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International audience; Assessment of human exposure to atmospheric metals is a challenge, and mosses seem to be good biomonitors to help this purpose. Lacking roots, they are easy to collect and analyze. However, to our knowledge, no formal comparison was made between cadmium (Cd) measurements in Grimmia mosses and alternative forecasts of atmospheric Cd pollution as those produced by the CHIMERE chemistry transport model. This work aims at studying this link to improve further biomonitoring. We compare 128 Cd measurements in the cemetery mosses of Paris and Lyon metropolitan areas (France) to CHIMERE Cd atmospheric forecasts. The area to consider around the cemetery for the CHIMERE forecasts has been defined by Kendall rank correlations between both information sources—Cd in mosses and CHIMERE Cd forecasts—from different area sizes. Then, we fit linear models to those two data sets including step-by-step different sources of uncertainty. Finally, we calculate moss predictions to compare predictions and measurements in the two cities. The results show an apparent link between the Cd concentrations in mosses and CHIMERE Cd forecasts including in addition the same unique covariate, the moss support (grave or wall), in the two cities. However, this model cannot be directly transposed from region to region because the strength of the link appears to be regional.

International audience; The formulation of variable selection has been widely developed in the Bayesian literature by linking a random binary indicator to each variable. This Bayesian inference has the advantage of stochastically exploring the set of possible sub-models, whatever their dimension. Bayesian selection approaches, appropriate for categorical predictors, are generally beyond the scope of the standard Bayesian selection of regressors in the linear model since all levels of a categorical variable should be jointly handled in the selection procedure. For categorical covariates, new strategies have been developed to detect the effect of grouped covariates rather than the single effect of a quantitative regressor. In this paper, we review three Bayesian selection methods for categorical predictors: Bayesian Group Lasso with Spike and Slab priors, Bayesian Sparse Group Selection and Bayesian Effect Fusion using model-based clustering. The motivation behind this paper is to provide detailed information about the implementation of the three Bayesian selection methods mentioned above, appropriate for categorical predictors, using the JAGS software. Selection performance and sensitivity analysis of the hyperparameters tuning for prior specifications are assessed under various simulated scenarios. JAGS helps user implement these three Bayesian selection methods for more complex model structures such as hierarchical ones with latent layers.

Meteorological ensemble members are a collection of scenarios for future weather issued by a meteorological center. Such ensembles nowadays form the main source of valuable information for probabilistic forecasting which aims at producing a predictive probability distribution of the quantity of interest instead of a single best guess point-wise estimate. Unfortunately, ensemble members cannot generally be considered as a sample from such a predictive probability distribution without a preliminary post-processing treatment to re-calibrate the ensemble. Two main families of post-processing methods, either competing such as the BMA or collaborative such as the EMOS, can be found in the literature. This paper proposes a mixed-effect model belonging to the collaborative family. The structure of the model is formally justified by Bruno de Finetti’s representation theorem which shows how to construct operational statistical models of ensemble based on judgments of invariance under the relabeling of the members. Its interesting specificities are as follows: (1) exchangeability contributes to parsimony, with an interpretation of the latent pivot of the ensemble in terms of a statistical synthesis of the essential meteorological features of the ensemble members, (2) a multiensemble implementation is straightforward, allowing to take advantage of various information so as to increase the sharpness of the forecasting procedure. Focus is cast onto normal statistical structures, first with a direct application for temperatures, then with its very convenient Tobit extension for precipitation. Inference is performed by expectation maximization (EM) algorithms with both steps leading to explicit analytic expressions in the Gaussian temperature case, and recourse is made to stochastic conditional simulations in the zero-inflated precipitation case. After checking its good behavior on artificial data, the proposed post-processing technique is applied to temperature and precipitation ensemble forecasts produced for lead times from 1 to 9 days over five river basins managed by Hydro-Quebec, which ranks among the world’s largest electric companies. These ensemble forecasts, provided by three meteorological global forecast centers (Canadian, USA and European), were extracted from the THORPEX Interactive Grand Global Ensemble (TIGGE) database. The results indicate that post-processed ensembles are calibrated and generally sharper than the raw ensembles for the five watersheds under study. Supplementary materials accompanying this paper appear on-line.

