Damien Givry
email: d.givry@aix-mrs.iufm.fr

Panagiotis Pantidos
email: ppantidos@nured.auth.gr

Toward a Multimodal Approach of Science Teaching

Keywords:

Major studies in science education have analyzed teaching based on verbal or written mode. Some researches suggest a multimodal approach. Our research studies how a Greek teacher of Physics in a ninth grade classroom uses several modalities to teach the concept of potential energy. Based on the precepts of Interaction Analysis, we analyzed video until a common agreement about the criteria was established. The results show that teacher performed different aspects of potential energy by using scenery, scenic objects and iconic bodily movements. The concept of potential energy can be more effective if teachers take into consideration these modalities.

Introduction

For decades, major studies in science education have analyzed teaching only with some aspects of language. Indeed, verbal or written texts were the dominant mode used to analyze teachers' or students' activity. It is only recently that researchers have focused on a multimodal approach of science teaching and learning (e.g. [START_REF] Kress | Multimodal Teaching and Learning: The Rhetorics of the Science Classroom[END_REF]. Thus, novel perspectives put to the foreground all the semiotic resources perceiving them as "grammatical" genres of making sense, interplayed one another (e.g. [START_REF] Pozzer-Ardenghi | How do we know he is not talking about himself? Demonstrations in science classroom[END_REF]. Speech, human body or spatial entities can be understood as vehicles of signs (i.e. semiotics resources) which support in different ways the construction of meanings. From this point of view, in any teaching event, scientific concepts are shaped by means of heterogeneous performances [START_REF] Pozzer-Ardenghi | On performing concepts in science lectures[END_REF] which are materialized in the classroom. The main idea behind such view is that semiotic resources situate teaching contexts which give knowledge shape (e.g., [START_REF] Kress | Multimodal Teaching and Learning: The Rhetorics of the Science Classroom[END_REF] affecting the way of students' thinking.

Theoretical background

In the context of adopting a multimodal approach with respect to science teaching [START_REF] Kress | Multimodal Teaching and Learning: The Rhetorics of the Science Classroom[END_REF], it sounds promising to focus our research interest on verbal and visual (non verbal) modalities that teachers use in order to communicate scientific concepts. In this sense, we argue that the meaning is distributed among various semiotic resources (verbal and nonverbal), which are essentially raised by teacher's performance. On that basis, an attempt is made to highlight the complex ways in which modalities are rhetorically orchestrated in science classroom.

According to previous work about semiotic approach in science teaching [START_REF] Givry | Toward a new conception of conceptions: Interplay of talk, gestures, and structures in the setting[END_REF][START_REF] Pantidos | The constitution of a "dictionary" for the semiotic analysis of physics teaching: a context of studying teaching practices by means of theatre semiotics[END_REF], our study focuses on: (1) acoustic signs (linguistic and paralinguistic signs), (2) kinesic signs (gestural and mimic signs, proxemics), (3) spatial signs (scenery, scenic objects). The discussion on linguistic signs relies on [START_REF] Jakobson | Essais de Linguistique Générale[END_REF] view on six functions of language (emotive, referential, conative, metalingual, poetic, phatic), while paralinguistic signs refer to prosody. Gestural signs rest on the movements of the whole body (i.e. hands, head, torso, feet et al.). These signs include gestures, i.e. semiotic movement of hands and arms, and specifically such forms which are called gesticulation: iconic (descriptive) and deictic (pointing) gestures (Mc Neil, 1992). Mimic signs are connected with facial expressions, while proxemic with the displacements of the human body. Finally, spatial signs concern scenery, i.e. anything that grounds a setting which cannot be moved (e.g. a board with a drawing on it), and scenic objects which are considered as material, moving, entities which one can manipulate with ergotic gestures (e.g. experimental artifacts). Our research focuses on three relevant signs linked to the speech: the scenery, the scenic objects, and the movements of the whole human body.

Research questions

This article emphasizes on how a physics teacher constructs his rhetorical style through various semiotic resources in a teaching about energy. More specifically our research needs to answer the following questions: Is this teaching of energy multimodal or not? Does teacher use only speech and written texts to teach the concepts about energy? What are the others modalities used by the teacher? The farther purpose is to examine how the teacher uses specific semiotic resources (i.e. different types of representational forms) in explanatory frameworks to perform various aspects of this physics concept. Although the above questions concern the topic of energy in general, we mention that, our analysis focused on several aspects of potential energy. Such a view does not essentially limit our research perspective for two reasons. First, in the specific lesson, the teacher takes advantage of the potential energy in order to exemplify 'how the concept of energy is conceptually organized' (e.g. conversion, store). Second, the kind of modes used in the episodes related to potential energy, are representative compared to the modes used in the entire teaching.

Research Design

Concerning the methodological context of the study, we collected video data from a physics lesson about energy, which took place in a ninth grade classroom in Greece. The video analysis is based on three stages. First, we recognized various aspects of the concept of energy which occur in the lesson. Second, we detected the video clips in which teacher explains these specific aspects. Third, we identified the semiotic resources used by the teacher to perform each feature of the concept of energy. Although, tools of semiotic analysis of the verbal mode were available to us (i.e. speech analysis context based on Jakobson's functions of language), we preferred to concentrate our analysis on the interplay between talk, scenery, scenic objects and body movements. We consider these elements as the protagonists of the 'story' of potential energy. Furthermore, following the precepts of Interaction Analysis proposed by [START_REF] Jordan | Interaction analysis: Foundations and practice[END_REF], both authors established a common agreement about the interpretation of each video clip. This collective interpretation allows us to explicit the criteria used for the analysis of the video, and to put these criteria into our transcriptions.

Results

Our point is to argue towards a multimodal approach for science teaching. In that way, our research shows that teacher uses more than speech and written texts to describe different aspects of the concept of potential energy. More specifically, our results illustrate how the teacher exposes the concept of potential energy by using (a) the scenery, (b) scenic objects and (c) iconic movements of body. We present our findings in terms of four assertions:

1. Teacher uses actively some elements of the scenery to express that potential energy is also converted into kinetic energy.

2. Teacher uses simultaneously elements of scenery and scenic object to illustrate that potential energy can be stored.

3. Teacher uses scenic objects to explain that various forms of energy can be converted into potential energy.

4. Teacher uses iconic bodily movements to describe situations from everyday life in which potential energy is stored or converted into another form.

Teacher uses some elements of SCENERY to express a new aspect of the potential energy

As far as spatiality concerns it should be mentioned that the blackboard is an important element of the scenery of the classroom. In our video, the lesson began when the teacher asked students to gradually construct a kind of conceptual map interconnecting the word ''energy'' with the verbs ''produced'', ''consumed'', ''transported'', ''stored'' and ''converted'' (figure 1). After that, he focused the discussion on the notion of ''converted energy'' by giving two examples (see figure 4 and 7 below). Sequentially, he wrote ''K => U'' above the verb ''converted''.

When the teacher finished to complete the kind of conceptual map on the blackboard (figure 1), he asked students to give examples about kinetic energy converted into potential energy.

Figure 1 Conceptual map of the concept of energy written on the blackboard

The figure 1 shows the written text on the blackboard concerning some aspects of the concepts of energy.

Traditionally, writing on the blackboard is perceived as a passive action which merely supports the explanations of the teacher. However, our data clearly demonstrates that scenery starts to be an active part of teacher's discourse. In this case, the deictic gestures (i.e. action of pointing) is the agent that joints teacher with blackboard and thus making him to use actively the written text on it.

Indeed, during the lesson, teacher points (deictic gesture) several times on specific words or relations on the blackboard. In episode 1, he uses the relation ''K => U'' written on the blackboard to express more than the idea of the kinetic energy is converted to potential energy. He uses simultaneously speech, deictic gestures and the text ''K=>U'' on the blackboard (scenery) to frame a question about the opposite relation (U=>K), i.e. potential energy is converted to kinetic energy (figure 2).

Episode 1:

Teacher: Is there an opposite example? This example shows that teacher's deictic gesture allows him to express more than what is contained separately in his speech and the written relation. That happens, because the meaning is conveyed simultaneously by three modalities. Actually, this episode illustrates how teacher's deictic gestures function as a bridge between speech and written text constructing a compact ensemble of meaning about a new aspect of potential energy (i.e. U=>K).

Teacher uses SCENIC OBJECT and SCENERY to express the concept of potential energy

This part shows how teacher uses a chalk (scenic object) and the blackboard (scenery) to convince students that an object (i.e. the chalk) can store potential energy. In this example, we argue that teacher expresses some aspect of the concept of potential energy by using scenic object and scenery in a specific way. Just before the episode 2, the teacher discussed with students on examples of stored energy. He made the following questions: ''What potential energy is?'' and, ''Is it a form of stored energy?'' The majority of students answered that potential energy is not a form of stored energy. Then, teacher by means of the simultaneous use of (a) a scenic object, (i.e. a chalk), and (b) the scenery, (i.e. the blackboard) attempted to demonstrate to students that an object can really store potential energy.

Episode 2 :

Teacher puts the chalk on the upper side of the blackboard and explains that the chalk has stored potential energy. He demonstrates this point by hitting the blackboard with his fist, which is causing the fall of the chalk (figure 3).

