We used 488 topsoil samples from 275 sites across Australia (Fig. ). The soils were sampled from three depth layers (0–10, 10–20 and 20–30 cm). All soil orders in the Australian soil classification were present, except Anthroposol and Organosol . Kandosols were the most abundant soil type, followed by Tenosols and Calcarosols, Chromosols and Vertosols, while Rudosols, Dermodols, Kurosols, Ferrosols, and Podosols were present in smaller numbers. Three Hydrosols were excluded from further analysis due to the distinct C storage mechanisms in anoxic soils .

The sampling area spans the main Köppen-Geiger climate zones , with most of the samples collected from arid hot deserts, with smaller proportions from arid hot steppes and tropical savannahs. Samples were primarily collected from areas with minimal human impact, particularly nature conservation sites, native vegetation grazing lands, and other minimally used areas. Only a small proportion of samples came from production or intensive land use. The vegetation at the sampling sites was diverse, comprising 24 major vegetation groups, with eucalyptus woodlands being the most common . Most samples were taken from native vegetation or natural bare land, with the rest from non-native vegetation or cleared land .

Soil samples were fractionated through physical granulometric separation. The samples were dispersed in deionised water using an ultrasonic probe (Sonics VCX 500 Sonicator, Newtown, Connecticut) with an energy output of 500 J mL⁻¹ for 200 s . After dispersion, the samples were fractionated using an automated wet sieving apparatus (Analysette 3 Pro, Fritsch GmbH, IdarOberstein, Germany) with 250 and 50 µm sieves. The resulting soils were in three size fractions: macroaggregates (2000–250 µm), microaggregates (250–50 µm), and the fine fraction (≤ 50 µm). The fractionated samples were then oven-dried at 60 °C overnight and ground to approximately ≤ 80 µm, before the organic C content of each size fraction was measured using an elemental analyser (SoliTOC Cube, Elementar Analysensysteme, Hanau, Germany). The organic C content of the fine fraction, representing MAOC, was recorded in grams per kilogram of whole soil.

The whole soils (sieved to ≤ 2 mm) were air-dried before fine grinding to ≈<80 µm. The mid-IR spectra of the finely ground samples were measured with a diffuse reflectance infrared Fourier transform (DRIFT) spectrometer (Bruker Invenio HTS-XT, Massachusetts, United States). Spectra were recorded from 4000–450 cm⁻¹ with a spectral resolution of 4 cm⁻¹ and measuring 64 scans per sample. The spectrometer was calibrated with a gold standard before measuring each sample plate with 23 samples (Bruker, Massachusetts, United States). Reflectance spectra were recorded in log⁡1R (apparent absorbance).

The MAOC content of samples displayed a log-normal distribution. We performed a log_e transformation on the MAOC content and removed three outliers that were more than 1.5 times the interquartile range above Q3 or below Q1. We proceeded with the analysis of the remaining 482 samples from 270 sites.

We fitted a monotonically increasing and concave frontier line to the relationship between log(MAOC) and clay + silt content of the samples using the smooth, non-parametric frontier line analysis with the R package SNFA . We calculated the CAmax and Cdef following the approach described in . Each point on the frontier line represents the maximum attainable amount of MAOC that soil could store for a particular clay and silt content.

To estimate uncertainty, we performed 100 non-parametric bootstrap resamples to fit the frontier lines, keeping samples from the same site together during resampling to prevent data leakage. We then averaged all 100 frontier-line fits from the bootstraps. The Cdef was calculated as the difference between the estimated mean frontier line and the MAOC content. We also computed the uncertainties of our frontier line estimate by calculating the 95 % confidence limits. All values were then back-transformed to their original units for the spectroscopic modelling.

The mid-IR spectra were interpolated to 32 cm⁻¹ wavenumber intervals to reduce inherent collinearity. Since mid-IR spectra are highly collinear and contain broad absorption features, we interpolated the spectra to 32 cm⁻¹ to reduce the redundant information passed into the machine learning model . Visual checks confirmed relevant absorption features remained distinguishable at this resolution. We also checked Cdef model performance using spectra interpolated to 8, 16, 24, and 32 cm⁻¹ resolutions and found no significant difference between these resolutions. Preprocessing consisted of an initial offset correction, in which the minimum spectral value minus 0.01 was subtracted from all measurements so that each spectrum was shifted to a common baseline just above zero, followed by a standard normal variate (SNV) transformation, and a final offset correction to address the baseline shift introduced by the SNV transformation. Spectral regions that were either featureless (4000 to 3746 cm⁻¹) or containing distracting features from noise and artefacts from water and CO₂ (2370 to 2082 cm⁻¹) were removed before modelling.

