Partitioning soil organic carbon into its centennially stable and active fractions with statistical machine-learning models based on Rock-Eval® thermal analysis (PARTY SOC v2.0 and PARTY SOC v2.0 EU )

Partitioning soil organic carbon (SOC) into two kinetically different fractions that are centennially stable or active on a 30 century scale is key information for an improved monitoring of soil health and for a more accurate modelsling of the carbon cycle. However, all existing SOC fractionation methods isolate SOC fractions that are mixtures of centennially stable and active SOC. If the stable SOC fraction cannot be isolated, it has specific chemical and thermal characteristics that are quickly ( ca . 1 h per sample) measureable using Rock-Eval® thermal analysis. An alternative would thus be to (1) train a machine-learning model on the Rock-Eval® thermal analysis data of soil samples from long-term experiments where the size of the 35 centennially stable and active SOC fractions can be estimated, and (2) apply this model on the Rock-Eval® data of unknown soils, to partition SOC into its centennially stable and active fractions. Here, we significantly extend the validity range of the a previously published machine-learning model published by Cécillon et al. [Biogeosciences, 15, 2835–2849, 2018, https://doi.org/10.5194/bg-15-2835-2018], and that is built upon this strategy. The second version of this statistical model, which we propose to name PARTY SOC , uses six European long-term agricultural sites including a bare fallow treatment and 40 one South American vegetation change (C 4 to C 3 plants) site as reference sites. The European version of the model (PARTY SOC v2.0 EU ) predicts the proportion of the centennially stable SOC fraction with a conservative root-mean-square error of 0.15 (relative root-mean-square error of 0.27) at six independent validation sites. More specifically, our results show that PARTY SOC v2.0 EU reliably partitions SOC kinetic fractions at its Northwestern European validation sites on Cambisols and Luvisols, which are the two dominant soil groups in this regionin a wide range of agricultural topsoils from 45 Northwestern Europe. We plan future expansions developments of the PARTY SOC global model using additional reference soils developed under diverse pedoclimates and ecosystems to further expand its domain of application while reducing its prediction error., and we already recommend the application of PARTY SOC


Introduction
Soil organic carbon (SOC) is identified as a key element contributing to soil functions such as primary productivity, water purification and regulation, carbon sequestration and climate regulation, habitat for biodiversity and recycling of nutrients (Keesstra et al., 2016;Koch et al., 2013;Schulte et al., 2014;Wiesmeier et al., 2019) .While the magnitude and the historical dimension of the decrease in SOC at the global level are progressively being unveiled (IPBES, 2018;Sanderman et al., 2017;Stoorvogel et al., 2017), SOC stocks' preservation and even increase is a major challenge for human societies in the 21 st century (Amundson et al., 2015).With widespread beneficial effects on soil functioning at the local level (Pellerin et al., 2019), increasing the size of the global SOC reservoir contributes directly to the Sustainable Development Goal related to life on land (https://www.globalgoals.org/15-life-on-land).It is also one of the few land management-based intervention options that has a broad and positive impact on food security and climate change mitigation and adaptation, two other Sustainable Development Goals set by the United Nations (IPCC, 2019;Lal, 2004).
There is experimental evidence showing that in all soils, SOC is made of carbon atoms with highly contrasting residence times, ranging from hours to millennia (Balesdent et al., 1987;Trumbore et al., 1989).This continuum in SOC persistence is often simplified by considering SOC as a mixture formed of several fractions, also called kinetic pools by modelers (Hénin and Dupuis, 1945;Jenkinson, 1990;Nikiforoff, 1936).The most drastic conceptual simplification of SOC persistence considers only two pools: (1) one made of young SOC with a short turnover rate (typically three decades on average; the active or labile SOC pool) and (2) one made of older SOC that persists much longer in the soil (more than a century; the stable, passive or persistent SOC pool).This dualistic representation of SOC persistence was considered as "a necessary simplification, but certainly not a utopian one" four decades ago (Balesdent and Guillet, 1982) and is still considered as meaningful (e.g., Lavallee et al., 2020).The active and stable soil organic matter pools contribute differently to the various soil functions (Hsieh, 1992).The active organic matter pool efficiently fuels soil biological activity (with carbon, nutrients and energy) and plant growth (with nutrients) through its rapid decay, and it sustains soil structure development (Abiven et al., 2009;Janzen, 2006).Conversely, the potential contribution of a soil to climate regulation would be most dependent on its stable organic matter pool size (He et al., 2016;Shi et al., 2020).
A myriad of methods has been developed and tested to partition SOC into active and stable fractions, that would match kinetic pools for the assessment of SOC dynamics and related soil functions, since the second half of the 20 th century (Balesdent, 1996;Hénin and Turc, 1949;Monnier et al., 1962;Poeplau et al., 2018) .Some of these methods based on chemical or physical (size, density or thermal) fractionation schemes can separate SOC fractions with, on average, different turnover rates (Balesdent, 1996;Plante et al., 2013;Poeplau et al., 2018;Trumbore et al., 1989).Of these methods, only a few are reasonably reproducible and easy to implement such as the ones based on rapid thermal analysis and chemical extractions (Gregorich et al., 2015;Poeplau et al., 2013Poeplau et al., , 2018;;Soucémarianadin et al., 2018a) .Other methods, such as size and density SOC fractionation, need to be inferred from statistical machine-learning models or infrared spectroscopy to be implemented on large soil sample sets (Baldock et al., 2013;Cotrufo et al., 2019;Jaconi et al., 2019;Viscarra Rossel et al., 2019;Viscarra Rossel and Hicks, 2015;Vos et al., 2018;Zimmermann et al., 2007b) .However, all SOC fractionation methods fail to achieve a proper separation of stable from active SOC, and the isolated SOC fractions are thus mixtures of centennially stable and active SOC (Fig. 1; Balesdent, 1996;Hsieh, 1992;von Lützow et al., 2007;Sanderman and Grandy, 2020).This limitation is common to all existing SOC fractionation methods and compromises the results of any work using them directly to quantify soil functions specifically related to SOC fractions or to parameterize SOC partitioning in multicompartmental models of SOC dynamics (Luo et al., 2016).Simulations of SOC stocks changes by multi-compartmental models are very sensitive to the initial proportion of the centennially stable SOC fraction, underlining the importance of its accurate estimation (Clivot et al., 2019;Falloon and Smith, 2000;Jenkinson et al., 1991;Taghizadeh -Toosi et al., 2020).quantify the size of the centennially stable and active soil organic carbon fractions.All existing soil organic carbon fractionation methods isolate fractions that are mixtures of centennially stable and active soil organic carbon.PARTY SOC is a machine-learning model trained on the Rock-Eval® thermal analysis data of soil samples from long-term experiments where the size of the centennially stable SOC fraction can be estimated.When applied on the Rock-Eval® data of unknown topsoils, PARTY SOC partitions soil organic carbon into its active and stable fractions (i.e., without isolating soil organic carbon fractions from each other).Abbreviation: SOC, soil organic carbon.
If the stable SOC fraction cannot be isolated, it has specific chemical and thermal characteristics: stable SOC is depleted in hydrogen and thermally stable (Barré et al., 2016;Gregorich et al., 2015).These characteristics are measurable quickly (ca. 1 h per sample) and at a reasonable cost (less than 60 USD per sample in private laboratories) measureable using Rock-Eval® thermal analysis, and they could be of use to identify the quantitative contribution of stable SOC to total SOC.An alternative to the elusive proper separation of stable and active SOC pools could thus be to directly predict their sizes by training a machine-learning model based on Rock-Eval® data to estimate the size of the stable and active SOC fractions, without isolating them from each other (Fig. 1).This statistical model would need a learning training set of soil samples for which SOC partitioning into its active and stable pools can be fairly estimated.Such soil samples are available in long-term (i.e., at least longer than three decades) bare fallow experiments (LTBF; soils kept free of vegetation and thus with negligible SOC inputs), or long-term vegetation change (C 3 plants to C 4 plants or vice versa) experiments, as described by Balesdent et al. (1987Balesdent et al. ( , 2018)), Barré et al. (2010), Cerri et al. (1985) or Rühlmann (1999).Cécillon et al. (2018) used this strategy, developing a machine-learning random forests regression model on topsoil samples obtained from the archives of four European long-term agricultural sites including an LTBF treatment.This statistical model, which we propose to name PARTY SOC , related thermal analysis parameters of topsoils measured with Rock-Eval® to their estimated proportion of the centennially stable SOC fraction (Fig. 1).This previous work positioned PARTY SOC as the first operational method quantifying the centennially stable and active SOC fractions in agricultural topsoils from Northwestern Europe.However, the ability of this machine-learning model to fairly partition the centennially stable and the active SOC fractions of soil samples from new sites in and outside Northwestern Europe is largely unknown because its learning sampletraining set is (1) rather limited, with a low number of reference sites and (2) based on centennially stable SOC contents that are exclusively inferred from plant-free LTBF treatments.In this study, we aimed to improve the accuracy and the genericity of the PARTY SOC statistical machine-learning model partitioning SOC into its centennially stable and active fractions developed by Cécillon et al. (2018).(1) We increased the range of soil typesgroups, soil texture classes, climates and types of long-term experiments, through the addition to the learning sampletraining set of topsoils from three new reference sites (two additional European long-term agricultural sites with an LTBF treatment and one South-American long-term vegetation change site).( 2) We integrated new predictor variables derived from Rock-Eval® thermal analysis.(3) In this second version of the model, we also changed the following series of technical details.We added a new criterion based on observed SOC content to estimate of the size of the centennially stable SOC fraction at reference sites, to reduce the risk of overestimating this site-specific parameter.We calculated the proportion of the centennially stable SOC fraction differently in reference topsoil samples, using SOC content estimated by Rock-Eval® rather than by dry combustion.We changed some criteria regarding the selection of reference topsoils in the learning training set of the model: we removed samples from agronomical treatments with compost or manure amendments, and preference was given to samples with good organic carbon yield of their Rock-Eval® thermal analysis.We better balanced the contribution of each reference site to PARTY SOC v2.0.(4) We also aimed to build a regional version of the statistical model restricted to the references sites available in Europe (named PARTY SOC v2.0 EU ). ( 5) Finally, we carefully evaluated the performance of the statistical models on unknown reference sitessoils, and we further investigated the sensitivity of model performance to the reference sites included in the learning training and test sets.For clarity, the main changes between the first version of PARTY SOC (Cécillon et al., 2018) and this second version of the model are summarized in supplementary Table S1.