Probabilistic forecasting aims at producing a predictive distribution of the quantity of interest instead of a single best guess point-wise estimate. With regard to water flow forecasts, the two main sources of uncertainty stem from unknown future rainfall and temperature (input error, i.e., meteorological uncertainty) and from the inadequacy of the deterministic simulator mimicking the rainfall-runoff (RR) transformation (hydrological uncertainty or RR error). These two sources of uncertainty can be dealt with separately and only the latter will be considered here. Only hydrological uncertainty is at stake when recorded meteorological data (instead of meteorological forecasts) are used as inputs to feed the RR simulator (RRS) for probabilistic predictions. The predictive performance of the RRS may strongly depend on the hydrological regimes: rapid flood variations induce large errors of anticipation but a series of dry events will translate into a much more smoother sequence of river levels due to the easily predictable behavior of the soil reservoir emptying. Consequently, a model with several regimes adapted to different error structures appears as a solution to cope with the issue of unstationary predictive variance. The river regime is modeled as a latent variable, the distribution of which is based on additional outputs of the RRS to be selected. Inference is performed by the EM algorithm with both steps leading to explicit analytic expressions. Asymptotic confidence regions for the estimates are provided within the same EM framework. Model selection is also performed, including the length of the model memory as well as the choice of explanatory variables for the latent regimes. The model is applied to a series of water flow forecasts routinely issued by two hydroelectricity producers in France and in Qu,bec and compared with their present operational forecasting methods.

[Departement_IRSTEA]Eaux [TR1_IRSTEA]RIVAGE; In this paper, we propose a novel approach for generating avalanche hazard maps based on the spatial dependence of avalanche runout altitudes. The right-truncated data are described with a Bayesian hierarchical model in which the spatio-temporal process is assumed to be the sum of independent spatial and temporal terms. Topography is roughly taken into account according to valley altitude and path exposition, and the spatial dependence is modelled with a Matérn covariance function. An application is performed to the Haute-Savoie region, French Alps. A spatial dependence in runout altitudes is identified, and an effective range of about 10 km is inferred. The temporal trend extracted highlights the increase of avalanche runout altitudes from 1955, attributed to both anthropogenic factors and climate warming. In a cross validation scheme, spatial predictions are provided on undocumented paths using kriging equations. All in all, although our model is unable to take into account small topographic features, it is a first-ever approach that produces very encouraging results. It could be enhanced in future work by incorporating a numerical physically-based code into the modelling.

Complex physical systems are increasingly modeled by computer codes which aim at predicting the reality as accurately as possible. During the last decade, code validation has benefited from a large interest within the scientific community because of the requirement to assess the uncertainty affecting the code outputs. Inspiring frompast contributions to this task, a testing procedure is proposed in this paper to decide either a pure code prediction or a discrepancy-corrected one should be used to provide the best approximation of the physical system. In a particular case where the computer code depends on uncertain parameters, this problem of model selection can be carried out in a Bayesian setting. It requires the specification of proper prior distributions that are well known as having a strong impact on the results. Another way consists in specifying non-informative priors. However, they are sometimes improper, which is a major barrier for computing the Bayes factor. A way to overcome this issue is to use the so-called intrinsic Bayes factor (IBF) in order to replace the ill-defined Bayes factor when improper priors are used. For computer codes which depend linearly on their parameters, the computation of the IBF is made easier, thanks to some explicit marginalization. In the paper, we present a special case where the IBF is equal to the standard Bayes factor when the right-Haar prior is specified on the code parameters and the scale of the code discrepancy. On simulated data, the IBF has been computed for several prior distributions. A confounding effect between the code discrepancy and the linear code is pointed out. Finally, the IBF is computed for an industrial computer code used for monitoring power plant production.

To fit a lognormal distribution to a complex set of microbial data, including detection data (e.g. presence or absence in 25 g) and enumeration data (e.g. 30 cfu/g), we compared two models: a model called M CLD based on data expressed as concentrations (in cfu/g) or censored concentrations (e.g. 1 cfu/25 g) versus a model called M RD that directly uses raw data (presence/absence in test portions, and plate colony counts). We used these two models to simulated data sets, under standard conditions (limit of detection (LOD) = 1 cfu/25 g; limit of quantification (LOQ) = 10 cfu/g) and used a maximum likelihood estimation method (directly for the model M CLD and via the Expectation–Maximisation (EM) algorithm for the model M RD . The comparison suggests that in most cases estimates provided by the proposed model M RD are similar to those obtained by model M CLD accounting for censorship. Nevertheless, in some cases, the proposed model M RD leads to less biased and more precise estimates than model M CLD .

