# Predicting Rock-Eval® thermal analysis parameters of a soil layer based on samples from its sublayers; an experimental study on forest soils

Eva Kanari, Pierre Barré, François Baudin, Alain Berthelot, Nicolas Bouton, Frédéric Gosselin, Laure Soucémarianadin, Florence Savignac, Lauric Cécillon

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## ► To cite this version:

Eva Kanari, Pierre Barré, François Baudin, Alain Berthelot, Nicolas Bouton, et al. Predicting Rock-Eval® thermal analysis parameters of a soil layer based on samples from its sublayers; an experimental study on forest soils. Organic Geochemistry, 2021, 160, pp.104289. 10.1016/j.orggeochem.2021.104289. hal-03978825

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https://ens.hal.science/hal-03978825v1

Submitted on 2 Aug 2025

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1 **Predicting Rock-Eval® thermal analysis parameters of a soil layer based on samples from its sublayers; an experimental study on forest soils.**

2 Eva Kanari<sup>a,b*</sup>, Pierre Barré<sup>b</sup>, François Baudin<sup>a</sup>, Alain Berthelot<sup>c</sup>, Nicolas Bouton<sup>d</sup>, Frédéric

4 Gosselin<sup>e</sup>, Laure Soucémarianadin<sup>f</sup>, Florence Savignac<sup>a</sup>, Lauric Cécillon<sup>b,g</sup>

5 <sup>a</sup>Institut des Sciences de la Terre de Paris, Sorbonne Université, CNRS, 75005 Paris, France

6 <sup>b</sup>Laboratoire de Géologie, CNRS, École normale supérieure, PSL University, IPSL, Paris, France

7 <sup>c</sup>FCBA, Délégation territoriale Nord-Est, 21170 Charrey-sur-Saône, France

8 <sup>d</sup>VINCI Technologies, 92022 Nanterre, France

9 <sup>e</sup>INRAE, UR Ecosystèmes Forestiers, 45290 Nogent-sur-Vernisson, France

10 <sup>f</sup>ACTA – les instituts techniques agricoles, 75595 Paris, France

11 <sup>g</sup>Univ. Normandie, UNIROUEN, INRAE, ECODIV, Rouen, France

12 * Corresponding author.

13 E-mail address: kanari@geologie.ens.fr (E. Kanari).

14

15 **Abstract**

16 Soil sampling depths strongly vary across soil studies. Stocks of elements (such as C, N) or
17 organic matter in a soil layer can be simply calculated from stocks measured in its sublayers.

18 This calculation is less obvious for other soil characteristics, such as soil organic carbon
19 (SOC) persistence, complicating the comparison of results from different studies. Here, we
20 tested whether Rock-Eval® parameters of a soil layer, characterizing soil organic matter and
21 its biogeochemical stability, can be determined using Rock-Eval® data measured on its
22 sublayers. Soil samples collected in 10 plots located in eight French forest sites, taken up at
23 two different depths (0–30 cm, 30–50 cm), and their mixtures were analysed with Rock-
24 Eval®. Expected values for the Rock-Eval® parameters of the soil mixtures were calculated
25 either: (1) as the weighted mean of Rock-Eval® parameters measured on the two sublayers, or
26 (2) based on a signal reconstructed as the weighted mean of Rock-Eval® thermograms
recorded on the two sublayers. Our results showed a good agreement between measured and expected Rock-Eval® parameter values. However, when the clay content strongly differed between the two soil sublayers, the amount of pyrolyzed hydrocarbons measured on the soil mixtures was slightly lower than expected. We conclude that it is reasonable to calculate Rock-Eval® parameters of a soil layer, from the Rock-Eval® signature of its sublayers. Our findings facilitate the harmonization of Rock-Eval® data from large scale soil studies using different sampling depths.

Keywords: Soil organic carbon, Pyrolysis, Soil mixing, Mineral matrix effect, Hydrocarbon retention, Clay content

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# 1. Introduction

Recognition of the central role of soil and soil organic matter (SOM) for food security and ecosystem functioning (FAO, 2005, 2017) has led to enhanced political and scientific attention on soil health and SOM dynamics (e.g., Global Soil Partnership (Montanarella, 2015), International Year of Soils 2015 (FAO, 2015), 4per1000 initiative (4p1000, 2018; Rumpel et al., 2018)). As a result, over the last five decades the number of studies focusing on SOM has grown exponentially (Smith et al., 2017). The first large-scale soil monitoring projects with focus on soil organic carbon (SOC) were initiated (e.g., RMQS in France (Arrouays et al., 2003), LUCAS in Europe (European Commission Joint Research Centre, 2021; Orgiazzi et al., 2018), WoSIS a worldwide soil profile database (ISRIC, 2020; Batjes et al., 2020)) and an enormous amount of soil samples and data were collected worldwide, without any harmonization regarding the depth of the sampled soil layers. According to the research question, each soil study may follow a different strategy for the selected sampling depths, with possible complications regarding the comparability of available information. For instance, in some studies the 0–30 cm layer is divided in several sublayers (e.g., 0–10 cm, 10–20 cm and 20–30 cm) or sampled according to pedogenetic horizons, whereas in some other cases the 0–30 cm layer is sampled as one homogeneous layer. Independent of the sampling method, the SOC stock of a soil profile is calculated as the sum of the SOC stocks obtained in the layers comprising that profile (FAO, 2018). Even though determining SOC stock of a given layer is straightforward, it may be much less obvious for other parameters such as SOM characterization results.