Figure 3 Teacher has put a chalk on the upper side of the blackboard. The chalk falls when he hits slightly on the blackboard

The fact that the chalk is falling down provides evidence that it had stored potential energy. More generally, teacher explained to students that objects contain energy (e.g., potential energy) when they are able to produce an action, or a change in their state or in their position. Teacher's performance underscored this change in terms of the conversion to another form (i.e., from potential to kinetic energy).

Teacher performed his demonstration by using simultaneously scenic object and scenery through ergotic gestures (i.e. movements of hands and arms to handle objects). In this example, teacher uses ergotic gestures to put the chalk on the upper side of the blackboard and to hit the blackboard. These gestures have a central role in teacher's performance. They show that he uses more than speech to explain that potential energy can be stored.

Teacher uses SCENIC OBJECTS to express the concept of potential energy

In this part, we show how teacher explains two aspects of the potential energy by handling some scenic objects. Indeed, episode 3 presents how the teacher chooses to toss a book in order to exemplify the conversion from kinetic to potential energy, and episode 4 shows how he lifts up a chair to illustrate how chemical energy is converted into potential energy.

Episode 3:

A student spoke about the conversion from kinetic to potential energy. Teacher illustrates this issue by tossing up a book (figure 4).

Figure 4 Teacher is tossing a book to exemplify the conversion from kinetic to potential energy

Episode 4 :

Providing another example teacher talked with students about the conversion from chemical to potential energy. He illustrated this specific relation between the two forms of energy by lifting a chair up (figure 5).

Figure 5 eacher lifts up a chair to illustrate how chemical energy is converted into potential energy

Besides, the action to elevate a chair also brings out some other aspects of the concept of energy, as for instance is the conversion from kinetic to potential energy, or the fact that an object can store energy. However, from a multimodal approach, the figure 5 describes in which way teacher is putting the chair up. Namely, he puts the chair up, while, at the same time he places his second hand on his arm. We consider that teacher refers to his body by doing this second gesture (glossed as a kind of deictic gesture). This second gesture underlines that the body of the teacher (specifically his arm) contained chemical energy, whereas the other ergotic gesture supports the idea about the potential energy. The general picture conveys the meaning of the chemical energy is converted into potential energy.

Both examples demonstrate how teacher expresses that various forms of energy can be converted into potential energy by using different scenic objects. In these examples the teacher's body movements, especially the ergotic gestures, are essential to understand his explanation.

Teacher uses ICONIC BODILY MOVEMENTS to express the concept of potential energy

In the previous episodes, we showed how teacher used real material (as scenic objects and scenery) to express some aspects of the potential energy. In this part, we pay attention on how the teacher explains some aspects of the potential energy when scenic objects and scenery are absent from the classroom's setting. We present two examples in which teacher illustrates aspects of the potential energy by means of iconic bodily movements.

Representing a bowman stretching a bow (figure 6) and an oscillated swing (figure 7). Both examples illustrate that teacher uses more than speech to teach concepts about potential energy.

Iconic bodily movements depict objects or events through human body movements. Such visualizations are not just mere representations of human actions or objects activities. They obtain a dynamic role in the teaching process since they gradually construct aspects of physics knowledge.

Episode 5 :

Students and teacher discussed about how the potential energy can be stored. Teacher performed this idea with iconic bodily movement of "stretching the string of a bow" (figure 6).

Figure 6 Teacher performs iconic bodily movement to stretch the string of a bow in order to illustrate how potential energy is stored

Episode 5 shows how the teacher adopts with his body the posture of a bowman and does simultaneously the iconic gesture to stretch the string of a bow. This somatic figure on the stage illustrates the concept of stored energy by iconically reflecting to the property of a bow.

Episode 6 :

In the same way, teacher performed the conversion from kinetic to potential energy by describing the movement of an imaginary swing (figure 7). In figure 7 (a) teacher pushes an imaginary swing using simultaneously the utterance: "I have a swing... I'am pushing it" and an iconic movement of pushing. In Figure 7(b), teacher's utterance: ''the swing is going up'' defines him as a moving swing. Additionally, his bodily functionality represents the features of a moving swing. By performing multimodal explanation, the teacher attempts to describe a situation in which the kinetic energy is converted into potential energy. However, the trajectory of the "swing" needs to go up to illustrate the conversion from kinetic to potential energy. But, as we can see in figure 7 (b), the horizontal body movement has a more important role than the hands' movement of going up. In that way, students could understand that the conversion from kinetic into potential energy happens when a swing is moving horizontally. This kind of misunderstanding can appear when students focus on the movement of teacher's body instead of his gestures. Maybe teacher could prepare some additional iconic gestures about potential energy to avoid the ambiguity with others gestures or body movements.

Discussion

Our results indicate that teacher takes advantage of more than speech and written text to perform some aspects of the concept of potential energy. Indeed, he actively used (a) the scenery (e.g. blackboard) in relation with deictic gestures, (b) scenic objects (e.g. chalk, book and chair) framed by ergotic gestures and (c) iconic gestures or body movements to refer to imaginary objects or events (e.g. swing or bow). The implications for science teaching are important, because the modalities used to describe aspects of energy could be directly available to other teachers for adapting them into their instructions. Thus, teachers, by taking advantage from this, are getting aware that anything is communicated cannot be confined in the verbal mode.

In general, it is our strong belief that a meaningful ensemble of semiotic resources such as gestures, displacements of teacher's body, material objects, drawings and verbal co-text can be significant in introducing a new concept, or approaching "hidden" aspects of it. However, teachers generally prepare their patterns of explanations and the written texts before the lesson. That is why, we propose that teachers have to design each lesson taking into consideration of a multimodal approach, i.e. they have to (a) select around scenery, scenic objects and iconic gestures, those which are the most relevant to explain some aspects of the concept, and (b) try also to minimize the ambiguous gestures.

Figure 2

 2 Figure 2 Teacher expresses another aspect of the potential energy through speech, deictic gestures and the written text on the blackboard (scenery) Figure 2 shows how teacher expresses a new link between kinetic and potential energy through: (a) his speech (''is there an opposite example?''), (b) his deictic gesture (his finger is pointing on the blackboard) and (c) the written relation ''K=>U'' (scenery). We interpret the figure 2 as teacher asks students to give an example of the conversion of potential energy into kinetic one.

Figure 7

 7 Figure 7 Teacher illustrates with iconic gestures (bodily movements) how kinetic energy is converted to potential energy.

Acknowledgements

We are grateful to Psychico College Middle School, as well as our colleague Fotis Vallinas for crucially contributing to this study.


Emna Sellami-Kaaniche

Bernard De Gouvello

Marie-Christine Gromaire

Ghassan Chebbo

A new method for modelling roofing materials emissions on the city scale: Application for zinc in the city of Créteil (France)

Keywords: City scale, modelling, emissions, roofing material, zinc, contaminant 1 Introduction

Today, urban runoff is considered as an important source of environmental pollution. Roofing materials, in particular the metallic ones, are considered as a major source of urban runoff metal contaminations. In the context of the European Water Directive (2000/60 CE), an accurate evaluation of contaminant flows from roofs is thus required on the city scale, and therefore the development of assessment tools is needed. However, on this scale, there is an important diversity of roofing materials. In addition, given the size of a city, a complete census of the materials of the different roofing elements represents a difficult task. Informations relating roofing materials and their surfaces on an urban district do not currently exist in urban databases. The objective of this paper is to develop a new method of evaluating annual contaminant flow emissions from the different roofing material elements (ex: gutter, rooftop) on the city scale. This method is based on using and adapting existing urban databases combined with a statistical approach. Different rules for identifying the materials of the different roofing elements on the city scale have been defined. The methodology is explained through its application to the evaluation of zinc emissions on the scale of the city of Créteil.

limited to the input data. For example, if three types of roofing materials are defined in the input data, the model will try to classify all roofing materials into the three types and will not be able to recognize another material. Moreover, the roofing material age is not identified. Finally, from an aerial image, only rooftop material areas can be evaluated. Besides, roof is also composed of other small elements (ex: gutter and valley) which can be a large source of runoff contamination. These elements are generally not visible on the aerial photography. Therefore, a method must be developed to evaluate roofing material contaminant emissions on the city scale. This method is based on the use of urban knowledge, the adaptation of existing urban databanks in the city and the definition of new approaches. The objective of this paper is to describe the method evaluating roofing material emissions on the city scale by studying the zinc emissions in the city of Créteil. This application in Créteil has two objectives. The first one is to validate the methodology. The second one is to analyze the transferability of the method to other cities and also to other contaminants. The development of the method from Créteil has enabled us to produce different methodological principles and practical rules.

Methodological Principles

This part describes the general methodology of the work, applicable to any contaminant. It is thus illustrated by examples for different contaminants.

General method to evaluate contaminant annual flow emitted by roofing material on the city scale

To evaluate roofing material contaminant emission on the city scale, the equation of its annual flow emitted by roofing material on the city scale is needed.

On the city scale, two parameters which determine the roofing material contaminant emissions have been retained: the surface or the length of the different materials used for the different roofing elements and the annual runoff rate for each contaminant from these materials.

