Pauline Rasset
email: pauline.rasset@unicaen.fr

Jessica Mange

Benoît Montalan

Distinct Feelings: a Typology of Affective Reactions While Meeting People With Facial Disfigurement for the First Time

Keywords: facial difference, affective states, self-presentation paradigm, social stigma

(Un)veiling distinct feelings: A typology of affective reactions while meeting people with facial disfigurement

for the first time

Introduction

In 2018, a cancer survivor was being told by the owner of a store that 'if he was going to eat in here he would have to cover his face', apparently in order to prevent the customers to run off [START_REF] O'kane | Cancer survivor says he was asked to cover face at South Carolina store[END_REF]. As this man's daughter created a page for donations, telling her father's experience of discrimination, she raised more than $80,000 from more than 2700 people (GoFundMe). As illustrated here, facial difference (FD) elicits ambivalence, ranging from discriminatory to supporting reactions according to the context. This paper thus aims to provide an overview of the stigmatizing and/or supporting affective reactions to this disabling -yet understudied -condition through the perceivers' perspective [START_REF] Yaron | Recognizing difference: In/visibility in the everyday life of individuals with facial limb absence[END_REF].

Faces influence social cognition in multiple ways (for a review, see [START_REF] Hugenberg | Faces are central to social cognition[END_REF]. Despite the key role faces play in social and nonverbal communication, few studies have investigated the impact of a visible FD. Yet, research based on testimonies of people living with a FD show that they endure prejudices and discriminations, ranging from a lack in social acceptance to harassment and bullying (for reviews see [START_REF] Thompson | Adjusting to disfigurement: Processes involved in dealing with being visibly different[END_REF][START_REF] Wali | People living with facial disfigurement after having had noma disease: A systematic review of the literature[END_REF]. Generally speaking, they must confront public stigma, through the perceivers' cognitive (e.g., stereotypes), behavioral (e.g. glances) and affective reactions (e.g., aversion; for reviews see [START_REF] Macgregor | Facial disfigurement: Problems and management of social interaction and implications for mental health[END_REF][START_REF] Rumsey | Body image and disfigurement: Issues and interventions[END_REF].

As regards this last dimension, [START_REF] Partridge | Changing faces[END_REF] has described the SCARED syndrome on the basis of his own experience as a person with a FD and of multiple testimonies from charity Changing Faces beneficiaries. This syndrome would consist of the affective states (SCARED meaning 'Sorry or Shocked, Curious or Confused, Anxious, Repelled, Embarrassed, Distressed') which seem to be experienced by the perceiver of people with FD when the communication goes wrong between two individuals, one of whom has a FD. Yet, if the experience of people with FD, as reported by Partridge, provides a strong support to understand affective issues related to FD self-stigma (i.e., the social and psychological impact on the stigmatized person), empirical studies on public stigma (i.e., the social and psychological reactions of perceivers to stigma) remain rather scarce. This research focuses specifically on affective reactions elicited by people with FD as described by the perceivers themselves.

Most researchers have investigated the arousal of one specific -in most cases of a negative valence -emotion or affective state triggered by FD (e.g., disgust, fear; [START_REF] Blascovich | Perceiver threat in social interactions with stigmatized others[END_REF][START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF]). Yet, reactions toward stigmatized individuals are often an ambivalent mixture of negative and positive feelings [START_REF] Bos | Stigma: Advances in theory and research[END_REF][START_REF] Dovidio | Stigma : Introduction and overview[END_REF][START_REF] Pryor | A dual-process model of reactions to perceived stigma[END_REF]. For example, an automatic feeling of disgust elicited by a hypothesized contact with an individual living with HIV might be counterbalanced by a controlled and thoughtful reaction of pity [START_REF] Pryor | A dual-process model of reactions to perceived stigma[END_REF]. This ambivalence was found to also characterize reactions towards people with FD [START_REF] Macgregor | Facial disfigurement: Problems and management of social interaction and implications for mental health[END_REF].

By adopting a more comprehensive approach, [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF] asked their participants to report their subjective experience when confronting either faces pretested as being attractive, unattractive or faces with disfigurement. Their scales included 21 emotions selected from the emotions literature that were not restricted to negative affective reactions. These emotions comprised negative ones (i.e., anger, fear, disgust, anxiety, embarrassment, repulsion), but also positive ones (i.e., happiness, joy, relaxation, attraction, comfort, calm, pleasure, confidence, delight), emotions related to sorrow (i.e., sorrow, sadness, distress) and to curiosity (i.e., curiosity, surprise, nonindifference). Participants reported higher levels of sorrow, and curiosity emotions but also lower levels of positive emotions such as joy or delight when looking at a face with FD (for a replication of difference on emotions, see also [START_REF] Stone | Emotional responses to disfigured faces and disgust sensitivity: An eye-tracking study[END_REF]. They also showed that people with FD elicit higher levels of negative emotions, but only when they experimentally lowered social desirability biases (i.e., condition of high anonymity). However, social desirability may have hindered the identification of other affective states. For instance, people with FD are targets of antisocial behaviors (e.g., hate crime, harassment; Changing Faces, 2020), which could be related to emotions having social distancing functions, like anger but also hate or contempt (see [START_REF] Fischer | Social functions of emotion and emotion regulation[END_REF]). Yet, these affective reactions remain underexplored. On the other hand, some affective states seem redundant (e.g., repulsion, disgust) and the concomitant presentation of these affective states might lead to a focus on certain feelings to the detriment of others.

In order to follow-on the work and findings initiated by [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF], the present research aimed at generating a complete set of emotional responses to an individual with FD, and to classify them into a smaller number of factors. To this end, it was decided to complement the deductive approach previously used by researchers with an inductive approach. In other words, it was investigated whether putting individuals in a specific context, specifically associated with people with FD on the one hand, and allowing people to express themselves spontaneously and without any restraints hampered by social desirability on the other hand, would lead to identify more clearly the variety of potential affective states actually felt by people encountering a person with FD.

In sum, the objective of this paper is to identify the diversity of affective states spontaneously experienced by people meeting a person with FD (Study 1) and use it as a basis to propose a typology of these affective states (Study 2), which could in the end constitute either an empirical tool for future empirical research on this issue, or an indicator for evaluation purpose (e.g., for psychosocial interventions targeting stigma prevention).

Study 1

The aim of this study was to set out a more exhaustive list of all potential affective states, including negative ones, spontaneously experienced by people meeting a person with FD. To this end, we opted for a qualitative approach. A vignette study, describing a situation in which someone comes face to face with a person with a FD on a bus, was submitted to the participants including various instructions. Indeed, in order to ease both desirable and undesirable responses, a self-presentation paradigm was used (i.e., a paradigm with varying instructions to present oneself in a good vs. bad light; [START_REF] Gilibert | Paradigms of the sociocognitive approach[END_REF][START_REF] Jellison | A self-presentation approach to the fundamental attribution error: The norm of internality[END_REF]. This study has two main advantages in the collection of all potential affective states experienced while encountering a person with FD. Firstly, negative / positive incentive conditions were specifically used to ease the expression of socially undesirable / desirable affective states. Secondly, no preestablished emotions list was submitted to the participants. These two protocol features were intended to foster the production of new affective states in comparison with earlier empirical studies on this issue.

Method

Participants

Participants were 47 graduate students in psychology who volunteered to participate to the study prior to their course without any financial counterpart (mean age = 22.45 years; SD = 2.54; Females = 45). These students' profile, i.e., enrolled in a master's program in psychology, was selected because of their assumed basic knowledge of the emotions lexical field. We assumed that it would be easier for them to identify their affective reactions. Since FD stigma was not expected to be related to sociodemographic characteristics, we supposed that the findings obtained from this sample could be generalized to the rest of the population (see Goode et al., 2008cited by Stone, 2021;[START_REF] Stone | Emotional responses to disfigured faces and disgust sensitivity: An eye-tracking study[END_REF].

Procedure and Material

After having been provided with an informed consent, participants were asked to read a vignette study (describing an imaginary situation in which they would notice a disfigurement on the face of the nearby sitting person on a bus) and then to list all the affective states they may feel in that situation. No images were presented so that the participants could not focus on affected states elicited by one type of disfigurement and to circumvent biases related to characteristics of the face observed (e.g., gender, age, ethnicity; see [START_REF] Zebrowitz | First impressions from faces[END_REF]. Based on a self-presentation paradigm [START_REF] Jellison | A self-presentation approach to the fundamental attribution error: The norm of internality[END_REF], participants were asked to write three times all the affective states they could feel in the situation they had previously read. The first time (standard condition), they just had to write what spontaneously came to their mind. The second and third times (positive vs. negative incentive conditions), they were asked to report the affective states as if they were attempting to make a good vs. bad impression when answering the question (the order of positive and negative incentive conditions was counterbalanced among the participants). The assignment was collective but participants were asked not to interact with each other. After providing sociodemographic information, participants were fully debriefed and thanked.

Results

First, the data base was cleaned and standardized. More specifically, we changed the grammatical class and replaced the past participle by the noun (e.g., 'surprised' replaced by 'surprise'). As participants were asked to answer with a single word, we replaced the nominal sentences by words referring to an affective state (e.g., 'shame of the way I gaze' by 'shame') in a few cases.

Afterwards, a lexical analysis was conducted (IRaMuTeQ program;[START_REF] Ratinaud | IRaMuTeQ : Interface de r pour les analyses multidimensionnelles de textes et de questionnaires[END_REF]. The classic lexicographical analysis revealed 537 occurrences resulting in 86 different words. A Factorial Correspondence Analysis (FCA) was conducted in order to investigate the lexical relationships between the three modalities of our "instruction" variable regarding words production. We obtained the number of occurrences for each word depending on the condition (see Table 1). The lexical extension was determined by type-token ratio (TTR) as a percentage ratio between the vocabulary size (V) and the size of the corpus (N), indicating the lexical richness of the textual repertoire. The computed value for the analyzed texts were 17.67% for the standard incentive data, 27.01 and 26.19, respectively for the positive and negative ones. These results suggest a higher lexical richness in the two last conditions. FCA also allows a Cartesian graphical visualization of the proximities, oppositions and tendencies of the words. This analysis mostly indicated clear divide across the conditions (see Figure 1). As each of the 86 words were not all related to affective states, we decided to separately evaluate them in order to state whether they could be considered as affective states or not. As the intercoder agreement was moderate (Cohen's κ = .43), we decided to remove all words that were identified as not revealing any affective state by at least one expert. Hence, the remaining list consisted of 72 words including 31 appearing only once (see Table 1). Among these 72 words, only 36 were elicited in the standard condition. Considering the 36 remaining words that have emerged from the incentive conditions, 15 were elicited only in the positive incentive condition (e.g., 'understanding', 'nothing'), 20 only in the negative incentive condition (e.g., 'rejection', 'mockery') and one in both conditions (e.g., 'joy').