In the context of risk analysis under uncertainty, we focus here on the problem of estimating a so-called quantity of interest of an uncertainty analysis problem, i.e. a given feature of the probability distribution function (pdf) of the output of a deterministic model with uncertain inputs. We will stay here in a fully probabilistic setting. A common problem is how to account for epistemic uncertainty tainting the parameter of the probability distribution of the inputs. In the standard practice, this uncertainty is often neglected (plug-in approach). When a specific uncertainty assessment is made, under the basis of the available information (expertise and/or data), a common solution consists in marginalizing the joint distribution of both observable inputs and parameters of the probabilistic model (i.e. computing the predictive pdf of the inputs), then propagating it through the deterministic model. We will reinterpret this approach in the light of Bayesian decision theory, and will put into evidence that this practice leads the analyst to adopt implicitly a specific loss function which may be inappropriate for the problem under investigation, and suboptimal from a decisional perspective. These concepts are illustrated on a simple numerical example, concerning a case of flood risk assessment.

Standard engineering procedures, such as adopting high return periods as reference events, are a simplified means of handling the complex and multivariate nature of snow avalanches. Furthermore, such methods do not explicitly take into account the elements at risk and/or possible budgetary constraints. In recent years, many authors from a variety of fields have tried to overcome these limitations with quantitative risk evaluations including cost-benefit analyses. Their proposals are based on different modelling assumptions, and often on different definitions for certain important concepts including scenarios, vulnerability relations and time effects. The first goal of this paper is to propose a state of the art, and to discuss the common points, advantages and drawbacks of the various proposals within a unified formal framework based on decision theory. Most of the applications already in use concern long term risk assessment in land use planning and traffic road regulation, but some potential also exists for short term problems including risk assessment to back-country skiing. In a second time, new extensions of a simple decisional model for the optimal design of an avalanche dam are proposed to illustrate the key point of the place of uncertainty in risk analyses. Finally, to stimulate further research efforts, other important outlooks including computational issues, multivariate optimal design and measures of risk alternative to the standard expected loss minimisation are discussed. (C) 2012 Elsevier B.V. rights reserved.

Hierarchical Bayesian Modelling is powerful however under-used to model and evaluate the risks associated with the development of pathogens in food industry, to predict exotic invasions, species extinctions and development of emerging diseases, or to assess chemical risks. Modelling population dynamics of Saccharomyces cerevisiae considering its biodiversity and other sources of variability is crucial for selecting strains meeting industrial needs. Using this approach, we studied the population dynamics of S. cerevisiae, the domesticated yeast. widely encountered in food industry, notably in brewery, vinery, bakery and distillery. We relied on a logistic equation to estimate the key variables of population growth, but we took also into account factors able to affect them, namely environmental effects, genetic diversity and measurement errors. Our probabilistic approach allowed us: (i) to model the dynamical behaviour of strains in a given condition under some uncertainty, (ii) to measure environmental effects and (iii) to evaluate genetic variability of the growth key variables.

A parsimonious model is presented as an alternative to delta approaches to modelling zero-inflated continuous data. The data model relies on an exponentially compound Poisson process, also called the law of leaks (LOL). It represents the process of sampling resources that are spatially distributed as Poisson distributed patches, each containing a certain quantity of biomass drawn from an exponential distribution. In an application of the LOL, two latent structures are proposed to account for spatial dependencies between zero values at different scales within a hierarchical Bayesian framework. The LOL is compared to the delta-gamma (Delta I") distribution using bottom-trawl survey data. Results of this case study emphasize that the LOL provides slightly better fits to learning samples with a very high proportion of zero values and small strictly positive abundance data. Additionally, it offers better predictions of validation samples.