We modelled the MAOC and the estimated Cdef with CUBIST. CUBIST is a rule-based regression tree algorithm . CUBIST creates a tree structure, with branches as a series of “if-then” conditions, then reduced into rules. Each CUBIST rule corresponds to a subset of the data that satisfies the rule's condition. For each rule, a linear regression model is fit to the data using relevant predictors . CUBIST balances accurate predictions and model interpretability through its rule-based structure. CUBIST is tuned by two parameters: committees and neighbours. The number of committees specifies the number of ensembles contributing to the final prediction, with more committees typically improving performance but reducing interpretability, and the number of neighbours specifies how many nearest-neighbours of a sample CUBIST uses to adjust its rule-based predictions. described the method for spectroscopic modelling. In our experiments, since our goal was to understand which spectral regions influence predictions and how they relate to soil properties, we prioritised model interpretability by using a single committee to maintain model transparency, avoiding the added complexity of ensemble averaging. We optimised the number of neighbours by testing all values from 0 to 9. Model fitting and validation were carried out using 10-fold cross-validation grouped by site, in which the 270 sampling sites were randomly assigned to 10 folds to ensure that samples from the same site and the three depth layers were kept together within the same fold. We assessed the models based on their coefficient of determination (R2), Lin's concordance correlation coefficient (CCC) and the root mean squared error (RMSE).

We propagated the uncertainty of the frontier line fitting and the CUBIST modelling. From the 100 frontier line fits made with the bootstraps, we derived the upper and lower 95 % confidence intervals (CI) for the frontier line fit and calculated the upper and lower limit of Cdef. The upper and lower limits of Cdef were also modelled with CUBIST following the same method described above.

To interpret the models, we extracted each CUBIST rule from the MAOC and Cdef models to analyse their rule partitioning. For the MAOC model, we examined the distribution of MAOC values within each rule, while for the Cdef model, we analysed the distributions of both MAOC and Cdef values within each rule. For the linear models in each CUBIST rule, we examined the wavenumber corresponding to specific absorptions of soil constituents and their coefficients. Furthermore, we calculated the SHAP (SHapley Additive exPlanations) values for each sample for each linear model of the CUBIST rules, focusing the analysis on the Cdef model. (SHAP analysis results of MAOC CUBIST model provided in the Supplement) The SHAP values are used to explain the outputs of machine learning models. SHAP is based on game theory and assigns an importance value to each instance at each feature (in our case, each sample's absorptions at specific wavenumbers) in a model. While the regression coefficients summarise the average effect of a wavenumber within a given rule, SHAP values provide instance-level attributions that quantify each wavenumber's contribution to the prediction for each individual sample. Positive SHAP values indicate a positive impact on the prediction, while those with negative values indicate a negative impact. The magnitude measures the strength of the effect.

All statistical analyses were performed using R .

Our samples represent a wide geographical area in Australia (Fig. ) with large variations in MAOC content and texture (Table ). The MAOC content ranges from 0.27 to 50.04 g kg soil⁻¹, while silt content ranges from 0.54 % to 31.81 %, and clay content ranges from 2.34 % to 54.25 % (Table ). The frontier line estimates the maximum C that can be stored in their current environments over their range of clay + silt contents for all 482 samples, with their 95 % confidence intervals shown in Fig. . The frontier line increases with increasing clay + silt content to around 20 %–45 %, after which the rate of increase slows. The CAmax ranges from 5.29 to 45.79 g kg soil⁻¹ with a mean of 32.76 g kg soil⁻¹ (Table ). The Cdef ranges from none to 45.17 g kg soil⁻¹ with a mean of 26.31 g kg soil⁻¹ (Table ).

The CUBIST model predicts MAOC with an RMSE of 2.77 g kg soil⁻¹, is unbiased with R2 of 0.86, and CCC of 0.91 (Table , Fig.  b). The model partitions the data into four rule sets, corresponding to different MAOC content levels, which increase from Rule 1 to Rule 4 (Fig. a). Samples in Rule 1 have the least MAOC and are not significantly different from Rule 2 (Fig. a). Rule 3 samples have significantly more MAOC than Rule 1 but are not significantly different from Rule 2 (Fig. a). Rule 4 samples have significantly more MAOC than all other rules and exhibit the largest spread (Fig. a).

