the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 12 Jun 2026
Modelling and Interpreting Thermal Stability Indices to Understand Soil Carbon Stabilization Using Soil Properties Data
Abstract. Soil organic carbon (SOC) sequestration and nutrient cycling are related to the susceptibility of soil organic matter to biological decomposition. Several studies have demonstrated associations between biological stability and thermal stability, as assessed using programmed pyrolysis. We sought to develop parsimonious machine learning (ML) models to predict SOC stability indices from measured soil properties. The study analyzed indices such as S1, S2, and S3; the oxygen index (OI); the hydrogen index (HI); and T50, which reflect SOC composition, thermal behaviour, and stability. A total of 203 soil samples collected at 0–15cm depth increments from agricultural, forest, and wetland landscapes in New Brunswick, Canada, were analyzed. Feature selection techniques optimized predictive models, and a random forest (RF) was used to develop one. Correlation results revealed that HI was negatively associated with pH (r = –0.35) and bulk density (r = –0.33), whereas OI showed a positive correlation with pH (r = 0.34). Thermal indices were more strongly related to soil chemistry and texture, with S1 closely correlated with total carbon (r = 0.88) and nitrogen, and S2 negatively associated with sand (r = –0.66) but positively associated with clay (r = 0.24) and POXC (r = 0.84). T50 showed positive correlations with both pH (r = 0.48) and bulk density (r = 0.36), indicating greater thermal stability in higher pH, compacted soils, though these patterns varied by land use. Random Forest (RF) model predicted S1 S3 indices with high accuracy (CCC = 0.83–0.86), while HI and OI were more difficult to model (CCC = 0.44–0.48), suggesting missing biological or environmental predictors; NH₄⁺ and POXC emerged as key predictors. Structural equation modeling (SEM), after addressing multicollinearity, supported a hypothesis driven model that explained ~54% of T50 variation. Clay dissolved organic carbon, pH, and aluminum showed significant direct associations with T50 (β for pH = 0.44), whereas bulk density showed no meaningful relationship. Our study demonstrates that ML and SEM can reveal patterns and associations between soil properties and thermal stability indices, offering insight into understanding the SOC stability under a changing climate as well as presenting a framework for rapid estimation of SOC stability proxies.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2849', Anonymous Referee #1, 19 Jun 2026
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CC1: 'Comment on egusphere-2026-2849', Pierre Barré, 28 Jul 2026
This study presents the results of thermal analyses of more than 200 topsoil samples collected in the New Brunswick region of Canada. The authors attempted to predict some selected thermal variables from soil characteristics using ML approaches and to identify the most influential predictors of each thermal variable. Finally, they used SEM to explore causal pathways linking soil properties to thermal stability. This study is original, particularly with regard to the causal models. I recommend its publication following a few minor comments that can nonetheless take some time to address.
Previous studies have linked biogeochemical stability observed in the field to thermal indicators (Barré et al., 2016; Cécillon et al., 2021). These studies could have served as a basis for selecting the indicators to be considered in the present draft. Furthermore, the T50 indicator is not described in sufficient detail. Is this the T50 calculated from S2 or from the entire pyrolysis signal? If it is the T50 measured from the S2 signal, that is unfortunate because it is really not the best indicator of biogeochemical stability (Cécillon et al., 2021). If it is the T50 calculated from the entire pyrolysis signal, it is necessary to better explain how this signal is constructed so that it incorporates both S2 and S3 (in particular, how were the CO2 and HC signals converted into carbon in order to determine the temperature at which half of the pyrolyzable C was emitted?)
The authors considered numerous soil characteristics to predict thermal indicators. Why didn’t they consider total organic carbon? Total organic carbon is a good indicator of biogeochemical stability (Zhao et al., 2026). I believe that adding TOC should improve the models’ metrics.
Delahaie et al. (2023) presented a study reporting the results of more than 1,700 thermal analyses and linking them to pedoclimatic variables. Delahaie et al. (2023) is cited in the introduction but is not referenced again in the discussion of the results. This is regrettable given the close relationship between the two studies.
Given the model metrics, at this stage, I would continue to recommend actually conducting the thermal measurement rather than predicting the result based on soil characteristics. It would be interesting for the authors to discuss this point.
Cited references
Barré et al. (2016) The energetic and chemical signatures of persistent soil organic matter. Biogeochemistry, 130 :1-12.
Cécillon et al. (2021) Partitioning soil organic carbon into its centennially stable and active fractions with machine-learning models based on Rock-Eval® thermal analysis. Geoscientific Model Development, 14 :3879-3898.
