Changes in global soil carbon stocks have considerable potential to influence
the course of future climate change. However, a portion of soil organic
carbon (SOC) has a very long residence time (

Soils exert a key regulation on atmospheric greenhouse gas concentrations
on a decadal timescale through the net carbon source and sink status of their
organic carbon reservoir (Amundson, 2001; Eglin et al., 2010). However, a
portion of the soil organic carbon (SOC) reservoir may not contribute
significantly to the net exchange of

In the past decade, the thermal stability of organic carbon has been proposed as
a good surrogate for its biogeochemical stability in litter and soils (e.g.,
Rovira et al., 2008; Plante et al., 2009; Gregorich et al., 2015). Several
studies using thermal analysis techniques, such as thermogravimetry and
differential scanning calorimetry with ramped combustion, have shown that the
fast-cycling SOC pool determined as the amount

The objective of this work was to design a reliable, routine method based on a thermal analysis technique (Rock-Eval 6; RE6) to quantify centennially persistent SOC in a range of temperate soil types. First, we compiled a set of reference soil samples from four long-term agronomic experiments in northwestern Europe with long-term bare fallow treatments. The SOC concentration of LTBF treatments can be used to estimate the size of the persistent SOC pool of a particular site, as proposed by Rühlmann (1999) and Barré et al. (2010). Here, we refined estimates of the persistent SOC concentration previously published by Barré et al. (2010) for the four sites used in this study. We then used these values to estimate the proportion of centennially persistent SOC in 118 archived soil samples (time series) from LTBF and non-LTBF treatments of these four sites. The last step consisted of analyzing these reference samples using RE6 thermal analysis and building a multivariate regression model to relate RE6 information on SOC thermal stability and bulk chemistry to the estimated proportion of centennially persistent SOC. In this work, we aimed to deliver a model based on thermal analysis with reliable prediction intervals around the predicted values of the size of the centennially persistent SOC pool. We thus focused on the uncertainty in the estimated proportion of centennially persistent SOC and its propagation in the multivariate regression model.

The reference soil sample set was built using samples from four long-term
agronomic experimental sites in northwestern Europe (Versailles and Grignon in France,
Rothamsted in the United Kingdom and Ultuna in Sweden; Supplement,
Table S1). Each of the four sites includes an LTBF
treatment, with bare fallow duration ranging from 48 years at Grignon to
79 years at Versailles. For all experimental sites, we also included non-LTBF
treatments that have increased or maintained their total SOC concentrations
over time or sustained smaller losses than the LTBF treatment. The selected
non-LTBF treatments included manure amendments (Versailles), straw or
composted straw amendments (Grignon), continuous grassland (Rothamsted) and
continuous cropland (Ultuna). Soil samples from each site and treatment have
been regularly collected and archived since the initiation of the
experiments. A total of 118 topsoil samples (0–20 to 0–25 cm of depth;
Table S1) were selected from the archives of LTBF and non-LTBF treatments to
build the reference sample set. Samples were selected from two or three field
replicate plots with a decadal frequency from the initiation of the
experiments up to 2007 (Grignon), 2008 (Versailles, Rothamsted) or 2009
(Ultuna) to obtain a sample set with the widest possible range of proportions
of centennially persistent SOC. The non-LTBF treatments and multiple sites
also added to the diversity of land-use, climate and parent material. For
each sample, total SOC concentration was measured by dry combustion with an
elemental analyzer (SOC

Based on the decline in total SOC concentration over the duration of the LTBF treatment, Barré et al. (2010) estimated the concentration of centennially persistent SOC at each site using a Bayesian curve-fitting method applied to each LTBF field replicate plot. Here, we refined those site-specific estimates by (i) applying a similar Bayesian curve-fitting method to combined SOC concentration data from all LTBF field replicate plots of each site (four field replicate plots for Ultuna and Rothamsted, six field replicate plots for Versailles and Grignon) and (ii) using new SOC concentration data up to 2014 for Rothamsted and 2015 for Ultuna, increasing their LTBF duration to 55 years for Rothamsted and 59 years for Ultuna.

