by a linear model. For each soil, linear regressions were fitted to successive segments of the titration curve by progressively increasing the number of consecutive titration points included. The segment yielding the highest coefficient of determination (R²) was retained as the optimal linear interval. For each soil, a linear regression model was fitted according to:

where x represents the cumulative amount of Ca(OH)₂ added. The linear buffering capacity was calculated as the inverse of the slope of the regression line:

BCL represents the average buffering capacity over the selected titration interval and is computed directly from the titration sequence used to construct the regression (13).

2.3.3 Integral buffering capacity

The integral buffering capacity (BCI) was computed following the method proposed by Masso and Khiari (13), adapted to the incubation lime response curves. For each soil, the lime response curve describes the evolution of pH as a function of cumulative CaCO₃ addition. A reference curve was established using the pH response of deionized water subjected to the same incremental CaCO₃ additions. The BCI was then calculated as the relative difference between the area under the reference curve and the area under the soil lime response curve, divided by the area under the reference curve, and expressed as a percentage. Mathematically, this is equivalent to computing the ratio of the integral of the soil curve to the integral of the reference curve over the same interval of CaCO₃ addition, and subtracting this ratio from unity. A soil with negligible buffering capacity would follow the reference curve closely, yielding a BCI near zero, whereas a strongly buffered soil would resist pH change, causing its curve to deviate markedly from the reference, and yielding a BCI approaching 100%. The BCI therefore provides a global, dimensionless measure of the overall resistance of a soil to pH change across the entire range of CaCO₃ doses applied during the incubation (13).

2.3.4 Reference water titration curve

A distilled-water titration curve was generated using the same Ca(OH)₂ solution, and the cumulative incremental additions were the same as those in the soil titration procedure. The water titration was continued until a stable pH plateau was reached, defined as the point at which additional Ca(OH)₂ did not produce a measurable change in pH.

The use of a distilled-water reference curve serves both a chemical and an agronomic purpose. Chemically, the water curve represents the theoretical maximum pH response to Ca(OH)₂ addition in the absence of any buffering constituents that is, without the proton-exchange reactions, surface complexation, and mineral dissolution that occur in soil (P. N. 4). By comparing the soil titration response to this unbuffered reference, the integral index isolates the fraction of the applied base that is consumed by the soil’s acid-neutralizing components rather than by the solution itself. This principle follows the integral framework developed by Masso and Khiari (13), in which a pure water titration curve f(x) was used as the lower boundary of buffering capacity (BC = 0%), representing a substance with negligible resistance to pH change, while a hypothetical maximum-buffered substance m(x) with ΔpH = 0 across the full titration range served as the upper boundary (BC = 100%). The soil titration curve g(x) is then positioned between these two extremes, and the integral ratio quantifies the relative resistance of the soil compared with the unbuffered reference. From an agronomic standpoint, this normalization enables direct comparison of buffering intensity across soils with different initial pH values and titration ranges, expressing cumulative resistance as a dimensionless percentage that is independent of the absolute quantity of base applied (13). This makes BCI interpretable across contrasting soil types and management contexts without requiring standardization to a fixed dose.

The resulting ΔpH–dose relationship for water was used as the reference function f(x). This curve represents the theoretical maximum pH response under identical chemical input and defines the upper boundary of titration responsiveness.

2.3.5 Mathematical expression of BCI

For each soil, the ΔpH titration curve was denoted g(x). The integral buffering capacity was computed by comparing the area under the absolute ΔpH curve of the soil to that of the water reference over the common domain [0,a]:

Absolute values of ΔpH were used in the integration to ensure that the cumulative area was positive across the domain.

BCI therefore expresses the relative reduction in cumulative pH change of the soil compared with water under identical alkaline input (13). A high BCI value indicates strong resistance to pH increase (high buffering capacity), whereas values approaching zero indicate weak buffering behavior.

2.4 Spectral data acquisition

Mid-infrared (MIR) spectra were acquired on air-dried soil samples (< 2 mm fraction) that were further finely ground using an agate mortar and pestle to reduce particle size heterogeneity and ensure uniform contact with the spectrometer crystal prior to analysis. Spectral measurements were performed using a TENSOR II Fourier-transform infrared spectrometer (Bruker Optics), equipped with an HTS-XT high-throughput sampling module and a mercury–cadmium–telluride (MCT) detector. Spectra were collected over the wavenumber range approximately 600 to 4000 cm⁻¹, with a nominal spectral sampling interval of about 1.4–1.5 cm⁻¹ and an instrument spectral resolution of 4 cm⁻¹, as configured in the OPUS acquisition software. For each soil sample, material was loaded into four independent wells, and four replicate spectra were recorded. The replicate scans were subsequently averaged to obtain a single representative spectrum per sample, thereby improving signal stability and reducing random instrumental noise. All spectra were expressed as absorbance units and stored for subsequent preprocessing and modeling.

