Théophane Nicolas

Ronan Gaugne

Cédric Tavernier

Valérie Gouranton

Bruno Arnaldi

Internal 3D Printing of Intricate Structures

Keywords: Archaeology, Tomography, 3D printing

come

Introduction

Cultural Heritage professionals such as archaeologists and conservators regularly experience the problem of working on concealed artefacts and face the potential destruction of source material without real understanding of internal structure or state of decay. For example, artefacts may be encased in corroded materials or a block of ash, or integrated with, and inseparable from, larger assemblies, such as manufactured objects composed of several pieces. The work presented in this paper aims to develop a non-destructive workflow for analysing and documenting the internal structure of artefacts, improving diagnostic techniques and knowledge by combining medical imaging technologies such as Computed Tomography (CT) with 3D printing. Our methodology allows to create digital and physical 3D surrogates of objects to investigate, analyse and interpret their internal structure through volumetric scanning, 3D image rendering, and 3D printing.

Combinations of CT scan and 3D printing technologies have already been proposed in CH contexts. The projects presented in [START_REF] Laycock | Using a Combination of Micro--Computed Tomography, CAD and 3D Printing Techniques to Reconstruct Incomplete 19th-Century Cantonese Chess Pieces[END_REF] and [START_REF] Haßmann | Der bronzezeitliche Hortfund von Gessel[END_REF] both propose the use of 3D printers, combined with CT images, to reproduce high-value pieces, Chinese chess pieces in the first case, and Gold jewels in the second case. In [START_REF] Mitsopoulou | Digitizing, modelling and 3D printing of skeletal digital models of Palaeoloxodon tiliensis (Tilos, Dodecanese, Greece)[END_REF], copies of fragile bones are used for sharing during study process and for exhibition.

This methodology was also successfully applied to physically access to encased artefacts through 3D images, and 3D printed replications without any irreversible physical action on the original material [START_REF] Nicolas | Preservative Approach to Study Encased Archaeological Artefacts[END_REF], even in the case of a disaggregated artefact [START_REF] Nicolas | Touching and interacting with inaccessible cultural heritage, in Presence: Teleoperators and Virtual Environments[END_REF]. In particular, in the first work, a removable copy of a Gallic weight illustrates how this technique allowed to better understand the internal structure of an artefact. This is also the case in the work of McKnight et al. [START_REF] Mcknight | Application of clinical imaging and 3D printing to the identification of anomalies in an ancient Egyptian animal mummy[END_REF] where a bones assembly from an animal mummy has been reconstituted for scientific analysis and public exhibition purpose. In both [START_REF] Nicolas | Tomography and 3D printing for the study of archaeological artefacts[END_REF] and [START_REF] Haßmann | Der bronzezeitliche Hortfund von Gessel[END_REF], a 3D print of the original shape of the archaeological material composed of an aggregate of several objects is proposed. This kind of production is useful to study the shape of disaggregated container.

In addition to these different works, it can also be interesting to have a view of both the external and internal structure of archaeological material in order to understand its production process, or to spatially localize the different notable internal items. The goal of the work presented in this paper is to propose a tangible representation of a complex intricate structure through advanced 3D printing. The process is applied to a funeral urn, and combines CT scan, 3D model processing, and 3D printing.

Archaeological context

The excavation of the site of Domaine de la Bizaie in Guipry (Brittany, France, Fig. 1, Left) in a preventive archaeological context uncovered a trapezoidal shaped funerary enclosure. The central area housed ten cremation burials containing pottery vessels from the Iron Age (Excavation L. Aubry, Inrap, [START_REF] Puil-Texier | Un enclos funéraire de l'âge du Fer, Domaine de La Bizaie[END_REF]). The exceptional state of preservation of some of these cremations prompted us to use tomography to analyse their contents. It allowed to highlight a number of metal objects as in the F42A cremation (Fig. 1, Right).

Description of the work

The process used in this study is based on a combination of CT scan, 3D processing and 3D printing. The main goal of the process is to physically display the internal structure of the archaeological material. We thus chose to explore two possibilities offered by 3D printing: physical copy of a part of the initial material and global printing with transparency. The process follows these different steps:

1. A computed tomodensitometry of the archaeological material was performed generating a database of X-Ray images, with density data. 2. Surface 3D meshes are generated from the previous database. Each mesh corresponds to a density range. 3. The 3D models are processed to fit 3D printing constraints. 4. The resulting 3D models are 3D printed.

Technical Environment

CT scan: The CT scanner used in this study is a Siemens SOMATOM sensation 16 owned by the French company Image ET (http://www.image-et.fr/) who delivers services and expertise on X-Ray images and associated tools.

The three-dimensional explorations were performed through two passes (acquisition) and 2D/3D images post-processing. The two acquisitions were a topogram (or radio mode) for positioning the slices to be realized and a helix scan.

The scan generates a dataset under DICOM format [START_REF] Mustra | Overview of the DICOM Standard[END_REF] of 512x512 pixels 2D slice images.

3D data processing. The data generated during the CT scan was processed with the free software Osirix, an image processing application for Mac dedicated to DICOM images. The 3D surface rendering functionality was used to generate 3D meshes cor-responding to different density ranges. This functionality allows to generate the surface of a set of points whose density value is within a defined range.

The 3D model was then manually processed in order to remove unwanted data and automatically processed in order to get a ready-to print file. 3D printing. We performed two different tasks of 3D printing on the urn, using two technologies: 3D printing of an internal artefact, and 3D printing of a whole material with transparency. The first 3D printer was a Stratasys Mojo owned by our institute. This 3D printer uses Plastic Jet Printing to print objects from ABS, in layers as thin as 178!, with a maximum dimension of 12.7cm x 12.7cm x 12.7cm. For the second printing, transparent 3D printing for complex objects appeared to be a not very developed technique. We contacted several Companies delivering advanced 3D printing services and only one, the CADindus Company (www.cadindus.fr), positively answered to our request. It uses a technology of multimaterial and multicolor additive manufacturing by resin polymerization for the production of the copies, on a Stratasys Objet500 Connex3 3D printer. This printer has a printing capacity of 49cm x 35cm x 25cm, with an accuracy of 30!.

Application of the process to the urn

Scan of the urn. The urn was scanned as a whole at one time. As the sediments inside the urn were not too dense, the scan was performed with the values of 120 kV and 350 mAs. In order to scan the entire urn, the field of view was sized to 320mm x 320mm, resulting in a resolution of 625!. We worked in an extended Hounsfield scale (from -10.000 to +40.000), in order to distinguish between fragments of bones and metallic parts and get a finer view of the metallic objects. A volume rendering is presented in Fig. 2.

Fig. 2. Volume rendering of the urn

The three views of volume rendering of the urn presented in Fig. 2 highlight the metal parts in blue, with two notable objects, a fibula and a knife blade. The red parts are fragments of bones. The sediments are displayed in transparent grey.

3D data generation and processing. Three meshes were generated from the data with the Osirix software (Fig. 3). The first mesh, for the metallic parts, corresponds to the points whose radio-density is between 4500 and 10950, the second mesh, for the urn shape and sediments, between 700 and 1300, and the last mesh, for the bones parts, between 1600 and 2300. Two issues arose after the generation of the meshes. First, corrosion gangues on the knife blade and fibula (Fig. 4, left) had a radio-density within the range of bones, visible in the mesh of the bones (Fig. 3, right). These gangues were easily removed as they were completely separated from other bones. Second, the mesh of the urn and ashes contained many galleries and cavities due to worms and insects (Fig. 4, right). All the galleries had to be manually removed and closed in order to get a clean transparency inside the urn. This task took several weeks, with many exchanges with the archaeologists in order to validate the modifications of the model. The targeted impression technique for the full urn required filling the volume of the urn, with a negative print of the metallic objects and bones fragments. This task was performed with 3D Boolean operations in a 3D modeling tool.

Printing of the fibula. The mesh of the fibula was isolated in order to propose a physical virtual extraction of this object whose shape appeared to be very well preserved. The process of producing the physical copy of the fibula from the digital data appeared to be very simple and fast (less than one day). The resulting copy of the fibula is presented in Fig. 5.

Fig. 5. 3D printing of the fibula

Printing of the urn. In order to keep close to the initial volume renderings from tomography (Fig. 2), we chose to render the bones in magenta and the metallic parts in cyan. The printing phase took 50 hours and required 8 kg of matter. It was printed with successive layers, bottom up (Fig. 6 left). The resulting printed object was covered with a pink support matter (Fig. 6 right) Fig. 6. Left: On-going 3D printing of the urn. Right: The printed urn with its support matter Post-processing. An important post-processing of the object produced by the 3D printer is required to obtain a good transparency rendering (Fig. 7). This post processing, which lasted one week, consisted in four phases: (i) Removal of the support matter, (ii) Photo-bleaching during 72h at 6500 kelvins (« day light »), (iii) Sanding cycles with different size grit (from 180 to 800), (iv) Coating in sterile conditions.