For each site, we assumed that the temporal evolution of LTBF SOC
concentration,

The proportion of centennially persistent SOC (CP

Detail of the sequential pyrolysis and oxidation stages of Rock-Eval 6 (RE6) thermal analysis and of the five thermograms used to derive the 30 RE6 parameters reflecting SOC thermal stability and bulk chemistry. The grey area under each RE6 thermogram represents the portion of the signal unaffected by soil carbonates that was used to calculate RE6 temperature parameters (modified after Behar et al., 2001; Saenger et al., 2013).

The 118 soil samples from the reference set were analyzed with an RE6 Turbo
device (Vinci Technologies) using the basic setup for the analysis of soil
organic matter (Behar et al., 2001; Disnar et al., 2003). The RE6 technique
provided measurements from the sequential pyrolysis and oxidation of ca.
40 mg of finely ground (

For each RE6 thermogram, we determined the temperatures corresponding to each
incremental proportion of the amount of gases evolved during the pyrolysis
and oxidation stages. Upper temperatures of 850

For the HC pyrolysis thermogram we also determined three parameters
reflecting a proportion of thermally resistant or labile hydrocarbons: a
parameter representing the proportion of hydrocarbons evolved between 200 and
450

Overall, we thus calculated for each soil sample a series of 30 RE6 parameters reflecting SOC thermal stability and bulk chemistry to be used in subsequent statistical and modeling analyses.

The signal integration of the RE6 thermograms and the calculation of the RE6 temperature parameters were performed with R v.3.4.3 (R Core Team, 2017) and the hyperSpec (Beleites and Sergo, 2014), pracma (Borchers, 2015) and stringr (Wickham, 2015) packages.

At each site, the CP

We chose uniform PDFs for the model parameters

Based on our assessment of the uncertainties in SOC concentration data and
site-specific CP

The reference sample set was randomly split into a calibration set
(

A multivariate regression model was built to relate the CP

The performance of the random forests regression model for predicting
CP

Additionally, the sensitivity of the RF regression model to pedoclimate was
assessed by examining its predictive performance for a calibration set based
on soils from three sites (Versailles, Grignon, Rothamsted,

Since our objective was to deliver a model based on thermal analysis with
reliable prediction intervals around the predicted values of the
CP

Briefly, we sampled with replacement (i.e., bootstrapped) the calibration set
(

Measured total SOC concentrations, estimated site-specific
CP

The Bayesian inference method was performed with Python 2.7 and the PyMC library (Patil et al., 2010). All other statistical analyses were performed with R v.3.4.3 (R Core Team, 2017) and the factoextra package for running PCA (Kassambara, 2015), the randomForest package for running the random forests regression models (Liaw and Wiener, 2002) and the boot package for bootstrapping (Davison and Hinkley, 1997; Canty and Ripley, 2015).

The Bayesian inference of the parameter

Evolution of SOC concentration (g C kg

Overall, the wide range in total SOC concentrations within and across sites
(from 5 to 46 g C kg

Spearman's rank correlation coefficient test between the 30 RE6
parameters and the CP

The random splitting of the reference sample set generated calibration and
validation sample sets with similar mean values, range of values and standard
deviations for both total SOC concentration and CP

The 30 RE6 parameters showed very different and even contrasting correlations
with the CP

Conversely, five RE6 temperature parameters showed significant negative
correlations with the CP

Principal component analysis (PCA) of the 30 RE6 parameters of the
calibration sample set with soils from all sites (

The PCA of the centered and scaled RE6 parameters illustrates the
correlations among those 30 variables in the calibration set with soils from
all sites (Fig. 3). A continuum of CP

The random splitting of the reference sample set generated calibration and
validation sample sets with similar RE6 thermal characteristics as
illustrated by their similar distribution on the factorial map of the first
two principal components of the PCA (Fig. 3a). Soils from the site of Grignon
(with carbonates) showed RE6 thermal characteristics different from the other
sites (Fig. 3a). Some soils from the sites of Rothamsted and Versailles with
high CP

The random forests regression model performed very well in predicting the
CP

Performance of the random forests regression model based on
Rock-Eval 6 thermal analysis (RE6-RF) for predicting the CP

Propagating the estimated uncertainties in the values of CP

Performance of the random forests regression model based on
Rock-Eval 6 thermal analysis (RE6-RF) for predicting the CP

Out of the 30 RE6 parameters tested by the random forests model as possible
predictor variables of the CP