One promising analytical technique in SOM research is Rock-Eval® thermal analysis. A time-efficient and inexpensive method, it can be used on large sample sets to quantify soil organic and inorganic carbon and characterize SOC bulk chemistry and thermal stability (Saenger et al., 2013; Gregorich et al., 2015; Sebag et al., 2016; Soucémarianadin et al.,
2018). Moreover, a strong empirical link exists between parameters obtained with this method and in situ observed SOM biogeochemical stability (Barré et al., 2016; Poeplau et al., 2019). Encouraged by this observation, Rock-Eval® thermal analysis was used to build a non-parametric random forests algorithm, PARTY<sub>SOC</sub>, providing quantitative information on SOC biogeochemical stability, by predicting the proportion of centennial stable SOC (Cécillon et al., 2018, 2021). As the application range of the Rock-Eval® method is increasingly expanding, samples from different projects and different sampling strategies are being analysed. Therefore, it is of great importance to determine whether Rock-Eval® parameters characterizing SOM of a given soil layer can be determined from Rock-Eval® parameters measured on its sublayers and, similarly, if centennial stable SOC assessed using PARTY<sub>SOC</sub> in a given soil layer can be determined from PARTY<sub>SOC</sub> estimates based on measurements on its sublayers. If true, this would simplify the comparison of data between studies and the building of datasets on harmonized sampling depths, for instance the 0–30 cm layer, a standard for soil studies (IPCC, 2008; FAO, 2018).

Rock-Eval® analysis consists of thermal treatment of a soil sample following a predefined temperature ramp. Simultaneous and continuous detection of effluents generates five thermograms in total that describe the evolution of carbon containing gases (HC, CO and CO<sub>2</sub>) during the analysis. A large number of Rock-Eval® parameters can be calculated from the five thermograms (Behar et al., 2001; Saenger et al., 2013; Sebag et al., 2016; Cécillon et al., 2018, 2021; Khedim et al., 2021). Parameters obtained with this method are characteristic of the SOM and its interaction with the soil mineral matrix, since soil samples are analysed with no previous isolation of SOM or removal of carbonates. We hypothesised that, in a large variety of temperate forest soils Rock-Eval® parameters characteristic of SOM of a given soil layer could be obtained from Rock-Eval® parameters measured on its sublayers. This hypothesis is far from trivial as differences in the composition of the mineral matrix can
influence the Rock-Eval® signal (Espitalié et al., 1980, 1984). This could considerably complicate the assessment of Rock-Eval® parameters of a given soil layer from Rock-Eval® parameters measured on its sublayers and comparison of results amongst studies with different sampling depth protocols.

To test this hypothesis, we conducted Rock-Eval® analysis of surface (0–30 cm) and deeper (30–50 cm) samples from 10 plots located in eight forest sites in France as well as various binary mixtures of the two soil layers. Some parameters (i.e., ratios) required a minor adaptation of the calculation method used to determine Rock-Eval® parameters of the mixtures based on Rock-Eval® results obtained for the two sublayers, while for other parameters (i.e., temperature parameters) a new calculation method was introduced. Finally, this study provides some basic guidelines that facilitate the direct comparison of Rock-Eval® data of samples from different depths.

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## 2. Materials and methods

### 2.1. Sampling sites and soil characteristics

Samples used in this study belong to 10 contrasting plots distributed amongst seven forest sites of the French “GNB” network (Paillet, 2021; 9 plots) and one site of the “FCBA” network (Berthelot, 2018; 1 plot; part of the IN-SYLVA France national research facility (INRAE, 2020)) (Fig. 1, site map; Cécillon et al., 2017; Gosselin et al., 2015). At each plot, two composite soil layers (layer A (0–30 cm) and layer B (30–50 cm)) were sampled, resulting in two “natural” samples per plot (n = 20 samples for the 10 plots). Soil samples were dried, sieved to < 2 mm and ground to < 250 µm before further processing. Basic characteristics of the 20 “natural” samples are provided in Table 1. Soil bulk chemistry was highly variable with organic carbon content ranging from 0.38 to 11.28 wt.%, pH measured in
water was between 4.1 and 8.2 and carbonate content was negligible in all samples except one that contained 35 wt.% CaCO₃. The sample selection covered a wide range of soil textures with sand content varying between 4 and 85 wt.% and clay content between 2 and 55 wt.% (Table 1).

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## 2.2. Soil mixtures

Using the two “natural” soil samples available from each plot, we composed five binary soil mixtures per plot by combining 90:10, 75:25, 50:50, 25:75 and 90:10 in mass proportion of soil from layer A and layer B (Equation 1; n = 50 binary mixtures for the 10 plots). The exact used soil mass was measured using a precision scale whereas the weighting error allowed was in average 0.39% (calculated as the mean weighted error). In addition, two pure end-member samples per plot were set aside, composed of 100% layer A and 100% layer B soil respectively, resulting in a total number of 70 samples.

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$$Mixture_{AB} = Layer_A \cdot f_i + Layer_B \cdot (1 - f_i) \quad (1)$$

where Layer_A: soil surface layer (0–30 cm), Layer_B: soil sub-surface layer (30–50 cm), f_i: mixing ratio = 1, 0.9, 0.75, 0.5, 0.25, 0.1, 0 ± 0.39%

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## 2.3. Rock-Eval® thermal analysis

All 70 soil samples including the 20 “natural” samples and the 50 composed mixtures were analysed using a Rock-Eval® 6 Turbo apparatus (Vinci Technologies). A small amount of soil (approx. 60 mg), was required for the analysis that took place in two consecutive steps, during which carbon-containing effluents were directly detected. First, the sample underwent
pyrolysis in an inert (N₂) atmosphere, and then oxidation in the presence of O₂ (ambient air).

The heating routine applied during pyrolysis was as proposed by Disnar et al. (2003), including a three-minute isotherm at 200 °C, succeeded by a heating ramp of 30 °C·min⁻¹ up to 650 °C. Oxidation started with a one-minute 300 °C isotherm followed by a heating ramp of 20 °C·min⁻¹ up to 850 °C and a final five-minute isotherm at 850 °C (oxidation routine presented in Baudin et al. (2015) as “bulk rock/basic” method). Simultaneous detection of effluents during both analysis steps generated five thermograms per sample in total describing the evolution of hydrocarbons during pyrolysis (HC PYR), and CO and CO₂ during both pyrolysis and oxidation steps (CO PYR, CO₂ PYR, CO_OX, CO₂_OX). A schematic representation of the analysis steps and the generated thermograms is presented in Supplementary Fig. 1.