Reference sites and estimation of the centennially stable SOC fraction content at each site
This second version of PARTY SOC uses seven long-term study sites as reference sites (i.e., sites where the size of the centennially stable SOC fraction can be estimated).The main characteristics of these seven reference sites and their respective soil type group and basic topsoil properties are presented in supplementary Table S2, and more thoroughly in the references cited below.Six reference sites of PARTY SOC v2.0 are long-term agricultural experiments located in Northwestern Europe that include at least one LTBF treatment.(1) The long-term experiment on animal manure and mineral fertilizers (B3-and B4-fields) and its adjacent LTBF experiment started in 1956 and terminated in 1985, at the Lermarken site of Askov in Denmark (Christensen et al., 2019;Christensen and Johnston, 1997).( 2) The static fertilization experiment (V120) started in 1902 and the fallow experiment (V505a) started in 1988 at Bad Lauchstädt in Germany (Franko and Merbach, 2017;Körschens et al., 1998;Ludwig et al., 2007).(3) The "36 parcelles" experiment, started in 1959 at Grignon in France (Cardinael et al., 2015;Houot et al., 1989).(4) The "42 parcelles" experiment, started in 1928 at Versailles in France (van Oort et al., 2018).( 5) The Highfield bare fallow experiment, started in 1959 at Rothamsted in England (Johnston et al., 2009).( 6) The Ultuna continuous soil organic matter field experiment, started in 1956 in Sweden (Kätterer et al., 2011).
These six reference sites are used in the European version of the statistical machine-learning model, PARTY SOC v2.0 EU .One additional long-term vegetation change site completes the reference sites list of the PARTY SOC v2.0 global statistical model.This site is a 56-year chronosequence of oil palm plantations (with C 3 plants) established on former pastures (with C 4 plants), located in South-America (La Cabaña in Colombia), and sampled as a space-for-time substitution (Quezada et al., 2019).
For each reference site, data on total SOC content in topsoil (0-10 cm to 0-30 cm depending on the site; supplementary Table S2) were obtained from previously published studies (Barré et al., 2010;Cécillon et al., 2018;Franko and Merbach, 2017;Körschens et al., 1998;Quezada et al., 2019).Total SOC content was measured by dry combustion with an elemental analyzer (SOC EA , g C kg −1 ) according to ISO 10694 (1995), after the removal of soil carbonates using an HCl treatment for the topsoils of Grignon.For the site of La Cabaña, data on 13 C content (measured using an isotope-ratio mass spectrometer coupled to the elemental analyzer, the results being expressed in δ 13 C abundance ratio (‰ relative to the international standard)) were obtained from Quezada et al. (2019), and the relative contributions of new (C 3 -plant derived) and old (C 4plant derived) carbon to total SOC in topsoils (0-10 cm) were calculated using the Equation 3 of the paper published by Balesdent and Mariotti (1996), as done in Quezada et al. (2019).
Based on these published data, the content of the centennially stable SOC fraction (g C kg -1 ) at each reference site was estimated by modelling the decline of total SOC present at the onset of the experiment with time (sites with an LTBF treatment; as SOC inputs are negligible in bare fallow systems) or by modelling the decline of C 4 -plant derived SOC present at the time of vegetation change with time (La Cabaña site; as SOC inputs from C 4 plants are negligible after pasture conversion to oil palm plantation).For the seven reference sites, the decline in total SOC or C 4 -plant derived SOC over time had a similar shape, as shown in Barré et al. (2010), Cécillon et al. (2018), Franko and Merbach (2017) and Quezada et al. (2019) and could be modelled using a first-order exponential decay with a constant term following Eq.(1): where γ(t) (g C kg −1 ) is the total (sites with an LTBF treatment) or C 4 -plant derived (La Cabaña site) SOC content at time t, t (year) is the time under bare fallow (sites with an LTBF treatment) or since pasture conversion to oil palm plantation (La Cabaña site), and a, b and c are fitting parameters.Parameter a (g C kg −1 ) corresponds to the content of the active SOC fraction and b (yr −1 ) is the characteristic decay rate.The parameter c (g C kg −1 ) represents the content of theoretically inert SOC.Following Barré et al. (2010), Cécillon et al. (2018) and Franko and Merbach (2017), we considered this parameter c as a site-specific metric of the centennially stable SOC fraction content.As already stated in Cécillon et al. (2018), in our view, the centennially stable SOC fraction is not biogeochemically inert; its mean age and mean residence time in soil are both assumed to be high (centuries), though not precisely defined here.As a result, its decline with time is negligible at the timescale of the long-term agricultural experiments or the long-term vegetation change site.We thus considered the centennially stable SOC fraction content at each experimental site to be constant.In this study, we used the centennially stable SOC fraction content already estimated by Franko and Merbach (2017) for the site of Bad Lauchstädt (on the LTBF experiment started in 1988), and by Cécillon et al. (2018) for the sites of Versailles, Grignon, Rothamsted and Ultuna.We estimated the content of the centennially stable SOC fraction for Askov and La Cabaña sites using the same Bayesian curvefitting method described by Cécillon et al. (2018).The Bayesian inference method was performed using Python 2.7 and the PyMC library (Patil et al., 2010).
For the second version of PARTY SOC , we aimed at reducing the potential bias towards an overestimation of the centennially stable SOC fraction content at reference sites using the Eq.(1) (supplementary Table S1).This overestimation is possible at reference sites with an LTBF treatment, as SOC inputs to bare fallow topsoils are low but not null (e.g., Jenkinson and Coleman, 1994;Petersen et al., 2005).Similarly, C 4 -plant derived SOC inputs are possible after conversion to C 3 plants at the site of La Cabaña.We thus used the lowest observed total (sites with an LTBF treatment) or C 4 -plant derived (La Cabaña site) topsoil SOC content value as the best estimate of the centennially stable SOC fraction content in reference sites where this measured value was lower than the fitted value of the site-specific parameter c of Eq. (1).