Adding new SOC concentration data for Rothamsted (up to 2014) and Ultuna (up
to 2015) and combining SOC concentration data from all LTBF field replicate
plots of each site decreased the uncertainty in the site-specific estimates
of the CP

Our results obtained under four contrasting pedoclimates of northwestern
Europe indicate a minimum value of 5 g C kg

Among the wide range of CP

Overall, those combined results illustrate the wide range of
CP

This work reinforces the evidence that there is a link between SOC
persistence in ecosystems and its thermal stability, providing evidence of
the first quantitative link between thermal and in situ long-term
(

Our results also highlight the sensitivity of the RE6-RF regression model to
pedoclimate. Decreased predictive performance of the model (as assessed by
the coefficient of determination) was indeed observed when predicting the
CP

Our results also illustrate the complex relationships between thermal-analysis-based parameters of SOC stability and the CP

Despite the fact that the TLHC index, the

The two RE6 parameters reflecting SOC bulk chemistry showed highly
significant correlations with the CP

Future developments of this work must extend the Rock-Eval 6 thermal analysis
regression model to a wider range of pedoclimates and to other biomes. As
sites with LTBF treatments are not widespread, complementing the reference
sample set may be achieved by using soils that have different soil forming
factors (e.g., climate, parent material) and (i) which are sampled from
long-term (

Another development of this work will involve elucidating the fundamental
mechanisms linking the biogeochemical stability of SOC with its thermal
stability (e.g., Leifeld and von Lützow, 2014). This was beyond the scope
of this work, yet it constitutes an exciting field of research that should be
addressed in the future, as highlighted by the unexpected observations
discussed in Sect. 4.2 and by other recent works that found no relationships
between the thermal oxidation of SOC between 200 and 400

Overall, this work demonstrates the value of Rock-Eval 6 as a routine method
for quantifying the size of the centennially persistent SOC pool with known
uncertainty in temperate soils. The relatively low cost of the Rock-Eval 6
technique and the robustness of the thermal analysis regression model make
it possible to apply it to soil monitoring networks across a continuum of
scales as a reliable proxy for SOC persistence. This may be part of the
framework proposed by O'Rourke et al. (2015) to better understand SOC
processes at the biosphere to biome scale and should be added to the soil
carbon cycling proxies recently listed by Bailey et al. (2018). Mapping
persistent SOC at large scales may allow for the identification of regional
hotspots of centennially persistent SOC that may contribute little to climate
change by 2100. It may also provide information on the sustainability of
additional SOC storage from soil carbon sequestration strategies such as
those promoted by the international 4 per 1000 initiative in agriculture and
forestry (

Data can be accessed upon request to Lauric Cécillon and Pierre Barré.

The supplement related to this article is available online at:

LC and PB designed the study. PB and CC collected the archived soils. TK, SH, FvO and AM provided the archived soils and associated metadata. FB and FS performed the RE6 thermal analyses. RJ wrote the Python code. LC wrote the R codes and performed all statistical analysis. All authors contributed to the interpretation of the results. LC prepared the paper with contributions from all coauthors.

The authors declare that they have no conflict of interest.

This work was funded by ADEME and EC2CO (CARACAS project). Pierre Barré, Lauric Cécillon, Laure Soucémarianadin and Suzanne Lutfalla thank the Mairie de Paris (Emergences Programme) for financial support. We thank Thomas Eglin (ADEME), Nicolas Bouton and Jean Espitalié (Vinci Technologies), David Sebag (Normandie Univ., University of Lausanne), the associate editor and two anonymous reviewers for their valuable suggestions on this work. We thank INRA and AgroParisTech for access to and maintenance of the Versailles 42 plots and the Grignon 36 plots with their long-term experiments and sample archives. We thank Rothamsted Research and the Lawes Agricultural Trust for access to archived samples and the BBSRC for support under the Institute National Capabilities program grant (BBS/E/C/000J0300). We gratefully acknowledge the Faculty of Natural Resources and Agricultural Sciences of the Swedish University of Agricultural Sciences (SLU) for providing funds for the maintenance of the Ultuna long-term field experiment and for its sample archive. Edited by: Marcel van der Meer Reviewed by: two anonymous referees