Discussions on the results

Before its actual excavation, the cremation 42A was the subject of a CT and a 3D reconstruction. 3D volume rendering informs on the preservation of the burial, the urn and the cremated bone block (its fragmentation and the deformations of the internal masses bioturbations ...). It allows the identification, location and orientation in space of each artifact in a sustainable manner, the visualization and localization of the bone mass in its entirety and the observation of the nature of the sediment's components in the urn. These elements offer the possibility of taking immediate precautionary measures before any manual intervention. Furthermore, the digitization permits operations of "virtual" manipulation of artifacts to increase the observation providing the first interpretations before excavation. It also serves as supporting tangible "evidence" for elements that are difficult to characterize in 2D. With the segmentation tools, it is possible to obtain an independent 3D model of an artifact that can be virtually manipulated before its excavation. The additive techniques allow tangible handling and initial observations before the provision of the original. This process allows the provision of information within hours, which is not the case for the "operational chain" commonly implemented that can take months if protective measures are implemented, prior to the study of the archaeological material, as presented in Fig. 8. The CT scan provided information on the structural state of the object, and allowed the identification of the cluster type of the fibula. Nevertheless, the observation of 2D sections and 3D reconstruction did not make possible to truly characterize the number of turns of the spring and the pin holder. Different segmentations were performed resulting in a restitution of the object with an approximate resolution of the details, which requires a systematic return to the real object in fine. This model has been the subject of a 3D impression (Fig. 9 left) that allowed to corroborate a number of observations from CT scans but also to confirm with certainty the number of turns of the spring and the shape of the. Also of note is the tangible nature of 3D printing with respect to the digital model. These comments have all been confirmed after the implementation of protective measures (Fig. 9 right and Fig. 10 left). The characterization of the initial surface condition during manual cleaning by a conservator revealed a setting of longitudinal striations on the arc (Fig. 10 right). Only this manual intervention may allow detection of such a setting very difficult to determine virtually on a small object. The CT scan reveals the different elements using an arbitrary color application (bone remains in red, metal in blue, biological indices in grey, etc.). For the neophyte, this palette can disturb, but is quickly understood. For the anthropologist, while ordinarily the information is supplied layer by layer in stratigraphic excavation, this comprehensive 3D visualization is more interactive. Translating from 2D to 3D, is none other than the transition from virtual to real and requires each expert to integrate this type of imaging. The complex 3D printing digital model overcomes this difficulty. After treatment, the printing transparency provides a 3D print of the container and contents (here funeral-deposit burned bones and iron objects knife rivet and fibula, Fig. 11).

Printing on both its tangible nature allows "direct" access to information and the physical handling of cremation deposit. It allows viewing and manipulation of the vessel and its contents in full and with integrity. Printing allows visualization of burned bones that are imperceptible when excavating (too small, fragile, or appearing negative, to be taken), but also some well-preserved bones (at least here, a long bone) and the determination of iron artefacts (here released from their mineralization). 3D printing also provides information for the reconstruction of the funerary urn. This tangible medium allows a manipulation / simple visualization to work on the analysis (such as the distribution of artifacts and the burial gestures) but also as a support for the excavation [START_REF] Haßmann | Der bronzezeitliche Hortfund von Gessel[END_REF]. Indeed, 3D printing is the only tangible medium of context preserved after the excavation of the incineration.

Conclusion and future works

For the archaeologist, the first asset of the scanner remains the immediacy of information, essential in the case of diagnostics where time is short. Well before the excavation of a container (funeral vase...), imaging allows the establishment of a protocol, the scheduling of specialists' intervention, the possible solicitation of a conservator curator to keep the fluidity of the scientific treatment of the remains [START_REF] Biron | La tomographie des objets archéologiques complexes et /ou altérés : outil d'identification, d'analyse et d'aide à la décision pour les mesures conservatoires[END_REF].

In this process, the substitution of the original by certified copies can be attractive for a valuation framework, given the fragility of unstable materials to exhibit. The archaeological sensitive materials suffer during traveling. Accidents due to manipulation (packaging, transport and installations) are inevitable. 3D printing offers promising perspectives regarding the diversity of materials faithful to the look, the weight, the texture of the original... From the image to the copy of an original, it takes an average a half-day with an easy correction of the design since we can re-intervene in the template file at any time. We also underline its importance in an educational set-

Fig. 1 .

 1 Fig. 1. Left: Domaine de la Bizaie, Guipry, France. Right: The F42 cremation, in situ

Fig. 3 .

 3 Fig. 3. Left: Meshes for the urn and sediments, Middle: metallic parts, Right: bones

Fig. 4 .

 4 Fig. 4. Left: Gangue of corrosion for the metallic parts. Right: Worms and insect galleries inside the urn

Fig. 7 .

 7 Fig. 7. Transparency view in the 3D printed urn

Fig. 8 .

 8 Fig. 8. Timelines of digital (blue) and physical (red) excavations

Fig. 9 .

 9 Fig. 9. Left: the 3D printed fibula Right: the real fibula, after its excavation, and before the restoration process.

Fig. 10 .

 10 Fig. 10. Left: The fibula after restoration. Right: Details of the etched patterns on the fibula

Fig. 11 .

 11 Fig. 11. Front and bottom views of the 3D printed urn

tions, but also for people with disabilities.

The processes used open up new exploratory research. For example, the possibility of obtaining a model of old or recent bioturbations (earthworms galleries ...) in a funerary urn provides information on the presence of a perishable container and 3D printing of a model provides access to "all" of the skeletal remains.

Aknowledgement

This project was funded by the CNRS Imag'In IRMA project, France. References


Vulnerability to heat waves: impact of urban expansion scenarios on urban heat island and heat stress in Paris (France)

Keywords: Urban sprawl, Densification, Urban Heat Island, Heat wave, Vulnerability indicators, Adaptation to climate change

Heat-wave risk in cities is determined both by regional climate evolutions and by cities size and shape change, because they can impact heat island effect. Land planning and urban transport policies, due to their long-lasting impact on cities shape, can therefore play a role in heat-wave risk mitigation. However, the link between these policies and resulting change in urban heat island is far from direct, and not yet clearly understood. Using Paris urban area as a case study, we show that evolutions towards a denser city could indeed lead to increased heat wave exposure when compared with urban sprawl evolutions. However, this increase depends strongly on the way heat-wave risk is measured, and on the indicators used to characterize heat island effect. Using an interdisciplinary modeling chain, including a socio-economic model of urban expansion and a physically-based model of urban climate, air temperature in the city during heat waves is simulated for five prospective scenarios of Paris urban area expansion and development. These scenarios differ in terms of land planning policies simulated, but are otherwise similar (e.g. in terms of total population evolution). Their impacts on urban heat island and population heat stress are evaluated and compared through different indicators. The urban heat island is always higher at night and hits preferentially the small area of the city centre, whereas it more widely affects the residential areas during the day. However, the concentration of population in the historic centre and the first suburbs makes these districts quite vulnerable. This is especially the case for the compact city scenario, whereas the greening strategies allow to mitigate urban heat island and consequently to insure better thermal comfort. The efficiency of such strategies is however strongly dependent on water availability for evapotranspiration of plants. Finally, it should be kept in mind that the method and choice of indicators are crucial in the process of adaptation strategies analysis.

Introduction

The global warming induced by greenhouse gases emissions is already observed and is going to intensify during the 21 st century according to climate projections at the global scale [START_REF] Meehl | More intense, more frequent, and longer lasting heat waves in the 21st century[END_REF][START_REF] Schär | The role of increasing temperature variability in European summer heat waves[END_REF]IPCC, 2013). One of the expected consequences is the raise of occurrences of heat waves, that has been highlighted at global and regional scale by numerous studies [START_REF] Huth | A GCM simulation of heatwaves, dry spells and their relationship to circulation[END_REF][START_REF] Beniston | Future extreme events in European climate: an exploration of regional climate model projections[END_REF][START_REF] Chauvin | Changes in severe indices as simulated by two French coupled global climate models[END_REF][START_REF] Vautard | Summertime European heat and drought waves induced by wintertime Mediterranean rainfall deficit[END_REF]. This issue has for instance been investigated for France by the IMFREX project [START_REF] Déqué | Frequency of precipitation and temperature extremes over France in an anthropogenic scenario: model results and statistical correction according to observed values[END_REF][START_REF] Planton | Expected impacts of climate change on extreme climate events[END_REF], as well as for the Paris region by [START_REF] Lemonsu | Evolution of the Parisian urban climate under a global changing climate[END_REF][START_REF] Lemonsu | Evolution of occurrences of heat waves over the Paris basin (France) in the 21st century[END_REF]. Especially, [START_REF] Lemonsu | Evolution of occurrences of heat waves over the Paris basin (France) in the 21st century[END_REF] indicate that heat waves will become more frequent at the end of the century (at least one event per year), but also they will last longer and will be more intense than today.