(Neutralité) 1 7 0 1.49% Fright (Effroi) 2 0 5 1.30% Sorrow (Peine) 5 1 0 1.12% Interest (Intérêt) 4 2 0 1.12% Shame (Honte) 1 0 5 1.12% Shock (Choc) 3 0 3 1.12% Rejection (Rejet) 0 0 6 1.12% Mockery (Moquerie) 0 0 6 1.12% Contempt (Mépris) 0 0 5 0.93% Understanding (Compréhension) 0 5 0 0.93% Stupor (Stupeur) 2 0 1 0.56% Horror (Horreur) 0 0 3 0.56% Intrigue (Intrigue) 3 0 0 0.56% Guilt (Culpabilité) 3 0 0 0.56% Aggressiveness (Agressivité) 0 0 3 0.56% Questioning (Questionnement) 2 0 0 0.37% Query (Interrogation) 2 0 0 0.37% Acceptance (Acceptation) 1 1 0 0.37% Trouble (Confusion) 1 0 1 0.37% Strangeness (Étrangeté) 2 0 0 0.37% Kickback (Recul) 0 0 2 0.37% Startle (Sursaut) 2 0 0 0.37% Grief (Chagrin) 1 1 0 0.37% Apprehension (Crainte) 1 0 1 0.37% Anger (Colère) 0 0 2 0.37% Security (Sécurité) 0 1 0 0.19% Nausea (Écoeurement) 0 0 1 0.19% Tolerance (Tolérance) 0 1 0 0.19% Indignation (Indignation) 0 0 1 0.19% Envy (Envie) 0 1 0 0.19% Ease (Aisance) 0 1 0 0.19% Intimidation (Intimidation) 1 0 0 0.19% Warmth (Chaleur) 0 1 0 0.19% Comfort (Réconfort) 0 1 0 0.19% Uncertainty (Insécurité) 0 0 1 0.19% Fun (Amusement) 0 0 1 0.19% Injustice (Injustice) 0 1 0 0.19% Disconsideration (Déconsidération) 1 0 0 0.19% Coldness (Froideur) 0 0 1 0.19% Ignorance (Ignorance) 0 0 1 0.19% Altruism (Altruisme) 0 1 0 0.19% Distancing (Eloignement) 0 0 1 0.19% Disdain (Dédain) 0 0 1 0.19% Malice (Méchanceté) 0 0 1 0.19% Satisfaction (Satisfaction) 0 0 1 0.19% Respect (Respect) 0 1 0 0.19% Consideration (Égard) 0 1 0 0.19% Distress (Bouleversement) 1 0 0 0.19% Solidarity (Solidarité) 0 1 0 0.19% Tenderness (Tendresse) 0 1 0 0.19% Anxiety (Angoisse) 1 0 0 0.19% Concern (Préoccupation) 1 0 0 0.19% Affection (Affection) 0 1 0 0.19% Condescension (Condescendance) 0 0 1 0.19% Obsession (Obnubilation) 0 0 1 0.19% Calm (Calme) 0 1 0 0.19% Hate (Haine) 0 0 1 0.19% Smile (Sourire)* 1 4 0 0.93% Laughter (Rire)* 1 1 1 0.56% Welcoming ('Accueillance')* 1 2 0 0.56% Nothing (Rien)* 0 3 0 0.56% Flight (Fuite)* 0 0 2 0.37% Violence (Violence)* 0 0 1 0.19% Avoidance (Evitement)* 0 0 1 0.19% Help (Aide)* 1 0 0 0.19% Sociability (Sociabilité)* 0 1 0 0.19% Funny (Drôle)* 0 1 0 0.19% Judgment (Jugement)* 0 0 1 0.19% Intrusiveness (Indiscrétion)* 0 0 1 0.19% Dreaming (Songe)* 1 0 0 0.19% Arrogance (Hautain)* 0 0 1 0.

Discussion

All of these results highlight the benefit of a self-presentation paradigm to produce a real variety of affective states elicited by people with FD. The CFA showed that the incentives eased the production of distinct and even sometimes opposed words.

Although we did not use visual stimuli, the affective states previously highlighted in the literature were again elicited in this study, supporting the applicability of the results (e.g., fear, disgust, curiosity, surprise; see [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF]. Moreover, a high proportion of words (20 out of 72) have emerged from the negative incentive condition.

As expected, the strategy facilitated the expression of socially undesirable affective states and the discrimination among negatively valanced affective states (e.g., disdain, fright, aggressiveness).

The remaining list consisted of 72 affective states spontaneously produced by the participants as they imagined themselves confronting a person with FD in an everyday situation. Nevertheless, it was unusable as such for future empirical studies because it was too long and some affective states were overlapping. In addition, because some of them were related to the same affective state, the list was redundant. Our approach, after benefiting from a qualitative perspective, had now reached a stage requiring a quantitative approach in order to group the 72 identified affective states into affective factors.

Study 2

Building on the 72 affective states formerly identified in Study 1, the aim of this second study was to propose an empirical tool to measure affective states elicited by people with FD in future empirical research. For this purpose, we opted for a quantitative approach. In the same manner as in Study 1, a vignette study describing a situation in which someone comes face to face with a person with a FD on a bus, was submitted to all participants who were asked to what extent they would experience each one of the listed affective states in the described situation. The set of affective states was composed of the affective states identified in Study 1. We opted for a self-presentation paradigm in Study 1 in order to ease the spontaneous production of negatively-valenced affective states, whereas Study 2 only required the standard condition. Indeed, as the aim here was to identify affective states overlapping or correlating in a same single factor, no variation in instruction was considered useful for this purpose.

Method

Participants

Three hundred eighty-five undergraduate students from different backgrounds volunteered to participate to the study prior to their course without any financial counterpart (mean age = 19.20 years; SD = 1.82; Females = 262). The sample size was computed based on a minimal subject to item ratio at 5:1 [START_REF] Costello | Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis[END_REF].

The data of four participants signaling a personal disfigurement were withdrawn from the study as well as three incomplete questionnaires. On the whole, participants mostly imagined mild to severe disfigurement 1 .

Procedure and Material

Participants provided an informed consent. After that, they were asked to read the same vignette as in Study 1. They were then asked to fill in a paper-and-pencil questionnaire composed of the 72 previously generated affective states listed in fixed order (i.e., in alphabetical order). The assignment was collective but participants were asked not to interact with each other. Since previous research evidenced that 'embarrassment' and 'repulsion' are invoked by the perception of people with FD [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF], 2019; see also [START_REF] Macgregor | Facial disfigurement: Problems and management of social interaction and implications for mental health[END_REF][START_REF] Rumsey | Body image and disfigurement: Issues and interventions[END_REF], these words were added to the list. Participants were asked to rate the extent to which they might feel each of the proposed 74 affective states in the situation described in the vignette on a scale ranging from 1 ('does not fit at all') to 7 ('fits totally'). After providing socio-demographic information, participants were fully debriefed and thanked.

Results

In a first step, to assess the underlying factor structure of the collected items, we conducted an exploratory factor analysis (EFA) with the 74 items. The Kaiser-Meyer-Olkin measure (KMO) of sampling adequacy for the EFA was .89, which suggested that the data was adequate to run the EFA. Moreover, a significant Bartlett's Test of 1 Severity was assessed based on the drawings and comments provided by participants (N = 311, 74 participants did not report any drawing or comment) in the debriefing section of the questionnaire by four independent judges with an adapted version of the Observer-rated disfigurement scale [START_REF] Katz | Reliability and validity of an observer-rated disfigurement scale for head and neck cancer patients[END_REF]. We computed inter-rater agreement using intraclass correlations (ICC; [START_REF] Koo | A guideline of selecting and reporting intraclass correlation coefficients for reliability research[END_REF]. ICC estimate was calculated using Jamovi and "seolmatrix" statistical package (The Jamovi project, 2021) based on a mean-rating (k = 4), consistency, 2-way mixed-effects model. We obtained an ICC = .63 which indicates moderate reliability. A mean score of severity was then computed for each participant by averaging the scores attributed by raters. To conclude, this exploratory analysis shows that participants mostly imagined mild to severe disfigurements (M = 6.70, SD = 1.50).

Sphericity indicated that the data were suitable, χ²(2701) = 12521, p < .001. Since

Skewness tests revealed a lack of multivariate normality for a minority of items (16/74; see Table 2), we tested the factor structure of the questionnaire with an EFA and the maximum likelihood extraction method [START_REF] Costello | Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis[END_REF]. As regards factor extraction, we investigated the values of the Kaisers' criterion, the scree plots, as well as the results of parallel analyses. As we aimed at developing a compound measure of affective states toward people with FD, we applied Oblimin factor rotation, which allows the factors to correlate with each other.

According to Kaiser's criterion and to the scree-plot, the EFA resulted in five factors.

The parallel-analysis pointed to six factors. As the cumulative percentage of variance was low for five factors (38.89%) and because the highest item among the sixth factor's loading was the emotion of disgustwhich is known to be a particularly relevant affective state when interacting with people with FD (e.g., [START_REF] Ryan | Facial disfigurement is treated like an infectious disease[END_REF][START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF] and which was the most cited word in the first study -we decided to keep the six-factor structure, accounting for 44.81% of the variance. We named those factors after the main affective state associated to them: 'sympathyrelated', 'anxiety-and embarrassment related', 'surprise-related', 'hostility-related', 'neutrality-related', and 'disgust-related' (see Table 2 for a summary of the EFA). In a second step, based on the exploratory factor structure evidenced, we conducted a Confirmatory Factor Analysis (CFA) to examine the model fit using Full Information Maximum Likelihood method (FIML). Considering the parsimony issue, we only submitted 18 items assessing the participant's affective states (for each factor, the three items with the highest factor's load were selected, except that we used 'calm' instead of 'joy' since the former was more congruent with the dimension called 'neutrality'). The CFA indicated acceptable fit statistics (χ 2 (120) = 323.0, p < 001, CFI = .93, TLI = .92, RMSEA range 0.06-0.07; [START_REF] Hu | Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives[END_REF]. In addition, the factor loadings for sympathy-related (.70-.85), anxiety-and embarrassment-related (.66-.84), surpriserelated (.75-.93), hostility-related (.71-.89), neutrality-related (.56-.62), and disgustrelated affective states (.74-.91) were all sizeable and statistically reliable (all p < .001).