The method developed to evaluate these parameters is described in figure 1. The different parts of this method will be explained in the following sections of this paper. In order to model the contaminant emissions on the city scale, describing and understanding the emission on the roof scale is needed. Thus, a new concept called typical situation of contaminant emission from roofing material on the roof scale has been defined. This concept allows the transition between the roof scale and the city scale. For each typical situation a contaminant annual runoff rate is associated.

A new method has been developed to identify and quantify roofing material surfaces or lengths on the city scale. This method is based on two main steps. The first one consists in quantifying the surfaces of rooftop materials classes1 and their associated valley and gutter lengths. The second one is the quantification of the rooftop material surfaces, gutter material lengths and valley material lengths using specific rules (Figure 1).

Annual runoff rates and typical situations of contaminant emission from roofing materials

A typical situation of contaminant emission from roofing materials on the roof scale is a situation for which a unique annual runoff rate for a contaminant is associated. On the roof scale, different parameters influence the contaminant runoff rate from roofing materials. These parameters can be classified into parameters related to the roof characteristics and parameters related to the exposure conditions and the time-related factors. The roof characteristics include material characteristics (age, type and composition) [START_REF] Bertling | Occurence and fate of corrosion-induced zinc in runoff water from external structures Science of the Total Environment[END_REF][START_REF] Wallinder | Atmospheric corrosion of zinc-based materials: runoff rates, chemical speciation and ecotoxicity effects[END_REF], the roofing element (gutter, rooftop…) [START_REF] Robert-Sainte | Annual metallic flows in roof runoff from different materials: test bed scale in Paris Conurbation[END_REF], inclination and orientation [START_REF] Wallinder | Effects of exposure direction and inclination on the runoff rates of zinc and copper roofs[END_REF]. On the city scale, the material characteristics should be taken into account. However, the orientation effects become smoothed as all types of roof orientations are combined. The roof slope was shown to be determinant for the runoff rate per m² of exposed material yet does not significantly affects the runoff rate per m² of projected area [START_REF] Wallinder | Effects of exposure direction and inclination on the runoff rates of zinc and copper roofs[END_REF]. On the city scale, identifying roofing materials is based on aerial photography databases which provide only projected area measurements. Thus, roof inclination will not be taken into account. The different roofing elements do not have the same contaminant runoff rate [START_REF] Robert-Sainte | Annual metallic flows in roof runoff from different materials: test bed scale in Paris Conurbation[END_REF] due to different collected runoff volumes, so the contaminant location on the roof is an important parameter to be taken into consideration on the city scale. In addition, contaminant runoff rates depend on exposure duration, rainfall characteristics (value, intensity, duration, pH) and a parameter considering previous exposure period [START_REF] Gromaire | Zn and Pb emissions from roofing materials-Modelling and mass balance attempt at the scale of a small urban catchment[END_REF]. These parameters are not taken into account in our case because we are focusing on annual contaminant runoff rate values. So for a city scale evaluation, two types of parameters seem relevant. The first one concerns material characteristics (age, type and composition) and the second one is the location on the roof. Thus, each typical situation of contaminant emission from roofing materials on the roof scale is defined as a simple case of a contaminant emission characterized by its belonging to a specific material and its location on the roof (see Table 1). The contaminant runoff rate for this typical situation will be noted r material, roof location .

2.2.1

Belonging to a specific material -Material age Runoff rates depend on the age of the material. On the one hand, the material composition depends on the period of its production. For example, a tin-lead component was added to the stainless steel composition in 1971 [START_REF] Invernizzi | Les couvertures métalliques : matériaux et techniques, L'inox en couverture[END_REF]. On the other hand, old materials present different runoff rates from the new material. For example, copper emission are higher for the older material (2,1 g.m -2 an -1 for copper 40 year old and 1,3 g.m -2 an -1 for new copper) [START_REF] He | A comparison between corrosion rates and runoff rates from new and aged copper and zinc as roofing material: Water[END_REF], whereas for paint containing biocides, the biocide runoff rate decreases from rain to another due to the limited quantity of biocide in the paint [START_REF] Jungnickel | Risk assessment of biocides in roof paint -Part 1: Experimental determination and modelling of biocides leaching from roof paint[END_REF].

-Sources of pollutants in roofing materials A pollutant released from a roofing material has a specific form of presence in the material. The pollutant can be the principal or a secondary component in the material composition. This is the case of metal materials (e.g. zinc, copper and lead) which are based on specific alloys composed of different components with different proportions. For example, steel is an alloy of iron and other elements such as nickel [START_REF] Invernizzi | Les couvertures métalliques : matériaux et techniques, L'inox en couverture[END_REF]. This is also the case of other roofing materials. For instance, bituminous membranes contain polycyclic aromatic hydrocarbons (PAHs) [START_REF] Bowen | Health safety and the enviroment-aqueous leaching of pac's from bitumen[END_REF]. The pollutant can also be a component in the coating added to the material during the production process. For example, zinc as a pollutant, releases from galvanized steel [START_REF] Bertling | Occurence and fate of corrosion-induced zinc in runoff water from external structures Science of the Total Environment[END_REF], i.e. steel coated with a thin zinc layer.

In addition, roofing material maintenance practises may be sources of pollutants. For example, renders and paints contain biocides which leached during rainfall periods [START_REF] Burkhardt | Biocides used in building materials and their leaching behavior to sewer systems[END_REF][START_REF] Jungnickel | Risk assessment of biocides in roof paint -Part 1: Experimental determination and modelling of biocides leaching from roof paint[END_REF][START_REF] Schoknecht | Leaching of Biocides Used in Facade Coatings under laboratory Test Conditions[END_REF]. Benzalkonium is a pollutant widely used as a demossing agent for cleaning tile roofs. This practice leads to benzalkonium transfer into stormwater (Van de Voorde et al., 2012). To conclude, a pollutant may come from three different sources: the material itself, the coating of the material and the roofing maintenance practices.

2.2.2

Location on the roof A roof is composed of four main elements: the rooftop, the tightness elements (valley, ridge, hips…), the evacuation of rainwater elements (gutter, pipes…) and accessories items (fixing components for slates…). For the same material, each element of the roof has a specific runoff rate. For instance, runoff rate for lead flashing against sidewall (0,88 g.m -².y -1 ) is very much lower than from rooftop lead (5,23 g.m -².y -1 ) due to orientation and shelter effect [START_REF] Wilson | Atmospheric corrosion of lead, Release of metals due to corrosion of materials[END_REF]. In addition, runoff rate from zinc rooftop (3,868 g.m -².y -1 ) is higher than from gutter zinc (1,654 g.m -².y -1 ) [START_REF] Robert-Sainte | Annual metallic flows in roof runoff from different materials: test bed scale in Paris Conurbation[END_REF]. We should note that the production of runoff rates on the roof scale is not the objective of our work. However, the existing runoff rates in the literature will be used to model the contaminant flow on the city scale.

Identification and quantification of roofing material elements on the city scale

A new method has been developed to identify and quantify roofing material surfaces or lengths on the city scale. This method is based on two approaches. The first one is a survey made by conducting interviews with the actors of the roofing material sector (industrials, master work, architect...) and consulting different documents (e.g. town planning regulation framework, construction laws, standardized technical documents). From this survey, concrete rules for the identification of roofing materials on the city scale have been established. The second one is a statistical approach for estimating the distribution of the materials of the different roofing elements on the city scale. The two approaches are combined in the method.

In figure 1, the first step of the method consists in dividing the city into homogeneous urban units. Each unit is obtained by crossing: -"Building classes" established through the adaptation of an existing land use database which allows us to connect building scale and urban scale; -With the historical urbanization process of the city. The crossing is conducted using specific rules which are based on three hypotheses: -The choice of a roofing material depends on the building typology.

-The spatial and temporal urban evolution of the city influences the use of roofing materials.

-The town regulation framework allows/recommends some roofing materials in the city. Each "Building class" located in an historical area represents a unit. For each unit, a random sampling technique is elaborated from the available building database. To ensure an absolute error less than 3%, the number of the selected random building depends on the total number of the existing building in the unit. This step provides the distribution of the rooftop material classes (ex: zinc, tile) and the gutter and valley lengths for each rooftop material class in each unit. In a second step, the material of the different roofing elements in each unit is quantified using a new set of rules. Three types of rules have been used: -Rules linking the rooftop material class to the rooftop material: these rules allow us to distinguish between the different varieties of the material class. For example, if the proportion of steel (as a material class) was identified in a specific unit, the objective is to get the distribution between galvanised steel, coated steel and stainless steel. In the case of units based on industrial building, the obtained rule is "coated steel is used in industrial unit".

-Rules linking the rooftop material to the gutter material: for a rooftop material there is a specific use of the gutter material. Thus, the obtained rule is "in metallic roof the gutter has the same material as the rooftop".