These extreme meteorological events are a source of growing concern for cities and urban populations, because high temperatures reached during heat waves are often exacerbated due to urban heat island (UHI) effect [START_REF] Basara | The Impact of the urban heat island during an intense heat wave in Oklahoma City[END_REF][START_REF] Tan | The urban heat island and its impact on heat waves and human health in Shanghai[END_REF][START_REF] Gabriel | Urban and rural mortality rates during heat waves in Berlin and Brandenburg, Germany[END_REF][START_REF] Li | Synergistic Interactions between Urban Heat Islands and Heat Waves: The Impact in Cities Is Larger than the Sum of Its Parts[END_REF]. As a result, there are rising concerns of public and institutional stakeholders about the vulnerability of urban areas facing these events (see for instance, [START_REF] Stone | Urban form and thermal efficiency: how the design of cities can influence the urban heat island effect[END_REF][START_REF] Solecki | Mitigation of the heat island effect in urban New Jersey[END_REF][START_REF] Hamin | Urban form and climate change: Balancing Adaptation and mitigation in the U.S. and Australia[END_REF][START_REF] Lambert-Habib | How is climatic adaptation taken into account by legal tools? Introduction of water and vegetation by French town planning documents[END_REF].

The specificities of urban climate and the resulting UHI are strongly determined by both morphological characteristics and material properties of the urban landscape. Some localscale action levers are already considered by architects and urban planners for a better thermal regulation of microclimate; for example the use of light-color materials favoring the reflective properties [START_REF] Santamouris | Using advanced cool materials in the urban built environment to mitigate heat islands and improve thermal comfort conditions[END_REF][START_REF] Kolokotsa | Green and cool roofs' urban heat island mitigation potential in European climates for office buildings under free floating conditions[END_REF] or the implementation of urban vegetation either ground-based (Potcher et al., 2006;[START_REF] Shashua-Bar | The cooling efficiency of urban landscape strategies in a hot dry climate[END_REF] or on building envelope (Harazano et al., 1991;[START_REF] Wong | Investigation of thermal benefits of rooftop garden in the tropical environment[END_REF].

In addition, at any given place in the city, the UHI can be impacted by the characteristics of the city as a whole, e.g. its size and shape or the composition and arrangement of the neighborhoods within it. The choices of urban planning at the scale of a city or of a community of conurbations may consequently play a key role in adaptation strategies [START_REF] Bass | The impact of green roofs on Toronto's urban heat island[END_REF][START_REF] Rosenzweig | Mitigating New York city's heat island[END_REF]Masson et al., 2013). The effects of actions led at cityscale, however, may be tricky to understand and evaluate due to the interaction of multiscale physical processes (i.e. a local action can influence a place far from it due to atmospheric processes) but also of socio-economical mechanisms (i.e. a local action can induce a change in inhabitants behaviors or choices, such as for instance a relocalization in the city).

We propose here to study this question, and to examine to what extent city-wide actions can have an impact on urban heat island effect and heat wave vulnerability. We focus on a representative issue: whether compact or spread-out city developments can have a positive or negative impact on UHI and heat wave risk. The comparison between advantages and costs of compact and spread-out city developments has nourished a long-standing academic debate (see for example [START_REF] Newman | Cities and automobile dependence: a sourcebook[END_REF][START_REF] Ewing | Is Los Angeles-style sprawl desirable?[END_REF][START_REF] Gordon | Are compact cities a desirable planning goal?[END_REF][START_REF] Ewing | Relationship between urban sprawl and physical activity, obesity, and morbidity[END_REF][START_REF] Eid | Fat city: questioning the relationship between urban sprawl and obesity[END_REF][START_REF] Brueckner | Social Interaction and Urban Sprawl[END_REF]. This has been recently revived by climate issues and greenhouse gases emissions reduction concerns (see for instance OECD 2012; [START_REF] Viguié | Trade-Offs and Synergies in Urban Climate Policies[END_REF]. City shape influence on UHI and, consequently, on heat wave vulnerability has been proposed as an important element of the debate [START_REF] Mcevoy | Adaptation and mitigation in urban areas: synergies and conflicts[END_REF][START_REF] Hamin | Urban form and climate change: Balancing Adaptation and mitigation in the U.S. and Australia[END_REF].

There is however no real consensus so far, and the present study tries to shed new light on how different urban planning policies, leading to more or less compact city shapes, can impact the UHI. This impact is a priori not trivial to infer. Broadly speaking, in a spread-out city, more space is available for urban vegetation, but sky-view factor is higher and artificialized surface larger. We study this question using Paris urban area as a case study, and compare the impact on UHI and heat wave vulnerability of different prospective city development scenarios.

This work is a result of a French research project (VURCA) that aimed at assessing the vulnerability and possible adaptation strategies of Paris metropolitan area to future heat waves. This issue has been investigated by accounting for the interactions of urban climate, local impacts of climate change, and the evolution of the city itself, thanks to an interdisciplinary approach involving researchers in climate, urban meteorology, economy, and buildings sciences and techniques.

The next section describes the numerical modeling methodology, more particularly the tools used for the production of urban expansion scenarios and the modeling of urban climate. Model evaluation is then presented in Section 3. Section 4 is dedicated to the presentation of indicators used to quantify and compare UHI effects. Finally, Sections 5 and 6 investigate how urban sprawl strategies impact the UHI and urban population. Section 7 concludes.

Modeling city evolution and urban climate

Overall methodology

The climate of Paris region -as it could be in 2100 under heat wave conditions -is studied by combining the local-scale effects of climate change on such extreme meteorological events and the impacts of urban sprawl. This analysis is carried out using a bottom-up approach. We use three steps simulations (see Fig. 1) in which both urban expansion scenarios and regional meteorological forcing conditions are used to feed a physically-based urban climate model. We review in this section each of these three steps: maps of city evolution and sprawl scenarios are first created using a socio-economic land-use transport interaction model, NEDUM-2D, and technical assumptions about future buildings characteristics (Section 2.2, Step 1 in Fig. 1). Meteorological forcings are then built for an ensemble of heat-wave conditions varying in intensity and duration and defined starting from the analysis of regional climate projections (Section 2.3, Step 2 in Fig. 1). Finally, these two inputs are used by physically-based Town Energy Balance (TEB) urban canopy model in order to simulate the urban climate of Paris, especially the urban heat island (UHI), as well as the thermal comfort conditions for indoor and outdoor environments (Section 2.4, Step 3 in Fig. 1).

City evolution scenarios

Paris urban area will evolve by the end of the century, as a result of macro-economic trends and demographic pressure, as well as under the influence of local urban planning policies, evolution of technologies and lifestyles. These combined effects can play a significant role on the structure of the city and, therefore, potentially, on the microclimate.

Urban expansion

To construct the urban expansion scenarios that we use here, long term socio-economic scenarios are downscaled at city scale using the method developed in [START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF]. To do that, the land-use transport interaction model NEDUM-2D is used (see Appendix A). This model is based on a dynamic extension of the classical urban economic theory [START_REF] Fujita | Urban economic theory: land use and city size[END_REF], and explains the spatial distribution of land and real estate values, dwelling surfaces, population density and buildings heights and density across the city. A validation over the 1900-2010 period shows that the model reproduces available data and captures the main determinants of city shape evolution over this period. A detailed description of the model and of its calibration can be found in [START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF]. In this study, a simple reference city expansion scenario is used, called the "spread-out city" scenario and referred to as SPR afterwards. This scenario follows broadly current trends in terms of total population increase and population density decrease, leading to urban sprawl1 . Fig. 2 shows a map of projected Paris urban area extension between 2010 and 2100 in this scenario. It is assumed in this case that the extension of the city is entirely guided by the market: we introduce no policy or regulation limiting the extension of the city or preferentially developing certain areas. The idea is that this scenario is used here to represent the "natural" trend of development of the city; this trend does not necessarily match the development that will occur in practice, but it allows understanding and anticipating land pressures, and therefore future local challenges.

Based on this scenario, we have then built four alternate city expansion scenarios, in which we make different assumptions about local land-use regulations (Fig. 3 and Fig. 4). In the "compact city" scenario (COM), strict urban containment policies are implemented in 2020, to control urban sprawl and protect natural areas and agriculture activity. From that year on, building is only possible through a densification of existing built spaces, but is prohibited elsewhere. In "green city" scenarios, no effective containment policy is carried out, but numerous parks are introduced in the city: in 2020, respectively 10% (G10), 30% (G30) or 50% (G50) of all built surfaces is uniformly destroyed to leave space for urban parks. After 2020, respectively 10%, 30% or 50% of all newly urbanized surfaces have to be urban parks (Fig. 3). These scenarios are of course somehow extreme, and unrealistic. They only aim to highlight what could be the impact of extreme theoretical greening scenarios. As can be seen in Fig. 3 and Fig. 4, urban extension is larger in green city scenarios than in the spread-out city scenario, in which urban extension is itself larger than in the compact city scenario. Population is the same in each scenario, and built densities are consequently in the reverse order. Table 1 sums up main characteristics of the projected city development in 2100 in the five scenarios, and of the simulated urban area in 2008 (see also Appendix A). The urban area simulated by NEDUM-2D in 2008 is used in this study as a reference of the today city (REF). The state of the city for this date is exactly the same whatever the urban expansion scenario, since (as explained just above) the different hypotheses of urban planning applied in the scenarios only differ from 2020.