Rock-Eval® thermal analysis of topsoil samples available from reference sites
Surface soil samples (0-10 cm to 0-30 cm depending on the site; see supplementary Table S2) were obtained from the seven reference sites described in Sect.2.1.As described in Cécillon et al. (2018), the first version of the PARTY SOC statistical model was based on a set of 118 topsoil samples corresponding to time series obtained from the soil archives of the sites of Rothamsted (12 samples from the LTBF treatment and eight samples from the adjacent long-term grassland treatment), Ultuna (23 samples from the LTBF treatment and 11 samples from the associated long-term cropland treatments), Grignon (12 samples from the LTBF treatment, six samples from the LTBF plus straw amendment treatment and six samples from the LTBF plus composted straw amendment treatment) and Versailles (20 samples from the LTBF treatment and 20 samples from the LTBF plus manure amendment treatment).All 118 topsoil samples were previously analyszed using Rock-Eval® thermal analysis (Cécillon et al., 2018).
For the second version of the statistical machine-learning model, 78 additional topsoil samples were provided by managers of the three new reference sites.Thirty-five topsoil samples were obtained from the soil archives of the Askov site (19 samples corresponding to different dates of the LTBF treatment and 16 samples corresponding to different dates of the associated long-term cropland treatments).Twenty-seven topsoil samples were obtained from the soil archives of the Bad Lauchstädt site (eight samples from two dates of the mechanical LTBF treatment, eight samples from two dates of the chemical LTBF treatment and eleven samples from two dates of several long-term cropland treatments of the static fertilization experiment, eight out of the latter coming from treatments with manure applications).Sixteen topsoil samples were obtained from the site of La Cabaña (13 samples from different C 3 -plant oil palm fields planted at different dates and three samples from different long-term C 4 -plant pastures).
The 78 additional topsoil samples from Askov, Bad Lauchstädt and La Cabaña were analyszed using the same Rock-Eval® 6 Turbo device (Vinci Technologies, France; see Behar et al., 2001 for a description of the apparatus) and the same setup as the one used for the sample set of the first version of the PARTY SOC statistical model, described by Cécillon et al. (2018).
Briefly, ca.60 mg of ground (< 250 µm) topsoil samples were subjected to sequential pyrolysis and oxidation phases.The Rock-Eval® pyrolysis phase was carried out in an N 2 atmosphere (3 min isotherm at 200 °C followed by a temperature ramp from 200 to 650 °C at a heating rate of 30 °C min -1 ).The Rock-Eval® oxidation phase was carried out in laboratory air atmosphere (1 min isotherm at 300 °C followed by a temperature ramp from 300 to 850 °C at a heating rate of 20 °C min -1 and a final 5 min isotherm at 850 °C).Each Rock-Eval® analysis generated five thermograms corresponding to the volatile hydrocarbon effluents (HC_PYR thermogram), CO (CO_PYR thermogram) and CO 2 (CO2_PYR thermogram) measured at each second during the pyrolysis phase, and to the CO (CO_OX thermogram) and CO 2 (CO2_OX thermogram) measured at each second during the oxidation phase (Behar et al., 2001).
A series of Rock-Eval® parameters were calculated from these five thermograms.For each thermogram, five temperature parameters (all in °C) were retained: T10, T30, T50, T70 and T90, which respectively represent the temperatures corresponding to the evolution of 10, 30, 50, 70 and 90% of the total amount of evolved gas.The calculation of Rock-Eval® temperature parameters was performed using different intervals of integration depending on the thermogram.The integration omitted the first 200 seconds of the analysis for the three thermograms of the pyrolysis phase.The integration ended at the time of analysis corresponding to the maximum oven temperatures of 650 °C (HC_PYR thermogram), 560 °C (CO_PYR and CO2_PYR thermograms), 850 °C (CO_OX thermogram) and 611 °C (CO2_OX thermogram).These intervals of integration prevented any interference by inorganic carbon from most soil carbonates, and they ensured comparability with previous studies (Barré et al., 2016;Cécillon et al., 2018;Poeplau et al., 2019;Soucémarianadin et al., 2 018b).Automatic baseline correction (as calculated by the software of the Rock-Eval® apparatus; Vinci Technologies, France) was performed for all thermograms but the CO_PYR and the CO2_PYR thermograms.This correction can yield some negative values for the CO_PYR and CO2_PYR thermograms of soil samples with very low SOC content (data not shown).For the HC_PYR 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 °C (thermo-labile hydrocarbons, TLHC-index, unitless; modified from Saenger et al. (2013Saenger et al. ( , 2015) ) as described by Cécillon et al. (2018); a parameter representing the preservation of thermally labile hydrocarbons (I-index, unitless, after Sebag et al., 2016); and a parameter representing the proportion of hydrocarbons thermally stable at 400 °C (R-index, unitless, after Sebag et al., 2016).We also considered the hydrogen index (HI, mg HC g -1 C) and oxygen index (OI RE6 , mg O 2 g -1 C) that respectively describe the relative elemental hydrogen and oxygen enrichment of soil organic matter (see e.g., Barré et al., 2016).These 30 Rock-Eval® parameters are not directly related to total SOC content and were all included in the first version of the PARTY SOC model developed by Cécillon et al. (2018).
In this second version of PARTY SOC , we considered ten additional Rock-Eval® parameters as possible predictors, some of these being directly linked to SOC content (supplementary Table S1).These ten parameters were calculated for all the 196 topsoil samples available from the seven reference sites.They included: the content of SOC as determined by Rock-Eval® (TOC RE6 , g C kg -1 ); the content of soil inorganic carbon as determined by Rock-Eval® (MinC, g C kg -1 ); the content of SOC evolved as HC, CO or CO 2 during the pyrolysis phase of Rock-Eval® (PC, g C kg -1 ); the content of SOC evolved as HC during the temperature ramp (200-650 °C) of the pyrolysis phase of Rock-Eval® (S2, g C kg -1 ); the content of SOC that evolved as HC, CO or CO 2 during the first 200 seconds of the pyrolysis phase (at ca.200 °C) of Rock-Eval® (PseudoS1, g C kg -1 , after Khedim et al., 2020); the ratio of PseudoS1 to PC (PseudoS1/PC, unitless); the ratio of PseudoS1 to TOC RE6 (PseudoS1/TOC RE6 , unitless); the ratio of S2 to PC (S2/PC, unitless, after Poeplau et al., 2019); the ratio of PC to TOC RE6 (PC/TOC RE6 , unitless); and the ratio of HI to OI RE6 (HI/OI RE6 , mg HC mg -1 O 2 ).TOC RE6 , MinC, PC, HI and OI RE6 were obtained as default parameters from the software of the Rock-Eval® apparatus (Vinci Technologies, France).All other Rock-Eval® parameters were calculated from the integration of the five thermograms using R version 4.0.0 (R Core Team, 2020; RStudio Team, 2020) and functions from the R packages hyperSpec (Beleites and Sergo, 2020), pracma (Borchers, 2019) and stringr (Wickham, 2019).