Except for the inter-correlations between disgust-related and anxiety/embarrassmentrelated affective states, and between disgust-related and hostility-related affective states (respectively .61 and .63), the inter-correlations between the factors were low (.07-.37).

Discussion

The affective states that emerged from Study 1 were clustered in six factors in this second study: 'sympathy-related', 'anxietyand embarrassment-related', 'surpriserelated', 'hostility-related', 'neutrality-related', and 'disgust-related'. The first 'sympathy-related' factor is made of affective states such as 'solidarity', 'sympathy', or 'benevolence' which express other-oriented affective states [START_REF] Goetz | Compassion: An evolutionary analysis and empirical review[END_REF]. They express sorrow for the other. From this standpoint, two affective states may be missing in this dimension: pity and (social) warmth (Eisenberg, 2016;[START_REF] Pryor | A dual-process model of reactions to perceived stigma[END_REF][START_REF] Weiner | An attributional analysis of reactions to stigmas[END_REF]. This may be due to linguistic changes in the meaning of affective states (e.g., 'to pity somebody' may be perceived as having a rather derogatory connotation in the French language). The second 'anxietyand embarrassment-related' factor, refers simultaneously to affective states centered on threat (e.g., fear, apprehension, anxiety) and on self-conscious affective states (e.g., embarrassment, discomfort; [START_REF] Lewis | Self-conscious emotions: Embarrassment, pride, shame, and guilt[END_REF][START_REF] Öhman | Fear and anxiety: Overlaps and dissociations[END_REF]. Although combining these seemingly different groups of affective states may be surprising at first glance, some affective states are known to be closely related (e.g., shyness; Öhman, 2008). Moreover, fear about interpersonal interactions is one of the most commonly feared situation [START_REF] Arrindell | Phobic dimensions: III. factor analytic approaches to the study of common phobic fears; An updated review of findings obtained with adult subjects[END_REF]. Thus, anxiety could be triggered by uncertainty about how social interactions with people with FD would proceed [START_REF] Hebl | Awkward moments in interactions between nonstigmatized and stigmatized individuals[END_REF][START_REF] Stone | Changing negative perceptions of individuals with facial disfigurement: The effectiveness of a brief intervention[END_REF]. The third 'surprise-related' factor, refers to affective states showing reactions towards an unexpected situation (e.g., intrigue, curiosity, strangeness). The fourth 'hostility-related' factor, gathers affective states that facilitate active rejection (e.g., hate, anger, mockery). The fifth 'neutralityrelated' factor gathers affective states that reflect a lack of change or self-control (e.g., indifference, ease, calm). The last 'disgust-related' factor, gathers different affective states related to disgust and aversion. Six items fell under the threshold of .30 for factor loading. This typology is thus in line with but also extends to former research. Indeed, we replicated previous work regarding the content of the affective reactions elicited by FD (for a review, see [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF]. Additionally, we proposed a classification into a reduced number of factors.

Interestingly this typology distinguishes affective states related to disgust, anxiety, and hostility. Yet, disgust-related affective states were strongly correlated with anxiety-related affective states on the one hand and hostility-related affective states on the other hand, while anxiety-related and hostility-related affective states displayed much lower correlations. These correlations may be at least partly explained by the behavioral component of disgust, which distances individuals from objects [START_REF] Rozin | Disgust[END_REF]. Distancing may thus imply either avoidance in embarrassment-and anxietyrelated affective states, or rejection in hostility-related affective states.

General Discussion

There is a need for a better understanding of individuals' affective reactions when encountering people with FD. Although negative reactions towards FD are ubiquitous and appear early in the development of individuals (e.g., [START_REF] Sigelman | The early development of stigmatizing reactions to physical differences[END_REF], the study of emotional responsiveness has received relatively little interest (see [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF]. This exploratory qualitative and quantitative study investigated the affective states felt when simulating a confrontation with an unknown person with FD, whilst taking into consideration social desirability biases. A comprehensive list of 74 affective states was proposed and 65 of these partially overlapping states were clustered in six factors and can even be reduced to 18 items. On the whole, this research mostly confirms previous work regarding the content of stigmatizing affective reactions (for a review, see [START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF] but also improves them by proposing an organization of these affective reactions through a six-factors typology. A discussion on these two points and on the benefits of this organization for the study of the stigmatizing affective reactions to FD will be provided.

First, this research highlights the formerly well evidenced affective states, such as 'anxiety', 'fear', 'curiosity', 'surprise', 'embarrassment' or 'disgust' (e.g., [START_REF] Blascovich | Perceiver threat in social interactions with stigmatized others[END_REF][START_REF] Partridge | Changing faces[END_REF][START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF][START_REF] Stone | Changing negative perceptions of individuals with facial disfigurement: The effectiveness of a brief intervention[END_REF]. The mention of disfigurement is highly associated with the emotion of disgust [START_REF] Ryan | Facial disfigurement is treated like an infectious disease[END_REF][START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF]. These affective states also comprise those showing the ambivalence aroused by FD, such as 'sympathy', 'compassion', 'benevolence' or 'sorrow' [START_REF] Bonanno | Mapping out the social experience of cancer patients with facial disfigurement[END_REF][START_REF] Stone | Emotional responses to disfigured faces: The influences of perceived anonymity, empathy, and disgust sensitivity[END_REF], 2019). Our study contributed to complete this list, while evidencing antisocial affective states formerly evidenced from the perspective of people with FD only, such as 'malice ', 'disdain', 'hate' (Changing Faces, 2020;[START_REF] Macgregor | Facial disfigurement: Problems and management of social interaction and implications for mental health[END_REF]. On another note, this study also stressed the presence of 'neutrality', 'indifference', and other affective states denoting a lowered emotional arousal. Thus, this research replicated and completed previous work regarding the content of stigmatizing affective reactions.

Second, this research organized affective reactions towards people with FD in a six-factors typology, including 'sympathy-related ', 'anxietyand embarrassmentrelated', 'surprise-related', 'hostility-related', 'neutrality-related', and 'disgust-related' affective states. Frequently, affective states are gathered according to their valence although a valence-based approach built upon the positive and negative aspects lacks differentiation and nuances reactions [START_REF] Lerner | Beyond valence: Toward a model of emotionspecific influences on judgement and choice[END_REF]. Exploring the affective reactions towards people with FD through the prism of valence creates the risk of missing their specific influence on the perceivers' cognitive and behavioral reactions.

As FD elicited ambivalent affective states, like other social stigmas (e.g., HIV; [START_REF] Pryor | A dual-process model of reactions to perceived stigma[END_REF], this research confirms that the investigation of affective reactions to people with FD needs to go beyond a valence scale. Yet, many of the remaining affective states are negative and the small but steady correlations between the different factors point to a broad factor of negative emotionality. Valence should therefore be questioned, but maybe more at the level of moral goodness than at the level of pleasantness [START_REF] Shuman | Levels of valence[END_REF].

Finally, this research contributes to stress the importance to study these six groups of affective reactions in the stigmatizing reactions to FD, which paves the way for future research. Indeed, this research highlights that invoking disfigurement is highly associated with the emotion of disgust [START_REF] Ryan | Facial disfigurement is treated like an infectious disease[END_REF][START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF]. Whereas some theorists argue for evolutionary reasons that people avoid those who are supposed to carry pathogens (see [START_REF] Kurzban | Evolutionary origins of stigmatization: The functions of social exclusion[END_REF], societal, social and individual explanations might be questioned too. For example, the media may contribute to FD stigma through the isolated representation of rare disfigurement or movie villain's representations (e.g., zombies; [START_REF] Croley | Dermatologic features of classic movie villains[END_REF][START_REF] Gunter | The role of the media[END_REF][START_REF] Reese | Dermatology in the cinema[END_REF]. Some individual differences were evidenced too, such as the individual sensibility to disgust [START_REF] Shanmugarajah | The role of disgust emotions in the observer response to facial disfigurement[END_REF]. Interestingly, in this research, disgust-related affective states were correlated with anxiety/embarrassment-related and hostility-related affective states. Anxiety/embarrassment-related affective states stress the disruptiveness of FD in the social interactions, which may lead individuals with and without FD to put an end to it [START_REF] Hebl | Awkward moments in interactions between nonstigmatized and stigmatized individuals[END_REF][START_REF] Partridge | Changing faces[END_REF][START_REF] Stone | Changing negative perceptions of individuals with facial disfigurement: The effectiveness of a brief intervention[END_REF]. In a more radical fashion, hostility-related affective states imply rejection and antisocial behaviors. Although these affective reactions help to understand the antisocial behaviors people with FD endure (see Changing Faces, 2020; [START_REF] Macgregor | Facial disfigurement: Problems and management of social interaction and implications for mental health[END_REF], the emphasis on 'disgust', 'horror' or 'hate' raises questions: do people with FD actually engender such a terrifying perception from people and not only from highly prejudiced individuals? Yet, this study has also evidenced that neutrality-related and sympathyrelated affective states contribute to a broader understanding of the affective reactions to FD. As both of these affective states were mainly evidenced thanks to the positiveincentive' condition of our first study, they probably reflect what the participants think they would like to feel in such given situations or even how they would actually feel.

The least consideration of these affective states in previous research may be due to an excessive focus on problems and difficulties of social interactions with people with FD (see [START_REF] Rumsey | The psychology of appearence[END_REF]). Yet, this pattern of affective states is not always beneficial and desired or requested by people with FD. For example, [START_REF] Bonanno | Mapping out the social experience of cancer patients with facial disfigurement[END_REF] revealed that expressions of unnecessary sympathy in a large group may make them feel uncomfortable. In the same vein, indifference may lead to benign neglect (i.e., individuals are not subject to particular attention), which can make people with FD feel uncomfortable if they feel ignored [START_REF] Bonanno | Mapping out the social experience of cancer patients with facial disfigurement[END_REF]. In other words, seemingly prosocial or neutral affective states may still be stigmatizing if they remind the bearer of his/her 'mark', and may thus lead to self-stigmatization [START_REF] Chaudoir | Discredited" versus "discreditable": Understanding how shared and unique stigma mechanisms affect psychological and physical health disparities[END_REF][START_REF] Goffman | Stigma. Notes on the management of spoiled identity[END_REF].

Limitations and future directions

Some limitations regarding the context, the FD, the perceivers, and the affective states should be noted. First, as this study focused on a specific social situation (i.e., standing close to a stranger in a public place) and because social stigma is context-specific, we have probably not evidenced all possible affective states [START_REF] Major | The social psychology of stigma[END_REF]. The grouping of affective states centered on threat and self-conscious affective states may have been guided by the story told on the vignette and would have not occurred if the participants had to picture themselves interacting with the person and not only sitting next to him/her. Further studies should thus try to explore some more varied situations, especially in real settings.