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## 2.4. Measured Rock-Eval® parameters

Although these parameters are calculated on the thermograms obtained from Rock-Eval® analysis of the “natural” samples and the composed mixtures, they will be referred to as “measured parameters” in this manuscript to avoid confusion with “calculated parameters” (defined in section 3). Classic Rock-Eval® parameters were acquired using the RockSix software (Vinci Technologies). These included: six automatically generated “peaks” defined as specific areas of the three pyrolysis thermograms (S1, S2, S3, S3’, S3CO and S3’CO; Supplementary Fig. 1, Supplementary Table 1), the amount of pyrolyzed carbon (PC corresponding to the sum of organic C released as HC, CO and CO₂ during pyrolysis), total organic carbon (TOC corresponding to the amount of organic C released during the analysis), mineral carbon (MinC corresponding to the amount of C released through carbonate cracking), hydrogen index (HI corresponding to the ratio of released hydrocarbons to TOC),
and oxygen index ($OI_{RE6}$ corresponding to the ratio of the amount of oxygen of organic origin released to TOC). In addition, further parameters used as predictors by the $PARTY_{SOCV2.0EU}$ model were calculated based on the obtained thermograms using R scripts available on Zenodo (https://zenodo.org/record/4446138#.YDe84Xlw2SQ) (Cécillon et al., 2021). These included: PseudoS1 (the sum of carbon released during the first 200 seconds of pyrolysis—200 °C isotherm—in form of HC, CO and $CO_2$), the ratio S2/PC (ratio of the amount of hydrocarbons released excluding the first 200 seconds of pyrolysis to pyrolyzed carbon), the ratio PC/TOC, the ratio HI/$OI_{RE6}$, and ten temperature parameters (e.g., T30, T50, T70, T90) that describe evolution steps, i.e., at which temperature 30, 50, 70 and 90% of a given gas was released. Finally, we calculated three additional parameters proposed in previous soil studies using the Rock-Eval® technique. These were: The I-index (assessing the preservation of thermally labile “immature” hydrocarbons; Sebag et al., 2016), the R-index (describing the proportion of refractory SOM released as hydrocarbons after 400 °C; Sebag et al., 2016), and the thermolabile hydrocarbon index (TLHC-index corresponding to the proportion of hydrocarbons evolved between 200 °C and 450 °C; Saenger et al., 2015). A detailed description of the definition, units and equations used to calculate all parameters can be found in Supplementary Table 1.

## 2.5. The Rock-Eval®-based $PARTY_{soc}$ model

In this study, we used the Rock-Eval®-based random forest model $PARTY_{SOCV2.0EU}$ (https://zenodo.org/record/4446138#.YDe84Xlw2SQ) proposed by Cécillon et al. (2021). This model was calibrated on data from 6 long-term agricultural experiments including a bare fallow treatment in Northwestern Europe and can predict the centennial persisting SOC proportion in a topsoil sample (0–30 cm). The model requires a set of 18 Rock-Eval®
parameters (Supplementary Table 1) characteristic of a sample and provides a prediction of
the stable SOC proportion for soils from similar pedoclimates. Here we run the model three
times, first using measured Rock-Eval® parameters as predictors (obtained as described in
section 2.4.) and then calculated ones obtained by two different methods (defined in section
3). The result of the first run was treated as one of the measured parameters during data
processing. In the context of this work we merely aimed at evaluating the possibility of
calculating the centennial stable SOC proportion of a soil profile based on its sublayers. As
this statistical model does not include any forest or deep soil samples in its learning set nor
has it been tested or validated on forest or deeper soil samples, we could not provide any
interpretation regarding the absolute measured centennial stable SOC proportion values.
Instead, we investigated the possible ways of using the model when combining several soil
layers.

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197 **2.6. Statistics**

198 To evaluate the performance of the two calculation methods in predicting measured Rock-Eval® parameters for soil mixtures we conducted a statistical assessment of the relationship
199 between measured and calculated values for each parameter. "Natural" samples were
200 excluded from all calculations. The coefficient of determination R² was estimated to assess
201 the existence and strength of a correlation between the measured and calculated values. R²
202 was accompanied by the *p*-value, indicating the probability of a statistically significant
203 relationship, whereas the threshold of significance level was set at 0.05. The mean difference
204 between calculated and measured values (BIAS) was used to test if the relationship was
205 biased. The root mean square error (RMSE) was used as an expression of the magnitude of
206 the error of prediction, as it is defined as a sum of the residuals or deviations between
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calculated and measured parameters. To compare not only the two calculation methods but also the uncertainty associated with each parameter independent of unit or range, we estimated the normalized root mean square error (NRMSE) defined as the RMSE divided by the range of observations.

$$R^2 = \left( \frac{\sum_{i=1}^{n} ((M_i - \bar{M}) \cdot (C_i - \bar{C}))}{\sqrt{\sum_{i=1}^{n} (M_i - \bar{M})^2 \cdot \sum_{i=1}^{n} (C_i - \bar{C})^2}} \right)^2$$

$$BIAS = \frac{1}{n} \sum_{i=1}^{n} (C_i - M_i)$$

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (C_i - M_i)^2}$$

$$NRMSE = \frac{RMSE}{M_{max} - M_{min}}$$

where: $M_i$ and $C_i$ are the measured and calculated values, n is the number of observations, $\bar{M}$ and $\bar{C}$ are the means of measurements and calculations, respectively and $M_{max}$ and $M_{min}$ are the maximum and minimum of measured values.

## 3. Calculation
The central idea of our experiment is that by knowing the exact mixing ratios used to prepare the soil mixtures and having analysed “natural” samples composed only of Layer A or Layer B we can calculate expected values of Rock-Eval® parameters for the mixtures as a weighted mean of the recorded signals. Since many of the parameters are composite terms, involving multiple thermogram areas, mass balance corrections and ratios (Supplementary Table 1), we had to resort to their defining equations to find the most appropriate way of calculating expected parameters. According to the type of parameter, we calculated expected parameters for soil mixtures: (1) based on acquisition parameters (AP) and (2) for temperature parameters only, based on reconstructed thermograms (RT).