-Rules linking the rooftop material to the valley material: for a rooftop material there is a specific use of the valley material. Thus, the obtained rule is "in metallic roof the valley has the same material as the rooftop". Finally, for each unit the rooftop material surface area distributions and the valley and gutter material lengths are computed. Thus, contaminant annual flow emitted in roofing material runoff on the city scale is computed by multiplying the surface or the length of the material element by its associated runoff contaminant rate. All of these rules will be explained in the next part by studying the zinc emission in the city of Créteil. In fact, the different rules are sometimes global or specific to the site. Thus, it will be easier to understand them by studying a case study. complex case study should be chosen in order to represent most of the urban functions of any city. In fact, the city should present a sufficient urban diversity. The selected city is Créteil located about 10 km from Paris (France). Créteil with a total area of 11.5 km² (INSEE, 2008), presents a big diversity and a large number of buildings which represents about 24% of the city area. This city also presents an interesting urban and functional diversity (residential area, industrial area...). To quantify the different roofing material surfaces or lengths, urban data banks (historical urban map), land use database MOS-IAU2 have been reorganized in order to match with our objective and interviews that have been conducted with various actors such as masters of work, contracting authorities and architects. These interviews showed that information relating roofing materials and their surfaces on an urban district does not currently exist in urban databases. In the city of Créteil, different urban data (historical urban evolution, land use…) are available but they are not sufficient to achieve our objective to evaluate roofing material emissions. In this context, data acquired on Créteil have been adapted and transformed to provide new useful data that will be used in our work.

Annual runoff rates and typical situations of zinc emission from roofing materials

In the city of Créteil, zinc annual runoff rates have been produced for different metallic materials (Robert-Sainte et al., 2009) (see Table 2). We should note that zinc runoff rates from roof did not include atmospheric deposition. In fact, Robert-Sainte et al ( 2009) have firstly evaluated atmospheric input values on Plexiglas panels. Then, they have directly deduced these values from concentration levels before the calculation of zinc runoff rates. The studied new stainless steel, coated steel, new zinc, new aluminium and coated aluminium samples were standard products. Thus, they are considered as representatives for the hole of Créteil. However, for the preweathered zinc, the process depends on the producer and the product. The market share between the different producers is 70% for VMZINC, 20% for RHEINZINK and 10% for the others (MSI, 2012). In Paris area, the market share of VMZINC is even higher (information given by producer). VMZINC produces two types of pre-weathered zinc: Anthra zinc and Quartz zinc. Robert-Sainte et al. (2009) only tested Anthra zinc. Literature data in other countries do not allow concluding on the difference of zinc runoff between anthra zinc and quartz zinc.

Dividing the city into homogeneous urban units

To develop the method to evaluate roofing material surfaces or lengths on the city scale, specific urban data are needed. Thus, a survey has been established by consulting different urban databases, scientific literature, technical documents and interviews. The results of this survey enable us to define new rules for identifying the use of a roofing material on the city scale. In what follows, rules will be described and applied to Créteil city.

Rule 1: A specific roofing material distribution is associated to each "Building class"

The choice of a roofing material depends on the building typology. For example, in France, individual housing roofs are mostly covered with concrete or clay tiles. In Créteil, a land use database named MOS-IAU is available. This database is very detailed and describes all types of land uses such as green space and roads. To optimize the use of this database for our objective, different operations have been elaborated [START_REF] Belmeziti | A New Methodology for Evaluating Potential for Potable Water Savings (PPWS) by Using Rainwater Harvesting at the Urban Level: The Case of the Municipality of Colombes (Paris Region) Water[END_REF]. The first one is to focus only on building land use which still very detailed. Then, the building land use data are organized by gathering all buildings with the same use of roofing materials. Therefore, new building types have been created called "Building class" characterized by a specific roofing material distribution. Thirteen "Building classes" have been created: individual houses, apartment, secondary activities, administrations, sports, commercial space, education, cultural, offices, health equipment, transport, other building (ex: jail), other equipment (water, gas…). Finally, a new map of Créteil has been elaborated describing the different "Building classes" (see Figure 2). This map has been associated via QGIS4 software with a numerical cadastre named BD-topo database [START_REF] Ign | Institut national de l'information géographique et forestière: www[END_REF], which contains a vector description of the building layer. BD-topo database provides the roofing surface for each building. Thus, by crossing "Building classes" map and the BD-topo, roofing surface areas are computed for each "Building class".

3.3.2

Rule 2: A specific roofing material distribution is associated to each historic urban area The spatial and temporal urban evolution of the city affects the use of roofing material. For example, in central Paris, roughly 40% of all roofing surfaces are covered with rolled zinc, due to the urban planning made by Haussmann in the 19's century [START_REF] Gromaire | Incidence of zinc roofing on urban runoff pollutant loads: The case of Paris: Water[END_REF]. The city of Créteil is divided into four major historical urban areas: Old center, Mont Mesly, New Creteil I, New Créteil II. This division is however not perfectly relevant to identify roofing materials. The urban survey made in the city, enabled us to divide the city into 3 historical urban areas corresponding to different periods of construction (see Figure 2).

-Area 1 from 19th century to 1950: characterized by downtown and a majority of individual houses.

-Area 2 from 1951 to 1980: construction of economic buildings with several floors and flat roof.

-Area 3 from 1981 to 2008: great urbanization of the city (mainly apartment buildings) with specific requirement of the mayor: each new building should be with a pitched roof in order to get an urban continuity with the downtown. Architects who preferred flat roofs tried to build flat roof with slate or tile roof breaks.

3.3.3

Rule 3: The town regulation framework allows/ prohibits roofing materials in the city. In central Paris, architectural rules concerning the protection of historical monuments and their environment prevent any changes for many years [START_REF] Gromaire | Incidence of zinc roofing on urban runoff pollutant loads: The case of Paris: Water[END_REF]. In the city of Créteil, there is no specific recommendation for the roofing material use. The only restriction is the mayor requirements to have pitched roofs to preserve the identity of the old Créteil of the 19th century. The application of the different rules enables us to produce two different maps. The first map is an historical map and the second one is the "Building classes" map (see Figure 2). Homogeneous urban units By overlaying these two maps (see Figure 2); each building class located in an historical area is a homogeneous urban unit in terms of building types and historical location. In what follows the term unit will be used. To optimize the computation time, only the most important "Building classes" corresponding to a cumulated surface of at least 95% of the total roofing surface of the considered historical area are selected (see Figure 3). Three different units have been selected to study the influence of building typology and surfaces on the zinc emission: Unit 1: "individual houses class" located in area 1 (58.5% of the area 1 roofing surface) Unit 2: "apartment class" located in area 1 (37% of the area 1 roofing surface) Unit 3: "health equipment class" located in area 1(4.5% of the area 1 roofing surface). This unit has been selected because it presents many zinc roofs.

Quantification of rooftop material class surfaces and their associated valley and gutter lengths

This method is based on a stratified random sampling technique in conjunction with aerial photograph interpretation of the rooftop material class and their surfaces and measuring the gutter and valley lengths.

In this part, the statistical approach will be applied for the selected units. By overlying the unit map and the BDtopo database, the roof surface for each unit (N (m²)) is obtained. The sampling strategy is based on randomly generating independent buildings. Each selected building (b) has a specific roofing material. So, a database of buildings sampled in the unit with their roof surfaces S b (m²) is generated. By associating BD-topo and BDortho5 [START_REF] Ign | Institut national de l'information géographique et forestière: www[END_REF], for each sampled building (b), its valley length l v,b (m) and gutter length l g,b (m) are measured with QGIS and its rooftop material class is identified by looking to the image. In the sample s the total building surfaces S s (m²), the total valley lengths l v,s (m) and the total gutter lengths l g,s (m) are evaluated. Finally, for each rooftop material class i in the sample, the rooftop surface area S s,i (m²) and its proportion p s,i (%), the gutter length l g,s,i (m) and the valley length l v,s,i (m) are computed. These results are then extrapolated to the unit with uncertainty calculations.

Uncertainty calculations

The sampling strategy uncertainties were computed for: -p s,i : proportion of rooftop material class i in the sample s -The ratio between the valley length for each material class i and the total valley length in the sample s:

s v i s v l l , , , i s, v, R =
-The ratio between the gutter length for each material class i and the total gutter length in the sample s:

s g i s g l l , , , i s, g,

R =

The Theorem for Proportions [START_REF] Saporta | Probabilités analyse des données et statistiques[END_REF] is applied, in which the sampling distribution for samples with size n ≥ 30 (generated without replacement) is approximately normal, so:

        - × - = → ) 1 ( ) 1 ( ; T i s, N n n T T T N i i T i i σ where { } { } i s, g, i s, v, , i s, i g, i v, i R ; R ; T ; ; R ; T i s i p R p ∈ ∈
p i : the material proportion in the unit R v,i : the material valley ratio in the unit R g,i : the material gutter ratio in the unit The point estimate of T i is T s,i and an estimation of standard error is given by:

) 1 ( ) 1 ( , , N n n T T i s i s T i - × - = σ
At the confidence-level coefficient of α= 0.05:

[ ] i i T i s T i s i T T T CI σ σ × + × - ∈ = 96 . 1 , 96 . 1 , ,
Results are illustrated in Table 3.