The mean mid-IR spectra of the samples of the four rule sets show overall consistent patterns, with differences in absorption intensities at 3700–3500, 2946–2850, 1986–1794, and 1634–1300 cm⁻¹) (Fig. c).

Specifically, the mean spectrum of Rule 4 has the highest absorption in the 2946–2850 cm⁻¹ region associated with organic C (C–H vibrations of alkyl CH₂), corresponding to having the highest MAOC content (Fig. a, c).

The wavenumbers selected for linear models of the four rules differ, although there is some overlap. All rules use wavenumbers between 2946–2850 cm⁻¹, organic C–H vibrations of alkyl CH₂ groups , though the specific selections vary (Fig. c), suggesting that the models rely directly on spectral signals from organic C to predict MAOC content. Rule 1 exhibits densely distributed wavenumbers across both these regions with high coefficient values. Rule 3 shows a similarly dense distribution, concentrated primarily in the 2946–2850 cm⁻¹ region, with the largest coefficient values. Rule 2 displays more sparsely distributed wavenumbers across both regions, while Rule 4 uses only a few select wavenumbers around 2946–2850 cm⁻¹.

Rules 1, 2, and 3 with the smallest MAOC values all use the region between 1986–1794 cm⁻¹, associated with quartz, whereas Rule 4 does not (Fig. c). Quartz is chemically inert, carries negligible surface charge, and has a low specific surface area compared to clay minerals, which limits the reactive surface area available for organo-mineral bonding and thus associated with low MAOC content, as found in coarser-textured soils dominated by quartz. Rules 1, 2, and 3 also use region 2515 cm⁻¹ associated with carbonate , as soils with more carbonate commonly form in arid or semi-arid regions with low plant productivity and rainfall, and therefore low organic C.

Rule 4 uniquely includes absorptions at the 3750 cm⁻¹ region, associated with the hydroxyl stretching vibrations of clay minerals . Clay minerals provide a more mineralogically reactive soil matrix that facilitates greater organo-mineral bonding, and the model's use of spectral signals reflecting mineral surface reactivity is particularly informative in soils where mineral-organic associations are most developed. Rule 4 also uses wavenumbers between 1762–1634 cm⁻¹, associated with amide C=O bond , as well as wavenumbers around 1154 cm⁻¹, which correspond to the SiO₂ lattice and C-OH stretch of aliphatic O–H (Fig. c), with Rule 3 also using these latter wavenumbers to a lesser extent. SiO₂ lattice indicating the silicate mineral of the soil matrix, while aliphatic C-OH groups indicate polysaccharide-derived and carbohydrate-like organic matter, and amide indicates protein-derived organic matter. Taken together, this suggests that the model draws on both organic-matter and mineral-related absorptions to estimate MAOC content.

The model predicts Cdef with an RMSE of 3.72 g kg soil⁻¹, R2 of 0.89, and CCC of 0.94 while also being unbiased (Table , Fig. c). The model partitions the data into 3 rule sets, and the linear models of each CUBIST rule also show good precision (Table ).

Rule 1 includes samples with the lowest Cdef and the highest MAOC content, representing samples that have smaller C sequestration potential, as these samples contain more MAOC (Fig. a, b). Rule 2 represents samples with intermediate Cdef, and contains little MAOC and clay and silt content, representing coarser-textured soils with more C sequestration potential than samples in Rule 1 because they hold less MAOC (Fig. a, b). Rule 3 includes samples with high Cdef, low MAOC content and the most clay and silt content. Since these samples contain the finest particles, their capacity is largest and is thus undersaturated with C relative to their potential (Fig. a, b).

The three rule sets show similar overall mean spectral patterns but with distinct differences in absorption intensities at key regions, including 2946–2850 cm⁻¹ associated with organic C, 1986–1794 cm⁻¹ associated with SiO₂ overtone and combination bands, and 1538–1218 cm⁻¹) region associated with various organic and mineral absorptions (Fig. d). The wavenumbers selected for the models in each CUBIST rule are generally consistent, with the magnitude of the coefficient decreasing from Rule 1 to Rule 3 (Fig. d).

In the 2946–2850 cm⁻¹ region, associated with organic C–H vibrations of alkyl CH₂ groups , Rule 1 shows greater average absorption compared to Rule 2 and Rule 3 consistent with Rule 1 having the highest MAOC content (Fig. b, d). All three CUBIST rules use wavenumbers within and near this region with relatively large coefficients, but the coefficient magnitude decreases from Rule 1 to Rule 3 (Fig. b, d). This pattern reflects that the model predicts Cdef by leveraging the spectral signal of existing organic C (MAOC) already occupying reactive mineral surfaces. As Cdef represents the remaining sequestration potential, more existing MAOC implies less remaining capacity. Thus, Rule 1 with the highest MAOC and largest organic-region coefficient has the lowest Cdef. Rule 2 has intermediate MAOC and coefficient magnitude, and Rule 3 has the lowest MAOC, smallest coefficient, and consequently the highest Cdef (Fig. a, b, d).