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### 3.1. Rock-Eval® parameters calculated based on acquisition parameters (AP)

Expected values of Rock-Eval® parameters defined as single thermogram areas (e.g., S1, S2, S3, etc.; Supplementary Fig. 1), as a sum of multiple thermogram areas (e.g., PC, TOC; Supplementary Table 1) or as evolution steps (e.g., T90<sub>HC_PYR</sub>; Supplementary Table 1) were calculated as a weighted mean, following Equation 2. For each parameter and each soil mixture we applied a weighting directly on the corresponding Rock-Eval® parameters measured for the two pure “natural” samples (100% Layer A, 100% Layer B) according to the known exact mixing ratio used for the mixture preparation.

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$$ \text{Calculated Rock-Eval® parameter}_{\text{Mixture}_{AB}}(\text{AP}) = \text{AP}_{\text{LayerA}} \cdot f_i + \text{AP}_{\text{LayerB}} \cdot (1 - f_i) \quad (2) $$

where AP: Measured Rock-Eval® acquisition parameter

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For parameters that represent ratios, a different procedure was followed. Directly applying a weighted mean equation on parameters that represent ratios (i.e., HI, OI<sub>RE6</sub>, S2/PC, PC/TOC, HI/OI<sub>RE6</sub>, R-index and TLHC-index; Supplementary Table 1) often leads to mathematical errors (Perdue and Koprivnjak, 2007). More precisely, following Equation 2 would mean neglecting to apply the weighted mean correction on the denominator of the ratio (see Equation 3 below for the basic application of equation 2 to OI<sub>RE6</sub> — defined as the proportion of O<sub>2</sub> of organic origin relatively to TOC).

$$OI_{RE6 \ Layer_A} \cdot f_i + OI_{RE6 \ Layer_B} \cdot (1 - f_i) = \frac{O_{2 \ Layer_A} \cdot f_i}{TOC_{Layer_A}} + \frac{O_{2 \ Layer_B} \cdot (1 - f_i)}{TOC_{Layer_B}} \neq 0$$

Calculated OI<sub>RE6 Mixture<sub>AB</sub></sub> (AP) (3)

In this case, this would lead to an overestimation of OI<sub>RE6</sub>. The correct Equation for ratios Perdue & Koprivnjak (2007), is presented below for OI<sub>RE6</sub> (Equation 4):

$$Calculated OI_{RE6 \ Mixture_{AB}} (AP) = \frac{O_{2 \ Mixture_{AB}}}{TOC_{Mixture_{AB}}} = \frac{O_{2 \ Layer_A} \cdot f_i + O_{2 \ Layer_B} \cdot (1-f_i)}{TOC_{Layer_A} \cdot f_i + TOC_{Layer_B} \cdot (1-f_i)} \quad (4)$$

Having already calculated expected values of thermogram areas with the AP-based method, we made use of them to simplify the calculation approach. We calculated Rock-Eval® parameters representing ratios based on their defining equations (e.g., Equation 5 for OI<sub>RE6</sub>; or Supplementary Table 1 for further parameters). We simply replaced basic terms in the defining equation (e.g., S3, S3CO, TOC) with previously calculated expected values of Rock-Eval® parameters for the soil mixtures (e.g., S3<sub>Mixture AB</sub> (AP), S3CO<sub>Mixture AB</sub> (AP), TOC<sub>Mixture AB</sub> (AP)).
$$ 269 \quad Calculated \ OI_{RE6 \ Mixture_{AB}}(AP) = \frac{[S_{3Mixture_{AB}}(AP) \times \frac{32}{44}] + [S_{3CO_{Mixture_{AB}}}(AP) \times \frac{16}{28}]}{TOC_{Mixture_{AB}}(AP)} \quad (5) $$

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271 Similarly, when calculating the I-index, applying a weighting to the logarithm itself would not have been mathematically correct, thus the weighting was applied on the areas of the 272 HC_PYR thermogram that are used in the I-index formula (areas used to calculate A1, A2, 273 A3; Sebag et al., 2016). 274

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### 3.2. Rock-Eval® parameters calculated based on reconstructed thermograms (RT)

276 The above described way of calculating expected values for temperature parameters, as the 277 weighted mean of temperature parameters measured on “natural” samples, is not 278 mathematically correct. Expected values for temperature parameters of soil mixtures were 279 therefore calculated following a reconstructed thermograms (RT) approach. Based on the 280 mixing ratio that was used to compose each mixture we reconstructed the expected shape of 281 the five thermograms of each soil mixture as the weighted mean of the shapes of the 282 thermograms obtained for the two “natural” samples (Equation 6). 283

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$$ 285 \quad Thermogram_{Mixture_{AB}} = Thermogram_{Layer_A} \cdot f_i + Thermogram_{Layer_B} \cdot (1 - f_i) \quad (6) $$

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287 The RT method was used to calculate expected values for temperature parameters only (Cécillon et al., 2018, 2021; Supplementary Table 1), as by definition the AP and RT 288 approaches are equivalent when considering all other parameters, whose calculation is based 289 on thermograms areas. Since the RT approach is more complicated to implement, we also 290 kept the AP method for the calculation of temperature parameters, to test whether the results
291 were very different from what can be obtained using a correct but more time-consuming
292 approach.

293 Signal processing, integrations of thermogram areas and calculation of Rock-Eval®
294 parameters were conducted using R version 3.4.2 (2017), the trapz function of the pracma
295 package (Borchers, 2018) and the hyperSpec package (Beleites and Sergo, 2018). The R
296 script used to calculate the reconstructed thermograms is provided as supplementary material
297 (Supplementary R script 1).