Quantification of rooftop material surfaces, gutter material lengths and the valley material lengths for the selected units

A survey was made by conducting interviews with experts of the roofing material sector (industrials, masters of work, architects...). Different documents have been consulted: town planning regulation framework, construction laws, standardized technical documents (in France, DTU: Documents Techniques Unifiés), marketing research (MSI, 2006(MSI, , 2012)). A historical study was made concerning the roofing material evolution (appearance, disappearance, evolution characteristics …). In fact, the rapid development of industrial technologies affects the use and the material characteristics. Thus, an historical table was elaborated for roofing material historical evolution. The objective of this survey is to identify the different parameters influencing the choice of a material from the different material class varieties. Different hypotheses have been identified from this survey; they allow us to define rules. These latter enable us to get a first distribution of the material in the different roofing elements. In what follows, the different rules to evaluate materials in the selected unit are described. The first step was to cross roofing material historical evolution with the city of Créteil urban history. This work allows us to identify the roofing materials potentially existing in an historical area. Figure 4 describes the history of the different materials found in the city of Créteil and which emit the zinc contaminant [START_REF] Aocdtf | Encyclopédie des métiers -L'art du Couvreur[END_REF][START_REF] Lamesch | Histoire mondiale de la galvanisation: Arcelor[END_REF][START_REF] Hartmann | L'aluminium historique[END_REF][START_REF] Hartmann | L'acier historique[END_REF][START_REF] Invernizzi | Les couvertures métalliques : matériaux et techniques, L'inox en couverture[END_REF][START_REF] Payet-Gaspard | Célébration du 100e anniversaire de l'acier inoxydable : L'histoire de sa création, Les grandes étapes par secteur[END_REF][START_REF] Schonnenbeck | Histoire du zinc, sa production, sa mise en oeuvre[END_REF]. In addition, in France, roofing techniques are described in details in standardized technical documents (DTU), addressed to professional roofers. Indeed, all roofing techniques are indexed: materials that may be used and the way of their implementation (DTU 40.1,40.2,40.3,40.4,40.5 and 43). All constructions are expected to respect these reference documents. Thus, these documents have been used in order to identify the roofing material used for the different roofing elements. In DTU documents, gutter material is not specified for each rooftop material class. The roofer has the choice between five gutter materials: zinc, copper, stainless steel, PVC and aluminium. For metal rooftops, valley is considered as a part of the rooftop and thus has the same metal material, whereas for the other rooftop material classes, valley materials could be zinc or lead or the same material as the rooftop (tile, stales...). 3 and Table 2 show that the roofing material classes that emit zinc are galvanized steel, zinc, and coated steel. The zinc material class presents different material varieties: natural zinc, pre-weathered zinc, coated zinc and coloured zinc. During the identification of rooftop material from aerial images, all collared materials were classified into "other material class''. Thus, collared zinc will be ignored. To distinguish between the other zinc varieties, other information is needed. The selected units: individual housing class, apartment class and health equipment class, are located in area 1. In this latter, by looking to Figure 4, the only zinc existing variety is natural zinc. Buildings located in area 1 are however old and their roofing materials have probably been renewed at least once time. The zinc cycle life is about 50 years (MSI, 2006). The zinc producers (e.g. VMZINC) say that old natural zinc renewal is usually done with the same zinc variety. To conclude, in area 1 the zinc variety used is natural zinc. The natural zinc age is less than 58 years if we consider that it was renewed once. For coated and galvanized steel they are appeared in roofs in 1975, their age is about 33 years. The life cycle of steel is about 100 years (MSI, 2006).

3.5.2

Rules linking the rooftop material to the gutter material Gutter materials are of six different types (DTU). The used zinc is mainly natural zinc. The survey shows that today, the gutter market in France is divided between three principal materials: natural zinc, PVC and coated aluminium. The other gutter materials represent only 5% of the market and therefore, their contribution can be neglected in a first approach. Figure 4 shows that PVC appeared in the 1980's and coated aluminium in 2000. Therefore, in area 1 these two materials are not originally present: the existing gutter materials are copper and natural zinc. If we consider the cycle life of natural zinc (50 years) and of copper (70 years) (MSI, 2006), thus, the gutters have been renewed at least once. Zinc and copper are noble materials, gutter with those materials are generally renewed by the same material (according to interview with roofing material experts). In selected units, gutters are linked to the rooftop material: tile, coated steel, galvanized steel zinc, slates and shingles. Coated steel and galvanized steel are economic roofing solution appeared in 1975. Such roofs are strongly correlated with PVC gutters, in the proportion of about 80% in PVC, the 20% remaining being mostly in natural zinc (according to interview with roofing material experts). For natural zinc rooftop, the gutter material is old natural zinc. For shingles which are mainly used during the 1980's and are considered as economic materials, the gutter material distribution is probably the same as for coated steel. Finally, for old tile and old slates rooftops, the considered materials are natural zinc and copper. Copper is an expensive material and its use in gutter will be very limited compared to natural zinc. In addition, as our objective is to evaluate zinc emission, we assume, using a first overestimation approach [START_REF] Belmeziti | A New Methodology for Evaluating Potential for Potable Water Savings (PPWS) by Using Rainwater Harvesting at the Urban Level: The Case of the Municipality of Colombes (Paris Region) Water[END_REF], that gutter material distribution for old tile rooftop is 95% in natural old zinc and 5% in old copper.

3.5.3

Rules linking the rooftop material to the valley material The survey made with the actors of the material sector shows that for metal rooftop, valley materials are the same as the rooftop materials. The obtained rule is: "For metal rooftop, the valley is a part of the rooftop". Thus, valley will be computed only for non metal rooftop (tile, slates, shingle). In this case, valley material could be zinc or lead or the rooftop material (tile, slates, and shingle). The survey shows that the zinc used for valleys is then natural zinc. For lead, it was used in very old building built before the 19 th century. In addition, in area 1, the oldest building is dating from 1900 and then lead in valley was not used. To have an estimation of the tile valley proportion, natural zinc valley proportion and slates valley proportion, we adopt here again an overestimation approach [START_REF] Belmeziti | A New Methodology for Evaluating Potential for Potable Water Savings (PPWS) by Using Rainwater Harvesting at the Urban Level: The Case of the Municipality of Colombes (Paris Region) Water[END_REF]. It means that, as our objective is to evaluate zinc emission, the quantification of valley lengths will be majored by considering that all valleys are made in natural zinc.

Zinc annual flow calculation for the selected units

The zinc annual flow emits by rooftop, gutter and valley material will be computed using the following equation: Where D represents the roof location dimension: area for rooftop (m²) and length for gutter and valley (m)). r zinc, roof location is the zinc annual runoff rate emitted by the different roofing material elements. Runoff rates are taken from Table 2.

Results and discussion

The evaluation of zinc emissions from roofing materials on a city scale shows that zinc emissions depend not only on the surface of the considered unit but, also on the building typology (see Table 4) . In addition, the principal source of zinc emissions is the rooftop. However, other elements of the roof such as gutters and valleys may contribute significantly to zinc emissions. For instance, for the individual housing unit with rooftops with a majority of tiles (83% tile roof, 2% zinc roof), the principal source of zinc emissions is the gutter (23.7% of the whole zinc emissions from the three units versus 15.7% providing by rooftop) (see Figure 5). Besides, although the zinc emissions from valleys are the lowest (3.23% of the total for the three units), the valley emissions in the individual houses (2.64% of the total) are of the same order of magnitude as the rooftop emissions in the health equipment unit (3.7%). Thus, the zinc emission from tightness elements such as valleys should not be neglected. Therefore, the contribution of the different elements of the roof (rooftop, gutter and valley) to zinc emissions strongly depends on building typology and the unit area. The validation of this method is difficult. In fact, it is impossible to experimentally measure roof emissions on a city scale. In addition, stormwater collected in the drainage systems are a mixture of the different types of urban surfaces. Moreover, in Créteil, no experimental data of zinc emissions from roofs or from other sources have been found. Nevertheless, some literature zinc fluxes data can be found. In fact, zinc emissions can be measured in some experimental roof runoff, sometimes with a rough extrapolation to the whole roofing area of a catchment scale.

In addition, measurements can be made in the stormwater sewer on a catchment scale. Thus, annual zinc runoff rates from roofs, computed in this study, were compared to other values collected in the literature (see Table 5). We should note that annual zinc runoff load data are very limited in the literature. The comparison shows that results obtained from this method are promising. In Table 5, the mean zinc annual runoff rates from roofs have been elaborated by a rough extrapolation on the catchment scale of data measured from some experimental roofs. For stormwater catchment, measurements have been taken in separate sewer systems. This latter contains mixed urban runoff sources (roof, green space, road, sewer transfer...). Thus, the zinc runoff rates computed correspond to the whole zinc emissions on a catchment scale provided by different urban sources. In France, a residential site with 3.3% of zinc roof emits 478 mg/m²/year and a residential site with 50% of zinc roof emits 1062 mg/m²/year. Therefore, values computed in this study belong to the range elaborated for the different sites. Measurements of zinc in stormwater have been taken in different sites in France and the USA. For sites with a high zinc roof density (30%), zinc emissions in stormwater on a catchment scale are very high. For instance, the zinc emission values measured in stormwater catchments are evaluated throughout the whole catchment surface area, contrary to our study where the values are computed only for the roof area. Therefore, roofs are an important source of zinc emissions compared to the zinc emissions in stormwater on the catchment scale. Is important to note that this observation also remains valid even in the case where the zinc roof proportion is small. Finally, even if rooftops are the principal source of roof runoff contamination, the emissions of the other different roof elements (e.g. gutter and valley) should not be neglected.