Second, as participants were instructed to imagine a FD rather than to simply look at it, some variations may have occurred. We preferred these settings to avoid restricting the typology to one specific visible difference since FD comprises a wide range of conditions [START_REF] Krishna | Disfigurement: Psychosocial impact and coping[END_REF]. These variations were not supposed to impact the structure of the typology but rather the intensity and type of affective states elicited.

However, future studies should verify that this typology is applicable to all conditions that involve a visible difference.

Third, this study was conducted based on samples of French students and future studies are needed to determine whether our findings can really be generalized to other cultures. For instance, some variations in preferences toward peers with FD were found between children from different cultures (e.g., between Americans, Nepalese and Philippines' children; [START_REF] Harper | Children's attitudes toward physical disability in Nepal: A field study[END_REF][START_REF] Harper | Children of the Philippines: Attitudes toward visible physical impairment[END_REF]. Even if FD seems to be stigmatized across times and cultures [START_REF] Kurzban | Evolutionary origins of stigmatization: The functions of social exclusion[END_REF], the specific affective states aroused may differ depending on the culture. More generally, future research using this typology is needed to better prove its internal consistency.

Finally, we took a static picture of all possible affective states, notwithstanding their timing. Considering the dual process of reactions to stigma, it is most likely that all affective states do not arouse at the same time, at the same level [START_REF] Pryor | A dual-process model of reactions to perceived stigma[END_REF]. On the contrary, some affective states may arise reflexively (e.g., disgust, fear) and others more deliberately (e.g., sympathy, hate). Further studies should thus examine the possible dynamic evolution of those affective states.

Implications

This research has several implications. First, it focused on affective reactions as they may be highly stigmatizing, engendering awkward moments [START_REF] Hebl | Awkward moments in interactions between nonstigmatized and stigmatized individuals[END_REF] but also supportive, engendering acceptance in relationships [START_REF] Bogdan | Relationships with severely disabled people: The social construction of humanness[END_REF]. The wide variety of affective reactions that was evidenced could be used in clinical settings. Indeed, interventions targeting social skills were developed in order to help visibly different people to confront difficult social situations (e.g., 'Changing Faces Package'; [START_REF] Clarke | Psychosocial aspects of facial disfigurement: Problems, management and the role of a lay-led organization[END_REF]. A better understanding of 'how' -and further research on 'why' -people react that way could thus be helpful, notably in psychosocial training programs targeting these specific affective reactions.

Second, as Bogart (2020) emphasized, social policy is a powerful way to act upon stigma. Nevertheless, as when designing any behavior change strategy, an indicator providing evidence of its effectiveness is needed. Our typology has thus been designed for that purpose, as a possible empirical tool providing indicators for evaluation purpose. Our findings also provide a basis for further empirical work investigating the determinants, correlates, and consequences of these reactions separately and of their interactions.

Third, this research provides the perceiver's perspective. Indeed, while focusing solely on the people with FD perspective, two assumptions are made: 1) stigmatizing reactions are obvious, and 2) experience of people with FD is not biased (e.g., by beliefs, former experiences). As researchers have shown that stigma reactions can be subtle (see [START_REF] Bos | Stigma: Advances in theory and research[END_REF], and that the stigma felt might rather reflect anticipation than actual discrimination [START_REF] Katz | Reliability and validity of an observer-rated disfigurement scale for head and neck cancer patients[END_REF], evidences of perceivers' reactions are needed in order to complement people with FD's testimonies. They might even be crucial when tailoring behavior change strategies. Yet, further work is required to determine how a greater understanding of these reactions in the context of disfiguring conditions can be applied to develop prevention strategies.

Conclusion

As for disability in general, there are two ways of seeing disfigurement issues (see [START_REF] Bogart | Ableism special issue introduction[END_REF]. First, it can be seen as an individual issue: people living with a FD bear differences from a standard. The solution has thus to be found among these stigmatized people. Second, disfigurement can be seen as a social issue: people living with a FD live in a society, which is not sufficiently inclusive and even biased against them. Here, the solution has to be found in their environment. In line with this second approach, this research documents affective reactions towards people with FD. Based on the perceiver's perceptions, we provide in a first step a comprehensive list of affective states that might be felt by the perceivers, and, in a second step, a typology of the most relevant ones, covering the main affective reactions. We hope this work will enable future research investigating determinants, correlates, and consequences of affective reactions to people with FD to try preventing them. Its aim was thus to contribute to a better understanding of how we can promote a more 'face positive' society, which would benefit the many rather than the few.

Figure 1 .

 1 Figure 1. Relationships between conditions and words in Study 1. Red-condition

Table 1 .

 1 Summary of the occurrences (number and total percentage) for each word produced depending on the instruction condition in Study 1.

	Occurrences	Standard	Positive incentive	Negative incentive	Total
	English translation (original French word)				Number	Percentage
	Disgust (Dégout)	9	0	43		9.68%
	Surprise (Surprise)	35	7	9		9.50%
	Fear (Peur)	21	0	26		8.75%
	Compassion (Compassion)	23	20	1		8.19%
	Empathy (Empathie)	20	24	0		8.19%
	Sadness (Tristesse)	14	7	2		4.28%
	Pity (Pitié)	10	1	8		3.54%
	Discomfort (Gêne)	10	1	7		3.35%
	Astonishment (Etonnement)	18	0	0		3.35%
	Disregard (Indifférence)	6	7	1		2.61%
	Sympathy (Sympathie)	4	8	1		2.42%
	Curiosity (Curiosité)	11	1	0		2.23%
	Benevolence (Bienveillance)	1	10	0		2.05%
	Uneasiness (Malaise)	4	0	5		1.68%
	Joy (Joie)	0	8	1		1.68%
	Neutrality

Table 2 .

 2 Summary of Exploratory Factor Analysis results using Maximum LikelihoodFactoring and Oblimin Rotation in Study 2. Factor's loadings are sorted by size. Factor loadings over .30 are written in bold. Factors: 1.

	Occurrences (French)	Skewness (SE) Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6
	Solidarity (Solidarité)	-0.47 (0.13)	0.78	-0.09	-0.01	0.04	-0.03	0.08
	Benevolence
	(Bienveillance)	-0.80 (0.12)	0.73	-0.08	0.09	-0.09	0.02	-0.02
	Sympathy (Sympathie)	-0.56 (0.12)	0.72	0.07	-0.05	0.02	0.07	-0.18
	Tenderness (Tendresse)	0.25 (0.12)	0.67	0.09	-0.06	0.16	0.00	-0.16
	Altruism (Altruisme)	-0.58 (0.13)	0.66	0.00	0.00	-0.10	0.12	0,00
	Compassion (Compassion) -1.07 (0.12)	0.65	-0.03	0.09	-0.16	-0.22	0.02
	Respect (Respect)	-1.02 (0.12)	0.65	0.07	-0.06	-0.03	0.25	0.02
	Empathy (Empathie)	-0.89 (0.12)	0.63	-0.03	0.14	-0.14	-0.17	-0.02
	Tolerance (Tolérance)	-1.35 (0.12)	0.62	-0.11	0.18	-0.17	0.21	0.04
	Understanding (Compréhension)	-0.81 (0.13)	0.60	-0.01	-0.02	-0.11	0.09	-0.05
	Affection (Affection)	-0.12 (0.12)	0.60	-0.08	-0.07	0.05	-0.11	-0.03
	Sorrow (Peine)	-0.41 (0.12)	0.58	0.11	0.16	-0.02	-0.32	0.07
	Injustice (Injustice)	0.38 (0.12)	0.45	0.17	0.05	0.29	-0.15	0.03
	Sadness (Tristesse)	-0.06 (0.12)	0.45	0.20	0.10	0.09	-0.40	-0.04
	Grief (Chagrin)	0.18 (0.13)	0.44	0.14	0.06	0.13	-0.43	-0.06
	Acceptance (Acceptation) -0.88 (0.12)	0.34	-0.16	-0.01	-0.18	0.16	-0.2
	Comfort (Réconfort)	0.97 (0.13)	0.34	0.14	0.09	0.20	0.07	-0.25
	Pity (Pitié)	-0.02 (0.12)	0.30	0.15	0.26	-0.04	-0.23	0.16
	Condescension (Condescendance)	1.31 (0.13)	0.12	0.03	0.03	0.11	0.01	0.06
	Apprehension (Crainte)	1.12 (0.12)	0.03	0.76	0.01	0.06	0.03	0.01
	Fear (Peur)	1.35 (0.12)	0.04	0.73	-0.04	-0.11	0.03	0.24
	Anxiety (Angoisse)	0.63 (0.12)	-0.10	0.66	0.09	0.03	-0.13	-0.08
	Uncertainty (Insécurité)	0.10 (0.13)	0.01	0.65	-0.08	0.08	0.06	0.14
	Fright (Effroi)	1.26 (0.12)	0.05	0.58	0.00	0.00	-0.05	0.21
	Distancing (Eloignement) 1.11 (0.12)	-0.04	0.57	0.06	-0.07	0.07	0.35
	Embarrassment (Embarras)	0.19 (0.12)	-0.04	0.51	0.24	-0.07	-0.16	0.15
	Intimidation (Intimidation) -0.70 (0.12)	0.11	0.45	0.19	0.08	-0.05	0.01
	Guilt (Culpabilité)	0.90 (0.12)	0.21	0.45	0.09	0.17	-0.17	-0.23
	Discomfort (Gêne)	0.04 (0.12)	-0.09	0.41	0.29	-0.02	-0.15	0.13
	Uneasiness (Malaise)	0.05 (0.12)	-0.14	0.40	0.33	0.03	-0.25	0.07
	Backsliding (Recul)	0.70 (0.13)	0.17	0.37	0.00	-0.04	0.27	0.26
	Trouble (Confusion)	0.18 (0.12)	-0.06	0.36	0.32	-0.04	-0.15	-0.04
	Startle (Sursaut)	0.79 (0.12)	-0.01	0.34	0.28	-0.01	-0.10	0.14
	Intrigue (Intrigue)	-0.57 (0.13)	0.07	-0.17	0.81	0.00	0.10	0.11
	Enquiry (Interrogation)	0.26 (0.13)	0.05	0.00	0.80	-0.05	0.01	-0.02
	Questioning (Questionnement)	-0.65 (0.12)	0.08	-0.06	0.72	-0.06	0.01	0.01
	Astonishment (Etonnement)	-0.38 (0.12)	-0.08	0.22	0.57	-0.08	-0.07	-0.04

Acknowledgments

The authors thank Celine Quint for having provided language help and Maxime Mauduy for his help in revising the manuscript. (revised January, 13th, 2022)

All data and materials have been made publicly available via the Open Science Framework and can be accessed at: https://osf.io/ercp3/?view_only=a8ea943260614a9b916a4e835dadb8bc.