Based on a previous township-scale model, a spatio-temporal framework is proposed to study the fluctuations of avalanche occurrence possibly resulting from climate change. The regional annual component is isolated from the total variability using a two-factor nonlinear analysis of variance. Moreover, relying on a Conditional AutoRegressive sub-model for the spatial effects, the structured time trend is distinguished from the random noise with different time series sub-models including autocorrelative, periodic and change-point models. The hierarchical structure obtained takes into account the uncertainty related to the estimation of the annual component for the quantification of the time trend. Bayesian inference is performed using Monte Carlo simulations. This allows a comparison of the different time series models and the prediction of future activity in an explicit unsteady context. Application to the northern French Alps illustrates the information provided by the model's different components, mainly the spatial and temporal terms as well as the spatio-temporal fluctuation of the relative risk. For instance, it shows no strong modifications in mean avalanche activity or in the number of winters of low or high activity over the last 60 years. This suggests that climate change has recently had little impact on the avalanching rhythm in this region. However, significant temporal patterns are highlighted: a complex combination of abrupt changes and pseudo-periodic cycles of approximately 15 years. For anticipating the future response of snow avalanches to climate change, correlating them with fluctuations of the constraining climatic factors is now necessary.

For snow avalanches, passive defense structures are generally designed by considering high return period events. However, defining a return period turns out to be tricky as soon as different variables are simultaneously considered. This problem can be overcome by maximizing the expected economic benefit of the defense structure, but purely stochastic approaches are not possible for paths with a complex geometry in the runout zone. Therefore, in this paper, we include a multivariate numerical avalanche propagation model within a Bayesian decisional framework. The influence of a vertical dam on an avalanche flow is quantified in terms of local energy dissipation with a simple semi-empirical relation. Costs corresponding to dam construction and the damage to a building situated in the runout zone are roughly evaluated for each dam height-hazard value pair, with damage intensity depending on avalanche velocity. Special attention is given to the poor local information to be taken into account for the decision. Using a case study from the French avalanche database, the Bayesian optimal dam height is shown to be more pessimistic than the classical optimal height because of the increasing effect of parameter uncertainty. It also appears that the lack of local information is especially critical for a building exposed to the most extreme events only. The residual hazard after dam construction is analyzed and the sensitivity to the different modelling assumptions is evaluated. Finally, possible further developments of the approach are discussed.

International audience; For snow avalanches, passive defense structures are generally designed by considering high return period events. However, defining a return period turns out to be tricky as soon as different variables are simultaneously considered. This problem can be overcome by maximizing the expected economic benefit of the defense structure, but purely stochastic approaches are not possible for paths with a complex geometry in the runout zone. Therefore, in this paper, we include a multivariate numerical avalanche propagation model within a Bayesian decisional framework. The influence of a vertical dam on an avalanche flow is quantified in terms of local energy dissipation with a simple semi-empirical relation. Costs corresponding to dam construction and the damage to a building situated in the runout zone are roughly evaluated for each dam heighthazard value pair, with damage intensity depending on avalanche velocity. Special attention is given to the poor local information to be taken into account for the decision. Using a case study from the French avalanche database, the Bayesian optimal dam height is shown to be more pessimistic than the classical optimal height because of the increasing effect of parameter uncertainty. It also appears that the lack of local information is especially critical for a building exposed to the most extreme events only. The residual hazard after dam construction is analyzed and the sensitivity to the different modelling assumptions is evaluated. Finally, possible further developments of the approach are discussed.