2.5 Spectral preprocessing

Before developing the model, mid-infrared (MIR) spectra were trimmed at both edges and linearly interpolated to standardize the range from 650 to 3950 cm⁻¹, using a consistent spectral interval of 1.5 cm⁻¹. This process eliminated noisy edge regions and ensured consistent alignment of spectral features despite differences in original ranges and resolutions. Then, mid-infrared (MIR) spectra were subjected to spectral preprocessing techniques to generate alternative representations of the original signal. These preprocessing operations were designed to address common sources of variability in soil spectra, including baseline shifts, multiplicative scatter effects, and high-frequency noise, while preserving chemically meaningful information. All preprocessing strategies were applied consistently across the full spectral range and were evaluated independently, as illustrated in Figure 2. The raw spectra were retained as a reference representation, corresponding to the absorbance signal directly acquired by the spectrometer. A Savitzky–Golay smoothing filter (SG0) was applied using a window size of 11 points and a second-order polynomial to reduce high-frequency instrumental noise while maintaining the overall spectral shape and band positions (27). In addition to smoothing, first-order (SG1) and second-order (SG2) Savitzky–Golay derivatives were computed using the same window size and polynomial order. These derivative transformations modify the original spectra by emphasizing local changes in absorbance with respect to wavenumber, thereby reducing baseline offsets and enhancing fine spectral structures. To correct for multiplicative scatter effects related to particle size, surface roughness, and sample packing, Standard Normal Variate (SNV) transformation was applied. SNV standardizes each spectrum by centering it to zero mean and scaling it to unit variance, thereby reducing variability unrelated to chemical composition (28). Several preprocessing techniques were also combined sequentially to generate additional spectral representations. In these cases, transformations were applied in a defined order to target different sources of spectral variability. Specifically, SG0-SNV, SG1-SNV, and SG2-SNV correspond to spectra that were first smoothed or differentiated using the Savitzky–Golay filter and subsequently normalized using SNV. This sequential approach allows noise reduction or feature enhancement to be performed before scatter correction, ensuring that the normalization step operates on spectra with reduced baseline and noise. In addition, SNV followed by detrending (SNV-DT) was applied to further remove residual baseline curvature. Detrending consists of fitting a low-order polynomial to each spectrum and subtracting it from the normalized signal, thereby eliminating remaining large-scale trends that may persist after scatter correction (28). Each preprocessing strategy shown in Figure 2 was treated as a distinct spectral input for subsequent modeling steps. By applying individual and combined preprocessing techniques, multiple complementary representations of the same soil spectra were generated, enabling the modeling framework to exploit different aspects of the spectral information.

Figure 2

2.6 Model development

Predictive modeling of buffering capacity indices was structured according to the nature of the predictor datasets. Two complementary modeling frameworks were developed: (i) models based on soil chemical signatures and derived variables, and (ii) models based on mid-infrared (MIR) spectral data. This distinction reflects the contrasting statistical properties and mechanistic meaning of structured laboratory measurements versus high-dimensional spectral predictors.

2.6.1 Modeling based on soil chemical signature

Buffering capacity indices were predicted using soil chemical properties and derived variables. Two tree-based ensemble algorithms were implemented: Random Forest (29) and Extreme Gradient Boosting (30). These approaches are well-suited to structured environmental datasets because they capture nonlinear relationships and complex interactions without requiring strict distributional assumptions. Random Forest constructs multiple regression trees using bootstrap sampling and aggregates their predictions to improve robustness and reduce variance. XGBoost builds trees sequentially, with each new tree correcting residual errors from the previous ensemble while controlling model complexity through regularization. Hyperparameters for both algorithms were optimized via cross-validation to ensure stable, generalizable predictions. This framework allowed evaluation of both bagging- and boosting-based ensemble strategies for translating measurable soil chemical attributes into functional buffering indicators.

2.6.2 Modeling based on MIR spectral data

Buffering capacity indices were also predicted from mid-infrared (MIR) spectra. Spectral data are high-dimensional and strongly collinear, requiring modeling approaches that account for these characteristics. Partial Least Squares Regression (PLSR) (31) was applied as a multivariate linear method that projects spectral variables into a reduced set of latent components maximizing covariance with the response variable. The optimal number of components was determined by cross-validation to balance predictive performance and model complexity. In addition, Cubist regression (32) was implemented to account for potential nonlinear relationships between absorbance features and buffering behavior. Cubist combines rule-based partitioning of the predictor space with local linear regression models, enabling nonlinear global responses while preserving local interpretability. By combining PLSR and Cubist, both linear and hybrid nonlinear modeling strategies were evaluated for converting MIR spectral signatures into buffering capacity indices.