Buildings characteristics

Built-up areas in the simulated city can belong to one of four classes of urban typologies: Paris historic buildings ("Haussmannian architecture buildings"), collective housing, single housing and office buildings. Except for Paris historic buildings and office buildings, whose land-use maps are prescribed as input parameters and do not evolve with time, urban typology is endogenously determined as a function of the population density simulated by NEDUM-2D; so that, surface devoted to collective housing and single housing is slightly different in each scenario. Each urban typology has its own characteristics in terms of roof types, insulation etc. (see Appendix A for more details). Especially, collective housing is supposed to be better insulated than single housing. This hypothesis will be of importance when studying temperature inside the buildings (cf. Section 6.2).

Air conditioning use and vegetation watering

In this study, we suppose as a simplification that no building is equipped by air-conditioning system. We also suppose that urban vegetation (but not forests neither agricultural fields) is watered during heat waves. Watering is done through a program of daily sprinkling, from 21 pm to 05 am with a sprinkling rate of 1.2 10 -7 m 3 s -1 of water (de Munck, 2013). [START_REF] Lemonsu | Evolution of occurrences of heat waves over the Paris basin (France) in the 21st century[END_REF] showed from the analysis of a large set of regional climate model (RCM) projections that the Paris basin will be frequently affected at the end of the 21 st century by heat waves which will be in average longer and more intense than today. Each of these heat waves is characterized by a maximum intensity, i.e. maximum temperature TX reached during the event, and a duration in number of days. They are classified according to four classes of intensities, i.e. with TX between 32-36°C, 36-40°C, 40-44°C, and greater than 44°C. Starting from heat waves extracted from the RCM projections, the probabilities of heatwave occurrence over Paris region for time period 2070-2099 are computed for each class of intensities and all possible durations. This is done by considering either the ensemble of events (Fig. 5, left) or the 10% most extreme events in a meteorological sense (i.e. by considering the product intensity × duration) (Fig. 5, right). After this analysis of the characteristics of future heat waves at a regional scale, meteorological events are downscaled over Paris urban area. A set of idealized events varying in intensity and duration is built, based on the atmospheric modelling of a real meteorological event : the heat wave of year 2003. This is done for the four intensity classes with TX of 34, 36, 38, 42°C previously identified from the climate projections. These classes of heat waves are afterwards referred to as HW34, HW38, HW42, and HW46. For each of them, the durations can vary from three to 38 days. The complete methodology of idealized heatwave building is detailed in Appendix B, and the evaluation of the modelling exercise by comparison with meteorological observations is presented in Section 3.

Heat-waves modeling

Urban climate modeling

The urban climate is simulated by using the physically-based TEB urban canopy model [START_REF] Masson | A physically-based scheme for the urban energy budget in atmospheric models[END_REF][START_REF] Hamdi | Inclusion of a drag approach in the town energy balance (TEB) scheme: offline 1-d validation in a street canyon[END_REF]. It parameterizes the energy, water, and momentum exchanges between urban covers and atmosphere, so that it is able to simulate the urban climate from the neighbourhood to the city scale by distinguishing various typologies of urban blocks thanks to different sets of geometrical parameters and material properties. Recently, TEB has been improved in order to include a building energy module [START_REF] Bueno | Development and evaluation of a building energy model integrated in the TEB scheme[END_REF][START_REF] Pigeon | Improving the capabilities of the Town Energy Balance model with up-to-date building energy simulation algorithms: an application to a set of representative buildings in Paris[END_REF] and to simulate the evolution of air temperature inside buildings. By accounting for local interactions between built-up covers and urban green areas (Lemonsu et al., 2012), TEB coupled to the ISBA vegetation model [START_REF] Noilhan | A simple parameterization of land surface processes for meteorological models[END_REF] is also able to model the potential cooling effect of vegetation in urban environment linked to evapotranspiration process of plants.

The TEB model is run in offline mode to simulate the climate of Paris over a domain of 100 km ⋅ 100 km with an horizontal resolution of 1 km (see the domain in Fig. 2). It is forced by the atmospheric forcing coming from the idealized heat waves HW34, HW38, HW42, HW46. As output, TEB provides the near-surface meteorological fields (e.g., temperature, humidity, wind speed at street levels) with a one-hour timestep. Besides standard variables, TEB also computes the Universal Thermal Climate Index (UTCI, [START_REF] Fiala | UTCI-Fiala multi-node model of human heat transfer and temperature regulation[END_REF] -result of the European Cooperation in Scientific and Technical Research (COST Action 730, http://www.utci.org). This represents the "perceived" temperature of the people, and it takes into account four immediate meteorological condition variables: air temperature, humidity, wind, and radiation. This UTCI is computed both for indoor and outdoor environments.

Models evaluation

Methodology

Model evaluation is an important aspect of prospective studies. Both NEDUM-2D model (see [START_REF] Viguié | Trade-Offs and Synergies in Urban Climate Policies[END_REF][START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF] and TEB urban canopy model (see [START_REF] Masson | Evaluation of the Town Energy Balance (TEB) scheme with direct measurements from dry districts in two cities[END_REF][START_REF] Lemonsu | Modeling the surface energy balance of the core of an old Mediterranean city: Marseille[END_REF][START_REF] Pigeon | Simulation of fall and winter surface energy balance over a dense urban area using the TEB scheme[END_REF] have already been separately validated against empirical or experimental data. However these models do, of course, not exactly describe the reality, and errors from each model can propagate through the modelling chain. We therefore evaluate here the ability of the chain, i.e. TEB urban canopy model using as input the urban area simulated by NEDUM-2D, to simulate the urban climate of Paris.

It is not rigorously possible to prove that, using our methodology, the impacts of different scenarios of urban expansion on urban climate can be correctly simulated and quantified. What we can do, however, is to check whether our modelling chain is at least able to adequately model past heat waves. The evaluation exercise is done for the 10 th of August 2003, taken here as reference day of the 2003 heat wave. This is the day which is used in this study to build the idealized heat waves (see Section 2.3).

This event has been simulated with the Meso-NH atmospheric model [START_REF] Lafore | The Meso-NH atmospheric simulation system. Part I: adiabatic formulation and control simulation[END_REF]) coupled to the SURFEX surface module (Masson et al., 2013) including TEB (see Appendix B for details). TEB is initialized by the map of Paris urban area that NEDUM-2D simulates for the year 2008 (the simulated city is almost unchanged between 2003 and 2008). The starting point for this NEDUM-2D simulation is 1900, and the map used is the map obtained when simulating 108 years of city evolution after 1900. This map does share mainly similarities with actual Paris urban areas characteristics in 2008, but it is of course not exactly similar, due to NEDUM-2D approximations.

We have then compared with observed data, at the neighbourhood scale, resulting simulated urban climate of Paris for the 2003 heat wave, as well as its spatial variability. This simulation, which we call REF, will be used several times in the rest of this study as a benchmark for the assessment of the impacts on urban climate of the different urban planning scenarios.

Comparison to meteorological observations

Over the study area, 31 meteorological stations from the Météo-France operational network are available and provide the 2-m air temperature and humidity, as well as the 10-m wind speed and direction with a 1-hour time step (see Fig. 2 for the locations of stations). The records of each station can be compared to the model's outputs extracted at the grid point the closest to the station geographic location. However, a point-by-point comparison between modelled and observed data is not appropriate to the 1-km horizontal resolution of the model that can result in significant subgrid heterogeneity of surface characteristics. For this reason, the comparison is performed by gathering the stations (and by averaging the data) regarding to the building density in the corresponding model's grid point and the distance to the city core. Four zones are distinguished and presented in Fig. 2: (1) Paris historic city centre (3 stations), (2) high-density suburbs (6 stations), (3) low-density suburbs (10 stations), and (4) rural areas (12 stations), with respective building densities of 50-60%, 10-25%, 2-10%, and 0%. The daily evolution of the average temperature and the associated spatial variability (as error bars) of each zone for both observations and model's outputs are presented in Fig. 6. In addition, the statistical scores are computed over the nighttime (2200-0500 UTC) and daytime (0600-2100 UTC) periods and presented in Table 2. Based on the averaged values, the best results are obtained in the city center with biases and root mean square errors (RMSE) always lower than 1°C. They slightly deteriorate for low-and high-density suburbs but are still acceptable (1.5 and 2.1°C at maximum, respectively for biases and RMSE). Slight underestimation of temperature during daytime and slight overestimation at night are systematically observed in model outputs. This effect is more marked in the countryside where the model simulates too high air temperatures compared to observations due to a defect in the calculation of vertical exchanges in low atmosphere for stable conditions. It is important to notice that whatever the zone, the second simulated night is always closer to the observations than the first one. This systematic underestimation in nocturnal temperature (quite important in the most vegetated areas) between the 9 th and 10 th of August 2003 was already highlighted by the previous numerical studies CLIM2 (de Munck et al., 2013) and EPICEA (Kounkou-Arnaud et al., 2014). It might be due to the synoptic or regional-scale wind calculation that drives the horizontal advection or in soil water content conditions that initiates the surface exchanges. In the study area, however, no record is available for soil water content and too much data are missing in the radiosoundings daily launched at Trappes (South of Paris, see Fig. 2) in order to provide relevant information that could highlight model defects.