Zhao et al. (2026) Declines in organic carbon persistence with increased soil carbon. Nature communications. https://doi.org/10.1038/s41467-026-75185-4
Citation: https://doi.org/10.5194/egusphere-2026-2849-CC1 -
RC2: 'Comment on egusphere-2026-2849', Teneille Nel, 08 Oct 2026
General Comments
Thank you for the opportunity to review this manuscript. This is a comprehensive and well-designed study investigating the potential drivers of soil organic matter stability using thermal techniques across soils and land-use types in Eastern Canada. The manuscript addresses an important topic, and the combination of thermal indicators, soil physicochemical properties, correlation analyses, and machine-learning approaches provides a potentially valuable framework for identifying the factors associated with SOM persistence.
I particularly appreciated the thorough statistical analyses and the attention given to model diagnostics. The manuscript also makes a useful contribution by considering multiple indicators of SOM stability rather than relying on a single metric. However, I think the manuscript would benefit from a stronger mechanistic interpretation of the observed relationships. Soil stabilization mechanisms are frequently mentioned throughout the manuscript, but they are not always explained in sufficient detail or explicitly connected to the soil properties and soil types represented in this dataset.
In particular, I encourage the authors to consider whether the relative importance of the identified drivers differs among soil types and/or land-use types. Relationships identified across the entire dataset may reflect differences among soil groups rather than consistent relationships operating within each soil type. Exploring this possibility, where statistically feasible, would substantially strengthen the interpretation and help distinguish general controls on SOM stability from relationships that are specific to particular soil environments.
Specific Comments
Introduction
L22: Please define the S1–S3 parameters when they are first introduced.
L28: Please clarify: more strongly than what?
L73: Regarding the statement about “integrating their outputs,” I suggest mentioning Bayesian approaches as a potential avenue for future research, which could may provide a useful framework for simultaneously evaluating several complementary indicators of SOM stability.
Materials and Methods
Figure 1: Please ensure that there is at least one city or other recognizable location that is named legibly on the map.
L161–175: Is a summary of the physical and chemical properties of the soils provided elsewhere in the manuscript or supplementary material? If not, I strongly recommend including one. A table reporting the mean, range, and standard deviation of the major soil physical and chemical properties for the overall dataset, and preferably by soil type and/or land use, would substantially improve the manuscript.
Information about how the absolute range over which those properties vary, is important for interpreting the subsequent statistical relationships between soil properties and SOM stability indices. These summary statistics would also help establish whether the proposed physical and chemical processes are realistically plausible within the soils investigated.
L191–193: Please clarify whether the use of HI and OI as predictors in the machine-learning models introduces circularity in the machine-learning models, since HI and OI are derived from S1–S3 measurements and TOC content?
Results and discussion
Figure 3: Please indicate in the figure caption that these plots represent the full dataset, including all land-use types. This is important for interpreting the relationships shown. Please also add the appropriate units to the x-axis labels of the CDF plots.
Section 3.2: This section is currently quite lengthy and contains many individual correlation results. I suggest focusing the Results section on the clearest and most biologically or mechanistically meaningful relationships rather than reporting all correlations in detail.
An alternative approach would be to move some of the interpretation of individual correlations into the Discussion and integrate the correlation results with the machine-learning results. This would reduce repetition and allow the manuscript to develop a clearer mechanistic narrative. For example, correlations could be used primarily to establish broad relationships, while the discussion could then consider whether these relationships are supported by the predictive models and what mechanisms might explain them.
L382: The phrase “protecting the release of CO₂” is unclear in terms of functional interpretation. I suggest rephrasing this in terms of the established concept of clay-associated protection of organic matter from mineralization or decomposition.
L391: The statements regarding pH appear potentially contradictory. The manuscript states that “alkaline conditions favor oxidative transformations,” whereas later (L430) it states that higher pH promotes SOC preservation. Please reconcile these statements and clarify whether the effects of pH differ depending on the SOM fraction, the specific thermal stability indicator, or the mechanism being considered. It may be that pH has opposing effects on different processes. If so, this distinction should be made explicit rather than presenting the two statements as generally applicable.
L404–405: Please clarify the mechanism by which organo-mineral interactions are proposed to enhance oxidative transformation of SOM. If the intended mechanism involves preferential stabilization or transformation of particular organic compounds, altered microbial accessibility, catalytic effects of minerals, or selective preservation of oxidation-resistant compounds, please explain this more explicitly.
L413: Please specify how bulk density (BD) is expected to alter SOM protection mechanisms. For example, is the proposed relationship related to changes in pore structure, aggregate formation, oxygen diffusion, physical accessibility of SOM, or simply the association of BD with soil texture/mineralogy? It would be helpful to distinguish direct effects of BD from its potential role as a proxy for other soil properties.
L427: The relationship between CEC and SOM stability could potentially have an alternative explanation. Higher CEC may be associated with greater soil fertility and therefore greater plant productivity or fresh organic matter inputs. Thus, the observed relationship may not necessarily indicate a direct protective effect of CEC on SOM. If possible, discuss whether the available data allow these mechanisms to be distinguished.