Determination of the centennially stable SOC fraction proportion in topsoil samples from the reference sites
Following the first version of PARTY SOC (Cécillon et al., 2018), the proportion of the centennially stable SOC fraction in a topsoil sample of a reference site was calculated as the ratio of the site-specific centennially stable SOC fraction content (see Sect. 2.1) to the SOC content of this particular sample.We thus assume that the centennially stable SOC fraction content in topsoils is the same in the various agronomical treatments of a reference site and that it remains constant within the timeperiod studied at each site.
While for the first version of PARTY SOC , the proportion of the centennially stable SOC fraction in reference topsoils was calculated inferred usingwith SOC contents determined by elemental analysis (SOC EA ), in this second version, we preferred the SOC content determined by Rock-Eval® (supplementary Table S1).The reason behind this choice was to link the Rock-Eval® parameters measured on a reference topsoil sample to an inferredcalculated proportion of the centennially stable SOC fraction that better reflected the organic carbon that actually evolved during its Rock-Eval® analysis.This choice was possible for reference topsoil samples for which Rock-Eval® analyses showed a good organic carbon yield (TOC RE6 divided by SOC EA , and multiplied by 100).This is generally the case for most soils, with typical organic carbon yields of Rock-Eval® ranging from 90 to 100% of SOC EA (Disnar et al., 2003).For the topsoils of the sites of Grignon, Rothamsted, Ultuna and Versailles used in the first version of PARTY SOC , the organic carbon yield of Rock-Eval® was greater than 96% (linear regression model, R² = 0.97, n = 118; Cécillon et al., 2018).Similarly, Rock-Eval® analyses of topsoil samples from the site of La Cabaña showed very good organic carbon yields (95% on average, linear regression model R² = 0.95, n = 16).For these five reference sites (corresponding to 134 reference topsoil samples), we thus used the Rock-Eval® parameter TOC RE6 as a measure of the SOC content of topsoil samples to calculate their respective proportion of the centennially stable SOC fraction.Conversely, Rock-Eval® analyses of topsoil samples from the sites of Askov and Bad Lauchstädt showed moderate organic carbon yields (90% on average for topsoils of Askov, with a noisy linear regression model R² = 0.68, n = 30; and 92% on average for topsoils of Bad Lauchstädt, yet with a very good linear regression model R² = 0.96, n = 11).Using the total carbon measured by Rock-Eval® (i.e., the sum of TOC RE6 plus MinC Rock-Eval® parameters) as an estimate of the SOC content of topsoil samples for these two sites -that are not carbonated-increased the organic carbon yield of Rock-Eval® analyses (96% on average at Askov, still with a noisy linear regression model R² = 0.66, n = 30; and 101% on average at Bad Lauchstädt, with a very good linear regression model R² = 0.95, n = 11).For the two reference sites of Askov and Bad Lauchstädt (corresponding to 62 topsoil samples), we thus used the sum of Rock-Eval® parameters TOC RE6 plus MinC as a measure of the SOC content of topsoil samples to calculate their proportion of the centennially stable SOC fraction.
The uncertainty in the proportion of the centennially stable SOC fraction was calculated using Equation 6 of the paper published by Cécillon et al. (2018), propagating the uncertainties in SOC content data (using a standard error of 0.5 g C kg -1 , 305 following Barré et al., 2010) and in the site-specific contents of the centennially stable SOC fraction (see above and Table 1).
Table 1: Main statistics of soil organic carbon contents, site-specific contents of the centennially stable SOC fraction, and resulting proportions of centennially stable SOC fraction in topsoils of the seven reference sites used as the reference topsoil sampletraining sets offor the PARTY SOC v2.0 and PARTY SOC v2.0 EU models.More details on 310 agronomical treatments and sampling year of reference topsoil samples are provided in supplementary Table S3.

Reference site
For this second version of PARTY SOC , we changed some criteria regarding the inclusion of the available reference topsoil samples in the learning training set of the model (supplementary Table S1).We excluded from the learning training set all the topsoil samples experiencing agronomical treatments that may have changed the site-specific content of the centennially stable SOC fraction, in contradiction with our hypothesis of a constant content of this fraction at each reference site (see Sect. 2.3).These agronomical treatments concern the repeated application of some types of exogenous organic matter such as compost or manure, for which we suspect that they may increase the content of the centennially stable SOC fraction after several decades.Therefore, to increase the likelihood of verifying our hypothesis of a constant content of the centennially stable SOC fraction at each reference site in time and space (see Sect. 2.3), we excluded all reference topsoil samples from plots that experienceding repeated applications of composted straw (six samples from Grignon), or manure (20 samples from Versailles and eight samples from Bad Lauchstädt) from the learning training set of the statistical model.Yet, we kept some reference topsoil samples from Grignon and Ultuna experiencing repeated applications of straw.
We also excluded from the learning training set of the model the reference topsoil samples for which the organic carbon yield of Rock-Eval® is below 86% or above 116%.For the site of Askov with a noisy relationship between SOC EA and the sum TOC RE6 plus MinC (see Sect. 2.3), we excluded the five samples without a SOC EA measurement preventing the calculation of the organic carbon yield of their Rock-Eval® analysis.Conversely, for the site of Bad Lauchstädt we kept topsoil samples without available SOC EA measurements, as the linear relationship between SOC EA and the sum TOC RE6 plus MinC was very good for this site (see Sect. 2.3).These criteria regarding the organic carbon yield of Rock-Eval® lead to the exclusion of nine samples from the site of Askov, four additional samples from the site of Versailles and two from the site of Ultuna.
Contrary to the first version of PARTY SOC (Cécillon et al., 2018), this second version is based on a balanced contribution of each reference site to the statistical model (supplementary Table S1).S3.This list includes, for each reference topsoil sample, information on its reference site, land cover, agronomical treatment, sampling year and its values for the 40 Rock-Eval® parameters.
The 40 Rock-Eval® parameters calculated (see Sect. 2.2) captured most of the information related to SOC thermal stability, elemental stoichiometry and content that is contained in the five Rock-Eval® thermograms.However, not all Rock-Eval® parameters do necessarily carry meaningful information for partitioning SOC into its centennially stable and active fractions (Cécillon et al., 2018).The PARTY SOC v2.0 statistical model and its European version PARTY SOC v2.0 EU incorporate as predictor variables only the Rock-Eval® parameters showing a strong relationship with the proportion of the centennially stable SOC fraction (supplementary Table S1).The absolute value of 0.50 for the Spearman's rho (nonparametric and nonlinear correlation test) was used as a threshold to select meaningful Rock-Eval® predictor variables (calculated on the reference topsoil sample set of the PARTY SOC v2.0 model, n = 105).Basic statistics of all Rock-Eval® parameters (learning training set of PARTY SOC v2.0) are reported in supplementary Table S4.