Failing this, observed and modelled data of wind speed and direction, as well as water vapour mixing ratio, are compared for the two rural stations of Changis and Orcemont located respectively North-East and South-West of the city (see Fig. 2 for locations). Even if the wind speed measures recorded at the South-West station are lower than the model calculations, intensities keep the same magnitude order for both stations. Also, taking into account the weakness of the wind speed, both intensity and direction (Fig. 7) stick to the stations data even though the model does not get all the variability due to the instantaneous measures. The same behaviour appears whatever the station considered, either in the city centre or the suburbs (not shown here). For humidity, the main difference is observed during the day (Fig. 7) where air humidity is significantly higher in the model (+4 g kg -1 ). This is coherent with the underestimation of air temperature at the same time, since the near-surface conditions are strongly driven by the soil state and the partition between latent and sensible heat fluxes in the surface energy balance. Nonetheless, the systematic overestimation of the temperature during the night is not explained by these results.

Quantification of UHI effect

Different solutions exist to measure or more broadly to quantify UHI, either from observations or from modelling [START_REF] Schwarz | Exploring indicators for quantifying the surface urban heat island with MODIS land surface temperatures[END_REF]. In literature, the UHI is often defined as the difference in temperature between the city centre and a reference point in the surrounding countryside, i.e. it informs the maximum effect reached at city-scale but does not provide spatialized information on all areas potentially affected. We use here this indicator, but we also propose a more innovative approach, and measure also UHI importance -both at nighttime and daytime -based on other indicators of UHI and thermal stress (these indicators are all listed in Table 3). They enable to objectively assess the vulnerability of the city to heat waves, and to compare the various urban sprawl strategies (see Step 4 in Fig. 1).

Definition of indicators

• Temperature anomaly This is the standard difference in temperature between the city centre and a reference point in the surrounding countryside. By using the simulations of the various heat waves varying in intensity and duration, a relative nighttime or daytime temperature anomaly is calculated at a daily basis for each scenario at each grid point i as:

night rur night sc night sc T (i) T (i) ΔT - = day rur day sc day sc T ) i ( T ) i ( T Δ - = night rur T
and day rur T are the nighttime and daytime reference temperatures, respectively, of the rural environment. They are computed from the REF scenario by a spatial averaging of the nighttime and daytime temperatures, respectively, modelled at the non-urbanized grid points located at the boundaries of the domain.

• City fraction indicator

By considering several threshold values (from +0.5 to 2.5°C) which reflect the severity of the UHI, the city's area affected by UHI (referred to as AUHI in km 2 ) can be computed.

Since the spatial extent of the city varies with the urban expansion scenario, the fraction of the city affected by UHIs (referred to as FUHI) is also computed by normalizing AUHI by the city size. This indicator can be related to indicators of surface UHI [START_REF] Streutker | Satellite-measured growth of the urban heat island of Houston, Texas[END_REF][START_REF] Xu | Urban expansion and heat Island dynamics in the Quanzhou region, China[END_REF]) computed from satellite land surface temperature measurements [START_REF] Schwarz | Exploring indicators for quantifying the surface urban heat island with MODIS land surface temperatures[END_REF].

• Population fraction indicator To complete previous indicators, an indicator related to the affected population (referred to as PUHI in %) is defined as the proportion of the city inhabitants affected by the different thresholds of UHI. In this study, this can be done because NEDUM-2D model provides simulations of the spatial distribution of urban population over the study area.

• Heat stress duration indicators Two additional indicators are computed to assess potential health impacts of UHI. They are based on the UTCI computed by TEB inside buildings and in the streets. This UTCI can be associated to a scale of heat-stress levels, for extreme cold and especially for extreme heat [START_REF] Bröde | Deriving the operational procedure for the Universal Thermal Climate Index (UTCI)[END_REF]. The heat-stress indicators are calculated here as the number of hours per day that is spent in a level of strong heat stress (i.e. for UTCI>32°C) both for indoor conditions (referred to as SHSin) and shaded outdoor conditions (referred to as SHSout).

Application to the reference case

Let us illustrate these indicators in the reference scenario (REF). The maps of the various thresholds of UHI -both for night and day -obtained for this scenario after seven days of HW38 are presented in Fig. 8 (globally, similar patterns are noted for the other scenarios, and are not shown in this paper). Note that this idealized heat wave is rather close to the real conditions of the 2003 heat wave in Paris region that lasted about 8 days with slightly variable daily conditions.

The UHI systematically spreads more during the day than at night, and presents different patterns. As expected, the nocturnal UHI is concentrated over the city centre and the densely built-up suburbs but rapidly decreases and becomes insignificant (i.e. less than 0.5°C) beyond 5 km from the city core. This organization is driven by the process of heat release from urban infrastructures that occurs at night and that is mostly observed in dense urban areas. Inversely during the day, the city centre is less affected by UHI, because it is partially protected from incident radiation due to shading effects related to the high building density. Such effects have already been highlighted by [START_REF] Oke | The energetic basis of the urban heat island[END_REF] and Steenveld et al. (2011). Besides, as shown in Lemonsu et al. (2012), the residential districts are subject to cumulative effects of urban warming and soil drying under heat wave conditions. At night, the maximum UHI reaches 2.84°C for the city centre compared to the surrounding countryside. The proportion of the city hit by UHI is not very important: FUHI = 12 % if a 1.5°C threshold is used for ΔT. Nonetheless, this area concentrates urban population; this leads to a great proportion of inhabitants affected by UHI (PUHI = 42 % in this case). During daytime, whereas FUHI = 11 %, i.e. the same proportion of city than at night, the proportion of inhabitants affected by UHI is much lower (PUHI = 6 %) since the positive anomalies of temperatures are essentially observed over low-density urban areas. Note that we consider here the fraction of inhabitants as defined by their place of residence: we do not model in our simulations the fact that people can be outside their home (e.g., at work) during the day. So this fraction is actually a measure of the percentage of residences affected by the temperature. The heat stress level evolves with time according to the hour of the day but also day after day during the heat wave. This evolution is presented in Fig. 9 for indoor and outdoor environments after three, seven, and 14 days of heat waves. Inside buildings, the level of thermal comfort is rather stable during the day. This is due to thermal insulation and inertia of constructions. However, the thermal comfort deteriorates progressively day after day for long-lasting heat waves, as the buildings get warmer progressively. As an example, it is found that after seven days of HW38, people spend in average about nine hours per day in strong heat stress conditions with UTCI values varying between 32 and 33°C (according to Table 3). In the streets, the thermal comfort changes markedly during the day together with solar radiation. With the heat-wave duration, outdoor heat stress gradually accumulates day by day but does not amplify by contrary to the comfort in buildings, because the UTCI daily cycle for outside remains almost the same whatever the heat-wave duration. After seven days of HW38, people spend in average 12 hours and 30 minutes per day in strong heat stress conditions in the streets. On average, this result is comparable to what is obtained for indoor conditions but the heat stress is much higher outside than inside buildings in the middle of the day since the UTCI rises up to 42°C (see Fig. 9). Inversely, outdoor conditions are more comfortable than indoor conditions during night because the nocturnal cooling is more marked.

Impact of urban sprawl scenarios on UHI: amplitude and extension

UHI is affected by city expansion scenarios. We examine here how this is reflected by our indicators.

UHI amplitude for Paris city center

The city center of Paris is an area of specific interest because the highest values of UHI are observed there. Fig. 10 shows a comparison of UHI temperature anomaly (indicator ΔT) for the city-centre grid points, i.e. for which the urban typology is defined as Paris historic buildings (see urban typology map in Fig A3 of Appendix A). Let us first compare scenario SPR and the green city scenarios G10, G30 and G50. Night UHI intensity is equal to 2.78°C for SPR and appears to decrease with the implementation of greening strategies. Contrary to what could be expected, the development of new neighbourhoods which encroach on natural areas tends to limit the UHI. This effect is due to the low building density of these neighbourhoods and to the fact that gardens are supposed to be watered in the present study (Section 2.2.3). The UHI mitigation is also perceptible over the city centre where additional urban green areas are set-up. This mitigation reaches 0.19, 0.66, and 1.08°C for G10, G30, and G50, respectively, compared to SPR. The contrary, however, occurs during the day: the UHI magnitude in the city centre is reinforced for the greenest scenarios (Fig. 10) of +0.12, +0.24, and +0.61°C for G10, G30, and G50, respectively. This is due to the fact that the greening policies we consider here decrease urban compactness and lead to larger sky-view factors and a greater sun light exposure. Nonetheless, these UHI intensities are weaker than those reached at night whatever the scenario, and do not exceed 1.5°C.