In the region near 1986–1794 cm⁻¹, which is due to the overtones of Si-O vibrations , absorption intensity decreases from Rule 2 to Rule 1 to Rule 3, corresponding to decreasing sand content and increasing clay and silt content (Fig. d).

All three rules have prominent absorption at and near 1634 cm⁻¹, which are associated with amide, carboxylate and carboxylic acid , aromatic –C=C– stretch , HO–H stretch , N–H bend, C=O stretch and absorbed water (Fig. d). This indicates that organic matter types, including polysaccharide-derived, carbohydrate-like, and protein-derived organic C, are used across all three rules similarly to the 2946–2850 cm⁻¹ region, to predict whether the C saturation capacity is filled.

In the fingerprint region (1550–450 cm⁻¹), the band assignments are more challenging due to significant overlaps between mineral and organic absorptions . The region from 1538 to 1218 cm⁻¹, likely associated with quartz minerals as well as organic matter , is more prominent in Rule 2 and Rule 1, and lower in Rule 3 (Fig. d). Rule 3 exhibits proportionally larger coefficients for wavenumbers in the fingerprint region because of low organic C content and high fine mineral particle content (Fig. b, d).

The absorption near 2515 cm⁻¹ due to carbonates shows more prominent absorption in Rule 3. Where Cdef is high, and MAOC is low, which matches the tendency of higher carbonate soils from arid or semi-arid regions with low organic C input that leave mineral surfaces unsaturated.

The model statistics of the CUBIST models of Cdef estimated from the upper and lower 95 % CI of CAmax are shown in Table . The model for the Cdef estimated with the lower 95 % CI of the frontier line performs better than the model estimated with the upper 95 % CI. This can be attributed to the upper 95 % CI of the frontier line being more uncertain than the lower 95 % CI. Specifically, the upper uncertainty of the frontier line fit is high around 25 % clay + silt content due to the low sample number (Fig. ). The uncertainty of Cdef estimated from CUBIST models of Cdef calculated from the upper CI and lower CI of the CAmax is shown in Fig. .

The SHAP contribution of spectral absorption at each wavenumber for the linear model of each CUBIST rule is shown in Fig. . The SHAP values coincide with the regression coefficients of the CUBIST rules (Fig. ). The regression coefficients and SHAP values are generally consistent: large coefficients correspond to strong SHAP model contributions. Rule 1 shows strong contributions primarily from organic C features, and Rule 2 displays a similar pattern but with more contributions from the fingerprint region. For Rule 3, there is a relatively stronger contribution from the absorptions in the double bonds region (including absorption from quartz and the region associated with amide overlapping with other absorptions), and the fingerprint regions have a relatively stronger contribution (Fig. ).

The SHAP values indicate positive and negative contributions from spectral regions associated with characteristic absorption of clay minerals, organic matter, and quartz (Fig. ). Generally, peaks associated with organic C have a negative model contribution with an increase in absorbance, while the troughs have a positive contribution with increasing absorbance (Fig. ). Absorbance in these regions indicates existing MAOC that already occupies reactive mineral surface sites. As mineral binding sites fill, the remaining deficit diminishes. Similarly, absorptions associated with clay minerals and silicate have a positive model contribution, while the troughs have a negative contribution (Fig. ). Absorbance from clay minerals indicates abundant reactive surface area that is available but not yet occupied by organic matter. The positive SHAP contribution reflects unrealised adsorption capacity, whereas quartz has negligible reactive surface area and contributes to coarser texture without contributing to adsorption capacity, which constrains CAmax.

In comparison to SHAP analysis of the MAOC CUBIST model (Fig. S1 in the Supplement), both models draw heavily on the organic C-H region, but the Cdef model shows a progressive shift across rules from organic-C-dominated (Rule 1) to mineral-dominated (Rule 3), indicating the model increasingly relies on mineralogy for available surface in soil with higher Cdef. The MAOC model's contributions remain more consistently concentrated in the organic C-H region across all rules, with the fingerprint region playing a lesser role throughout. This reflects that the MAOC model is more driven by the organic C information in the spectra, whereas the Cdef model integrates both organic and mineral information.