2.7 Model training and evaluation

All predictive models were trained and evaluated using a consistent and reproducible framework (Figure 3). The dataset was randomly split into training (80%) and testing (20%) subsets using a fixed random seed (random_state = 42). The 80:20 partition is a widely adopted convention in chemometric and machine learning studies involving soil spectral data, providing a balance between sufficient training data for model calibration and a representative hold-out set for unbiased performance evaluation (19). The split was performed randomly and was not stratified by geographic location, soil type, or pH level. The test set was kept completely independent and was never used during model tuning. For PLSR, hyperparameter tuning consisted of selecting the optimal number of latent components. The number of components was varied from 1 to 20, Each candidate number of components defines a progressively more complex model that extracts additional covariance between the spectral predictors and the response variable. and for each candidate value, a PLSR pipeline was fitted and evaluated using 5-fold cross-validation on the training data. The value yielding the highest mean R² across the five folds was retained for final model training. For Random Forest, hyperparameter tuning was performed using a randomized search strategy, where 50 random combinations were sampled from a predefined parameter space. The tuned parameters included the number of trees, the maximum tree depth, the minimum number of samples required to split an internal node, the minimum number of samples required at a leaf node, and the number of features considered at each split. Each combination was evaluated using 5-fold cross-validation on the training data with R² as the scoring criterion, and the best-performing configuration was retained for final model training. Model performance was then assessed using two complementary approaches. First, 5-fold cross-validation was applied to the whole data, where each sample appeared in a test fold exactly once (Evaluation a). This provided an internal assessment of model performance across the full dataset. Second, the independent test set, comprising 20% of the samples and excluded prior to any model tuning, was used to evaluate model generalization in an unbiased manner (Evaluation b). The two evaluation approaches are intended to be compared to assess the consistency and reliability of model performance. All performance metrics reported in this study correspond to the testing folds in cross-validation (Evaluation a) or the independent test set (Evaluation b). Training performance was never reported. Model accuracy was quantified using the following complementary statistical indicators: the coefficient of determination (R²; (33)), which quantifies the proportion of variance in observed values explained by the model; the root mean square error (RMSE; (34)), which measures the average magnitude of prediction errors in the same units as the predicted variable; the regression slope and intercept between observed and predicted values, where a slope close to 1 and an intercept close to 0 indicate strong agreement across the full value range; the prediction bias (35), calculated as the mean difference between predicted and observed values, where values close to zero indicate the absence of systematic error; and the ratio of performance to interquartile distance (RPIQ; (36), which relates prediction error to the natural variability of the response variable and provides a scale-independent indicator of model performance. All performance metrics were computed consistently for the testing dataset and, where applicable, averaged across cross-validation folds to ensure comparability among models and preprocessing strategies.

Figure 3

2.8 Feature importance and model interpretation using SHAP values

Model interpretation was performed using two complementary approaches tailored to the nature of the predictor datasets: SHAP values for tree-based models using the chemical signature, and Variable Importance in Projection (VIP) scores for PLSR models using MIR spectral data.

2.8.1 SHAP analysis for chemical signature models

SHAP (SHAPley Additive exPlanations) values (37, 38) were used to interpret the Random Forest models retained for predicting the three buffering capacity indices (BCP, BCL, and BCI) from routine soil chemical properties. SHAP values quantify the average marginal contribution of each predictor to the model output, ensuring additivity such that the sum of all SHAP values equals the predicted value for each observation. This enables both local explanations at the individual soil level and global interpretation by aggregation across samples. SHAP values were computed using the TreeSHAP algorithm (39), which leverages the internal tree structure to efficiently compute exact predictor contributions. SHAP values were calculated on the testing folds of the 5-fold cross-validation procedure, ensuring that interpretations reflect model behavior on data not used during training. For each cross-validation iteration, the Random Forest model trained on the corresponding training fold was used to compute SHAP values on the held-out testing fold. The resulting SHAP values were then aggregated across all five folds to produce a global summary covering the entire dataset.

2.8.2 VIP analysis for MIR spectral models

Variable Importance in Projection (VIP) scores (31) were used to identify the most influential spectral regions in the PLSR models predicting BCP, BCL, and BCI from MIR spectra. VIP scores quantify the contribution of each spectral variable (wavenumber) to the PLSR model by summarizing its weighted loading across all retained latent components, relative to the total explained variance in the response variable. A VIP score greater than 1 indicates that the corresponding wavenumber contributes above average to the model and is considered influential (40). VIP scores were computed from the final PLSR models fitted with the optimal preprocessing (SG2–SNV) and the optimal number of latent components selected by cross-validation. The resulting VIP profiles were plotted across the full spectral range to identify wavelength regions most strongly associated with each buffering index, enabling spectroscopic interpretation of the compositional controls underlying soil buffering behavior.

Together, SHAP and VIP analyses provide complementary insights: SHAP links buffering predictions to individual chemical properties with directional and magnitude-specific contributions, while VIP identifies the spectral regions that encode functional buffering information, connecting model behavior to measurable soil attributes from both analytical perspectives.

2.9 Jenks natural breaks classification

To enhance the interpretability of buffering capacity across heterogeneous African soils, the three buffering indices (BCP, BCL, and BCI) were classified into three categories (low, medium, and high) using the Jenks Natural Breaks optimization method. Jenks classification is a variance-minimization approach that partitions continuous data into internally homogeneous and externally distinct groups. The algorithm iteratively determines breakpoints that minimize within-class variance while maximizing between-class variance, thereby identifying natural groupings inherent in the data distribution. This approach was preferred over equal-interval or quantile classifications because it better captures the intrinsic structure of highly variable soil datasets. Each buffering index was independently classified into three categories (k = 3): low, medium, and high buffering regimes. Break thresholds were computed using the full dataset for each index to ensure consistency and comparability across countries. The resulting classes were used exclusively for interpretative and comparative purposes, allowing clearer visualization of buffering patterns and facilitating agronomic interpretation of soil resistance to pH change across diverse agroecological contexts.