Comparing scenarios SPR and COM, i.e. analysing the impact of city densification, leads to a different result. Both at night and during the day, the temperature anomaly appears slightly higher in SPR scenario than in COM scenario (2.78 against 2.67°C, and 0.90 against 0.69°C, for night and day, respectively). These differences are small, however, and not strongly significant (lower than 0.2°C) because for these two scenarios, the morphology of the historic city centre remains unchanged, i.e. the local characteristics of the city at the point where the temperature anomaly is measured is the same in these scenarios. Consequently, the fact that the UHI computed for the city centre is higher for the spread-out city than for the compact city may be caused by the larger size of the city, but it is tricky to conclude on this issue.

Finally, the REF case gives the lowest intensity of UHI during the day, but the highest one at night. For the today city, building characteristics are slightly different than for city evolution scenarios, because the scenarios assume a progressive improvement of thermal regulation with time (see Appendix A). More especially, in the future some of buildings are equipped with reflective materials. As a result, they store less energy during the day and release less heat at night, which can explain that the nighttime UHI is the highest for REF.

Inversely, the fact that the city's size is smaller for REF than for all scenarios could explain the lowest value of daytime UHI.

Using UHI temperature anomaly as an indicator leads therefore to somehow inconclusive results. On the one hand, the effect of city densification cannot be significantly measured, and on the other hand the impact of the vegetation appears unclear, as it reduces UHI during the night but increases it during the day. Using alternative indicators can enable to get a clearer view of the differences between each scenario.

Fraction of city affected UHI at nighttime

Fig. 11 shows city fractions affected by UHI (indicator FUHI of Section 4.1) at nighttime, for different temperature thresholds, in the case of HW38 after seven days of heat wave. For each threshold, the same trend can be seen between scenarios : the denser the city, the most it is proportionately affected. COM is the most affected city, then SPR, G10, G30, and G50, whereas, conversely, these scenarios are more and more extended spatially. Contrary to the temperature anomaly indicator, FUHI shows a non-negligible impact of city densification (i.e. a significant difference between COM and SPR).

The main reason behind these results is that the new urban areas that develop around the existing city are mainly low-density residential districts (where vegetation is widely present) that are consequently minimally affected by the nocturnal UHI. Therefore, the more spreadout the city, the lower the fraction affected by different UHI thresholds. Similarly, in all scenarios, projected cities in 2100 appear less affected by UHI than present day city, even without specific adaptation. Both duration and intensity of heat waves have an impact on UHI because heat storage in soil and urban infrastructures, as well as soil water status, evolve during the event. By selecting the UHI threshold of 1.5°C, the FUHI indicator is computed day by day (from three days to three weeks) for the REF case and the five urban sprawl scenarios according to the four intensity classes (Fig. 12).

The fact that the city is proportionally less affected at night when it is wider is confirmed whatever the intensity and duration of heat waves. The values of FUHI reach rapidly an equilibrium value after few days of heat wave. Beyond the first week, FUHI varies only slightly and is very similar whatever the intensity of heat waves. Indeed, for long events, the potential of heat storage decreases as the buildings warm up and the UHI does not evolve anymore. As an example, for the most unfavourable case HW46, the fraction of the city affected by UHI is about 12 % for REF, 9 % for COM, 5 % for SPR, 5% for G10, and only 3 % for G30 and 1 % for G50. In conclusion, among the tested urban planning scenarios, the compact city appears the most subject to nighttime UHI. Inversely, the scenarios with vegetation reduce UHI spatial extension due to combined effects: the loose urban fabric reduces the heat storage in urban infrastructures, the green areas watering promotes transpiration of plants and evaporation of water intercepted by the foliage which cools the ambient.

Fraction of city affected by UHI at daytime

At daytime, the conclusions are different (Fig. 12). For HW34, for instance, COM is the least affected by UHI. It produces effects quite comparable to REF. Inversely, the SPR scenario corresponds to the most affected city. The green city scenarios give intermediate results with a positive effect of a greening rate increase from G10 to G50.

Let us look into the details at Fig. 12. Scenarios COM, SPR and G10 are a bit more affected by UHI when the intensity of heat waves increases, but FUHI mainly increases for G30 and G50 up to proportions which become very close to those of SPR and G10. In all scenarios, the values of FUHI strongly decrease during the first two weeks of heat wave, and then stabilize.

The dynamics of UHI (and of the city's fraction affected) according to the intensity and duration of heat waves is driven by the availability of water for vegetation both inside (urban parks) and outside (forests and crops) the city. For short events, the high evapotranspiration of the surrounding vegetation has a more efficient cooling effect than that of urban green areas, which reinforces the UHI effect. For the longer events, the natural soils become drier while the urban green areas are still watered, so that FUHI decreases. But after around two weeks of heat wave (depending on the intensity), this decrease in FUHI stops because the water supply for urban vegetation is no more sufficient. This effect is especially marked for the most intense heat waves (see HW46 in Fig. 12); the green scenarios become therefore significantly less effective.

In conclusion, the compact city COM clearly stands out from other urban expansion scenarios, more especially for long and/or intense events; by limiting the penetration of incoming solar radiation due to its dense urban form, it is the most efficient in mitigating UHI during daytime, regardless the intensity of heat wave. Compared to the temperature anomaly indicator, nighttime and daytime FUHI enable therefore to get a different view of the impact of the different scenarios. Whereas ΔT indicator gives non-significant results for the impact of densification, and inconclusive results about the impact of the vegetation (positive effect of UHI mitigation at night, negative effect during the day) FUHI highlights a different message: vegetation appears positive both days and nights, and densification now appears negative at night and positive during the day.

Impact of urban sprawl scenarios on UHI: link with population distribution

As we have shown in the last section, the analysis of the impact of urban form on UHI depends on the indicator which is used. The indicators that we have used so far (ΔT and FUHI) are related to the geometry of the urban micro-climate. In this section, we introduce in the analysis the spatial repartition of the population, and use the three last indicators of Table 3.

Fraction of population affected by UHI

Let us first translate the proportion of the city affected by UHI (FUHI) into the proportion of population that is subject to UHI (PUHI). To do that, we need to know the spatial distribution of the inhabitants, today and in the future. This can be done here thanks to the NEDUM-2D model that simulates the households' settlement dynamics (see [START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF].

The trends for the various heat waves are presented in Fig. 13. They are similar to those obtained for FUHI but the orders of magnitude are very different. Especially, whereas, with FUHI, the orders of magnitude of daytime and nighttime fractions are similar, this is no longer the case with PUHI. Comparing scenarios on day 21 in Fig. 13, nighttime fractions vary between 0% and 10%, whereas daytime fractions vary between 10% and 40%. Same comparison in Fig. 12 shows variations between 0% and 10% both in daytime and nighttime.

At night, the benefits brought by the greening scenarios, which seem rather limited when evaluated according to the city surface proportion, are much more significant when evaluated according to the city population proportion. The G50 green scenario, which is the most effective for mitigating the nocturnal UHI, leads to a reduction of more than 20% of the population affected by UHI (for a threshold of 1.5°C as shown in Fig. 13) compared to the compact city COM, because the effects are mostly perceived in the most populated areas. As for FUHI indicator, COM appears the best choice for limiting UHI in daytime, but the worst in nighttime. However, introducing in the analysis the repartition of the population in the city, i.e. using PUHI, has given information: it shows that daytime effect of scenario choice has, to some extent, a much lower magnitude than nighttime effect. Therefore, when considering PUHI indicator, the dense scenario seems in overall less desirable than spread-out city scenario. To go further, one needs indicators which integrate both nighttime and daytime effects. This is what is doing our last indicators SHSin and SHSout (Table 3).

Averaged thermal comfort

The last analysis framework that we consider in this study is the number of hours per day, on average for the whole heat-wave duration, that is spent in strong heat stress conditions. For each city scenario and each simulated heat wave (for the four intensity classes and all possible durations), this indicator is computed both for indoor and outdoor conditions (SHSin and SHSout indicators are more detailed in Section 4.1 and Table 3).

These indicators are spatially aggregated by accounting for the spatial distribution of population density, in order to attribute greater importance to the most populated areas. They are then weighted by the occurrence probabilities of the future heat waves. We also compute, for extra information, the average for only the 10% most extreme heat waves (see Section 2.3 and Fig. 5 for detail).

Outdoor thermal comfort

For REF case (i.e. today city), we simulate that about 35, 50, and 15% of inhabitants spend, respectively, 16, 14, and 12 hours per day in strong heat stress conditions (Fig. 14): heat waves can have an important effect on thermal comfort. The comparison of this REF case to the city scenarios in 2100 indicates that whatever the scenario, the outdoor thermal comfort is improved for a part of the population.