A deeper validation of this method could be done by its integration into a larger substance flow analysis model that estimates the whole contaminant emission provided by different sources on the city scale. But, even with such an approach, this validation may create a difficulty to describe the processes within the sewage network.

In the city of Créteil, Robert-Sainte (2009) evaluated the zinc annual atmospheric deposition rate (34.2 mg/m²/year). This value belongs to the range elaborated for different sites in France. Roofs are a large source of zinc emissions in Créteil compared to the atmosphere: industrial activities are very limited (14%of Créteil area) and consequently, the related zinc emissions in the atmosphere.

Conclusions

A new methodology evaluating contaminant flow emissions on the city scale has been developed by studying the zinc emissions in the city of Créteil. It is based on using and adapting existing urban databases in conjunction with a statistical approach. This method contributes to an assessment of pollutant flows on the city scale and then, the impact of a city or an urban area on the environment can be evaluated.

Our method can be used as a decision-making tool by urban planners at three levels to implement policies in order to reduce roofing pollutants emissions. This innovative method will firstly allow them to assess the state of the emissions for existing roofs all over the city. They will then be able to define a plan of renewing roofing materials on the urban scale. And finally, it will be also possible to define a roofing material choice strategy for the construction in new urban areas.

To conclude, some considerations should be taken into account to apply this method to other cities. Some adaptations need specific work. The historical urban evolution of the city map has to be elaborated for each studied city. This type of map can be available in the municipality library databases. It is also important to identify the different existing rules in the city related to the roofing materials use such as the town planning regulation framework (e.g. the Local Urban Planning scheme) and construction regulations. For the Ile-de-France cities, the building class databases are the same as Créteil. Elsewhere, land use databases are available but present some differences versus MOS-IAU. Whatever the land use database, it should be reorganized to get the thirteen "Building classes" created from the MOS-IAU land use database.

Other elements of the method can be applied with minor changes. Most of the rules linking the rooftop material classes and the material of the different roofing elements could be directly applied. The historical evolution of the roofing material table can be used in any city. Other rules are specific to Créteil, but they highlight some principles which can be adapted to other cities. The renewal process of the material because of its age strongly depends on the historical evolution of the city. Moreover, the specificities of the city can be used to optimize the computing process. For instance, one can find texts prohibiting roofing materials in urban planning city regulations: the number of roofing materials to be taken into account is therefore reduced. Finally, runoff rates for different contaminants emitted from roofing elements could be used in other cities except for those where very specific local conditions may affect emission processes. Actually, the practical table of runoff rates for different contaminants presented in this paper is not complete. The production of more runoff rates is still needed.

Figure 1 :

 1 Figure 1: General method to evaluate contaminant annual flow emitted by roofing material on the city scale

Figure 2 :

 2 Figure 2: (a) Historical map (b) "Building classes" map

Figure 3 :

 3 Figure 3: The distribution of roof surface "Building classes" in the area 1 (1900-1950)

Figure 4 :

 4 Figure 4: The historical evolution of roofing material emitting of zinc

Figure

  Figure 5: Distribution of the total zinc emissions Table 4: Results for annual zinc flow for the three selected units from the three units from the different sources

Table 1 : Examples of typical situations

 1

	Pollutant	Type	Age	Material	Form	Location on the roof	Annual runoff rate
	Chrome	Stainless steel	new	Component of stainless steel sheet	Rooftop	0,8 à 1,2 (mg.m -2 an -1 ) (Odnevall Wallinder et al., 2002)
	Lead	Copper	old	Component of copper sheet	Gutter	0,9 (mg.ml -1 .an -1 ) (Robert-Sainte et al., 2009)
	Zinc	Zinc natural	new	Principal component of zinc sheet	Gutter	0,871 (Robert-Sainte et al., 2009)

Table 2 : Typical situations of zinc emission

 2

		Material	Localisation on	Annual average runoff rate
	Type	Age	Form	the roof	(g/m²/year) (g/ml/year *)
	Zinc natural	New	Principal component of zinc sheet	Rooftop Sealing element 3 Gutter* Valley* 3	3.9 0.87
	Zinc old	35 years 40 years	Principal component of zinc sheet	Rooftop Gutter*	4.2 0.81
	Anthra zinc	New	Principal component of zinc sheet	Rooftop Gutter*	2.3 0.50
	Galvanised steel	New	Principal component of the coating the of galvanised steel sheet	Rooftop	2.0
	Coated galvanised steel	New	Principal component of the coating the of galvanised steel coated sheet	Rooftop	0.025
	Stainless Steel	New	Component of stainless steel sheet	Rooftop	No emission
	Lead	New 50 years	Component of lead sheet Component of lead sheet	Rooftop Rooftop	0.052 0.11
	Aluminium	New	Component of aluminium sheet Component of aluminium sheet	Rooftop Gutter*	0.034 No emission
	Aluminium coated	New	Component of aluminium coated sheet	Gutter*	No emission
	Copper	New 20 to 25 years	Component of copper sheet Component of copper sheet	Gutter* Gutter*	0.002 0.021

[START_REF] Robert-Sainte | Annual metallic flows in roof runoff from different materials: test bed scale in Paris Conurbation[END_REF]

Table 5 : Comparison of annual zinc runoff rates for different sites and different sources Sources Mean Zinc annual runoff rates (mg/m²/year) Site location References

 5

		333-673	Créteil (France)	This study
	Roofs	478	Residential site: 3.3% of zinc roofs (Nantes, France)	(Lamprea, 2009)
		1062	Residential site: about 50% of zinc roofs (Paris, France)	(Thévenot et al., 2007)
		34.2	Créteil (France)	(Robert-Sainte et al., 2009)
	Atmosphere	15 -140	France	(Azimi et al., 2005; Bressy, 2010; Garnaud et al., 1999; Lamprea,
				2009; Sabin et al., 2005)
	Stormwater on a catchment scale	240 -430 4 -80 39.8 50.2 54.8	Residential site: 30% of zinc roofs (Noisy-le-Grand, France) Residential (Florida, USA) Residential site: 3.3% of zinc roofs (Nantes, France) Mixed site (Nantes, France) Industrial site (Lyon, France)	(Bressy, 2010) (Wong et al., 2000) (Lamprea, 2009) (Becouze, 2010)

A material class is defined as the gathering of different materials having the same principal material. For example, steel is considered as a class which gathers different varieties of steel: natural steel, galvanised steel, stainless steel, coated steel.

Application of the methodology for zinc emissions in the city of Créteil3.1 Case Study SiteThe goal of our research work is to develop a general method to quantify roofing material surfaces or lengths on the city scale. In this context, a case study is needed to achieve two objectives. The first one is to validate the method. The second one is to make it possible to apply the method to other cities. Therefore, a sufficiently

IAU: Institut d'Aménagement et d'Urbanisme d'Ile-de-France: institute of planning and development for the Greater Paris region. http://www.iaurif.org/

For sealing element and valley, no runoff rates data have been produced. Thus, we propose an approximation for these two values. For sealing element they have been approximated by the rooftop runoff value and valley it was approximated by the gutter one.

Quantum GIS (often abbreviated QGIS) is a cross-platform free and open source desktop geographic information systems application that provides data viewing, editing, and analysis capabilities. http://www.qgis.org/

BD-ortho images come from IGN's (Institut Géographique National) which contains digital colour ortho-photos with three or four (redgreen-blue-near infrared) bands and with a 50 cm ground resolution.

Acknowledgements

This study has been conducted as part of the OPUR research program. The authors gratefully acknowledge the Centre Scientifique et Technique du Bâtiment (CSTB) for their financial support.

Table3 : Rooftop surface area, gutter length and valley length computed for each material class for three units: individual houses, apartment and health equipment classes located in area


Iza Marfisi-Schottman

Gunnar Karlsson

Jonas Celander Guss
email: jonascg@gmail.com

Demo: Opphosa participative light and sound show using mobile phones in crowds

Keywords: K.4.3 [Computer and society]: Organizational Impacts -Computer-supported collaborative work Algorithms, Performance, Design, Human Factors Opportunistic network, participative, smartphones, emergent art

Opphos is a mobile application that creates participative light and sound shows by using and coordinating the screens and speakers of smartphones of people in crowds. These shows are made up of waves of color and sound that are generated by the cheers and movements of the participants. Opphos is built on a peer-to-peer network middleware that provides communication between mobile phones in large crowds, where standard cellular networks would not be available or sufficient.