Field experiments are often difficult and expensive to make. To bypass these issues, industrial companies have developed computational codes. These codes intend to be representative of the physical system, but come with a certain amount of problems. The code intends to be as close as possible to the physical system. It turns out that, despite continuous code development, the difference between the code outputs and experiments can remain significant. Two kinds of uncertainties are observed. The first one comes from the difference between the physical phenomenon and the values recorded experimentally. The second concerns the gap between the code and the physical system. To reduce this difference, often named model bias, discrepancy, or model error, computer codes are generally complexified in order to make them more realistic. These improvements lead to time consuming codes. Moreover, a code often depends on parameters to be set by the user to make the code as close as possible to field data. This estimation task is called calibration. This thesis first proposes a review of the statistical methods necessary to understand Bayesian calibration. Then, a review of the main calibration methods is presented with a comparative example based on a numerical code used to predict the power of a photovoltaic plant. The package called CaliCo which allows to quickly perform a Bayesian calibration on a lot of numerical codes is then presented. Finally, a real case study of a large photovoltaic power plant will be introduced and the calibration carried out as part of a performance monitoring framework. This particular case of industrial code introduces numerical calibration specificities that will be discussed with two statistical models.; Les difficultés de mise en œuvre d'expériences de terrain ou de laboratoire, ainsi que les coûts associés, conduisent les sociétés industrielles à se tourner vers des codes numériques de calcul. Ces codes, censés être représentatifs des phénomènes physiques en jeu, entraînent néanmoins tout un cortège de problèmes. Le premier de ces problèmes provient de la volonté de prédire la réalité à partir d'un modèle informatique. En effet, le code doit être représentatif du phénomène et, par conséquent, être capable de simuler des données proches de la réalité. Or, malgré le constant développement du réalisme de ces codes, des erreurs de prédiction subsistent. Elles sont de deux natures différentes. La première provient de la différence entre le phénomène physique et les valeurs relevées expérimentalement. La deuxième concerne l'écart entre le code développé et le phénomène physique. Pour diminuer cet écart, souvent qualifié de biais ou d'erreur de modèle, les développeurs complexifient en général les codes, les rendant très chronophages dans certains cas. De plus, le code dépend de paramètres à fixer par l'utilisateur qui doivent être choisis pour correspondre au mieux aux données de terrain. L'estimation de ces paramètres propres au code s'appelle le calage. Cette thèse propose dans un premier temps une revue des méthodes statistiques nécessaires à la compréhension du calage Bayésien. Ensuite, une revue des principales méthodes de calage est présentée accompagnée d'un exemple comparatif basé sur un code de calcul servant à prédire la puissance d'une centrale photovoltaïque. Le package appelé CaliCo qui permet de réaliser un calage rapide de beaucoup de codes numériques est alors présenté. Enfin, un cas d'étude réel d'une grande centrale photovoltaïque sera introduit et le calage réalisé pour effectuer un suivi de performance de la centrale. Ce cas de code industriel particulier introduit des spécificités de calage numériques qui seront abordées et deux modèles statistiques y seront exposés.