Particularly, the implementation of large-scale greening policies seems quite efficient. For the highest greening rate, less than 10% of inhabitants spend 16 hours per day in SHSout (against about 30% for instance in the business-as-usual SPR scenario). The improvements brought by the green scenarios mainly concern the residential areas, considering that the lower the building density is, the less heat storage there is. In addition, as shown by the statistical distribution of future heat waves (Fig. 5), a large proportion of these events has a characteristic temperature TX lower than 40°C and a duration lower than two weeks. As a result, the water supply prescribed for green areas is enough to produce a significant cooling which still reduces the daytime heat storage in residential areas. In the densely built-up districts, the proportion of green areas is lower and consequently, the cooling effect induced by evapotranspiration is more limited. On the contrary, the compact city COM is the most unfavorable scenario: as was suggested by PUHI comparisons, nighttime increased UHI more than counterbalance daytime UHI decrease. The comparison of SHSout for the most extreme events (Fig. 14) leads to the same conclusions between scenarios. It can be however noted that for such heat waves, the heat stress conditions reach exceptional levels even for the most efficient urban planning scenarios: the entire city is subject to at least 18 hours of SHSout per day and 20% and more of population (according to the scenario) spends more than 22 hours per day in SHSout. In this case, alternative actions should be implemented in order to preserve the population-at-risk and to avoid serious sanitary consequences.

Indoor thermal comfort

With regard to indoor thermal comfort, the most unfavourable conditions also concern the city centre where people spend between 12 and 14 hours a day in SHSin (Fig. 14). This is related both to the UHI and to the bad energetic performances of buildings, so that the ambient warms rapidly. Inversely, the best conditions are observed in the multi-family blocks for which the level of renovation is greater. Finally, the residential areas present intermediate conditions. The different trends of urban sprawl have little impacts on indoor thermal comfort which is mostly driven by the quality of buildings' insulation that differs according to building typologies (see details in Appendix A).

The differences noted between scenarios (Fig. 14) are due only to the fact that inhabitants are not distributed the same way between multi-family housings and residential districts, whereas the proportion of inhabitants living in the historic city centre is about the same. The more the city is extended and greened, the more the residential areas cover an important part of the city. In this case, more people occupy single housings and are consequently subject to more uncomfortable thermal conditions than those living in multi-family housings.

Conclusion

In conclusion, we have tried here to shed new light on how different urban planning policies, leading to more or less compact city's shapes, can impact the UHI and heat waves risk. Using Paris urban area as a case study, five contrasted urban expansion scenarios have been built with the NEDUM-2D model. For each of them, the urban climate has been simulated with the physically-based TEB urban canopy model for a large set of heat-wave conditions. Here, different indicators (described in Table 3) are computed in order to measure and investigate UHI effect and heat-wave risk. Fig 15 shows a summary of the value of these indicators, when computed for the HW38 event after 14 days.

Whatever the scenario, nocturnal UHI is limited to the most densely built-up areas and reaches up to 2.5-3.0°C. Inversely, during the day the residential neighbourhoods, which are less protected by the shadow effects, are the warmest places, however in a lesser extend (between 1.0 and 1.5°C). As a result, the proportion of the city hit by UHI is greater during the day than during the night. However, taking into account the spatial distribution of population in the city brings a different perspective because the city centre is much more populated and consequently more vulnerable. Taking also into account UHI intensity reinforces this message, as UHI amplitude is higher at night than during the day. Due to UHI, city densification -a strategy widely supported by urban planners and stakeholders -appears to potentially lead to an increased heat wave risk, when compared to urban sprawl. However this conclusion is strongly impacted by the way heat wave risk is measured. In our simulations, the compact city gives rise to the most uncomfortable thermal conditions for outdoor environment, if one takes into account the population repartition in the city and integrate over both days and nights (indicator SHSout). Considering separately days and nights, or not taking into account the population repartition in the city, leads to different messages. This is due to the fact that, whereas the compact city reinforces the UHI at night, it favours solar protection, and therefore cool temperatures during the day.

One of the main results of this study is therefore the qualitatively difference in the messages that one can deduce from UHI simulations, when one consider different UHI or heat wave vulnerability indicators. The impact of a potential urban densification on UHI can either be measured as non-significant (using ΔT indicator), significant but uncertain (using FUHI or PUHI indicators) or strongly negative (using SHSout indicator). The extreme greening of the urban landscape that we analyse here appears significant for all our indicators, sometimes uncertain (using ΔT or FUHI indicator), sometimes strongly positive (PUHI and SHSout indicators).

It is difficult to say which indicator is the most meaningful, and it most certainly depends on the question one wants to answer. Day PUHI, for instance, can be considered of limited interest if people in the city do not stay at home during the day. Favoring FUHI over PUHI also means giving a heavier weight to dense city center over suburban areas, and this might not necessarily be politically or socially desirable. Considering that the choice of the period and criteria for evaluation is essential, it is consequently tricky to conclude on the most efficient strategy.

The greening of the urban landscape is an interesting option because it generates evapotranspiration while reducing the heat storage process by impervious surfaces. Land availability and water resource are nevertheless major issues in the implementation of such strategies. Their efficiency is dependent on both vegetation density and soil water status (in turn connected with meteorological conditions). In case of long periods of heat waves or hot spells, the benefit of greening strategies is lesser even if vegetation is irrigated.

Our analysis uses simplistic scenarios and hypotheses. Alternative scenarios and indicators are required to get a complete picture. For instance, it would be interesting to consider less extreme city greening scenarios and more extreme densification scenarios. It would also be interesting to repeat our study on other cities, with different sizes and climatic conditions. Other indicators could also be useful to consider, such as for instance potential electric consumption in the case of air conditioning general use in the city, or temperature increase in office districts.

Another important question is whether the differences that we measure here are relevant or not. The differences that we measure between scenarios COM and SPR, for instance, are small in absolute terms (less than 4% in PUHI and FUHI, 10 min more per day under strong heat stress conditions…). Is such a moderate variation of interest in the policy debate? Addressing this question requires doing a finer analysis of the mechanisms behind our vulnerability to heat, as well as taking into account the costs and obstacles associated with the evolution towards more or less dense urban shapes. These fundamental questions, however, are beyond the scope of this analysis.

Appendix A: Integrated city scenarios

Within the frameworks of the VURCA project [START_REF] Hallegatte | VURCA project, Cities vulnerability to future heat waves & adaptation strategies[END_REF], integrated city prospective scenarios have been built to translate a possible evolutions of the city at the end of the century. They combine four potential action levers: urban-planning policies to manage the future urban sprawl, adaptation measures for buildings, air-conditioning usage, and watering practices. Each of them consists in different alternatives or hypotheses. In this study, we use the following scenarios.

A.1. Urban sprawl

The urban sprawl is simulated by the NEDUM-2D socio-economic model, forced by macro-economic trends of energy costs especially for oil and demographic pressure [START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF]. NEDUM-2D is a dynamic model which relies on the classical urban economics framework, an economic modeling approach developed in the end of the 1960s [START_REF] Alonso | Location and Land Use[END_REF][START_REF] Mills | An aggregative model of resource allocation in a metropolitan area[END_REF][START_REF] Muth | Cities and housing; the spatial pattern of urban residential land use[END_REF] which explains the spatial distribution -across the city -of the costs of land and of real estate, housing surface, population density and buildings heights and density. It is based on three main mechanisms.

First, we suppose that households choose their accommodation location and size by making a trade-off between the time and money they spend in transport (i.e. to commute to their jobs) and the real estate price level (or, equivalently, between the proximity to the city center and the housing surface they can afford). Second, real estate developers choose to build more or less housing (i.e. larger or smaller building) at a specific location, depending on the local level of real estate prices. When these prices are low, developers tend to build low density buildings, and when these prices are high, they tend to build high density buildings. Third, we suppose that various city characteristics do not evolve and adjust at the same speed. For instance, rents can evolve very quickly, whereas buildings change with a much longer timescale. Building depreciation is also very low, leading to path dependency and lockins in city evolution. Using these mechanisms, it is possible to determine the structure of the city from information on population size, households' income, transport network location, building construction costs and developers behavior parameters.

The reference scenario (SPR) corresponds to the scenario called "SN with high demographic hypothesis" in [START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF]. Fig. A1 shows for instance the demographic scenario used in our simulations. The four other scenarios that we used in this study are identical to this scenario in terms of population evolution, transport prices and people and firms behavior. Local urban planning policies are however implemented through specific constraints (they are detailed in Section 2.2). Fig. A2 shows simulated city size and green area fraction in the scenarios.

A.2 Buildings characteristics

Four different typologies of buildings are defined over the study area (see Fig. A3): historic buildings located in the city centre (Haussmannian architecture buildings dating from 19 th century), collective housing, single housing, and office buildings. Materials characteristics of buildings and renovation techniques are specified differently for each typology on the basis of an inventory of the current Parisian buildings and the renovation trends. Projected buildings characteristics in 2100 are based on the assumption that the energetic performances of buildings are going to improve with time due to the technological progresses in construction and renovation methods, following the current trends. A complete database of buildings characteristics has thus been built within the framework of the VURCA project [START_REF] Marchadier | Les scénarios « bâti et usages de la climatisation » et leur simulation (Developing and modeling of scenarios for buildings and air-conditioning usage)[END_REF] and is used here.