3 Results

3.1 Variability of soil properties

Descriptive statistics of the studied soils are presented in Table 1. Across the six countries, the dataset exhibited substantial variability in texture, chemical properties, and soil acidity indicators. Sand content ranged widely, from predominantly sandy soils (with maximum values exceeding 90% in several countries) to more balanced textures. Mean sand content was generally high, particularly in Mozambique (779 g kg⁻¹), Zambia (741 g kg⁻¹), Malawi (704 g kg⁻¹), and Zimbabwe (701 g kg⁻¹), indicating a dominance of coarse-textured soils in the dataset. Clay content varied considerably, reaching maximum values above 500 g kg⁻¹ in several countries, with standard deviations indicating marked intra-country heterogeneity. Cation exchange capacity (CEC) showed strong dispersion, with minimum values near zero in some cases and maximum values exceeding 50 cmol(+) kg⁻¹ in Zimbabwe and Malawi. Mean CEC values ranged from 6.8 cmol(+) kg⁻¹ (Mozambique) to 13.5 cmol(+) kg⁻¹ (Malawi), reflecting contrasting soil reactivity levels. Soil pH_w ranged from strongly acidic (minimum values around 3.8–4.0) to near-neutral and moderately alkaline (maximum values up to 9.8 in Zimbabwe). Mean pH values remained within the acidic-to-slightly-acidic range across all countries. Similar variability patterns were observed for pH_smp, although within a narrower range. Organic matter content also showed notable dispersion, with mean values generally below 30 g kg⁻¹, but maximum values reaching nearly 66 g kg⁻¹ in Malawi, indicating the presence of both low- and relatively high-carbon soils within the dataset. Overall, the dataset encompasses a wide range of pedological conditions, ensuring that subsequent buffering capacity analyses are conducted across diverse soil chemical and textural contexts.

3.2 Comparative analysis of BCP, BCL, and BCI

Figure 4 illustrates the conceptual derivation of the three buffering capacity indices from a representative titration curve and highlights their distinct mathematical formulations. The punctual buffering capacity (BCP) corresponds to the local slope at a selected cumulative dose, reflecting the instantaneous pH response to the addition of Ca (OH)₂. The linear buffering capacity (BCL) is derived from the slope of a regression fitted across the titration range, representing the overall linear response of the soil. The integral buffering capacity (BCI) is calculated as the relative area under the titration curve and captures the cumulative neutralization behavior over the full dose interval. Statistical analysis revealed clear differences in magnitude and dispersion among the indices, as shown in Table 2. BCP ranged from 0.036 to 4.267 (mean = 0.945; SD = 0.601), while BCL varied between 0.099 and 3.296 (mean = 1.083; SD = 0.624), both exhibiting high relative variability. In contrast, BCI showed a narrower distribution, ranging from 69.96% to 99.52% (mean = 81.21%; SD = 5.82), indicating comparatively greater stability across soils. These results demonstrate that the three indices characterize buffering capacity from complementary but statistically distinct perspectives.

Figure 4

11). BCI is expressed as a dimensionless percentage (%) relative to the water reference curve. ΔpH, change in pH relative to initial soil pH.; BCL, linear buffering capacity (cmol H⁺ kg⁻¹ pH⁻¹); BCI, integral buffering capacity (%); ΔpH, change in pH relative to initial soil pH; Ca(OH)₂, calcium hydroxide. The shaded region in (c) represents the integrated buffering response, and annotations indicate the corresponding buffering indices.

3.3 Model evaluation

3.3.1 Chemical signature model.

3.3.1.1 Punctual buffering capacity model

Among the tree-based algorithms evaluated, Random Forest consistently outperformed XGBoost across all three buffering indices and was therefore retained for chemical signature analysis. A comparative summary of Random Forest and XGBoost performance for BCP, BCL, and BCI is provided in Supplementary Table 1. As shown in Figure 5a, the Random Forest model for BCP achieved a cross-validated R² of 0.73 and a CV RMSE of 0.26 cmol H⁺ kg⁻¹ pH⁻¹. The RPIQ value was 2.51, indicating good predictive performance. The regression slope was 0.72 with an intercept of 0.26, while the bias remained minimal (0.01 cmol H⁺ kg⁻¹ pH⁻¹), suggesting limited systematic deviation between measured and predicted values. The slope below unity indicates some compression of the predicted range, consistent with a tendency of ensemble models to underestimate high values and overestimate low values, particularly at the extremes of the distribution (41). On the independent test set (Evaluation b), the model achieved an R² of 0.70, an RMSE of 0.24 cmol H⁺ kg⁻¹ pH⁻¹, and an RPIQ of 2.44. These metrics were consistent with the cross-validated estimates, confirming model generalizability and the absence of overfitting (Table 3). Permutation importance results (Figure 6a) indicated that organic matter (OM%) was the most influential predictor, followed by pH_smp and clay content. CEC showed a moderate contribution, whereas sand, silt, and pH_w were comparatively less important. It should be noted that some predictors, particularly CEC and organic matter, may be partially correlated, as CEC is partly governed by organic matter and clay content. However, tree-based ensemble methods such as Random Forest are inherently robust to multicollinearity, as they construct individual trees using random subsets of features and do not rely on matrix inversion as in linear regression (29). SHAP value analysis (Figure 7a) confirmed the dominant role of OM% and pH_smp. Higher organic matter levels were generally associated with positive SHAP contributions, increasing predicted BCP values. Clay content also showed a positive influence at higher concentrations, while texture fractions such as sand and silt contributed less consistently.