Random forests regression models to predict the proportion of the centennially stable SOC fraction from Rock-Eval® parameters, performance assessment and error propagation in the statistical models
The PARTY SOC v2.0 statistical machine-learning model consists of a nonparametric and nonlinear multivariate regression model relating the proportion of the centennially stable SOC fraction (response vector or dependent variable y) of the reference soil sample set (n = 105 topsoil samples from the seven reference sites;, see Sect.2.4) to their Rock-Eval® parameters summarized by a matrix of predictor variables (X) made up of the selected centered and scaled Rock-Eval® parameters.As stated above, we also built a regional (European) version of the statistical model based on the six European reference sites only (PARTY SOC v2.0 EU , using the 90 reference topsoil samples from Askov, Bad Lauchstädt, Grignon, Rothamsted, Ultuna and Versailles).
Like the first version of the PARTY SOC statistical model, this second version uses the machine-learning algorithm of random forests-random inputs (hereafter termed random forests) proposed by Breiman (2001).This algorithm aggregates a collection of random regression trees (Breiman, 2001;Genuer and Poggi, 2020).The PARTY SOC v2.0 and its European version PARTY SOC v2.0 EU are based on a forest of 1000 different regression trees made of splits and nodes.The learning algorithm of random forests combines bootstrap resampling and random variable selection.Each of the 1000 regression trees was grown on a bootstrapped subset of the reference topsoil sample set (i.e., containing ca. two-thirds of "in-bag" samples).The algorithm randomly sampled one-third out of the selected Rock-Eval® parameters (see Sect. 2.4) as candidates at each split of the regression tree, and it used a minimum size of terminal tree nodes of five topsoil samples.The relative importance (i.e., ranking) of each selected Rock-Eval® parameters in the regression models was computed as the unscaled permutation accuracy (Strobl et al., 2009).
The performance of the PARTY SOC v2.0 and the PARTY SOC v2.0 EU random forests regression models was assessed by statistical metrics comparing the predicted vs. the estimated values of their reference topsoil sample set using three different strategiescomplementary validation procedures.First, the predictive ability of both models was assessed by an "internal" procedure that used their respective whole reference topsoil sample sets (n = 105 samples for PARTY SOC v2.0, n = 90 samples for PARTY SOC v2.0 EU ).For this procedure, performance statistics were calculated only on the "out-of-bag" topsoil samples of the whole reference sets, using a random seed of 1 to initialize the pseudorandom number generator of the R software.Out-of-bag samples are observations from the training sets not included in the learning topsoil sample setused for a specific regression tree that can be used as a "built-in" test set for calculating its prediction accuracy (Strobl et al., 2009).
Second, the predictive ability of the models was assessed by a "random splitting" procedure that split randomly their respective reference topsoil sample sets into a test set (made of n = 30 samples), and a training set (n = 75 samples for PARTY SOC v2.0, n = 60 samples for PARTY SOC v2.0 EU ).This procedure was repeated 15 times using random seeds from 1 to 15 in the R software.Third, a fully independent "leave-one-site-out" procedure was used to assess the predictive ability of the models.This procedure successively excluded topsoil samples of one reference site from the training set and uses them as a test set (n = 15) for the models.It used the random seed of 1 in the R software.For the second and third procedures, performance statistics were calculated (1) on the "out-of-bag" topsoil samples of the training sets and (2) on the topsoil samples of the test sets.The "leave-one-site-out" validation should be seen as the procedure giving the most accurate estimation of the uncertainty of both regression models on unknown topsoil samples.Several statistics were used to assess the predictive ability of the regression models.The coefficient of determination: R 2 OOB , calculated on the "out-of-bag" samples of the training sets; and R², calculated on the samples of the test sets.The root-meansquare error of prediction: RMSEP OOB , calculated on the "out-of-bag" samples of the training sets; and RMSEP, calculated on the samples of the test sets.The relative RMSEP: R RMSEP, calculated as the ratio of the RMSEP to the mean value of the test sets.The ratio of performance to interquartile range (RPIQ) was calculated as the ratio of the interquartile range of the test sets (Q3 -Q1; which gives the range accounting for 50% of the test sets around its median value) to the RMSEP (Bellon-Maurel et al., 2010).The bias of the random forests regression models was calculated as the mean of the model predictions on the test sets minus the actual mean of the test sets.Additionally, site-specific RMSEP and R RMSEP were calculated for the "leave-one-site-out" procedure (on the 15 independent test topsoil samples from each site).The uncertainty on the model predictions for new topsoils was determined using a methodology that was fully described by Cécillon et al. (2018).This methodology was adapted after the work of Coulston et al. (2016), to explicitly take into account the uncertainty in the reference values of the proportion of the centennially stable SOC fraction (see Sect. 2.3) that were used to build the models (Cécillon et al., 2018).PARTY SOC v2.0 and PARTY SOC v2.0 EU were programmed as R scripts in the RStudio environment software (RStudio Team, 2020), and were run using the R version 4.0.0 (R Core Team, 2020).The R scripts use the random forests algorithm of the randomForest R package (Liaw and Wiener, 2002) and the boot R package for bootstrapping (Canty and Ripley, 2020; Davison and Hinkley, 1997).

Content of the centennially stable SOC fraction at the reference sites
The two newly fitted values of the centennially stable SOC fraction content (i.e., parameter c in Eq. ( 1), see Sect.2.1) were 5.10 g C kg -1 at the site of Askov (standard deviation = 0.88 g C kg -1 ) and 5.12 g C kg -1 at the site of La Cabaña (standard deviation = 0.35 g C kg -1 ).The fitted values of parameter c in Eq. ( 1) for all reference sites and their standard errors are provided in supplementary Table S2.A total (reference sites with an LTBF treatment) or a C 4 -plant derived (La Cabaña site) SOC content value lower than the fitted value of the site-specific parameter c in Eq. ( 1) was measured in four out the seven reference sites of the PARTY SOC v2.0 model.At Bad Lauchstädt, a SOC EA value of 15.0 g C kg -1 was reported by Körschens et al. (1998) for topsoils of the well ring experiment (Ansorge, 1966).At Rothamsted, a SOC EA measurement of 9.72 g C kg - 1 was reported for topsoils of the Highfield LTBF experiment by Cécillon et al. (2018).At Versailles a SOC EA measurement of 5.50 g C kg -1 was reported after 80 years of bare fallow by Barré et al. (2010).At La Cabaña, a C 4 -plant derived SOC content of 4.75 g C kg -1 was calculated using data from Quezada et al. (2019).These values did not differ strongly from the values of the centennially stable SOC contents calculated from the Bayesian curve-fitting method (Table 1, Table S2).In particular, the hierarchy in the centennially stable SOC content of the seven reference sites was unchanged whatever the calculation method.These values were thus retained as the best estimates of the site-specific content of the centennially stable SOC fraction in topsoils of the four sites to reduce the risk of overestimating the actual value of the centennially stable SOC content, compared to the first published version of the model (see Sect. 2.1; Table 1 and supplementary Table S1).As these site-specific values of the centennially stable SOC fraction content were derived from SOC EA measurements, we attributed a standard deviation of 0.50 g C kg -1 to each of them, following Barré et al. (2010).The final estimates of the content of the centennially stable SOC fraction at the seven reference sites that were used in the PARTY SOC v2.0 statistical model are provided in Table 1.They varied by a factor of three across the reference sites, ranging from 4.75 g C kg -1 at La Cabaña to 15.00 g C kg -1 at Bad Lauchstädt.The lowest value of the topsoil content of the centennially stable SOC fraction used in the European version PARTY SOC v2.0 EU of the statistical model differed only slightly from the one of the PARTY SOC v2.0 model (5.10 g C kg -1 at the site of Askov).