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300

**3.3. Three ways of calculating stable SOC proportion of soil mixtures using the**
**PARTY<sub>SOCV2.0EU</sub> model**

301 Expected values of stable SOC proportion of soil mixtures were calculated in three different
302 ways. First, the stable SOC proportion of soil mixtures was calculated as a weighted average
303 of PARTY<sub>SOCV2.0EU</sub> predictions obtained for layer A and layer B. Second, the stable SOC
304 proportion of the soil mixtures was predicted by running the PARTY<sub>SOCV2.0EU</sub> model, using
305 calculated Rock-Eval® parameters as predictors, obtained with the AP method. Third, we run
306 the PARTY<sub>SOCV2.0EU</sub> model using the calculated predictors (AP method) but replacing
307 temperature parameters with ones obtained with the RT method.

308
309

**4. Results**

4.1. A general agreement between calculated and measured Rock-Eval® parameters

311 Comparison of calculated and measured Rock-Eval® parameters showed that the AP method
312 was able to accurately predict the values of Rock-Eval® parameters for the soil mixtures
313 (overall median NRMSE obtained for the 29 parameters of 8.5%; Supplementary Table 2).
314 For classic Rock-Eval® parameters such as TOC there was a perfect correlation between
measurements and predictions ($R^2_{AP} = 1$), with a negligible bias ($BIAS_{AP} = -0.47 \text{ g C} \cdot \text{kg}^{-1}$ soil) and a very low percentage error ($NRMSE_{AP} = 1.1\%$; Fig. 2a). The calculated values of $OI_{RE6}$ were also very close to the measured ones ($NRMSE_{AP} = 5.6\%$, Fig. 2b). An overestimation was observed for HI, for two out of ten plots ($BIAS_{AP} = 17 \text{ mg HC} \cdot \text{g}^{-1} \text{ C}$; Fig. 2c). This effect increased with distance of the mixture composition from the “natural” samples and was the strongest for the 50:50 soil mixtures. However, the overall observed relationship between calculated and measured values was still very strong ($R^2_{AP} = 0.90$). The correlation between measured $T90_{HC\_PYR}$ and calculated with the AP method was equally strong ($R^2_{AP} = 0.91$) and the relationship was unbiased with a low percentage error ($BIAS_{AP} = 1.66^\circ\text{C}$, $NRMSE = 8.8\%$; Fig. 2d).

Overall a strong agreement was also observed between measured temperature parameters and calculated with the RT method (Supplementary Table 2). Nonetheless, the RT calculation method resulted in a less strong correlation and slightly biased relationship for $T90_{HC\_PYR}$ ($R^2_{RT} = 0.78$, $BIAS_{RT} = -3.6^\circ\text{C}$, $NRMSE = 14\%$; Fig. 2e). $T90_{HC\_PYR}$ was underestimated by the RT calculation method for the same two plots, for which the HI overestimation was observed and the same pattern, with the prediction bias increase towards the 50:50 mixtures was evident.

Finally, all three ways of calculating the expected stable SOC proportion of soil mixtures using the $PARTY_{SOCv2.0}_{EU}$ model performed well. Values of stable SOC proportion calculated as a weighted average of $PARTY_{SOCv2.0}_{EU}$ predictions obtained for layer A and layer B were relatively close to the actual stable SOC proportion predictions obtained using the measured Rock-Eval® parameters as predictors in the $PARTY_{SOCv2.0}_{EU}$ model ($R^2 = 0.85$, $BIAS = 0.03$, $NRMSE = 13\%$; Supplementary Table 2). The relationship between theoretical and observed stable SOC proportions improved when Rock-Eval® parameters calculated with the AP method or with the RT method were used as predictors in the
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PARTYSOCV2.0EU model ($R^2_{AP} = 0.94$, $BIAS_{AP} = -0.01$, $NRMSE_{AP} = 7\%$, $R^2_{RT} = 0.94$, $BIAS_{RT} = -0.02$, $NRMSE_{RT} = 9\%$). An overview of summary statistics of Rock-Eval® parameter values measured on "natural" samples is presented in Supplementary Table 3.

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## 4.2. Clay content difference between sublayers explains the poorer agreement between calculated and measured HC_PYR thermogram-derived parameters

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Our results suggested a strong agreement between calculated and measured values for all Rock-Eval® parameters of soil mixtures except those derived from the HC_PYR thermogram. Calculated values of S2, HI (obtained with the AP calculation approach) and temperature parameters of the HC_PYR thermogram (obtained with the RT calculation approach) were either positively or negatively biased, leading to a slight overestimation of S2 and HI, and an underestimation of HC_PYR temperature parameters respectively (Fig. 2c and e; Supplementary Fig. 2; Supplementary Table 2). The overestimation bias observed for S2 was magnified for HI, which can be explained by the mathematical definition of the latter parameter (HI = S2/TOC × 100). We investigated the relationship of the overestimation of S2 and HI with various soil characteristics of each plot presented in Table 1. The mean difference between measured and calculated S2 and HI values was averaged per plot and it was compared to the difference in various soil characteristics between layer A and layer B (Table 1). This comparison revealed a strong correlation between overestimation of S2 and HI and difference in clay content between soil layers (Spearman rho = 0.90 and $R^2 = 0.71$ for S2, and Spearman rho = 0.85 and $R^2 = 0.84$ for HI; Fig. 3a and b). The bias was the highest for the two plots of the Parroy site, where the clay content difference between layer A and B was the

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highest (clay content difference > 20 wt.%). Investigation of the relationship of this bias with other soil characteristics, such as soil pH, and TOC content did not explain any of the observed variation. The clay content difference between the two layers was also negatively correlated with the bias observed for T90<sub>HC_PYR</sub> (not shown here).