Francois Pfister
email: francois.pfister@mines-ales.fr

A Design Pattern Metamodel and Use Mechanisms for Systems Engineering

In facing repetitive classes of problems during their projects, engineers need to combine practitioners' experience in design with solutions that are already capitalized, approved, and standardized. Sharing, interpreting, and applying this experience and these solutions allows engineers to improve their performance (including comprehensiveness and relevance) and their reliability (since they are using proven solutions that have been justified and argued contextually), while also raising their economic value (through time savings). In this way enterprises can capitalize on their engineers' experience.

The idea of using such "design patterns" is intended to help an engineer improve the nonfunctional features, quality of service, and "ilities" (Manola 1999) of a system under design. A design pattern is a simple and small artifact, linking a model of a problem noticed in a given context with a model of a well-known solution that has been already used to solve the problem in another but quite similar context on which the interest of the solution has been validated. This solution must then be imitated and adapted to another context. This approach is currently used in several engineering fields, such as traditional architecture [START_REF] Alexander | A Pattern Language: Towns, Buildings, Construction[END_REF], software engineering [START_REF] Gamma | Design Patterns: Elements of Reusable Object-Oriented Software[END_REF][START_REF] Coplien | Pattern Languages of Program Design[END_REF][START_REF] Harrison | The Language of Shepherding: A Pattern Language for Shepherds and Sheep[END_REF][START_REF] Fowler | Analysis Patterns: Reusable Object Models[END_REF], and process management [START_REF] Appleton | Patterns for Conducting Process Improvement[END_REF][START_REF] Van Der Aalst | Workflow Patterns[END_REF]). More recently it has been applied to systems engineering [START_REF] Barter | A Systems Engineering Pattern Language[END_REF][START_REF] Haskins | Using Patterns to Share Best Results: A Proposal to Codify the SEBOK[END_REF][START_REF] Haskins | Application of Patterns and Pattern Languages to Systems Engineering[END_REF]Schindel and Rogers 2005;[START_REF] Cloutier | Applicability of Patterns to Architecting Complex Systems[END_REF][START_REF] Cloutier | Applying the Concepts of Patterns to Systems Architecture[END_REF]. Despite this literature, however, the design-pattern concept remains poorly formalized for the systems engineering domain. Our research promotes a formalized metamodel for design patterns.

A System Pattern Metamodel

The proposed metamodel is a domain-specific language defined in ecore format shown in figure 1 and built taking into account a global systems engineering metamodel. So, the whole metamodel includes all entities needed to support a systems engineering process, as specified in the ISO 15288 standard.

The main concepts of the metamodel concern system-of-interest models and a catalogue of existing design patterns called system patterns. A system pattern is designed as a parameterized functional microarchitecture; in other words, a function graph in which some elements play given roles (pattern roles) linked by a parameter metaclass to roles (concrete roles) played by elements belonging to the model under study.

A system pattern identifies and describes a solution that addresses a problem in a given context. More precisely, a system pattern is characterized by a unique identifier, a short but evocative name, alternative aliases, a creation date, a textual description, and an author.

In the terms of the system pattern, a Problem describes the specified design problem that is motivating the system pattern. It is characterized by an informal description, a Feature to optimize, a set of competing Forces, and a use-case Model showing an elementary functional or organic architecture. A Force is a competing constraint which, when put in conflict with another constraint, is the cause from which the Problem arises. So the decision to apply a system-pattern depends from arbitration between the Forces. A Force is described by a challenge, a constraint and a Problem Type (which might include Fluid, Field, Structure, Security or others).

A Feature is an extra functional characteristic identified as an "ility". A Solution holds a Pattern Model, which is parameterized system architecture. It configures a design solution as a response to a Problem considering the given Context. There is only one solution for one pattern, but one Problem may have many solutions through several patterns by using equivalent patterns or related patterns.

Figure 1. A system-pattern metamodel

A Solution is illustrated by a use case showing a more relevant architecture and an Impact quantified by a Variation Sense (increase, decrease, equals) and a value on a scale. Impact is measured on a feature and allows one to quantify the influence of a system pattern on a system-of-interest model by detecting the optimized and degraded Feature. The Context is interpreted as a set of pre-conditions that define in what cases and in which conditions the System Pattern may be applied.

The Rationale justifies the system pattern by an explicit description and the associated argumentation; thus the rationale allows one to assume the system-pattern can be applied or not. This approach is different from a statistical observation which inventories known-uses in several Applications. Last Problems, Solutions, Contexts, Applications, and Rationales are indexable objects, described by Keywords.

A system pattern has a Domain that identifies a specific area in which a system pattern can be applied or is relevant, such as mechanics, electronics, software, civil engineering, organization and service, security, or pedagogy. System patterns are related to each other by several relationships: requested, related, and equivalent patterns, and antipatterns. Each system pattern references well-known cases (known uses).

Conclusion and Outlook

The proposed metamodel contributes to INCOSE's Model-Based Systems Engineering Initiative [START_REF] Estefan | Survey of Model-Based Systems Engineering (MBSE) Methodologies[END_REF]) by describing the required language that allows one to implement a catalog of systems engineering design patterns. This metamodel is currently under validation. The goal is now to provide mining techniques and models of alignment mechanisms to identify applicable design patterns in a given context. We have designed a software to support this meta model. The editor has to be fully interoperable with the main tools used by system architects. Mining and alignment mechanisms (based on model transformations) are under development.


Maxence Lafon
email: maxence.lafon@cea.fr

Vincent Chapurlat
email: vincent.chapurlat@mines-ales.fr

Jean-François Milot
email: jean-françois.milot@cea.fr

A model based approach to design, organize and monitor dismantling and decommissioning of nuclear facilities

Dismantling and Decommissioning (D&D) of nuclear facilities involves complex operations requiring the collaboration of a large number of stakeholders from various activities, and has to deal with numerous significant constraints. The CEA (French Alternative Energies and Atomic Energy Commission), is conducting research to better pilot these operations and reduce their costs and timeframes, and to improve overall performance. To this end, many issues remain to be solved, which lead to studying, then implementing in the form of a method with appropriate tools, the principles from systemics and the engineering of complex projects and systems. This method first consists in formalizing and specifying the entire set of requirements to be taken into consideration. Second, based on these requirements, the method will enable the project team to structure, check, and then to demonstrate the coherence and feasibility of the project from both the technological and organizational points of view. Lastly, the method should permit a constant re-evaluation of the D&D strategy and the management of its products, depending on the possible evolution of the D&D projects. Demonstration software is being developed, aiming to provide the functionalities requested for the design, implementation and maintenance of a future enterprise software, which should provide a complete D&D project Digital Mock-Up being interoperable and connected to the tools and databases of the stakeholders' information systems.

Introduction

Today, more and more nuclear facilities of various types are reaching their Dismantling and Decommissioning (D&D) phase. Managers must pay particular attention to the design and management of the D&D projects. They have to consider the inherent complexity and history of each nuclear facility, especially because it is difficult to generalize elements to all D&D projects despite significant capitalization and valorization of feedback.

Issues

Numerous complexity factors are met in D&D, such as:

• the many activities required to carry out D&D operations;

• the many stakeholders involved, and their various roles and responsibilities;

• the many and various interactions between these elements;

• the significant amount of data, information, and knowledge to handle;

• the strict requirements based on a strong risk culture;

• the project evolutions that require the models to be flexible and adaptable. At first, each nuclear facility may have been modified or impacted by incidents during its operation phase, which is often very long. These changes should thus be known and taken into account when designing and performing D&D projects, focusing among other constraints on ensuring safety at all times. In addition, designing a D&D project requests to take into consideration the variety of stakeholders and businesses involved: nuclear physics, nuclear chemistry, mechanics, robotics, nuclear instrumentation, computer science, etc. Indeed, they could express various requirements relating to their field of knowledge but dealing with the other fields. This imposes to improve the collaborative work and exchanges. Moreover, to meet the requirements, a large amount of data from different levels of detail should also be managed all along the D&D project life cycle. To this end, quite a few documents and deliverables of different kinds, involving skills from several businesses, are needed (OECD-NEA 2012) (IAEA 2013). Their creation, provisioning and updating are major stakes for managers. However, the quality and availability of data collected from the different phases of the facility's life cycle (including records, plans, etc.) represent a recurring issue for D&D projects. It is therefore particularly important to define the types of relevant raw data to be collected and traced for D&D projects as early as possible (IAEA 2014).

Towards a new method

Therefore, we have adopted Model Based Systems Engineering (MBSE) approach and principles (ISO, IEC, IEEE 2015) (NASA 2016) (INCOSE 2008). The purpose is to propose and promote a new method for D&D project engineering and monitoring, based on a systemic modeling framework and equipped with tools. This must support on the one hand nuclear facility description and characterization with a sufficient level of detail and considering the various data available, and on the other hand project description at a level of detail enabling first to design and to validate it before its deployment, then to monitor and adapt it in real time when it is in progress [START_REF] Nastov | Towards V&V Suitable Domain Specific Modeling Languages for MBSE: A Tooled Approach[END_REF].

The modeling framework takes care about the description of stakeholders' perspectives, aiming to be understandable and shareable, by guiding them throughout the classical functional, physical, requirements, behavioral and risks management points of view. This framework is based on systemic approach and is designed in order to integrate the D&D existing vocabulary or to emerge when requested a new common vocabulary. This has to be sufficient and unambiguous to support the collaboration between stakeholders and at the same time to take into account both the technical and organizational aspects of D&D projects.

Current existing standards or methods remain limited when considering various points of view, levels of detail, and modeling languages. Models are realized always using neither the same modeling language (conventionally denoted Domain Specific Modeling language DSML in MBSE context) nor interoperable languages nor even the same media over time. We may mention the case of the maps, which today are evolving on digital media. Models' federation is however requested for validation and monitoring, and more broadly for all activities involving decision-making strategies (Project Management Institute 2017). The goal of the new method is therefore to procure a D&D project "whole model" that is built step by step from the design phase. Especially this results from the federation or composition of current models in each point of view. The framework must integrate and enable the analysis of the interfaces, dependency relations (both from semantic or pragmatic aspect) and related links between all D&D models. This aims the whole project description to gain on relevance and accuracy when managers want to assess the global safety, security and performance of the project, to test and assess alternatives solutions, to trace the impact of some unforeseen events on the behavior of the whole project, and to validate in part or in whole the project.