Figure 5

Figure 6

Figure 7

3.3.1.2 Linear buffering capacity model

Random Forest was also retained for BCL prediction, as it provided marginally better error metrics than XGBoost (Supplementary Table 1). For BCL (Figure 5b), the model produced a cross-validated R² of 0.70 and a CV RMSE of 0.31 cmol H⁺ kg⁻¹ pH⁻¹. The RPIQ was 2.52. The regression slope was 0.69, the intercept was 0.33, and the bias was 0.01 cmol H⁺ kg⁻¹ pH⁻¹, indicating stable prediction with some compression of higher observed values, as expected from ensemble averaging. On the independent test set, the BCL model achieved an R² of 0.69, an RMSE of 0.29 cmol H⁺ kg⁻¹ pH⁻¹, and an RPIQ of 2.34, confirming stable generalization to unseen samples (Table 3). According to permutation importance (Figure 6b), pH_smp was the most influential variable, followed by organic matter and clay content. CEC exhibited moderate contribution, while sand, silt, and pH_w displayed lower relative importance. SHAP values (Figure 7b) indicated that higher pH_smp values were associated with increased predicted BCL. Organic matter also displayed positive SHAP contributions at elevated levels. Clay content showed a consistent positive influence, whereas sand and silt had comparatively minor effects.

3.3.1.3 Integral buffering capacity model

For BCI, Random Forest again demonstrated slightly better stability than XGBoost and was retained for subsequent analysis (Supplementary Table 1). For BCI (Figure 5c), the model achieved a cross-validated R² of 0.70, a CV RMSE of 2.99%, and an RPIQ of 2.60. The regression slope was 0.71, the intercept was 23.29, and the bias was −0.02%, indicating balanced prediction across the observed range with modest compression at the extremes. On the independent test set, the BCI model yielded an R² of 0.71, an RMSE of 3.20%, and an RPIQ of 2.42, indicating consistent performance between cross-validated and external evaluation (Table 3). Permutation importance (Figure 6c) revealed that pH_w was the most influential predictor, followed by pH_smp. Clay content was moderately important, whereas organic matter, CEC, sand, and silt contributed less than the pH-related variables. SHAP analysis (Figure 7c) demonstrated that higher pH_w and pH_smp values were associated with higher predicted BCI values. Clay content showed positive effects at higher levels, whereas organic matter and texture fractions showed smaller, more variable effects.

3.3.2 Spectral MIR model

3.3.2.1 Punctual buffering capacity

Two algorithms, PLSR and Cubist, were evaluated under multiple preprocessing strategies for MIR prediction of punctual buffering capacity. Among the tested configurations, the best predictive performance was obtained using PLSR combined with SG2–SNV preprocessing (Table 4). Under this configuration, the MIR-PLSR model achieved a CV R² of 0.81, a CV RMSE of 0.23 cmol H⁺ kg⁻¹ pH⁻¹ (Figure 8a), and an RPIQ of 2.73. The regression slope (0.80) and low bias (0.01 cmol H⁺ kg⁻¹ pH⁻¹) indicate strong agreement between measured and predicted values. In comparison, Cubist models showed lower predictive performance and higher prediction errors across preprocessing techniques (Table 4). When applied to the independent test set, the PLSR model with SG2–SNV preprocessing achieved an R² of 0.78, an RMSE of 0.32 cmol H⁺ kg⁻¹ pH⁻¹, and an RPIQ of 2.50, confirming the robustness of the spectral–buffering relationship (Table 3). Variable Importance in Projection (VIP) analysis (Figure 9a) identified wavelengths with VIP scores greater than 1 primarily around 3700–3500 cm⁻¹, 2920–2850 cm⁻¹, 1650–1550 cm⁻¹, and 1100–1000 cm⁻¹. These regions are broadly consistent with O–H stretching vibrations, aliphatic C–H groups associated with organic carbon, amide/aromatic functional groups, and Si–O stretching in silicate minerals, although spectral overlap between mineral and organic absorptions in these regions means that individual band assignments should be interpreted with caution given the multivariate nature of PLSR.

Figure 8

Figure 9

3.3.2.2 Linear buffering capacity

For linear buffering capacity, both PLSR and Cubist models were tested across several preprocessing strategies. The highest predictive performance was again achieved using PLSR with SG2–SNV preprocessing. The optimized MIR-PLSR model achieved a CV R² of 0.75 and a CV RMSE of 0.30 cmol H⁺ kg⁻¹ pH⁻¹ (Figure 8b), with an RPIQ of 2.53. The regression slope (0.81) and minimal bias (−0.01 cmol H⁺ kg⁻¹ pH⁻¹) indicate stable proportional prediction. Cubist models had lower coefficients of determination and higher prediction errors than the optimized PLSR model (Table 4). On the independent test set, the PLSR model for BCL achieved an R² of 0.70, an RMSE of 0.33 cmol H⁺ kg⁻¹ pH⁻¹, and an RPIQ of 2.40, supporting the generalizability of the spectral model for linear buffering prediction (Table 3). VIP scores greater than 1 (Figure 9b) were concentrated in spectral regions near 3600–3400 cm⁻¹, 2900 cm⁻¹, 1700–1600 cm⁻¹, and 1200–1000 cm⁻¹. These regions are broadly associated with hydroxyl groups in clay minerals, C–H stretching from organic matter, carbonate-related absorption, and silicate vibrations, though definitive assignments remain tentative due to spectral overlap among mineral and organic components.