Content and biogeochemical stability of SOC in the learning training sets, and selection of meaningful Rock-Eval® parameters as predictor variables for the PARTY SOC v2.0 and PARTY SOC v2.0 EU models
The SOC content in the topsoil samples of the seven reference sites ranged from 5.6 to 41.5 g C kg -1 in the learning training sets of the PARTY SOC v2.0 (n = 105) and PARTY SOC v2.0 EU (n = 90) models (Table 1).As showed in Table 1, 2).While the inorganic carbon content was not correlated to the proportion of the centennially stable SOC fraction, TOC RE6 was significantly and negatively correlated to the response variable of the PARTY SOC v2.0 model (Spearman's rho = -0.55;Table 2).Other Rock-Eval® parameters linked to soil carbon content showed a stronger relationship than TOC RE6 with the proportion of the centennially stable SOC fraction.This was the case for S2 and PC that showed the highest absolute Spearman's rho coefficients, with a highly significant negative relationship (Spearman's rho = -0.85;Table 2).Eighteen out of the 40 calculated Rock-Eval® parameters showed an absolute value of Spearman's rho above 0.5 with the proportion of the centennially stable SOC fraction in the learning training set of the PARTY SOC v2.0 model (n = 105; Table 2), and were thus retained as predictor variables for the models.
The most important Rock-Eval® parameter for predicting the proportion of the centennially stable SOC fraction is S2 for both PARTY SOC v2.0 and PARTY SOC v2.0 EU statistical models (Table 2).Conversely, the two models show only two Rock-Eval® parameters in common out of their five most important ones that are S2, PC, PC/TOC RE6 , T70 CO2_OX , T90 HC_PYR for PARTY SOC v2.0 and S2, T50 CO2_PYR , PC, S2/PC, HI/OI RE6 for PARTY SOC v2.0 EU (Table 2).

Sensitivity of model performance to the reference sites included in the learningtraining and the test sets
The sensitivity analysis to the training set showed that Rrestricting the learning model training set of the machine-learning model to topsoil samples from fewer reference sites with pedoclimatic conditions closer to the ones of a fully independent test site changed its performances (Fig. 3).Removing from the training set the a reference sites with a climate (i.e., La Cabaña) or a soil type group (i.e., Bad Lauchstädt) differing strongly from the independent test sites (here, Grignon or Versailles used as examples) reduced the site-specific RMSEP and R RMSEP of the model (supplementary Table S5).When Grignon or Versailles were used as independent test sites, the statistical model with the best predictive ability (i.e., the lowest site-specific RMSEP and R RMSEP) used a learning training set composed of 45 topsoil samples from three European reference sites (including the French site with the closest climate, despite its different soil typegroup; supplementary Table S2 and S5 S5 for more details on the learning training sets of the different statistical models and their site-specific performance statistics.Abbreviation: SOC, soil organic carbon. The sensitivity analysis to the test set showed that when excluding Chernozem samples from the test set (i.e., validating the model exclusively on independent samples from Cambisols or Luvisols), the performance statistics of PARTY SOC v2.0 EU were improved (leave-one-site-out validation procedure: R² of 0.56; RMSEP of 0.13; n = 75).The further removal of independent test soils that are unlikely to be encountered in agricultural Cambisols and Luvisols (soils sampled at late dates of bare fallow treatments, more than 25 years after the experiment onset) also improved the performance statistics of PARTY SOC v2.0 EU (supplementary Fig. S1; leave-one-site-out validation procedure: R² of 0.71; RMSEP of 0.11; n = 58).

Discussion
The second version of the PARTY SOC machine-learning model incorporates a large number of modifications and improvements (supplementary Table S1), and its predictive ability was more thoroughly assessed compared to the first version of the statistical model (Cécillon et al., 2018).The critical examination of the performance of PARTY SOC v2.0 and PARTY SOC v2.0 EU provides new insights: (1) on the relationships between Rock-Eval® parameters and the century-scale persistence of SOC; (2) on both current and potential capabilities of the model to partition the centennially stable and active organic carbon fraction in topsoils.Based on those insights, (3) we plan future expansions developments of the PARTY SOC global model to further expand its domain of application while reducing its prediction error., and we recommend the application of PARTY SOC v2.0 EU in European agricultural topsoils to provide accurate information on SOC kinetic pools partitioning that may improve the simulations of simple models of SOC dynamics.

Rock-Eval® chemical and thermal information are related to the century-scale persistence of SOC
The methodology used to estimate the centennially stable SOC proportion in reference topsoils has been revised for the second version of the PARTY SOC model (see Sect. 2.1 and 2.3 and supplementary Table S1), and the traininglearning set now integrates a wider range of centennially stable SOC contents [4.75-15.00g C kg -1 ] with a median value of 6.95 g C kg -1 (n = 7; Table 1).This range covers most of the published size estimates of this fraction in topsoils, estimated using different methods (Balesdent et al., 1988;Barré et al., 2010;Buyanovsky and Wagner, 1998b;Cécillon et al., 2018;Franko and Merbach, 2017;Hsieh, 1992;Huggins et al., 1998;Jenkinson and Coleman, 1994;Körschens et al., 1998;Rühlmann, 1999).
The contribution of each reference site to the learning training set and the inclusion criteria for topsoil samples were also modified, and ten Rock-Eval® parameters not considered in the first version of the model were proposed as potential predictor variables for this second version of the statistical model (see Sect. 2.2 and 2.4 and supplementary Table S1).
Using this improved design, all Rock-Eval® temperature parameters showed positive values of Spearman's rho coefficient with the proportion of the centennially stable SOC fraction in topsoils (Table 2), when a few of them showed counterintuitive significant negative correlations using the learning training set of the first version of PARTY SOC (Cécillon et al., 2018).This confirms the generic link between SOC thermal stability and its in situ biogeochemical stability: centennially stable SOC is thermally stable, even though thermostable SOC fractions are a mixture of centennially stable and active SOC (Fig. 1; Barré et al., 2016;Gregorich et al., 2015;Plante et al., 2013;Sanderman and Grandy, 2020;Schiedung et al., 2017) .Some Rock-Eval® temperature parameters were within the five most important predictor variables for both PARTY SOC v2.0 (T70 CO2_OX , T90 HC_PYR ) and PARTY SOC v2.0 EU (T50 CO2_PYR ; ) statistical models (Table 2).
Contrary to the first version of the PARTY SOC statistical model, the second version tested several Rock-Eval® parameters directly linked to soil carbon content as potential predictor variables.TOC RE6 was selected as a meaningful predictor variable for PARTY SOC v2.0 and PARTY SOC v2.0 EU .Its negative correlation with the centennially stable SOC proportion (Table 2) was expected, according to the calculation of the latter (see Sect. 2.3).This is in line with results from SOC-dating techniques and with most multi-compartmental models of SOC dynamics suggesting that the proportion of the most persistent SOC fraction is a decreasing function of total SOC (Huggins et al., 1998;Rühlmann, 1999).Indeed, the ex-post optimized optimised initial value of the proportion of the inert SOC fraction for the simple AMG model of SOC dynamics is higher (0.60 on average) for SOC-poor depleted temperate topsoils with a long-term arable history than for SOC-rich temperate topsoils with a long-term grassland history (0.47 on average; Clivot et al., 2019).Contrarily, the empirical function commonly used to initialize the size of the inert SOC fraction of the multi-compartmental RothC model predicts an increased proportion of inert SOC with increased total SOC (Falloon et al., 1998).This empirical function needs to be examined upon these results.
Interestingly, S2 (pyrolysable volatile hydrocarbon effluents) and PC (total pyrolysable organic carbon), two other Rock-Eval® parameters linked to SOC content showed a stronger negative relationship than TOC RE6 with the proportion of the centennially stable SOC fraction.Both variables are within the three most important predictor variables for PARTY SOC v2.0 and PARTY SOC v2.0 EU while TOC RE6 was ranked sixth or ninth out of the 18 predictor variables (Table 2).Other Rock-Eval® parameters related to the pyrolysable SOC fraction (PC/TOC RE6 and HI, both negatively related to the centennially stable SOC proportion) were also important predictor variables for both models.The results suggest that a simple decreasing function of total SOC content cannot accurately predict the centennially stable SOC proportion in topsoils, according to the recent report by Clivot et al. (2019).They also confirm the generic elemental stoichiometry of the centennially stable SOC fraction: it is consistently depleted in hydrogen (Barré et al., 2016;Gregorich et al., 2015;Poeplau et al., 2019); and they illustrate the usefulness of the pyrolysis step of Rock-Eval® thermal analysis and its volatile hydrocarbon effluents quantification to infer the proportion of the centennially stable SOC fraction in unknown topsoils.