L494: Please provide more detail regarding the statement that “interactions from N content” influence SOM stability. What specific interactions are being referred to? A more explicit mechanistic explanation would strengthen this section.
L510: Please clarify the proposed mechanisms through which trace metals influence SOM stability. Are the authors referring to direct complexation with organic compounds, association with mineral surfaces, catalytic effects on oxidative reactions, effects on microbial activity, or another mechanism? Please provide a more specific mechanistic explanation and appropriate references.
Organization of the Discussion
Sections 3.3.1, 3.3.2, and 3.3.3: These sections contain considerable repetition and discuss several similar mechanisms across the different models and thermal stability indices. I suggest restructuring these sections to provide a more integrated discussion. Rather than discussing each model or SOM fraction independently, the authors could first identify the major mechanisms consistently supported across multiple models/fractions. The authors could then discuss the exceptions and differences among individual indices. This type of organization would make the discussion more concise while also making the overarching conclusions easier to identify. It would also help avoid repeatedly explaining the same mechanism when it appears as an important predictor of several stability indicators.
Section 3.3.6: Please reduce repetition in this section. Consider focusing this section on the unique findings or implications that have not already been addressed.
Minor Editorial Comment
L593–594: This is an incomplete sentence. Please revise for grammatical completeness.
Overall Recommendation
Overall, I found this to be a strong and potentially valuable study. The experimental/data framework and statistical analyses are substantial, and the manuscript has the potential to make a useful contribution to our understanding of the controls on SOM stability as assessed through thermal techniques.
The main opportunity for improvement is to move beyond identifying statistical associations and develop a more integrated mechanistic interpretation of the results. Greater attention to the ranges of soil properties, differences among soil types and land uses, and the specific mechanisms underlying the observed relationships would considerably strengthen the manuscript.
I also recommend reducing repetition in the Results and Discussion and synthesizing the common mechanisms across SOM fractions and predictive models. Doing so would make the manuscript more concise while highlighting the most important findings and improving the overall narrative.
Citation: https://doi.org/10.5194/egusphere-2026-2849-RC2
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Using a dataset of n=203 samples from the New Brunswick province in Eastern Canada, the authors proposed a detailed modeling and analysis framework linking thermal stability indicators with soil organic matter (SOM) stability. The framework includes both a predictive model (using a Random Forest (RF) implementation in R), and a more analytical model that aims at removing the black-box quality so often associated with machine learning predictions (using Structural Equation Modeling (SEM)). The manuscript represents a scientific work of both good quality and significance. The presentation of this work, however, needs to be revised and, at times, restructured.
The RF modeling section presents a serious effort of finding the most parsimonious set of predictors, by both eliminating (multi)collinearity in the feature set before model training, and by applying recursive feature elimination to further eliminate less informative features. During the RF model training and selection, a grid search was used to find the best-fitting hyperparameters. The authors also included a posteriori analysis using partial dependence plots and individual conditional expectation plots. A detailed analysis of the relationships between the main thermal indicators (S1, S2, S3, OI, HI, T50) is introduced before presenting the modeling results, confirming pre-existing hypotheses about the links between SOM stability and thermal stability indicators.
In the modeling section, more effort should be put in detailing the exact parameters/libraries used, and explanations of common methods (like PDPs and ICEs) should be minimal and concise. A significant effort has been put into making the paper accessible to a wider audience, however the presentation of many modeling choices was omitted in doing so.
Regarding code and data availability, authors have declared that the data will be made available upon reasonable request (due to privacy concerns). Will the code be accessible online? If not, even more precisions need to be provided.
Metrics have to be systematically introduced and, when appropriate, references and/or equations should be provided. Certain metrics are never introduced, others change their nomenclature throughout the text, and some will depend on the code implementation used (thus, rendering code availability even more important).
In the results section, and particularly in the summary results of the thermal indicators of stability, authors need to make clearer distinctions between the conclusions from their own results and the overall consensus regarding the relationships between thermal indicators and SOM stability. In general, the results section (3.1, 3.2…) are very repetitive and contain lots of redundant information. The authors should consider rephrasing and shortening their result explanations so as to not repeat certain conclusions many times. Similar to the modeling section, the results are at times very elaborate while significant statistical/modeling choices are omitted.
Authors need to interpret PDP and ICE results with a grain of salt, as these can’t always be taken at face value due to the marginal effects they represent (as the authors have well explained in the modeling section).
Detailed corrections are provided in a commented pdf. I urge the authors to pay attention to having consistency in the introduction, repetition, and capitalization of acronyms and initialisms. Same goes for the introduction of new terms, chemical solutions, and references.