Progress

Currently, the proposed method is being studied at CEA [START_REF] Lafon | Nuclear Decommissioning: a Systemic Approach adapted to Project Dynamics[END_REF]) [START_REF] Lafon | Nuclear Decommissioning: a Systemic Approach adapted to Project Dynamics[END_REF]. For a given D&D project, it first consists in formalizing and specifying all the requirements to be taken into account to bring the project to a successful end. Secondly, based on these requirements, the method should enable to structure, verify, and validate the project while demonstrating its coherence and feasibility both from a technical and an organizational point of view [START_REF] Pesola | Building Framework for Early Product Verification and Validation[END_REF]. Finally, the method should permit a continuous reassessment of the dismantling plans and products (e.g. waste), depending on the possible evolution of projects (new stakeholders, unforeseen events, etc.).

The method, especially thanks to MBSE, enables the construction of a formal representation of a D&D system related to each project. Such a D&D system is defined as "a set of elements of various and heterogeneous nature that interact in order to decommission a nuclear facility". It implements a set of basic concepts through some points of view, including the classical points of view previously mentioned.

First, these concepts and relationships are collected, and syntactically and semantically described in a generic metamodel, which is as timeless as possible, and therefore adapted to various nuclear facilities and compatible with the project evolutions.

DSML are defined for each point of view. Project managers will be able to model D&D systems and share their models all along the projects. These DSML must therefore be ergonomic and understandable by experts from various businesses who are not necessarily modeling experts.

The proposed method, to be enforced, has taken into account two important concepts:

• From the modeling side, the formalization of a D&D System as a system of systems including the properties described by [START_REF] Maier | Architecting principles for systems-of-systems[END_REF]; • From the management side and especially during project piloting, the implementation of a process management based on the principle of adaptive workflow as proposed for instance by [START_REF] Samiri | Toward a Self-Adaptive Workflow Management System Through Learning and Prediction Models[END_REF]. These two concepts are used and needed throughout the life cycle of the D&D system. Finally, we have implemented in the method the concept of modeling patterns, describing elements common to a set of projects (such a dismantling technique that is used in several scenarios, and its different features, or a waste outlet, including technical specifications for a given type of waste that can be found, among others, in several D&D projects). Modeling patterns can be made and shared among the stakeholders of several projects. They allow in particular to facilitate the handling of the metamodel to cope with this heterogeneity of facilities which are decommissioned. They guide, or even compel managers to draw from past experiences. In addition, we can ensure, through especially quite a few features, some flexibility (e.g. by an adaptation to evolution) and some dynamism (e.g. by an automatic feedback or by the verification and the validation of models) to the organization and the monitoring of a specific D&D project. The use of modeling patterns aims to catalyze the reproducibility and reuse of experienced project elements, to justify their use and thereby to facilitate decision-making steps to achieve and improve in real time the dismantling solution i.e. the D&D system as a whole, with a multi-point of view and multidisciplinary approach.

These patterns are made and validated by defined users, often experts in the various businesses involved in the D&D: nuclear measurement and instrumentation, transportation, regulation, etc. They are stored in a database and then can be used by each project manager to feed his specific model, or by other experts to create new patterns.

The patterns can of course evolve over time, consequently it is necessary to guarantee the traceability of the modifications and to manage the impacts on each project having used them.

Prospects

The method is today partially equipped and a demo software has been developed, based on use cases to prove the meeting of conceptual, methodological, technical, economic and human challenges identified at the beginning of the project. Results provide features requested to handle the proposed design and monitoring framework, helpful for the design, implementation and maintenance of a future enterprise software. This last tool should provide a complete D&D project Digital Mock-Up being interoperable and connected to the tools and databases of the stakeholders' information systems [START_REF] Chapurlat | Revisiting Digital Mock-Up for SME involved in Systems Engineering Deployment[END_REF]. This should be particularly useful for the overall management of D&D projects, and should catalyze collaborative work in D&D projects.


Axelle Hego

Floriane Collin

Hugues Garnier

Rémy Claverie

Rémy Claverie How

How do the soil, the vegetation and the weather affect the water content of a green roof ?

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

GdR MASCOTNum 2022

How do the soil, the vegetation and the weather affect the water content of a green roof ?

Axelle HEGO 1 , Floriane COLLIN 1 , Hugues GARNIER 1 , Rémy CLAVERIE 2 1 Université de Lorraine, CRAN, CNRS UMR 7039, 2 Cerema Est, Team research group, F-54510, Tomblaine, France • Meteorological data and real water content measured in a green roof of the CEREMA of Nancy

• Simulation of the water infiltration into the layers using Hydrus-1D © software where these equations are implemented:

  ∂ ∂   ∂θ(h) ∂t   ∂ ∂   water content = ∂ ∂ ∂ ∂x K(θ)   ∂h ∂x -1   ∂ ∂ water infiltration in the soil (1) -   ∂ ∂   S(h)   ∂ ∂   plant effect (2) (1)

Generation of N samples

Computation of the output Y(ω,t) (Fig. 4) Computation of the sensitivity index S i (t) (Fig. 5) Model Uncertain static param. X i s (ω) i s =1,...,k s (N×1) Uncertain dynamic param. X i d (ω,t) i d =1,...,k d and t=1,...,T (N×T)

Input U(t) Output Y(ω,t) (N×T) X k X i X 1 ((k s +k d )× T) S i (t) 1 0.5 t 1 t T
Challenge 1: How to generate dynamic input ?

(1) Each dynamic param. can be defined as:

X i d (ω, t) = X(t) + ε(ω, t)
with ω the randomness, X(t) the time mean and ε(ω, t) a stochastic variable defined by a correlation function C ii (t, t ′ ) and a distribution h(t) for each instant.

(2) Extraction of the statistical information from a data set:

Observed data (N obs ×T)

Time mean X(t) (1×T)

Time variation (N obs ×T)

+ = Time distribution h(t) Time correlation C ii (t, t ′ ) (T×T)
(3) Generation of dynamic param. using Iman and Conover procedure (1982):

Figure 1 -Figure 2 -

 12 Figure 1 -Green roof located in Tomblaine (France)

  Time correlation C ii (t, t ′ ) (T×T) Tranformation matrix P (T×T) Cholesky decomp. Independant samples following h(t) (N×T) Time correlated samples ε (N×T)(4) Results: net radiation for a typical month of June in Fig.3

Challenge 2 :Figure 3 -

 23 Figure 3 -Observed net radiation R n (t) of June 2020 and some generated samples.

Figure 4 -Figure 5 -

 45 Figure 4 -Observed and simulated water content VWC and rainfall

parameters affect the water content (model output) ?

  Richards equation which describes water inflitration in the soil (2) combination of Feddes function and Penman-Monteith equation which describe plants effect

	Problem statement
	Methods: Generation of uncertain dynamic input for GSA
	Aim of Global Sensitivity Analysis (GSA) : Better understand the model behavior
	Definition of the
	uncertain paramaters X i

• Input: Rainfall; • Output: Volumetric water content θ(t) or VWC in the substrate (ii) (Fig.

2

); • 6 soil parameters: θ s , θ r , K s , l, n and α;

• 5 meteorological variables: temperatures T max , T min , radiation R n , air moisture, wind speed; • 4 vegetation parameters: crop height, LAI, albedo and root depth.

→ 5 parameters are considered uncertain: θ s , n, α, LAI and R n (t) What


Luc Malhautier
email: luc.malhautier@mines-ales.fr

Stéphane Cariou

Paul Legrand

Evelyne Touraud

Philippe Geiger

Jean-Louis Fanlo

Treatment of complex gaseous emissions emitted by a rendering facility using a semi-industrial biofilter

Keywords: exhaust gas, rendering plant, semi-industrial biofilter, performance, spatial distribution