Capability of the second version of PARTY SOC to partition the centennially stable and active SOC fractions
The learning training set of the second version of the PARTY SOC statistical model was significantly diversified compared with the first version.Its reference topsoil samples now represent wider pedoclimatic conditions (supplementary Table S2), and it includes one long-term vegetation change site as reference site (La Cabaña).Reference topsoils from the Colombian site of La Cabaña fitted well into the global learning training set of the statistical global model: they did not alter its overall performance, as.T the root-mean-square errors of PARTY SOC v2.0 (internal or random splitting validation procedures) are comparable to the ones of the model's first version, where the content of the centennially stable SOC fraction was inferred exclusively from plant-free soils (Fig. 2a, Table 3; Cécillon et al., 2018).Similarly, the expansion of the reference learning training topsoil sample set to new soil types (Acrisol at La Cabaña, Chernozem at Bad Lauchstädt; FAO, 2014), soil texture (loamy coarse sand at Askov; supplementary Table S2), soil pH (in H 2 O, with values as low as 4 at La Cabaña; supplementary Table S2) and pedoclimates (tropical at La Cabaña; supplementary Table S2) did not alter the performance of the model, when assessed using the internal or random splitting validation procedures ( Fig. 2a, Table 3).
The predictive ability of the second version of PARTY SOC was more thoroughly assessed compared to the first version of the statistical model.Specifically, the sensitivity of model performance to the reference sites included in the learningtraining set demonstrates that local models -with learningtraining sets composed of soils from pedoclimates similar to the ones of the soils from the prediction set-showed better predictive ability of the centennially stable SOC proportion compared to a global statistical model (Fig. 3).While the current traininglearning set is composed of too few reference sites to implement local modelling, this suggests that the European version PARTY SOC v2.0 EU should be preferred to the global version PARTY SOC v2.0 model when predicting the centennially stable SOC proportion in unknown soils from Europe.
On the other hand, Conversely, the leave-one-site-out validation procedure, the most robust validation procedure (see Sect. 2.5), illustrated demonstrates that the second version of PARTY SOC is currently not capable of accurately partitioning SOC into its centennially stable and active fractions in soil samples coming from pedoclimates that differ strongly from the ones included in the learning training set (sites of La Cabaña and Bad Lauchstädt; Fig. 2b, Table 3b).This indicates that like all machine-learning approaches, the PARTY SOC model gains progressively more genericity (i.e., capability to fairly predict the centennially stable SOC proportion in unknown soils) as its learning training set integrates soils from new pedoclimates.To this respect, we consider that applying the second version of PARTY SOC significantly extends the model's validity range to new pedoclimates (tropical Cambisols, continental Chernozems and temperate loamy coarse sand Luvisols)to unknown soils from pedoclimates outside its training set cannot be recommended.The sensitivity analysis to the test set, however, shows that PARTY SOC v2.0 EU reliably partitions SOC kinetic fractions at its validation sites on Cambisols and Luvisols (with a mean prediction error on the centennially stable SOC proportion of 0.11; see Sect.3.4 and supplementary Fig. S1).
Cambisols and Luvisols are the two dominant reference soil groups in Europe, covering more than 41% of European land areas (European Commission, 2008).Though the model test set does not include all the within-group pedological variability of Cambisols and Luvisols (FAO, 2014), this suggests that PARTY SOC v2.0 EU can accurately partition SOC into its centennially stable and active fractions on a significant portion of Northwestern European agricultural soils.Contrarily, tThe relatively high prediction error, however, of both PARTY SOC v2.0 and PARTY SOC v2.0 EU models at Rothamsted (high R RMSEP; Table 3), a site developed on a Chromic Luvisol, with a pedoclimate rather similar to some of the other European sites included in the learning set of PARTY SOC , may be due to an inaccurate estimate (overestimation) of the centennially stable SOC content at this site.Indeed, a report from an ancient LTBF trial at Rothamsted (drain gauge experiment; Jenkinson and Coleman, 1994), on the same soil type unit than as the Highfield bare fallow experiment, showed a measured total SOC content of 7.9 g C kg -1 , which is lower than our current estimate of the centennially stable SOC content (9.72 g C kg -1 ; Table 1).Yet, the conditions of the drain gauge experiment, with a basic soil pH value of 7.9 due to heavy dressing of chalk on Rothamsted's arable lands before the 19 th century (Avery and Catt, 1995;Jenkinson and Coleman, 1994), may not be directly comparable to the conditions of the Highfield bare fallow experiment showing acidic pH values r anging from 5.2 to 6.3 (supplementary Table S2).
The predictive ability of the second version of PARTY SOC was more thoroughly assessed compared to the first version of the statistical model.Specifically, the sensitivity of model performance to the reference sites included in the learning set demonstrates that local models -with learning sets composed of soils from pedoclimates similar to the ones of the soils from the prediction set-showed better predictive ability of the centennially stable SOC proportion compared to a global statistical model (Fig. 3).While the current learning set is composed of too few reference sites to implement local modelling, this suggests that the European version PARTY SOC v2.0 EU should be preferred to the global PARTY SOC v2.0 model when predicting the centennially stable SOC proportion in unknown soils from Europe.The mean prediction error of 0.15 obtained using the leave-one-site-out validation procedure of PARTY SOC v2.0 EU (with a R RMSEP of 0.27; Table 3a) is probably a conservative estimate of the accuracy of this model to partition the centennially stable and active SOC fractions over a wide pedoclimatic range of agricultural topsoils in Northwestern Europe.