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369

## 5. Discussion

371

### 5.1. Recommendations for inferring Rock-Eval® parameters of soil mixtures

According to the type of parameter, two calculation methods are discussed for combining Rock-Eval® analysis results of different sublayers to obtain the Rock-Eval® signature of a soil layer. The first method based on acquisition parameters (AP method; see section 3.1.) is fast and easy to implement, and perfectly adequate, when classic Rock-Eval® parameters (such as PC, TOC, $OI_{RE6}$, MinC, etc.) or results of the $PARTY_{SOCv2.0EU}$ model are of interest.

Even though this method is simple and effective, attention must be paid when applying weighting on parameters representing ratios (e.g., HI, $OI_{RE6}$; Perdue & Koprivnjak, 2007) or more complex terms such as logarithms (I-index). One drawback of this method is related to its use to predict temperature parameters. Although empirically in this work the AP method performed well for the calculation of temperature parameters, from a purely mathematical point of view it cannot be recommended. The accuracy of this method for the calculation of temperature parameters specifically is very sensitive to mineral-induced changes on the Rock-Eval® signal. Temperature parameters do not represent surface areas (like S1, S2, etc.) but instead they mark a limit on the x-axis of a thermogram (time axis), defining the moment (translated into the corresponding temperature) when a specific proportion of a thermogram
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surface area was reached. Therefore, if an interaction causes a change in the shape of a thermogram, this will not be reflected in the AP based calculation method.

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A second approach is presented (Section 3.2.) for the calculation of temperature parameters, based on signal processing. According to this method, the expected Rock-Eval® thermograms of a soil layer can be calculated based on the thermograms obtained on its sublayers (RT method; Supplementary Fig. 2). Rock-Eval® temperature parameters representative of a soil layer can subsequently be calculated on the reconstructed thermograms. This method might be considered as more demanding in terms of manipulation but it is also more suitable for the calculation of temperature parameters. In soils where a mineral matrix effect might be expected and in cases where precise information on the hydrocarbon signal is important, the RT method is more appropriate. However, in cases where the mineral matrix effect is expected to be low, or if the hydrocarbon signal is not particularly of interest, this approach might be unnecessarily cumbersome since its performance is expected to be equally good as the AP method.

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For the variety of soil types and the range of sampling depths studied here, the most appropriate way to combine Rock-Eval® results of sublayers to obtain the stable SOC proportion of a soil layer, is to follow the AP method to calculate values of Rock-Eval® parameters to be used as predictors by the PARTY<sub>SOC</sub>v2.0<sub>EU</sub> model.

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Regardless of the chosen calculation method, one additional aspect to consider when adding information obtained on sublayers, is the content of fine fraction in each sublayer. This study focuses on linear mixing regarding the concentration of SOC and other parameters measured on a given soil mass. However, when averaging existing data, a correction will have to be undertaken to account for the soil mass contribution of each soil layer to the final sample.

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Thus, information on the fine fraction content, and the density difference between layers when calculating stocks of elements, will be required.

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**5.2. Results should be considered with caution when mixing samples with contrasted clay contents**

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Our initial hypothesis, that classic Rock-Eval® parameters will be independent of the sampling strategy for temperate forest soils was confirmed, with one exception. Introducing a clay rich soil layer to a coarser soil layer through the mixing process caused changes in the hydrocarbon signal (Supplementary Fig. 2), and especially on the S2, HI and T90<sub>HC_PYR</sub> parameters. This effect was most pronounced for the two plots from Parroy, where the difference in clay content varied by more than 20% between layer A and layer B. After their release in the pyrolysis oven, hydrocarbon gases might be protected through retention by clay minerals (Espitalié et al., 1980). The observed increase in T90<sub>HC_PYR</sub> is an indication of a bulk increase in hydrocarbons thermal stability that could be explained by retention of light hydrocarbons on mineral surfaces causing them to evaporate at a higher temperature (Rahman et al., 2017). The decrease in S2 and HI however would require a sink in the total fraction of carbon released as HC, with a shift of the lost amount of carbon to the CO or CO<sub>2</sub> signal, since TOC remains constant. However, due to the relatively low fraction of carbon released as HC compared to CO<sub>2</sub> (in average ten times less) and the very low S2 overestimation bias, the difference is not detectable in any of the other signals. Previous studies involving Rock-Eval® analysis of soils before and after removal of the mineral matrix through acid hydrolysis support the hypothesis that clay particles may influence the detection of pyrolysis effluents (Zegouagh et al., 2004; Czirbus et al., 2016). Both studies showed that hydrocarbon yield increased in the absence of minerals, causing up to an 18-times increase in S2 (Zegouagh et

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al., 2004). Although qualitatively interesting, quantitative estimation of the mineral effect is problematic when the acid hydrolysis method is applied. While efficient for elimination of minerals, the acid attack also causes some loss of organic matter (e.g., 17% in Zegouagh et al. (2004)). Studies have shown that the occurring SOM loss is preferential, influencing the bulk composition of SOM (Rumpel et al., 2006; Spaccini et al., 2013). Future experimental work should focus on quantifying the effect of different minerals on the Rock-Eval® signal of SOM, using simple model systems. To better understand the interactions between SOM and minerals it would be of interest to examine how different minerals and different degrees of interaction might influence the detection of SOM.

For temperate forest soils, we can consider the difference in clay content (20%) observed in this study, as a first empirical threshold value, up to which the mineral matrix effect is insignificant. As the application range of the Rock-Eval® method extends to new climates and new soil types, it is important to know that the linear mixing assumption holds true in temperate forest soils. However, different guidelines might be necessary in tropical soils where, as shown by previous studies conducted on kerogens, the effect of more reactive clay minerals and iron oxides during pyrolysis of organic matter is expected to be stronger (Huizinga et al., 1987; Ma et al., 2018).