est destinée au dépôt

INTRODUCTION

From 2007 to 2013, the US rendering industry produced more than 8 million metric tons of rendered animal products, including tallow, meat and bone meal, poultry-byproduct-meal and feather mea1. [START_REF] Swisher | Market report: pressure is on US supplies, prices, and exports[END_REF] About 2.8 million tons of mainly meat by-products were treated in German animal-rendering plants in 1999 (German Federal Environment Ministry). [START_REF] Friedrich | Microbial community and physicochemical analysis of an industrial waste gas biofilter and design of 16S rRNA-targeting oligonucleotide probes[END_REF] In 2013, around 2.8 million metric tons of raw materials were processed by the French rendering industry (Syndicat des Industries Françaises des Coproduits animaux (SIFCO), www.sifco.fr). Although the products of these processes are no longer being used for animal feed production, rendering plants are still necessary for biologically safe waste treatment. [START_REF] Friedrich | Microbial community and physicochemical analysis of an industrial waste gas biofilter and design of 16S rRNA-targeting oligonucleotide probes[END_REF] During rendering, the heating of animal tissues liberates a variety of odorous organic and inorganic compounds, creating a significant source of odour nuisance. [START_REF] Luo | The use of pine bark and natural zeolite as biofilter media to remove animal rendering process odours[END_REF] The odour concentration of the encountered flow is generally between 20 000 and 1 100 000 OU E (European Odour Unit) m -3 . [START_REF] Luo | The use of pine bark and natural zeolite as biofilter media to remove animal rendering process odours[END_REF][START_REF] Anet | Characterization of gaseous odorous emissions from a rendering plant by GC/MS and treatment by biofiltration[END_REF] The composition of rendering gaseous emissions consists of a wide range of inorganic and organic compounds with about 300 identified compounds. [START_REF] Sironi | Odour emission factors for assessment and prediction of Italian rendering plants odour impact[END_REF] Moreover, it has been reported that the number of odorous compounds ranged between 20 and 50. [START_REF] Luo | The use of pine bark and natural zeolite as biofilter media to remove animal rendering process odours[END_REF][START_REF] Sironi | Odour emission factors for assessment and prediction of Italian rendering plants odour impact[END_REF][START_REF] Luo | Gas characteristics before and after biofiltration treating odorous emissions from animal rendering processes[END_REF][START_REF] Smet | Abatement of volatile organic sulfur compounds in odorous emissions from the bio-industry[END_REF] The odorous compounds that have been identified in gaseous emissions from rendering plants include hydrogen sulfide (H 2 S), ammonia (NH 3 ), organic sulphides (dimethylsulphide, diethyl sulphide), disulphides (dimethyl disulphide, diethyl disulphide), mercaptans (methanethiol), aldehydes (especially C-4 to C-7 aldehydes), amines (trimethylamine, C-4 amines), quinoline, dimethyl pyrazine, other pyrazines, indole, skatole and C-3 to C-6 organic acids. In addition, lesser amounts of C-4 to C-7 alcohols, ketones, aliphatic hydrocarbons, and aromatic compounds are potentially emitted. [START_REF] Sironi | Odour emission factors for assessment and prediction of Italian rendering plants odour impact[END_REF] More recently, other authors [START_REF] Anet | Characterization of gaseous odorous emissions from a rendering plant by GC/MS and treatment by biofiltration[END_REF] have identified and quantified the chemical compounds emitted by rendering plants causing odorant nuisance. Among the identified compounds, the most concentrated pollutants at the biofilter inlet were H 2 S, methanethiol, 3-methylbutanal, 2-methylpropanal and ethanal with concentrations generally above 10 mg m -3 . The treatment of these pollutants needs then to be efficient in order to reduce the olfactory impact of rendering plant. Over the last few decades, biofilters have become a popular means of odour control, particularly suitable for the treatment of malodorous gaseous effluents characterized by high flow rates (more than 100 000 m 3 h -1 ) and low contaminant concentration (from a few μg m -3 to 1-5 g m -3 ) such as rendering emissions. [START_REF] Friedrich | Microbial community and physicochemical analysis of an industrial waste gas biofilter and design of 16S rRNA-targeting oligonucleotide probes[END_REF][START_REF] Luo | The use of pine bark and natural zeolite as biofilter media to remove animal rendering process odours[END_REF][START_REF] Bourcier | Équarrissage : traitement des émissions gazeuses[END_REF] Open filterbed biofilters covering more than a 1000 m 2 area can be used. [START_REF] Friedrich | Microbial community and physicochemical analysis of an industrial waste gas biofilter and design of 16S rRNA-targeting oligonucleotide probes[END_REF][START_REF] Iranpour | Literature review of air pollution control biofilters and biotrickling filters for odour and VOCs removal[END_REF] The humidified waste gas is generally forced to flow upwards through the filterbed. Gaseous compounds transfer to the liquid phase of the biofilm where they are consumed as carbon, energy or nutrient source by the biomass. Nevertheless, some works contributing to the final objective of improving process design, and scale-up are really scarce. Hence, a thorough understanding of the compounds degradation mechanisms within model engineering biofilters continuously fed with industrial gaseous emissions is needed. When contaminants are introduced simultaneously into a biofilter, process performance is dependent on the interaction between the contaminants. [START_REF] Malhautier | Biofiltration of volatile organic compounds[END_REF] In the present study, the functional stratification of an experimental semi-industrial biofilter fed with an industrial gaseous effluent was thoroughly investigated by assessing the relative abundances of waste gas compounds using gas chromatography-mass spectrometry (GC-MS) and by quantifying sulphured compound concentrations (H 2 S, methylmercaptan, dimethysulphide, dimethyldisulphide (DMDS)) using gas chromatography. We focus on sulphured compounds since these volatiles have been identified as predominant odorants in the emission of a wide range of activities in bio-industry such as rendering plants.

MATERIALS AND METHODS

Inlet stream

A rendering process is defined as a process using high temperature and pressure to convert whole animal and poultry carcasses or their by-products with no or very low value to safe, nutritional, and economically valuable products. Raw material is dehydrated in continuous steam heated cookers. Condenser units are used to reduce the strongest odours which arise from cooking and reducing the temperature of the cooking steam to around 35-40 ∘ C. Remaining odorous gases (direct-fired meal dryers and workshops) can then be transferred to a biofilter bed constructed of materials such as concrete and layered products such as compost, coarse gravel, pinebark, and woodchips. [START_REF] Auvermann | Rendering[END_REF] The total flow rate emitted by the rendering plant chosen as study site was 180 000 m 3 h -1 .This waste gas was treated using a biofilter with a cross-section of 1720 m 2 and a bed height of 1 m.

Pilot-scale biofiltration unit

An outdoor pilot-scale biofilter (1.4 m internal diameter, 2 m height) and packed with sawmill chips (packing volume 3.1 m 3 ) was carried out for the treatment of the real and humidified (water content >97%) gaseous mixture emitted by the rendering plant. The gas flow rate, empty bed residence time (EBRT) and superficial gas velocity were 154 m 3 h -1 , 70 s and 100 m h -1 , respectively, which was representative of full-scale biofilter operation. At the bottom of the biofilter, a 0.2 m plenum and an above 0.2 m pebbles section were designed to homogenize the gas velocities before entering the filter. After dust removal in a water scrubber, the biofilter was continuously fed (except during maintenance of water scrubbers corresponding to 2-3 h per week), via a propeller (Invertek Drives, Welshpool, Great Britain), by the rendering emissions in upward flow mode. Even if the rendering activity was interrupted during the week-end, the pilot-scale biofilter was continuously fed with building ventilation airstreams. The mean characteristics of the packing material used are given in Table 1. The biofilter was inoculated by spraying packing material with supernatant (60 L) from activated sludge collected at the on-site wastewater treatment plant. The packing material was periodically sprayed with drill water (pH 7.7) (10 s every 5 h, corresponding to an inflow of 22 L m -2 day -1 ) to maintain constant high moisture content. During the experiment, the mean value of pH of the packing material and the pH of percolate waters were around 8 (Table 1). The biofilter operated for 600 days. Due to the size of the reactor, the complexity of the experimental device and the operation costs, only one biofilter could be implemented.

Sampling strategy

The performance of each compartment has been evaluated by gas sampling at three dates (7 April, 27 July and 6 October 2011) corresponding to a period of 6 months between 280 and 463 days of operation and to an usual operating activity (confidential data). Due to cost and time reasons, it has not been possible to carry out further gas samples over the total bed height and the biofilter operating period. Gas-sampling ports were located at 0, 0.2, 0.8, 1.6 and 2 m from the gas inlet. This enabled the biofilter performance to be assessed as a function of height. Gas sampling was carried out during functional steady state which corresponds to odour removal efficiency of 80% (data not shown). Gas samples were collected in laboratory-made 40 L Nalophan ® bags (for sulphur compounds quantification) or into a 1 L glass bubble (for gas chromatography-mass spectrometry analysis) using a KNF N86KN pump (Midisciences, Rousset, France).

Gas composition assessment

The extraction of pollutants from sampled gases was achieved according to the protocol developed by Lestremau. [START_REF] Lestremau | Development of a quantification method for the analysis of malodorous sulphur compounds in gaseous industrial effluents by solid-phase microextraction and gas chromatography-pulsed flame photometric detection[END_REF] Briefly, the extraction of pollutants was performed by SPME (Solid Phase MicroExtraction) in static mode using a PDMS/Carboxen (75 μm stableflex) fiber (Sigma-Aldrich, Saint-Louis, MO, USA). The SPME fiber was inserted in the 1 L sampling bulb through a suitable septum and was exposed for 10 min at 20 ∘ C. At the end of sampling, the fiber was retracted in the needle, removed from the bulb and thermal desorption was carried out in the gas chromatograph injection port which was held at 250 ∘ C.

The richness and the relative abundances of pollutants were determined by gas chromatography-mass spectrometry (trace gas chromatograph coupled with a DSQ mass detector (Thermo Fisher Scientific, Waltham, MA, USA)). An Optima 5-ms Accent analytical column, 0.25 mm internal diameter, 1 μm film thickness, 60 m (Macherey-Nagel, Düren, Germany) was used with carrier gas (helium 6.0) at a flow rate of 1.5 mL min -1 . The temperature of the detector was 200 ∘ C. The method used was as follows: 40 ∘ C for 9 min; 10 ∘ C min -1 from 40 to 90 ∘ C; 90 ∘ C for 6 min; 5 ∘ C min -1 from 90 to 250 ∘ C; 250 ∘ C for 10 min. The mass spectrometer was operated, by electronic impact, in full scan in the range of m/z 20-250.

Quantification of gaseous sulphured compounds

Gaseous concentrations of sulphured compounds were determined by connecting Nalophan ® bags to a gas chromatograph CHROMA-S (Chromatotech, Houston, TX, USA) with MXT-624 column (Øi 0.53 mm, length 30 m, stationary phase thickness 3 μm, Restek, Bellefonte, PA, USA) with a carrier gas (compressed air) at 130 hPa, and equipped with a flame photometric detector (FPD). The detector temperature was set at 150 ∘ C, and the oven temperature at 50 ∘ C. [START_REF] Zaouak | High performance cost effective miniature sensor for continuous network monitoring of H 2 S[END_REF] The calibration was realized using a certified gaseous mixture (Messer France, Puteaux, France) of hydrogen sulphide, methanethiol, ethanethiol, diethylsulphide, dimethylsulphide, dimethyl disulphide and carbon disulphide with a concentration of 100 mg m -3 each. The detection limit of each compound was 150 μg m -3 .

Determination of biofilter performance

For each compound i, the removal efficiency (RE i ) was calculated at the biofilter height h:

RE i,h = C i,inlet -C i,h C i,inlet (1)
where C i,inlet is the concentration of the compound i at the entrance of the biofilter.

RESULTS AND DISCUSSION

The aim of this study is to investigate the performance of a semi-industrial biofilter fed with a real (i.e. complex) gaseous mixture emitted by a rendering plant. Hence, we focus on compounds removal efficiency along biofilter bed height by comparing 'ionic current signals' for different compounds or families of compounds.

As the analysis of volatile sulphur compounds using PDMS (Polydimethylsiloxane)/Carboxen SPME (solid-phase microextraction) fiber is limited by the formation of artefacts such as the reaction of mercaptans to form the corresponding dimers (DMDS), we used another analytical system for this chemical family (direct quantification of gaseous sulphur compounds by connecting the sampling bag to a gas chromatograph equipped with a flame photometric detector). Moreover, the fingerprint of the inlet gas composition has been tentatively assessed (compounds identification and relative abundance expressed in percentage of total emitted compounds in the complex mixture) to check the composition similarity with other such gaseous industrial emissions.