3.3.2.3 Integral buffering capacity

For integral buffering capacity, PLSR and Cubist algorithms were evaluated under different preprocessing configurations. The best predictive performance was achieved using PLSR combined with SG2–SNV preprocessing, as summarized in Table 4. The MIR-PLSR model yielded a CV R² of 0.70, a CV RMSE of 3.01% (Figure 8c), and an RPIQ of 2.63. The regression slope (0.76) and low bias (−0.04%) indicate balanced prediction across the observed range. Cubist models showed lower explained variance and higher prediction errors than the optimized PLSR configuration (Table 4). On the independent test set, the PLSR model for BCI achieved an R² of 0.68, an RMSE of 3.03%, and an RPIQ of 2.49, confirming consistent predictive performance for integral buffering capacity across both evaluation approaches (Table 3). VIP analysis (Figure 9c) highlighted key wavelengths with VIP scores exceeding 1 around 3700–3500 cm⁻¹, 3000–2800 cm⁻¹, 1650 cm⁻¹, and 1100 cm⁻¹, broadly corresponding to structural hydroxyl groups, organic carbon functional groups, water-related absorptions, and silicate mineral vibrations, with the same caveats regarding spectral overlap and multivariate interpretation.

3.3.3 Classification of buffering capacity indices

The buffering capacity indices were classified into three categories (Low, Medium, and High) using the Jenks Natural Breaks optimization method, which partitions continuous data into internally homogeneous and externally distinct groups by minimizing within-class variance while maximizing between-class variance (see Section 2.9). The resulting classification is illustrated in Figure 10. Globally, BCP was predominantly classified as Low (69.40%), followed by Medium (25.41%) and High (5.19%) (Figure 10). For BCL, the classification was even more strongly skewed toward the Low class, which accounted for 82.47% of samples, while Medium and High accounted for 9.63% and 7.90%, respectively. In contrast, BCI exhibited a more balanced class distribution: Medium represented 43.44% of the samples, Low 31.88%, and High 24.68%. The contrast between BCP/BCL and BCI distributions carries direct agronomic significance. BCP and BCL characterize the instantaneous and average response of the titration curve, respectively; their dominance in the Low class indicates that most soils in the dataset exhibit limited immediate resistance to pH change and would respond rapidly to relatively small lime inputs. BCI, by contrast, captures the cumulative neutralization demand integrated across the full titration range. Its more balanced distribution indicates that soils with low instantaneous reactivity may nonetheless carry substantial total corrective demand. In practical terms, a soil classified as Low for BCP will respond quickly to lime application, but if its BCI is Medium or High, complete correction to the agronomic target will still require significant total amendment. This distinction is critical for liming management: BCP and BCL inform the rate and timing of lime application, while BCI determines the total quantity needed, thereby reducing the risk of both under- and over-application in heterogeneous smallholder systems.

Figure 10

4 Discussion

The dataset spans a wide range of pedological conditions across six African countries, including contrasting textures, cation exchange capacities, and acidity levels. A large proportion of the soils were acidic, with several samples falling within the strongly acidic range conditions that represent a persistent constraint on agricultural productivity across sub-Saharan Africa (42). While pH identifies this acidity status, it does not indicate how a soil will respond to corrective liming. In sandy, low-CEC systems, limited buffering capacity can lead to rapid pH shifts after amendment application, increasing the risk of overliming, while soils with higher clay or organic matter content may require more lime to reach agronomically optimal conditions (43). Evaluating BCP, BCL, and BCI therefore provides a structured framework for characterizing how these soils will respond to liming and for estimating their amendment requirements.

The three indices showed distinct statistical distributions, confirming that they capture complementary dimensions of buffering behavior. BCP exhibited the highest relative dispersion, consistent with its sensitivity to local variability in surface reactivity. BCL, by integrating multiple titration points into a single parameter, produced a smoother distribution. BCI, expressed as a percentage relative to the water reference, showed the narrowest range, suggesting that cumulative lime demand is more constrained than instantaneous responsiveness. These contrasting distributions demonstrate that a single parameter cannot adequately describe how a soil will respond to liming, as each index captures a different analytical scale of buffering behavior.

The buffering capacity indices were derived from controlled Ca(OH)₂ titration experiments that quantify the soil’s immediate chemical response to incremental base addition. This short-term perspective is particularly relevant for liming management, where the primary concern is the soil’s immediate response to amendment incorporation. The titration curves illustrate how soils with similar initial pH may diverge markedly in their response trajectories, reinforcing the need for differentiated indices (25). In practical agronomic systems, the initial pH adjustment following lime incorporation is crucial for alleviating aluminum toxicity, improving nutrient availability, and restoring favorable conditions for root development (44). By quantifying instantaneous sensitivity (BCP), average resistance (BCL), and cumulative neutralization demand (BCI), the framework offers a structured assessment of how soils will behave immediately following lime application. In acidic African soils characterized by strong variability in texture, exchange capacity, and reserve acidity (45), such differentiation reduces uncertainty in lime rate estimation and supports evidence-based management strategies.