INTRODUCTION

People like to gather in crowds at concerts and sports events, not only to watch the show, but also to be part of a collective and unique experience [START_REF] Reeves | Designing for crowds[END_REF]. Interactive systems that support such experiences have become increasingly popular, especially systems that create crowd-sourced light shows [START_REF] Reeves | Designing for crowds[END_REF]. However, as the size of a crowd increases, it becomes a technical challenge to capture and process the participants' actions and hence the level of interactivity might decrease or even disappear completely. The light show created with Mickey Mouse ears in California Disneyland 1 or the LED panels at the London 2012 Olympics closing ceremony 2 for example, are controlled by centralized systems that orchestrate the show and do not support interaction from the crowd. Because of their centralized structure, these systems require additional infrastructure (e.g., wired connections between devices, infrared emitters) and are therefore not affordable by most artists.

In this article, we present Opphos 3 , a mobile application that creates participative light and sound shows using the screens and speakers of smartphones in crowds, without the need for any infrastructure. We start by presenting the two modes of Opphos, 1 http://www.theverge.com/2012/8/13/3239390/disney-glow-with-the-show-led-ears 2 http://www.dezeen.com/2012/08/13/pixel-animations-at-london-2012-olympicclosing-ceremony-by-crystal-cg/ 3 Opphos comes from the words "opportunistic" and "phos" (light in Greek). designed to support participative and unique collective experiences. Then, we explain its adaptive mediation algorithm that enhances the cheers and movements of a crowd by creating artistic waves of color and sound. Subsequently, we describe the opportunistic network that our application is built on and that ensures communication between the mobile phones even in large crowds, where standard cellular networks would not be sufficient or where they are not available. Finally, we discuss the future evaluations of Opphos at ExtremeCom and in live concerts.

PARTICIPATIVE EXPERIENCE

Tomitsch et al.'s study [START_REF] Tomitsch | A Concept to Support Seamless Spectator Participation in Sports Events Based on Wearable Motion Sensors[END_REF] reveals that, in order to support participative experiences during large-crowd events, the interactions with the system should be intuitive and should not interfere with the natural interactions of the audience. In addition, the study emphasizes the fact that the system should enhance the audience's experience and give them an impression that they are being part of something unique.

After analyzing natural interactions in live concerts and conducting informal interviews with people who regularly go to concerts and soccer games, we have defined two modes of interaction that would enhance participants' experience during such events. The first mode, called battle mode, is triggered when the participants start a fist pumping movement. While the phones are in this mode, their screens light up with color when the ambient noise becomes louder than a certain threshold. As we will explain in the next section, this threshold is calculated so that the phones light up only if a significantly large group of people cheer at the same time. In addition, when the cheers of a group exceed the threshold, the phones also record the color that is shown on the screens, the strength of the cheering and the sound made by the participants. The phones then pass on this information to neighboring phones in order to produce a wave of light and sound that spreads thought the crowd via the screens and speakers of the phones. This mode is designed to encourage the crowd to make noise and to provide a diversion alongside the event. Typically, this mode would be used before the beginning of concerts, to heat up the ambiance, or during slow moments of sports events to motivate the athletes.

The second mode of Opphos, called ambiance mode, is triggered when participants sway their phones back and forth. The waves of light are created in the same way as for the battle mode, but the threshold is much lower so that new waves are constantly created by the sounds coming from the event (e.g., music coming out of speakers). In addition, the intensity of the lights increases when the phones are at the highest point of the swaying curve, creating a calm light show in rhythm with the swaying movements of the crowd. Since this mode is designed to be used during the event Iza Marfisi-Schottman, Gunnar Karlsson, Jonas Celander Guss, « Demo: Opphosa participative light and sound show using mobile phones in crowds », Proceedings of ExtremeCom, 24-30 August, Thórsmörk, Iceland, pp.47-48.

without interfering with it, the phones do not produce any sound. This mode is inspired by the swaying movements people used to do with lighters during the final song of a concert. In summary, Opphos empowers a crowd to generate a unique show with natural interactions. We will next discuss the way it adapts to the crowds size in order to maximize the participation and enhance the light and sound effects.

ADAPTIVE MEDIATION ALGORITHM

The battle mode is intended to promote a competitive and collaborative mechanism. Collaborative because a significantly large group of participants has to team up in order to cheer loud enough to reach the threshold that will light up the phones. And it is competitive because the cheers that are propagated through the crowd can be perceived as a provocation by people on the other side of the audience. Hopefully, this provocation will push them to shout back and initiate a one-upmanship game. However, the number of neighbor participants that defines a significantly large group and the diminishing speed with which the strength of the light and sound of the wave decrease each time it is passed on to the next phone, (i.e., the traveling distance of the wave) need to be carefully calibrated. In particular, they need to adapt to the size of the crowd so that the effects are neither insignificant nor overpowering. In the same way, the number of neighbor participants and the diminishing speed also need to be calibrated for the ambiance mode in order to generate new waves constantly.

We have decided to calibrate these two parameters heuristically by simulating various sizes of crowds and varying the parameters until we reached the desired effect. In order to do this, we modeled the crowd as a multi-agent system composed of phones to adjust the parameters; we used the Netlogo [START_REF] Wilensky | NetLogo. Center for Connected Learning and Computer-Based Modeling[END_REF] simulator. Figure 1 shows the data retrieved from the simulations of the battle mode and the linear functions that define the value of the two parameters depending on the size of the crowd. Following the two modes of interaction offered by Opphos and its adaptive mediation algorithm, we now discuss the technical solutions we have found to support the information transfer between phones, as required for the application.

CONNECTING LARGE CROWDS

As it has been shown in several recent events (e.g., London Olympics, Super Bowl, Mobile World Congress), cellular networks may not scale to support the connections of large crowds [START_REF] Kapustka | The Connected Event Dilemma[END_REF]. To ensure connectivity without any extra infrastructure, we have therefore decided to use the PodNet peer-to-peer network middleware [START_REF] Helgason | A mobile peer-to-peer system for opportunistic content-centric networking[END_REF] that allows phones to connect directly to one another via Wi-Fi Direct or ad-hoc mode. Even though the opportunistic network has not yet been tested in large crowds, the high density of phones should allow rapid data transfer and support interactive crowd applications such as Opphos.

CONCLUSION AND EVALUATION

In this article, we presented Opphos, a mobile application that enables people in crowds to generate light and sound shows by collaboratively waving and shouting. This application supports two types of participative experiences: a type of one-upmanship game in which groups of participants in a crowd send waves of light and sound at each other, and a light show that synchronizes to the colors of the screens of the phones in synchrony with swaying rhythm of the crowd. In order to connect the phones, Opphos uses an opportunistic peer-to-peer network that provides rapid data transfer in large crowds without any infrastructure.

The experimentation at ExtremeCom 2013 will focus on testing the robustness of the peer-to-peer network as a technical solution to support connectivity in large crowds (i.e., extreme in terms of human and device density); we will also demonstrate the visual effects of Opphos. During the summer of 2013, we plan complementary evaluations of Opphos' emotional impact, aiming at collecting enough data to interest artists in using the app for live concerts and other crowd events.

Figure 1 .

 1 Figure 1. Multi-agent simulation of a stadium using Opphos. The two curves in the graph show the parameters as function of crowd size.

ACKNOWLEDGMENTS

This work was carried out during the tenure of an ERCIM "Alain Bensoussan" Fellowship Programme. The research leading to these results has received funding from the European Union Seventh Framwork Programme (FP7/2007-2013) under grant agreement no 246016.


E Sellami-Kaaniche

B De Gouvello
email: bernard.degouvello@leesu.enpc.fr

M C Gromaire
email: gromaire@leesu.enpc.fr

G Chebbo
email: chebbo@leesu.enpc.fr

Evaluation of gutter and valley materials emissions at the city scale: Statistical approach for computing gutter and valley lengths

Keywords: City scale, gutter, roofing material, statistical approach, valley

Roofing materials are considered as a major source of urban runoff contamination. Today, in the context of the European Water Directive (2000/60 CE), an accurate evaluation of contaminant flows from roofs is thus required at the city scale, and therefore the development of assessment tools is needed. However, at the city scale, the important diversity of roofing materials represents a difficult task for the quantification. In fact, the most restrictive step when estimating contaminant flows for large-scale territories is the estimation of the roofing materials surfaces area, for which no direct data exists. This study focuses on describing the method to evaluate gutter and valley lengths at the city scale. The proposed approach relies uses a statistical framework. The city was divided into homogenous urban areas. Then, a stratified random sampling technique was employed. The reliability of the methodology has been proved for three different urban areas (drained by sewer system) with known roofing materials distribution and known gutter and valley lengths. The obtained results show that a sample representing R=4% of the urban area leads to an absolute error less than 2% for gutter and valley length values.