Assessment of the inlet gaseous effluent composition

Waste gas analyses at the biofilter inlet (Fig. 1(A)) reveal that the effluent mainly contains aldehydes (54.8 ± 2.8% of the total emitted compounds) and sulphur compounds (32.8 ± 4.9% of the total emitted compounds). The most abundant aldehydes (10-15 identified compounds) are 2-methyl butanal and 3-methyl butanal followed by 2-methyl propanal. Among ketones, the dominant compounds are acetone, methyl ethyl ketone, propyl methyl ketone and methyl isobutyl ketone. Different esters and VFA (around 8-12 compounds for each chemical family) are detected. The identified alcohols are ethanol, 1-propanol and 3-methyl-1-butanol. The detected nitrogenous compounds are pyrrole, pyrazine (degradation products of DNA bases or amino acids such as proline, histidine) and trimethylamine. Ammonia is not detected. Concerning sulphur compounds (Fig. 1(B)), the dominant compounds are hydrogen sulphide (3.6 ± 2.8 mg m -3 ) and methylmercaptan (5.1 ± 2.4 mg m -3 ). According to these data (three dates), the composition of the inlet gas remains globally unchanged corresponding to a fingerprint currently observed for rendering gaseous emissions. The detected compounds in this study have effectively been identified from such gaseous samples. 2 -4,6,7 As a given molecule is linked to characteristic fragment ions, the removal of each chemical family and associated compounds within the biofilter could be evaluated.

Spatial distribution of pollutants along the biofilter height

The analysis of Figs 2 and 3 reveals a stratification pattern of pollutants removal. It is apparent that different chemical families with nitrogenous compounds, esters, VFA, alcohols and aldehydes are completely or mostly removed especially in the lower layers of the biofilter (up to around 1 m depth). The ionic current observed for aldehydes at 1.6 m depth is only due to the detection of 3 methyl butanal from one gas sample (7 April 2011) while it was not identified for the others. The removal efficiency of ketones at the biofilter outlet is about 97-98%. The ionic current observed for ketones at 2 m depth is mainly due to the detection of acetone from all gas samples. Hence, among ketones, acetone penetrated down the filters in all layers until breakthrough while the others are eliminated up to 1 m depth. In return, sulphur compounds removal seems to begin when nitrogenous and oxygenated compounds are degraded (from 0.8 m depth to 2 m depth). This functional stratification obtained for an experimental pilot unit fed with a complex exhaust air stream (around 40-50 compounds) corroborates the results observed for duplicated laboratory scale biofilters (about 10 cm across) fed with synthetic gases containing a few compounds only (up to 10 pollutants). 8,15 -17 Under long-term stable operating conditions, the treatment of a gaseous mixture (including ammonia and a mixture of volatile organic compounds), representative of composting emissions, revealed the same stratification pattern of elimination capacity within both bioreactors, with better and faster elimination of ammonia and oxygenated compounds compared with organic sulphur compounds. [START_REF] Cabrol | Bacterial dynamics in steady-state biofilters: beyond functional stability[END_REF] Other work has reported the lower biodegradability of sulphur compounds compared with oxygenated compounds, of ketones compared with esters and aldehydes and of acetone compared with methyl ethyl ketone. [START_REF] Sempere | Performance evaluation of a biotrickling filter treating a mixture of oxygenated VOCs during intermittent loading[END_REF][START_REF] Smet | Abatement of high concentrated ammonia loaded waste gases in compost biofilters[END_REF] Friedrich 2 investigated the vertical profile of a full-scale industrial biofilter by assessing the concentrations of some waste gas compounds (aldehydes, ammonia, hydrogen sulphide and dimethyldisulphide) for different depths of the filterbed using gas chromatography-mass spectrometry (GC-MS).

The authors stated that the biofilter section near the gas inlet proved to be the most active part for the degradation of ammonia and aldehyde compounds, while dimethyldisulphide concentration revealed no consistent decrease throughout the filter bed. The differences of removal efficiency between different compounds mainly lay in mass transfer characteristics, with a positive correlation between the degradation order and the substrate availability in the liquid phase. In our study, the better elimination of oxygenated (aldehydes, VFA, esters and alcohols) compared with sulphured compounds (methanethiol, dimethyldisulphide) may be due to transfer limitation of poorly soluble sulphur compounds from the gas to the liquid phase (biofilm). [START_REF] Chen | Performance evaluation of a wood-chip based biofilter using solid-phase microextraction and gas chromatography-mass spectroscopy-olfactometry[END_REF] This difference can also be attributed to biological factors. This pattern can be explained by competition between substrates: inhibition of hydrophobic compounds (methanethiol, dimethyldisulphide) metabolism by preferential hydrophilic substrates (aldehydes, VFA, alcohols and some esters). 15,20 -22 This pattern could also result from competition between bacterial taxa, through the selection of specialized populations able to degrade the biodegradable compounds at sections near the gas inlet and to largely out-compete the other taxa for space, energy and oxygen. [START_REF] Cabrol | Integrating microbial ecology in bioprocess understanding: the case of gas biofiltration[END_REF] -25

Concentration profiles of sulphur compounds along the biofilter height

As has been underlined by Lestremau,[START_REF] Lestremau | Investigation of artefact formation during analysis of volatile sulphur compounds using solid phase microextraction (SPME)[END_REF] the analysis of volatile sulphur compounds using PDMS /Carboxen SPME fiber is limited by the formation of artefacts such as the reaction of mercaptans to form the corresponding dimers (DMDS). Nevertheless, because of their very low odour thresholds (around 1 μg Nm -3 ), these compounds deserve special attention. Hence, the analysis of these compounds has been determined by using an adapted gas chromatography apparatus. The vertical pattern of sulphur compounds is sharpened by determining the concentration of dominant sulphur compounds. The results (Fig. 4) reveal that sulphur compounds removal begins from 0.2 m height (i.e. h/h total = 0.1). A sequential degradation of sulphur compounds is also observed: hydrogen sulphide is mostly eliminated up to 1 m depth while methylmercaptan (removal efficiency of 87%) and DMDS (removal efficiency of 73%) are mainly eliminated in the second half of the column. This analysis corroborates the biodegradation order of sulphur compounds: hydrogen sulphide > methylmercaptan > DMDS. [START_REF] Cha | Removal of organo-sulphur odour compounds by Thiobacillus novellus SRM, sulphur-oxidizing microorganisms[END_REF][START_REF] Hirai | Removal kinetics of hydrogen sulfide, methanethiol and dimethyl sulfide by peat biofilter[END_REF] According to literature, different specialized groups able to degrade hydrogen sulphide and organic sulphur compounds have been identified. [START_REF] Schäfer | Microbial degradation of dimethylsulphide and related C1-sulphur compounds: organisms and pathways controlling fluxes of sulphur in the biosphere[END_REF] This stratification seems then to display the enrichment and dominance of specific populations, favored by specific operating conditions. In the section near the gas inlet, hydrogen sulphide oxidizing bacteria would then out-compete other populations able to use organic sulphur compounds for their growth. [START_REF] Soupramanien | Biological treatment of a mixture of gaseous sulfur reduced compounds: identification of the total bacterial community's structure[END_REF]

CONCLUSIONS

Little information is available concerning vertical degradation profiles of model engineering biofilters (1.54 m 2 section and 2 m height) fed with industrial gaseous emissions. As has been highlighted in laboratory-scale biofilters treating synthetic gaseous effluents, an on-site biofilter used for waste gas abatement in an animal-rendering plant also exhibited spatial distribution of compounds removal efficiency. These results then revealed that the removal efficiency depends on the type of pollutants. It has been reported, at laboratory scale, that gaseous concentration of compounds is also related to their abatement levels. [START_REF] Malhautier | Kinetic characterization of toluene biodegradation by Rhodococcus erythropolis: towards a rationale for microflora enhancement in bioreactors devoted to air treatment[END_REF][START_REF] Estrada | Influence of gaseous VOC concentration on the diversity and biodegradation performance of microbial communities[END_REF] For example, for a bioprocess operator, it remains difficult to maintain the stability of full-scale biofilters, as industrial waste streams are characterized by variability in terms of pollutants concentration. . The concentration ratio C h /C inlet was plotted against the height ratio h/h total , where C h is the outlet concentration (mg m -3 ) at the height h of the biofilter (m), C inlet the inlet concentration (mg m -3 ) and h total the total height of the column (2 m). For each compound, the results obtained for different gas samples were averaged.

Hence, appropriate efforts (semi-industrial biofilters implementation, reliable sampling strategies) to determine to what extent biofilters are able to cope with a fluctuating environment must be made. Moreover, this work emphasizes the importance of improving gas-biofilter performance to achieve complete elimination of pollutants causing unpleasant odours by developing long-term reliable microbial resource management strategies (using microbial ecology principles) as microbial communities are key players of these complex engineered ecosystems.

Figure 1 .

 1 Figure 1. Assessment of the waste gas composition. (A) GC-MS analysis. nitrogenous compounds , sulphured compounds , aldehydes , ketones , esters , volatile fatty acids alcohols . (B) Detailed composition of sulphur compounds: hydrogen sulphide , methylmercaptan , dimethyldisulphide , dimethylsulphide . For each group or individual compound, the results obtained for different gas samples were averaged. h total : total height of the column, i.e. 2 m.

Figure 2 .

 2 Figure 2. Spatial distribution of chemical families of compounds (nitrogenous , sulphured , oxygenated . For each chemical family, the results obtained for different gas samples were averaged. h total : total height of the column, i.e. 2 m.

Figure 3 .

 3 Figure 3. Spatial distribution of oxygenated compounds. Aldehydes , ketones , esters , volatile fatty acids (VFA) , alcohols . For each chemical group, the results obtained for different gas samples were averaged. h total : total height of the column, i.e. 2 m.

Figure 4 .

 4 Figure 4. Concentration profiles of sulphur compounds along biofilter height. Hydrogen sulphide , methylmercaptan , dimethyldisulphide. The concentration ratio C h /C inlet was plotted against the height ratio h/h total , where C h is the outlet concentration (mg m -3 ) at the height h of the biofilter (m), C inlet the inlet concentration (mg m -3 ) and h total the total height of the column (2 m). For each compound, the results obtained for different gas samples were averaged.

Table 1 .

 1 Packing material characteristics. These values were obtained for dry packing material ± 0.3 †The specific surface area (a vs ) was estimated by measurement as sawmill chips are parallelepiped-like particles (a vs = 2lL+2lh+2Lh Llh with h: height; l: width and L: length). ‡The pressure drop was measured periodically over the entire bed height of 2 m.

	Physical properties
	Specific surface area a vs (m 2 m -3 ) †	632 ± 284
	Diameter dp sv (mm)	9.6
	Bulk density (kg m -3 )	330 ± 17
	Bed void fraction (%)	67 ± 3
	Pressure drop (Pa) ‡	< 10
	Water-holding capacity (g H 2 O g -1 material)	0.67 ± 0.04
	Chemical property
	pH	8.1

ACKNOWLEDGEMENTS

The project funding for Paul Legrand was supplied by Europe-Environnement SA, Aspach-le-haut, France.