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## 6. Conclusion

Our study shows that the Rock-Eval® parameters of a soil layer, including the centennialy stable SOC proportion predicted by the PARTY<sub>SOCV2.0EU</sub> model, can be obtained on Rock-Eval® results of its composing sublayers. This observation has significant practical implications regarding the comparison of available Rock-Eval® soil data from studies applying different sampling depths. According to the parameter type, one of the two methods
of calculating expected values for the Rock-Eval® parameters of composite samples can be
recommended: (1) as the weighed mean of acquired Rock-Eval® parameters for classic and
some extended parameters (i.e., S1, S2, S3, S3', S3CO, S3'CO, PC, TOC, MinC, HI, OI<sub>RE6</sub>,
Pseudo S1, S2/PC, PC/TOC, HI/OI<sub>RE6</sub>, I-index, R-index, TLCH-index, centennialy stable
SOC proportion), and (2) based on a signal reconstructed using Rock-Eval® thermograms
measured on their composing endmembers for temperature parameters (i.e., T70<sub>HC_PYr</sub>,
T90<sub>HC_PYr</sub>, T30<sub>CO2_PYr</sub>, T50<sub>CO2_PYr</sub>, T70<sub>CO2_PYr</sub>, T90<sub>CO2_PYr</sub>, T70<sub>CO_ox</sub>, T50<sub>CO2_ox</sub>,
T70<sub>CO2_ox</sub>, T90<sub>CO2_ox</sub>). In the context of the ongoing work towards harmonization of
databases it is important to keep in mind that in temperate soils, the linear mixing hypothesis
is valid. However, in soils with pronounced clay content heterogeneities between sublayers
(clay content difference > 20 wt.%) averaging HC_PYR-derived parameters over a soil
profile might lead to biases. Although the reconstructed thermogram method is more
demanding, it is more appropriate for the calculation of temperature parameters and it can
offer valuable insight on mineral-induced changes in the Rock-Eval® signal. This work can
be considered as an empirical guide, paving the way towards harmonized Rock-Eval®
databases for soil studies.

474

475 Acknowledgments

476 The authors would like to thank the French ANR (project StoreSoilC; ANR-17-CE32-0005;
477 PhD thesis of Eva Kanari), ADEME (Agence de la transition écologique; piCaSo project and
478 PhD thesis of Eva Kanari) and the French Ministère de la transition écologique et solidaire
479 (DEB; GNB-sol project) for the financial support during this work. We would also like to
480 thank Jean-Maxime Gonzalez, Sébastien De Danieli, Thomas Goïtré, Nicolas Eisner, Audrey
481 Bonnelye, Yoan Paillet, Charlène Heiniger and Isabelle Bilger for their help in sampling and
482 processing soils. We deeply thank Julien Barré for his help in mathematical analysis. Finally,
483 the authors thank the anonymous reviewers and the editor for their valuable time and input.