Future developments and recommended applications of the second version of the PARTY SOC model
The second version of the PARTY SOC model is based on six long-term agricultural sites including an LTBF treatment located in Northwestern Europe and one vegetation change (C 4 to C 3 plants) site located in Colombia.The very first future improvements for to the PARTY SOC machine-learning model isare to increase the size and pursue the expansion offurther expand the pedoclimatic diversity of its learning training set.A few additional LTBF sites and several C 3 to C 4 plants (or C 4 to C 3 ) long-term vegetation change sites (including space-for-time substitution, like the site of La Cabaña) could be used to achieve this goal.A potential complement lies in a few long-term experimental sites with soil archives and treatments experiencing contrasting SOC stock changes.Radiocarbon measurements on recent and archived soil samples from such sites can be used to infer the content of the centennially stable SOC fraction in topsoils (Hsieh, 1992), but also in subsoils, to allow extending the model to deeper soil horizons.Following the method developed by Buyanovsky and Wagner (1998b, Mis en forme : Indice 1998a) and Huggins et al. (1998), the content of the centennially stable SOC fraction can also be estimated at a few additional long-term experiments with contrasted SOC inputs.A promising complement to these strategies lies in numerous long-term sites where time series of SOC inputs, outputs and stocks are well constrained (i.e., long-term experiments or long-term monitoring sites in various types of ecosystems including arable land, grassland and forest).It is possible to reliably infer the content of the centennially stable SOC fraction at these sites using simple models of SOC dynamics like AMG (Clivot et al., 2019).Combining all these strategies could help expanding significantly the learning training set of PARTY SOC to soil samples from diverse climates, ecosystems, soil types and soil depths.When the learning training set of PARTY SOC will integrate a sufficient diversity of soil samples, a second future improvement of the model lies in the comparison of different machine-learning algorithms as well as the testing of local modelling approaches, as commonly used in soil spectroscopy studies (Dangal et al., 2019;Gogé et al., 2012;Ramirez-Lopez et al., 2013b, a).
Meanwhile, the current version of the PARTY SOC v2.0 model and especially its European version PARTY SOC v2.0 EU already provide accurate predictions of the size of the centennially stable and active SOC fraction in agricultural topsoils of a large diversity of pedoclimatic conditions (Fig. 2; Table 3).We consider that PARTY SOC v2.0 EU is mature enough (see Sect. 3.3,3.4 and 4.2) to be reliably applied on agricultural topsoils in Northwestern Europe, or to be tested on topsoils of other ecosystems under similar pedoclimates for research purposes.The PARTY SOC v2.0 EU model is available on public repositories as an R script and an R data file (see Sect.Data and code availability).PARTY SOC v2.0 EU generates predictions of the centennially stable and active SOC proportions and contents (in g C kg -1 ; obtained by multiplying the centennially stable and active SOC proportions by TOC RE6 ) in unknown soil samples, using their measured Rock-Eval® parameters.
The second version of PARTY SOC enables the reliable partitioning of SOC into its centennially stable and active SOC fractions (Fig. 2).The independent validation of PARTY SOC v2.0 EU the model at five sites the scale of on the two dominant reference soil groups in Northwestern Europe presented here (PARTY SOC v2.0 EU Fig. 2 and supplementary Fig. S1) constitutes a breakthrough significant progress in the metrology of SOC kinetic pools.It represents an great improvement compared to other approaches that consistently fail to achieve a proper separation of active from stable SOC (Fig. 1; Hsieh, 1992;von Lützow et al., 2007).Those methods such as the physical or physico-chemical SOC fractionation schemes have been developed to initialize the size of SOC kinetic pools of models (Skjemstad et al., 2004;Zimmermann et al., 2007a) and some of them are now implemented on large topsoil sample sets at the national or continental scale in Europe (Cotrufo et al., 2019;Vos et al., 2018) and Australia (Gray et al., 2019;Viscarra Rossel et al., 2019).A similar implementation in soil monitoring networks of Rock-Eval® measurements combined with the second version of PARTY SOC will can provide a more accurate quantification of the functionally different SOC fractions that are centennially stable or active (Fig. 1), at least for a portion of Northwestern European agricultural land areas on Cambisols and Luvisols.Large-scale Rock-Eval® measurements and the combined application of the PARTY SOC v2.0 EU model are already ongoing in the French soil monitoring network for soil quality assessment (RMQS; Jolivet et al., 2018).We recommend undertaking similar works in other national and international soil monitoring networks.The second version of PARTY SOC can could also be directly employed as a SOC pools partitioning method for simple models of SOC dynamics that are built on the same dualistic conceptual approach of SOC persistence (i.e., active vs. inert stable SOC pools).The accuracy of these simple models, such as AMG, is highly sensitive to the proper partitioning of SOC kinetic pools (Clivot et al., 2019), and could thus strongly benefit from the second version of PARTY SOC .
We envision a significant contribution of the PARTY SOC machine-learning model based on Rock-Eval® thermal analysis to the forthcoming large-scale availability of accurate information on the size of the centennially stable or active SOC fractions.
Such accurate information will foster (1) the initiatives of soil health assessment and monitoring and (2) the modelling works of SOC dynamics and of the climate regulation function of soils.

Figure 1 :
Figure 1: Conceptual representation of soil organic carbon fractionation methods vs. the PARTY SOC approach to Each reference site contributes to the model with 15 samples, so that the reference sample set of the PARTY SOC v2.0 statistical model is composed of 105 topsoil samples (90 for the European version of the model PARTY SOC v2.0 EU ).Besides the above-mentioned exclusion criteria (that excluded 49 out of the 196 topsoil samples available from the seven reference sites), the 15 topsoil samples retained for each reference site were selected: (1) to have a range of proportion of centennially stable SOC fraction as wide as possible; (2) to have the best organic carbon yield of Rock-Eval® analysis.On average, the organic carbon yield of the Rock-Eval® analyses for the retained learning training set of reference topsoil samples (calculated as described above) was greater than 98% of SOC EA (SOC DETERMINED_BY_ROCK-EVAL® = 0.9924 SOC EA -0.1051, R² = 0.99, n = 91 topsoil samples with available SOC EA measurements).The list of the 105 reference topsoil samples retained as the learning training set of PARTY SOC v2.0 is provided in supplementary Table

Finally
, we assessed the sensitivity of model performance to the reference sites included in the learning training and the test sets.For both sensitivity analyses, only the leave-one-site-out validation procedure was used (based exclusively on independent training and test sets).First, model sensitivity of the random forests regression model to the training set was assessed as its sensitivity to the independent reference sites included in the training set.It was performed using successively, as examples, two different test sets consisting of on independent soils from two the reference sites , used as examples.For this sensitivity analysis, topsoil samples from of Grignon and Versailles (n = 15 samples) were successively used as fully independent test sets for several random forests regression models.Several random forests regression models were built using, as training sets, C combinations of topsoil samples from a decreasing number of the remaining reference sites were selected as training sets for the models, on the basis of their potential proximity to the topsoil samples of the test sets, regarding their pedological or climatic conditions.The size of the various training sets composed for the sensitivity analysis ranged from n = 90 samples (six training reference sites) to n = 30 samples (only two training reference sites this resulted in proportions of the centennially stable SOC fraction ranging from 0.15 to 0.98 (PARTY SOC v2.0 learning training set), and from 0.23 to 0.98 (PARTY SOC v2.0 EU learning training set).All the 25 calculated Rock-Eval® temperature parameters showed positive values of Spearman's rho coefficient with the response variable of the PARTY SOC v2.0 model (n = 105; with Spearman's rho values up to 0.81 for T90 HC_PYR ; Table

Table 2 :
Spearman's rank correlation coefficient test between the 40 calculated Rock-Eval® parameters and the proportion of the centennially stable organic carbon fraction in the reference topsoil sample set of the PARTY SOC v2.0 model (n = 105), and variable importance (ranking) of the 18 selected Rock-Eval® parameters for predicting the proportion of the centennially stable SOC fraction in the PARTY SOC v2.0 and PARTY SOC v2.0 EU random forests regression models.Symbols for p-values: *** p < 0.001; ** p < 0.01; * p < 0.05; NS p > 0.05 = not significant.See Section 2.2 for a description of the units of the 40 Rock-Eval® parameters.The 18 Rock-Eval® parameters retained as predictor variables for the second version of PARTY SOC are shown in bold.Abbreviation: SOC, soil organic carbon.

Figure 2 :
Figure 2: Performance of the PARTY SOC v2.0 and the PARTY SOC v2.0 EU statistical machine-learning models based on Rock-Eval® thermal analysis for predicting the centennially stable organic carbon proportion in topsoils.(a) Results of the internal validation procedure; (b) Results of the leave-one-site-out validation procedure (see Section 2.5 for more details on model performance assessment).Abbreviation: SOC, soil organic carbon.Table 3: Performance of the PARTY SOC v2.0 and the PARTY SOC v2.0 EU random forests regression models based on Rock-Eval® thermal analysis for predicting the proportion of the centennially stable organic carbon fraction in topsoils.(a) Performance statistics calculated for the internal, random splitting (mean statistics of 15 different models) and leave-one-site-out validation procedures; (b) Site-specific performance statistics calculated for the leave-one-site-out validation procedure.The performance statistics and their abbreviations are defined at Section 2.5.

Figure 3 :
Figure 3: Sensitivity of model performance to the reference sites included in the learning training set, using 15 topsoil samples from the sites of (a) Grignon or (b) Versailles as independent test sets.Predictions by statistical models showing the lowest RMSEP and R RMSEP are plotted in green (using a learning training set composed of three independent reference

Selection of the learning training set and of meaningful Rock-Eval® predictors variables for the PARTY SOC v2.0 model
In machine-learning, the selection of the model learning training set (here, the training and test sets of reference topsoil