Global warming is a major issue for both the scientific world and societies. The concentration of carbon dioxide has increased by 45% since the pre-industrial era (Harris, 2010) as a consequence of human activities, unbalancing the global carbon cycle. This results in global warming with dramatic impacts on the Earth, particularly for fragile populations.Amongst mitigation solutions, a better use of soil is proposed. Soils have the largest capacity of carbon exchanges with the atmosphere and contain a large stock of carbon. A tiny increase in this soil carbon stock and in carbon exchanges between atmosphere and soil would be more favorable to soil carbon sequestration and would compensate for carbon emissios from burning fossil fuel. However, soil carbon dynamics still suffers from insufficient knowledge. There remains therefore a huge uncertainty about the soil carbon response to climate and land-use changes.While several mechanistic models have been developed to better understand the dynamics of soil carbon, they provide an incomplete view of the physical processes affecting soil organic matter (OM). It will be long before a complete and updated soil dynamics model becomes available.In my thesis, I propose a Bayesian statistical model aiming at describing the vertical dynamics of soil carbon. This is done thanks to the modeling of both soil organic carbon and of radiocarbon data as they illustrate the residence time of organic matter and thus the soil carbon dynamics. The purpose of this statistical approach was to better represent the uncertainties on soil carbon dynamics and to quantify the effects of climatic and environmental factors on both surface and deep soil carbon.This meta-analysis was performed on a database of 344 profiles, collected from 87 soil science papers and the literature in archeology and paleoclimatology, under different climate conditions (temperature, precipitation, etc.) and environments (soil type and type of ecosystem).A hierarchical non-linear model with random effects was proposed to model the vertical dynamics of radiocarbon as a function of depth. Bayesian selection techniques, recently published, were applied to the latent layers of the model, which in turn are linked by a linear relationship to the climatic and environmental factors. The Bayesian Group Lasso with Spike and Slab Prior (BGL-SS), the Bayesian Sparse Group Selection (BSGS) and the Bayesian Effect Fusion model-based clustering (BEF) were tested to identify the significant categorical explanatory predictors (soil type, ecosystem type) and the Stochastic Search Variable Selection method to identify the influential numerical explanatory predictors. A comparison of these Bayesian techniques was made based on the Bayesian model selection criteria (the DIC (Deviance Information Criterion), the Posterior Predictive Check, etc.) to specify which model has the best predictive and adjustment power of the database profiles. In addition to selecting categorical predictors, the BSGS allows the formulation of an a posteriori inclusion probability for each level within the categorical predictors such as soil type and ecosystem type (9 soil types and 6 ecosystem types were considered in our study). Furthermore, the BEF made it possible to merge the types of soil as well as the types of ecosystem, which according to the BEF, are considered to have the same effects on the responses of interest here, such as the response of the topsoil radiocarbon.The application of these techniques allowed us to predict, on average and on a global level, the vertical dynamics of the radiocarbon in the case of a temperature increase of 1, 1.5 and 2 °C, and in the case of a change in vegetation cover. For example, we studied the impact of deforesting tropical forests and replacing them by cultivated land on soil carbon dynamics. The same statistical analysis was also done to better understand the vertical dynamics of soil carbon content., Le réchauffement climatique est un problème majeur pour le monde scientifique et les sociétés. La concentration de dioxyde de carbone a augmenté de 45% depuis la période préindustrielle (Harris, 2010), conséquence des activités humaines déséquilibrant le cycle du carbone mondial. Cela se traduit par un réchauffement de la planète avec des impacts dramatiques sur la terre et encore plus pour les populations fragiles.Parmi les solutions d'atténuation, une meilleure utilisation du sol est proposée. En effet, les sols ont la plus grande capacité d'échange de carbone avec l'atmosphère et renferment un stock important de carbone. Une augmentation minime du stock de carbone du sol, les échanges de carbone entre l'atmosphère et le sol plus favorables à la séquestration du carbone dans le sol compenseraient les émissions de carbone provenant de la combustion des combustibles fossiles. Cependant, la dynamique du carbone dans le sol souffre encore de connaissances insuffisantes. Il subsiste alors une grande incertitude quant à la réponse du carbone du sol aux changements climatiques et aux changements d'affectation des terres.Plusieurs modèles mécanistiques ont été développés pour mieux comprendre la dynamique du carbone du sol. Cependant, ces modèles mécanistes ont encore une vue incomplète des processus physiques affectant la matière organique (MO) du sol. Il faudra beaucoup de temps pour obtenir un modèle complet et à jour de la dynamique des sols.Dans ma thèse, nous avons proposé un modèle statistique bayésien visant à décrire la dynamique verticale du carbone du sol. Cela se fait grâce à la modélisation du carbone organique du sol et aussi des données radiocarbone, car elles illustrent le temps de séjour de la MO et donc la dynamique du carbone du sol. Cette approche statistique visait à mieux représenter les incertitudes sur la dynamique du carbone du sol et quantifier les effets des facteurs climatiques et environnementaux sur le carbone des sols superficiels et profonds.Cette méta-analyse a été réalisée sur une base de données de 344 profils, collectés à partir de 87 articles scientifiques et archéologiques et paléoclimatologiques, sous différentes conditions climatiques et environnementales.Un modèle non linéaire hiérarchique avec effets aléatoires a été proposé pour modéliser la dynamique verticale du radiocarbone en fonction de la profondeur. Les techniques de sélection bayésiennes, récemment publiées, ont été appliquées aux couches latentes de notre modèle, elles-mêmes liées par une relation linéaire aux facteurs climatiques et environnementaux. Le Bayesian Group Lasso, le Bayesian Sparse Group Selection(BSGS) et le Bayesian Effect Fusion(BEF) ont été testés pour identifier les principaux prédicteurs explicatifs catégoriels et le Stochastic Search Variable Selection pour identifier les prédicteurs explicatifs numériques influents. Une comparaison de ces techniques bayésiennes a été effectuée sur la base des critères de sélection du modèle bayésien pour spécifier quel modèle a le meilleur pouvoir prédictif En plus de la sélection de prédicteurs catégoriels, le BSGS permet de formuler une probabilité d'inclusion a posteriori pour chaque niveau dans les prédicteurs catégoriels comme type de sol et type d'écosystème. En outre, le BEF a permis de fusionner les types de sol et les types d’écosystèmes qui, selon le BEF, sont supposés avoir les mêmes effets sur nos réponses d’intérêts que la réponse du radiocarbone du sol arable.L'application de ces techniques a permis de prédire, en moyenne et au niveau mondial, la dynamique verticale du radiocarbone dans le cas d'une augmentation de température et de changement d’usage des sols. Par exemple, nous avons étudié l'impact de la déforestation des forêts tropicales et leur remplacement par des terres cultivées sur la dynamique du carbone du sol. La même analyse statistique a également été effectuée pour mieux comprendre la dynamique verticale de la teneur en carbone du sol.