INTRODUCTION

Many studies developed since 1970 have highlighted the pollution from urban wet weather discharge and its negative impact on receiving water [START_REF] Saget | Urban discharges during wet weather -what volumes have to be treated[END_REF][START_REF] Ellis | Urban drainage impacts on receiving waters[END_REF]. Roofing materials are considered as a major source of urban runoff metal contamination received by sewer system. This observation was revealed by several research programs conducted since the 1990s [START_REF] Förster | Patterns of roof runoff contamination and their potential implications on practice and regulation of treatment and local infiltration[END_REF][START_REF] Odnevall Wallinder | The influence of patina age and pollutant levels on the runoff rate of zinc from roofing materials[END_REF][START_REF] Gromaire-Mertz | Characterisation of urban runoff pollution in paris[END_REF]. In this context, annual metallic runoff rates at different scales (test-bed and roof) have been evaluated, for the different roofing materials commonly used in Paris and suburbs [START_REF] Robert-Sainte | Contribution des matériaux de couverture à la contamination métallique des eaux de ruissellement[END_REF]. Further undergoing research aims at extending runoff rates at the city scale [START_REF] Robert-Sainte | Contribution des matériaux de couverture à la contamination métallique des eaux de ruissellement[END_REF][START_REF] Gromaire | Zn and Pb emissions from roofing materials-Modelling and mass balance attempt at the scale of a small urban catchment[END_REF]. The roof area estimation is a fundamental input for evaluating roofing materials emissions. However, at the city scale, the information concerning roofing materials and their surfaces on an urban district does not exist currently in urban data banks. Some methods [START_REF] Gromaire | Incidence of zinc roofing on urban runoff pollutant loads: The case of Paris[END_REF][START_REF] Bris | Classification of roof materials for rainwater pollution modelization[END_REF] have evaluated roofing materials surfaces using data obtained from aerial photographs and image classification software. This classification method based on aerial images was applied to an urban catchment with 2.25 km² of surface. This method allows only identifying and quantifying roof area. For the other element of roof (ex: gutter and valley), no method has been found to identify and evaluate their materials surfaces. In this work, a methodology is developed to quantify gutter and valley lengths at the city scale. The method is based on a statistical approach and is applied to Créteil city (France). The data are processed with the aid of a Geographical Information System (QGIS) and Matlab is used to implement the statistical approach.

METHODOLOGY Case study site

The selected city is Créteil (Department 94) located about 10 km from Paris (France). Créteil has 89 304 inhabitants (INSEE, 2008) distributed over 11.5 km². Créteil city presents a big diversity and a large number of buildings which represent about 54% of the city area. In a previous work, we have developed a set of rules for identifying the use of a roofing material at the city scale. These rules have been applied to Créteil city. In this work, we have combined different databases for Créteil: land use database MOS-IAU1 , images database BDtopo2 and BD-ortho3 . The obtained results correspond to two maps of Créteil city (see Figure 1). The first map represents the roofing material historical distribution (see Figure 1

Method for gutter and valley lengths estimation and application to Créteil

Given the size of the city, a complete census of the roofing material surfaces was unfeasible. In a previous work (Sellami-Kaaniche et al., 2013, submitted), we have developed a statistical approach to evaluate roofing material area distribution at the city scale. This method was based on a stratified random sampling technique which was employed in conjunction with aerial photograph interpretation of surface roofing materials types (ex: zinc, tile). The city was divided into distinctive homogenous strata in order to accurately characterize it. The homogenous strata are obtained by overlaying the two previous maps (Figure 1). In fact, we consider that each building class in figure 1.b located in an area of the figure 1.a is a homogeneous urban area in terms of building types and the historical location. We define homogeneous urban area as an area representing specific probabilities of roofing material distribution. The statistical approach to evaluate roofing materials distribution for a stratum (roofs area (N (m²)) was based on two steps. The first one is the sampling theory which aims to determine the number of samples required n r for all roofing materials. The second step is the application of the estimation theory. Indeed, after determining the number of samples n r , we determine the proportion R = n r /N and then we estimate the unknown characteristics of a stratum by generating a sample representing R (%) from the total area of the new stratum. To validate this proportion R we have tested three stratums with different characteristics. The obtained results have shown that a random sample representing R=4% of the zone area could be draw with or without replacement. Then, the estimated roofing material distribution of the zone will be established by applying theorem for proportions. Thus, we will obtain an estimation of each roofing material proportion by computing the confidence interval. This statistical method will be applied to quantify gutter and valley lengths. We propose to evaluate gutter and valley lengths for each roofing material type. The sampling strategy is based on randomly generating independent individuals of 1 m² representing 4% of the stratum roofs area (N (m²)). Each 1 m² belongs to a specific building with specific roofing material. So, we obtain two databases, the first one is a database of different buildings (with their roof surface (S r,b (m²)) existing in the stratum, and the second one is composed of the selected surfaces for each building (S s,b (m²)) in the sample. By associating BD-topo and BD-ortho we can measure with QGIS the length of valley (l v,b (m)) and gutter (l g,b (m)) for each building and also identify its roofing material. For each 1 m² of roof surface (S r,b (m²),) we associate x r (m) of gutter length and y r (m) of valley length selected in each building. Then, in the sample, the length of gutter (l g,s (m)) and valley (l v,s (m)) will be evaluated as follow: Finally, we compute for each material i: -in the stratum: (area (N (m²)), proportion of different existing materials (p i (%)), surface area of each material i (S i ), the real gutter length l g,i (m) and the real valley length l v,i (m) -in the sample representing 4% of the stratum area (N) : surface area of each material i (S s,i ), gutter length l g,s,i (m) and valley length l v,s,i (m).

RESULTS

The method of evaluating gutter and valley lengths at the city scale was applied and validated for three strata with known and different characteristics.

Uncertainty in the gutter and valley lengths evaluation

Results obtained (see table1) in each sample have been compared to the real values in each stratum by computing an absolute error (E a,g and E a,v ). This latter is the difference between R g , r,i real ratio and R g , s,i ratio in the sample for gutter length and the difference between R v , r,i real ratio and R v , s,i ratio in the sample for valley length. 100 R , i r, g, Table 1 shows that for the three zones the absolute error for the gutter and valley lengths is less than 2%. Therefore, the developed method ensures good results in computing gutter and valley lengths at the city scale.

× = i i g S l ; 100 R , , , i s, g, × = i s i s g S l ; 100 R , i r, v, × = i i v S l ; 100 R , , , i s, v, × = i s i s v S l i s, g, i r, g, g a, R R - = E ; i s, v, i r, v, v a, R R - = E

CONCLUSION AND PERSPECTIVES

A method was proposed and applied to Créteil city to evaluate roofing material distribution and the gutter and valley lengths. The new question is "How to apply this method to other cities?"

Therefore, the first step is to divide the city into fairly homogenous urban areas by overlying two types of maps as illustrated in figure 1 for Créteil. The first map represents the roofing material historical distribution. This map should be elaborated for the case study city. To this end, we need an historical evolution of the city urbanization. This type of map can be available in the town halls databases or in the libraries of municipalities, etc. Besides, it is important to identify the different existing rules in the city related to the use of roofing materials such as the town planning regulation framework and the Local Urbanism Plan document.

For the Ile-de-France cities, the building class databases are the same as Créteil. Elsewhere, land use database are available but present some differences versus MOS-IAU that should be take into account to obtain the different established building classes.

The second step of the method is to apply the statistical approach. In fact, for each homogenous urban area (with known surface), a sample representing R=4% of the area surface is randomly generated. After that, using GIS software, we associate for each sample different maps BD-topo, BD-ortho and the strata one to identify the roofing material, the gutter and the valley lengths. Finally, we obtain the roofing material proportions, gutter and the valley lengths for each material type.

  .a). Each color represents an area with the same material historical distribution. The second one is a building classes map (see Figure 2.b) established from reorganizing the MOS-IAU database. Each color represents a building class.

Figure 1 :

 1 Figure 1 : (a) Material distribution map (b) Building classes map

  The three tested strata are described as follows: -Zone1 (N 1 =6256.84 m²): individual house class (Figure 1.b) located in area (1) (Figure 1.a). -Zone2 (N 2 =81100.11 m²): apartment class (Figure1.b) located in area (2) (Figure1.a) -Zone3 (N 3 =105304.04 m²): secondary activity class (Figure 1.b) located in area (2) (Figure1.a)

Table 1 : Absolute errors values computed for each material and for the three zones

 1

			Zone 1			Zone 2			Zone 3
	Material	Proportion p i (%)	E a,g (%) E v,n (%)	Proportion p i (%)	E a,g (%)	E v,n (%)	Proportion p i (%)	E a,g (%)	E v,n (%)
	Clear tile	33,7	0.51	1.55	x	x	x	x	x	x
	Dark tile	19,6	0.44	0.31	5,6	0.08	0.00	x	x	x
	Slates	14,2	1.25	2	1,2	1.73	0.04	x	x	x
	Zinc	13,3	0.98	0.50	x	x	x	1,1	0.46	0.00
	Flat roof	15,7	0.00	0.00	91,9	0.00	0.00	86,5	0.00	0.00
	Steel	1,9	0.00	0.80	0,7	0.01	1.03	8,8	0.17	0.00
	Other material	1,6	0.00	0.13	0,6	0.99	0.60	3,6	0.28	0.00

IAU: institute of planning and development for the Greater Paris region (http://www.iaurif.org)

BD-Topo is a database for Topographic Information IGN made from an aerial image. These images define only the built by masking inbuilt areas

BD-ortho images come from IGN's (Institut Géographique National) which contains digital colour ortho-photos with a 50 cm ground resolution.

ACKNOWLEDGEMENTS:This study has been conducted as part of the OPUR research program. The authors gratefully acknowledge the Centre Scientifique et Technique du Bâtiment (CSTB) for their financial support.