The Random Forest models achieved cross-validated R² values above 0.70, meaning that more than 70% of the variability in buffering indices was explained by measurable soil properties. This level of predictive performance is consistent with what has been reported for other functional soil properties predicted from chemical signatures in heterogeneous tropical datasets comparable or higher R² values have been obtained for CEC and organic carbon prediction using similar tree-based approaches (14, 45) suggesting that buffering capacity is no harder to predict than these established soil attributes. The regression slopes remained below unity for all three indices, indicating some compression of the predicted range. This pattern is consistent with the well-documented tendency of ensemble averaging methods to underestimate extreme values and overestimate low values (14), rather than reflecting a fundamental limitation of the chemical signature approach. Intercepts were small relative to the data ranges, and bias values were near zero, confirming the absence of systematic overestimation or underestimation. RPIQ values above 2.5 indicate good predictive discrimination according to the thresholds proposed by Bellon-Maurel et al. (36), confirming that model error is small relative to the dataset’s natural spread. Importantly, the consistency between cross-validated and independent test set metrics confirms that the models are not overfitting to the training data. The test set R² values for BCP, BCL, and BCI closely matched the CV estimates, demonstrating that the learned relationships generalize to unseen soil samples drawn from the same multi-country distribution. Similarly, RMSE values on the test set remained comparable to cross-validated errors, and RPIQ values confirmed that predictive discrimination was maintained. This consistency is particularly meaningful given the heterogeneity of the dataset, which spans six countries with contrasting pedological conditions, and indicates that the chemical signature captures structurally stable drivers of buffering behavior rather than dataset-specific artifacts.

For BCP, organic matter, pH_smp, and clay content emerged as the dominant predictors. At this shortest response scale, buffering is mainly governed by the density and reactivity of surface functional groups. Organic matter provides numerous pH-dependent charge sites that enable rapid proton exchange (46). Clay contributes additional exchange surfaces, while pH_smp reflects the accessible reserve acidity associated with these colloids (5). For BCL, pH_smp became the primary predictor, followed by organic matter and clay, reflecting greater control by reserve-acidity pools as buffering extends across a correction interval (46). For BCI, pH_w and pH_smp were the dominant predictors, while clay and organic matter played secondary roles — at this cumulative scale, active and reserve acidity together determine the total acid load to be neutralized (42). It should be noted that some predictors, particularly CEC and organic matter, may be partially correlated, as CEC is partly governed by organic matter and clay content. However, tree-based ensemble methods are inherently robust to multicollinearity (29), and feature-importance rankings reflect statistical associations rather than direct mechanistic confirmation. The interpretations provided should therefore be understood as consistent with modeling outcomes rather than as definitive causal proof.

To further clarify how these predictors influence buffering behavior, SHAP analysis was used to examine the direction and magnitude of their contributions across the three indices. For the punctual index (BCP), higher organic matter content consistently yielded positive SHAP contributions, indicating that carbon-rich soils increase immediate resistance to pH changes (10). Clay content exhibited a similar directional effect, consistent with the density of reactive surface sites. For the linear index (BCL), variations in pH_smp exerted the largest directional shifts in predicted values, suggesting that buffering across the correction interval is increasingly structured by the size of exchangeable acidity pools mobilized during titration. For the integral index (BCI), both active and reserve acidity indicators strongly influenced cumulative neutralization demand, confirming that this scale reflects the total acid load requiring correction (47). Taken together, the SHAP analysis reveals a progressive mechanistic shift across the three indices: surface reactivity dominates at the punctual scale, reserve acidity takes control across the linear interval, and integrated acidity status governs cumulative behavior. This transition from organic- and clay-controlled surface exchange to system-level acidity conditions reinforces the conceptual layering of the three indices and demonstrates that buffering capacity cannot be reduced to a single controlling property.

Mid-infrared (MIR) spectroscopy showed consistent, robust predictive performance across the three buffering indices, with PLSR achieving CV R² values of 0.81, 0.75, and 0.70 for BCP, BCL, and BCI, respectively. These values compare favorably with MIR-based predictions of other soil functional properties in African and tropical contexts 16 reported R² values in a similar range for soil hydraulic and chemical properties using MIR in Moroccan soils. The fact that buffering capacity, a dynamic functional property, can be predicted with accuracy on par with static compositional properties such as CEC or clay content underscores the strength of the MIR approach proposed here. Regression slopes were close to unity, intercepts were small, and bias remained negligible, confirming statistical calibration quality across all three indices.

Regarding spectral interpretation, the VIP-selected wavelengths provide insight into the compositional controls underlying each index, although individual band assignments should be interpreted with caution given the multivariate nature of PLSR and the spectral overlap that characterizes MIR soil spectra. For BCP, VIP scores were concentrated in regions broadly associated with organic functional groups (O–H, C–H, C=O vibrations) and clay-related bands (Si–O and Al–OH), consistent with the dominant role of organic matter and clay at this instantaneous scale (48). For BCL, VIP-selected wavelengths reflected a broader combination of organic and mineral bands, including structural hydroxyl groups and mineral lattice features, consistent with the more integrative nature of this index in which reserve acidity pools increasingly contribute (49). For BCI, VIP scores emphasized mineralogical regions and weathering-related bands, alongside secondary contributions from organic matter, reflecting the cumulative system-level control of acidity at this scale. Across all three indices, a clear spectral gradient emerges: organic-dominated absorption features are most influential where surface reactivity governs buffering, while mineralogical bands progressively dominate as the analytical scale shifts toward reserve and cumulative acidity. This spectral gradient is consistent with the mechanistic shift identified by SHAP analysis, suggesting that the three indices capture distinct chemical dimensions of soil liming behavior. The agreement between titration-derived indices and MIR-based predictions demonstrates that buffering capacity can be rapidly and cost-effectively assessed without extensive wet chemistry, with important logistical implications for large-scale soil monitoring in Africa, where laboratory infrastructure may be limited.