484

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<table><caption>Table 1: Information on the geographical location, soil type, soil texture and soil chemistry of the study plots. The reference coordinate system used here was WGS84 and texture analysis was done without previous decarbonisation of the samples. C org EA is the organic carbon content measured by Elemental Analysis.</caption><thead><tr><th>Plot ID</th><th>Sampling depth (cm)</th><th>Site</th><th>Latitude of the plot</th><th>Longitude of the plot</th><th>Soil type (WBR 2014)</th><th>Clay (wt.%)</th><th>Fine silt (wt.%)</th><th>Coarse silt (wt.%)</th><th>Total silt (wt.%)</th><th>Fine sand (wt.%)</th><th>Coarse sand (wt.%)</th><th>Total sand (wt.%)</th><th>pH (water)</th><th>CaCO<sub>3</sub> (wt.%)</th><th>C org EA (wt.%)</th></tr></thead><tbody><tr><td>ANO-2316</td><td>0-30</td><td rowspan="2">Anost</td><td rowspan="2">47.10216</td><td rowspan="2">4.06001</td><td rowspan="2">Dystric Cambisol</td><td>20.8</td><td>24.3</td><td>10.3</td><td>34.6</td><td>7.6</td><td>37.0</td><td>44.6</td><td>4.1</td><td>0</td><td>11.28</td></tr><tr><td>ANO-2316</td><td>30-50</td><td>9.8</td><td>28.1</td><td>12.0</td><td>40.1</td><td>8.2</td><td>42.0</td><td>50.2</td><td>4.49</td><td>0</td><td>5.23</td></tr><tr><td>CIT-463</td><td>0-30</td><td rowspan="2">Citeaux</td><td rowspan="2">47.07216</td><td rowspan="2">5.06185</td><td rowspan="2">Luvic Stagnosol</td><td>11.6</td><td>28.4</td><td>31.5</td><td>59.9</td><td>24.9</td><td>3.6</td><td>28.5</td><td>4.75</td><td>0</td><td>1.65</td></tr><tr><td>CIT-463</td><td>30-50</td><td>10.6</td><td>27.9</td><td>31.8</td><td>59.7</td><td>26.2</td><td>3.5</td><td>29.7</td><td>4.71</td><td>0</td><td>0.53</td></tr><tr><td>RNCL-1023</td><td>0-30</td><td rowspan="2">Combe Lavaux</td><td rowspan="2">47.21097</td><td rowspan="2">4.94095</td><td rowspan="2">Calcaric Cambisol (Colluvic)</td><td>44.7</td><td>35.3</td><td>16.5</td><td>51.8</td><td>2.6</td><td>0.9</td><td>3.5</td><td>6.6</td><td>0</td><td>3.42</td></tr><tr><td>RNCL-1023</td><td>30-50</td><td>33.9</td><td>26.8</td><td>14.4</td><td>41.2</td><td>11.4</td><td>13.5</td><td>24.9</td><td>8.19</td><td>35.2</td><td>0.38</td></tr><tr><td>ENG-RBI-294</td><td>0-30</td><td rowspan="2">Engins</td><td rowspan="2">45.23063</td><td rowspan="2">5.59497</td><td rowspan="2">Calcaric Cambisol</td><td>20.9</td><td>43.7</td><td>27.6</td><td>71.3</td><td>7.1</td><td>0.7</td><td>7.8</td><td>4.71</td><td>0</td><td>7.26</td></tr><tr><td>ENG-RBI-294</td><td>30-50</td><td>23.4</td><td>40.4</td><td>27.8</td><td>68.2</td><td>7.7</td><td>0.7</td><td>8.4</td><td>5.45</td><td>0</td><td>2.21</td></tr><tr><td>PAR-6316</td><td>0-30</td><td rowspan="2">Parroy</td><td rowspan="2">48.65225</td><td rowspan="2">6.61094</td><td rowspan="2">Vertic Cambisol</td><td>31.2</td><td>39.9</td><td>13.5</td><td>53.4</td><td>8.0</td><td>7.4</td><td>15.4</td><td>5.34</td><td>0</td><td>3.16</td></tr><tr><td>PAR-6316</td><td>30-50</td><td>55.1</td><td>25.1</td><td>7.8</td><td>32.9</td><td>5.2</td><td>6.7</td><td>11.9</td><td>6.6</td><td>0</td><td>0.86</td></tr><tr><td>PAR-RBI-301</td><td>0-30</td><td rowspan="2">Parroy</td><td rowspan="2">48.63205</td><td rowspan="2">6.65036</td><td rowspan="2">Vertic Cambisol</td><td>15.6</td><td>45.4</td><td>26.7</td><td>72.1</td><td>5.3</td><td>6.9</td><td>12.2</td><td>4.64</td><td>0</td><td>2.60</td></tr><tr><td>PAR-RBI-301</td><td>30-50</td><td>36.8</td><td>33.8</td><td>19.8</td><td>53.6</td><td>4.1</td><td>5.5</td><td>9.6</td><td>5.42</td><td>0</td><td>0.45</td></tr><tr><td>RMB-579</td><td>0-30</td><td rowspan="2">Rambouillet</td><td rowspan="2">48.66017</td><td rowspan="2">1.77172</td><td rowspan="2">Luvic Stagnosol</td><td>16.1</td><td>20.1</td><td>22.3</td><td>42.4</td><td>23.1</td><td>18.4</td><td>41.5</td><td>4.65</td><td>0</td><td>1.77</td></tr><tr><td>RMB-579</td><td>30-50</td><td>27.2</td><td>17.5</td><td>20.9</td><td>38.4</td><td>19.1</td><td>15.3</td><td>34.4</td><td>4.98</td><td>0</td><td>0.66</td></tr><tr><td>RMB-941</td><td>0-30</td><td rowspan="2">Rambouillet</td><td rowspan="2">48.67083</td><td rowspan="2">1.71289</td><td rowspan="2">Entic Podzol (Arenic)</td><td>2.3</td><td>5.8</td><td>8.0</td><td>13.8</td><td>55.9</td><td>28.0</td><td>83.9</td><td>4.23</td><td>0</td><td>1.66</td></tr><tr><td>RMB-941</td><td>30-50</td><td>3.3</td><td>4.7</td><td>7.3</td><td>12.0</td><td>54.2</td><td>30.6</td><td>84.8</td><td>4.73</td><td>0</td><td>0.45</td></tr><tr><td>SA_x1a</td><td>0-30</td><td rowspan="2">Saint-Amand</td><td rowspan="2">45.80000</td><td rowspan="2">1.77000</td><td rowspan="2">Dystric Cambisol</td><td>15.3</td><td>14.1</td><td>7.6</td><td>21.7</td><td>20.7</td><td>42.3</td><td>63.0</td><td>4.19</td><td>0</td><td>4.75</td></tr><tr><td>SA_x1a</td><td>30-50</td><td>11.8</td><td>11.1</td><td>6.2</td><td>17.3</td><td>21.7</td><td>49.2</td><td>70.9</td><td>4.54</td><td>0</td><td>1.18</td></tr><tr><td>VER-540</td><td>0-30</td><td rowspan="2">Verrières</td><td rowspan="2">48.75656</td><td rowspan="2">2.24006</td><td rowspan="2">Stagnic Luvisol</td><td>13.7</td><td>28.3</td><td>46.7</td><td>75.0</td><td>8.1</td><td>3.2</td><td>11.3</td><td>4.15</td><td>0</td><td>2.32</td></tr><tr><td>VER-540</td><td>30-50</td><td>18.2</td><td>26.3</td><td>44.9</td><td>71.2</td><td>8.0</td><td>2.6</td><td>10.6</td><td>4.27</td><td>0</td><td>0.60</td></tr></tbody></table>
<caption>Figure 1: Map of the 10 plots used in this study, located in eight forest sites in France.</caption>

623

<figure><img src="image_3.png" /></figure>

622

621
<figure><img src="image_4.png" /><figcaption>Figure 2a–d: Comparison of measured and calculated values for four Rock-Eval® parameters, presented in three simple plots and one twin plot. The measured values of Rock-Eval® parameters for TOC, $OI_{RE6}$, HI and $T90_{HC\_PYR}$ are plotted on the y-axes. On plots a, b and c and on the left side of the twin plot the x-axis represents values calculated on the acquisition parameters-based method (section 3.1.). On the right side of the twin plot the x-axis shows values obtained with the reconstructed thermograms method (section 3.2.).</figcaption></figure>

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<figure><img src="image_5.png" /></figure>

R² = 0.91

BIAS = 1.66

RMSE = 3.87

NRMSE = 8.79%

<figure><img src="image_6.png" /></figure>

R² = 0.78

BIAS = -3.65

RMSE = 6.21

NRMSE = 14.11%

Calculated T90<sub>CH_PYR</sub> (°C)

Plot

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>
Figure 3 a and b: Relationship between prediction bias in Rock-Eval® parameters (S2 and HI) and difference in clay content between soil layers (i.e., clay content of the surface layer – clay content of the subsurface layer) for each plot. Prediction error shown on the y-axis is calculated as the mean difference between calculated Rock-Eval® parameter values (obtained with the acquisition parameters-based method) and measured values per plot.

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

639

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Predicting Rock-Eval® characteristics of a soil layer from sublayers

<figure><img src="image_28.png" /></figure>

AB

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

Clays

<figure><img src="image_31.png" /></figure>