The independent test set evaluation confirmed the robustness of MIR-based predictions. For BCP, the test set R² remained close to the CV, indicating that the spectral–buffering relationship captured by PLSR is stable beyond the training folds. The comparable test set performance for BCL and BCI further demonstrates that MIR spectroscopy can serve as a reliable, rapid alternative to titration-based buffering assessment without substantial loss of accuracy when applied to new samples. RPIQ values on the test set for BCP, BCL, and BCI remained above 2.0, indicating adequate predictive discrimination according to the thresholds proposed by (36). The agreement between cross-validated and external metrics across all three indices reinforces the conclusion that MIR-encoded compositional features effectively capture the functional chemical behavior underlying soil buffering capacity.

From an agronomic perspective, the differentiation among BCP, BCL, and BCI provides operational guidance for lime rate calibration. The classification results reveal that most soils fall into the low-buffering class for both BCP and BCL, indicating limited immediate and average resistance to pH change meaning many soils will respond rapidly to relatively small lime inputs, requiring careful dose adjustment to avoid overshooting agronomic pH targets (46). The situation differs markedly for BCI, where soils are more evenly distributed across low, medium, and high classes, indicating that even soils with low instantaneous reactivity may still carry substantial cumulative lime demand (50). This contrast between BCP/BCL and BCI is agronomically critical: a soil classified as low BCP will respond quickly to lime, but if its BCI is medium or high, complete correction will still require significant total inputs. Conversely, a soil with moderate BCP but low BCI may respond more gradually yet require little overall amendment. Reducing buffering capacity to a single index would mask these distinctions and lead to systematic errors in lime planning — either underestimating total demand or misjudging the rate of response. BCP therefore functions as a reactivity indicator for fine-tuning lime rates, BCL as a stability indicator for planning the correction trajectory, and BCI as a demand indicator for estimating total amendment requirements. Used together, these indices enable more precise, economically efficient liming and reduce the risk of over- or under-application in heterogeneous smallholder systems across Africa.

While the proposed framework provides a robust and mechanistically interpretable foundation for liming management, several limitations should be acknowledged. First, the titration protocol uses a 25-minute equilibration time per increment, which captures rapid proton-exchange reactions but does not reflect slower processes such as gradual mineral dissolution or the re-equilibration of aluminum species that occur under field conditions over weeks or months. The indices therefore characterize short-term buffering behavior and should be interpreted as indicators of immediate liming response rather than long-term soil acidity dynamics. Second, the MIR predictive models were calibrated exclusively on soils from six African countries, and their generalizability to soils outside this geographic and pedological scope remains to be validated. External validation across a broader range of soil types and regions is therefore necessary before these models can be applied operationally at the continental scale. Third, although the independent test set evaluation demonstrated consistent performance for all three indices, the test set was drawn from the same multi-country distribution as the training data. True external validation using geographically independent soil datasets would provide a stronger assessment of model transferability and should be pursued in future work. Complementary incubation-based approaches would further help capture the kinetic dimensions of buffering that controlled titration cannot resolve. The present framework should thus be viewed as the short-term chemical component of a broader buffering assessment strategy, providing a structured and scalable foundation for future integration with long-term field-based evaluations in acidic African soils.

5 Conclusion

This study demonstrates that soil buffering capacity in heterogeneous African agroecosystems cannot be adequately described by a single operational parameter. By structuring buffering behavior into three complementary indices punctual (BCP), linear (BCL), and integral (BCI) derived from the same Ca(OH)₂ titration curves, we provide a multidimensional framework that distinguishes between instantaneous sensitivity, average resistance across the correction interval, and cumulative neutralization demand. The statistical independence and contrasting distributions of these indices confirm that soil resistance to pH change is scale-dependent and mechanistically layered.

The strong predictive performance obtained using both reduced chemical signatures and mid-infrared (MIR) spectroscopy demonstrates that buffering behavior is not an isolated empirical construct but is structurally governed by measurable soil attributes. Tree-based models identified organic matter, clay content, and pH-related variables as key drivers, with their relative importance varying systematically with the analytical scale of the buffering index from organic- and clay-controlled surface reactivity at the punctual scale to system-level acidity conditions at the integral scale. MIR-based PLSR models further improved prediction accuracy, particularly for punctual buffering capacity, confirming that compositional spectral features effectively encode functional chemical behavior. This represents an important step toward transitioning from labor-intensive wet titration methods to rapid, reagent-free, and scalable predictive approaches.

From an agronomic standpoint, the differentiation among BCP, BCL, and BCI provides operationally meaningful information for acidity management. Instantaneous responsiveness, average stability, and cumulative lime demand correspond to distinct management questions and risks, particularly in resource-constrained smallholder systems where inaccurate lime recommendations can lead to economic losses or reduced amendment efficiency. The classification framework further translates quantitative buffering indices into actionable categories, facilitating decision support across diverse soil contexts.

Although the indices capture short-term chemical buffering behavior under controlled conditions, they establish a mechanistically interpretable foundation for improved acidity management in strongly weathered soils. By integrating titration-based quantification with spectroscopic prediction and interpretable machine learning, this work advances both the conceptual understanding and the practical assessment of soil buffering capacity in African agroecosystems. Collectively, these findings confirm the study hypothesis that BCP, BCL, and BCI capture statistically independent dimensions of soil liming response governed by distinct but measurable physicochemical drivers, and that these indices can be reliably predicted from both routine chemical properties and mid-infrared spectral signatures across pedologically diverse African soils.

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