It is assumed that all collective housing and single housing follow the French thermal regulations fixed by the Grenelle Environmental Forum. The level of renovation is higher for office buildings which are equipped with high-performance vacuum insulation systems and reflective materials. Inversely, because of architectural and aesthetical reasons, the historic buildings are the least renovated ones (a simple interior thermal insulation is implemented in this case).

Appendix B: Building idealized heat waves

The objective of this stage is to produce meteorological conditions over Paris region that represent the future heat waves identified in Section 2.3. These meteorological conditions must be used afterwards to force the TEB urban canopy model. They must consist of hourly spatialized fields of incoming solar and infrared radiation, atmospheric pressure, air temperature, humidity, and wind speed above the top of urban canopy level.

With this aim, a complete three-dimensional atmospheric modelling of the 2003 heat wave (see Step 2 in Fig. 1) is carried out with the Meso-NH non-hydrostatic model [START_REF] Lafore | The Meso-NH atmospheric simulation system. Part I: adiabatic formulation and control simulation[END_REF]. The 10 th of August 2003 is selected as a reference real case, this being a sunny day with low winds of the 2003 heat wave according to the previous modelling exercises performed by [START_REF] Kounkou-Arnaud | Epicea: étude des impacts du changement climatique à Paris[END_REF]de Munck et al. (2013). The numerical setup is time-computing consuming but makes possible to take into account explicitly the retroactions of surface fluxes on the low atmosphere. This reference day of heat wave is consequently run for the today city as well as for each urban expansion scenario. Indeed, the low atmosphere is influenced in different way according to the size, shape, and other characteristics of the city coming from the studied scenarios.

The Meso-NH outputs, required to force TEB, are extracted and stored with a one-hour time step. One single atmospheric level is needed; it is taken 30 m above the top of the urban canopy. These meteorological conditions are then modified and adapted to correspond to different intensities of heat waves. First, the temperature fields provided by Meso-NH are linearly corrected in order to fit the middle value of TX of each intensity class, i.e. 34, 38, 42, and 46°C, respectively (see Step 3 in Fig. 1). These heat waves are afterwards referred to as HW34, HW38, HW42, and HW46. In order to account for the impact of the temperature modifications on other atmospheric parameters, the specific humidity is recomputed by considering that relative humidity is unchanged; the long-wave incoming radiation is also adjusted to reflect the additional atmospheric emission due to the increase in air temperature. Finally, all these conditions available for one daily cycle are duplicated to build three-week atmospheric forcing.

In the end, meteorological forcing are available for the six city scenarios (including the today city), for the four intensity classes of heat waves, and for events lasting up to three weeks (see Step 3 in Fig. 1). Note that beyond three weeks of heat wave, a sensitivity study (not presented here) indicates that the local meteorological parameters, especially air temperature in the streets and inside buildings, reach equilibrium or evolve linearly, so that the results can be extrapolated for longer events.

Fig. 1 .

 1 Fig. 1. Description of the interdisciplinary methodology implemented in the VURCA project.

Fig. 2 .

 2 Fig. 2. Example of simulated urban area extension, in Spread-out city (SPR) scenario. Reference case (REF) corresponds to simulated urban area in 2008. Locations of the meteorological stations presented in Section 3.2 are also indicated.

Fig. 3 .

 3 Fig. 3. Presentation of the REF case (in 2008) and the five urban sprawl scenarios, in 2100. The maps present the simulated fraction of impervious covers over the study area. The thick black line in the last map shows the line along which the profile graphs are computed in Fig. 4.

Fig. 4 .

 4 Fig. 4. Examples of impervious cover profiles over the study area.

Fig. 5 .

 5 Fig. 5. Statistical distribution of heat waves for 2070-2099 time period according to the four classes of intensity, and by considering all events (left) or the most extreme ones (right). These events have been extracted by Lemonsu et al. (2014) from regional climate model projections provided by the ENSEMBLES project.

Fig. 6 .

 6 Fig. 6. Comparison between observed and modeled 2-m air temperatures on the 10 August 2003 averaged for the four land cover classes. The standard deviations are also presented both for model outputs (black bars) and observations (gray envelop).

Fig. 7 .

 7 Fig. 7. Comparison between observed and modeled 2-m specific humidity, and 10-m wind speed and direction on the 10 August 2003 for the two rural stations of Changis (top) and Orcemont (bottom) located north-east and south-west of Paris, respectively.

Fig. 8 .

 8 Fig. 8. Spatial representation of the city's areas affected by UHI for the different thresholds in temperature anomaly. Example of the today city (REF scenario) for the HW38 after seven days of heat wave both for nighttime (left) and daytime (right) hours.

Fig. 9 .

 9 Fig. 9. Daily evolution of indoor and outdoor UTCI for HW38 after three, seven, and 14 days of heat waves, respectively. Indoor and outdoor UTCI are computed for each grid point of the domain and spatially aggregated at the city scale.

Fig. 10 .

 10 Fig. 10. Comparison of the values of UHI obtained by aggregating the results for the city-center grid points for each scenario for the HW38 after seven days of heat wave.

Fig. 11 .

 11 Fig. 11. Comparison of the proportion of the city affected by UHI according to the thresholds in temperature anomaly, for the today city and the future scenarios. Example of the HW38 after seven days of heat wave both for nighttime (left) and daytime (right) hours.

Fig. 12 .

 12 Fig. 12. Comparison of the evolution with time (from three to 21 days) of the proportion of the city affected by a UHI of 1.5°C for the today city and the future scenarios. The results are presented for the four classes of heat-wave intensity, and both for nighttime (top) and daytime (bottom) hours.

Fig. 13 .

 13 Fig. 13. Comparison of the evolution with time of the proportion of the population affected by a UHI of 1.5°C for the today city and the future scenarios. The results are presented for the four classes of heatwave intensity, and both for nighttime (top) and daytime (bottom) hours.

Fig. 14 .

 14 Fig. 14. Distribution of population according to the number of hours per day spent in strong heat stress for outdoor (left) and indoor (right) conditions for the different city scenarios. Results are weighted by the occurrence probabilities of all future heat waves (top) and of the most extreme ones (bottom).

Fig 15 .

 15 Fig 15. Example of the indicators computed for the HW38 event after 14 days for the five scenarios of urban expansion.

Fig. A1 .

 A1 Fig. A1. Demographic scenario used in the simulations.

Fig. A2 .

 A2 Fig. A2. City size (left) and green area fraction (right) in the scenarios.

Fig. A3 .

 A3 Fig. A3. Typologies of urban landscapes over the study domain, in the case of the spread-out city (SPR).

Table 1

 1 General characteristics of the reference city and of the urban sprawl scenarios simulated by the NEDUM-2D model.

	City	Description	Date	Population (inhab)	City size (km²)	Green areas (km²)
	REF	Today Paris	2008	11 800 000	1600	750
	SPR	Spread-out city	2100	13 400 000	2550	1250
	COM	Compact city	2100	13 400 000	1900	850
	G10	10% Green city	2100	13 400 000	2800	1500
	G30	30% Green city	2100	13 400 000	3450	2150
	G50	50% Green city	2100	13 400 000	4300	3050

Table 2

 2 Biases (Obs-Model) and root-mean square errors computed between observations and model outputs for the four land cover classes and separately for nighttime (2200-0500 UTC) and daytime (0600-2100 UTC) hours.

			City	High-density	Low-density	Rural
			center	suburbs	suburbs	areas
	Bias	Night	-0.41	-0.79	-1.51	-3.72
	(°C)	Day	+0.50	+0.62	+0.41	+0.57
	RMSE	Night	0.83	1.69	2.07	3.83
	(°C)	Day	0.78	0.94	1.08	2.06

  Table 3 summarizes indicator value in this REF case both for nighttime and daytime hours.

Table 3

 3 Description of indicators used for assessing urban sprawl strategies. The two last columns presents the indicators calculated for REF in the case of a seven-day HW38 and for a temperature threshold of 1.5°C.

	Indicator (Unit)	Definition

This scenario corresponds to the scenario SN with high demographic hypothesis in[START_REF] Viguié | Downscaling Long term socio-economic scenarios at city scale: a case study on Paris[END_REF]. See Annex A for more details.

Acknowledgments

This study benefited from funding by the French Agency for Research (ANR) through the VURCA project (ANR-08-VULN-013). The authors are grateful to the large VURCA's community, especially Stéphane Hallegatte for initiating the project. They also thank Colette Marchadier and Jean-Luc Salagnac for the elaboration of the database of building characteristics, as well as Anne-Lise Beaulant and Grégoire Pigeon for their contribution to the design and implementation of the modeling platform.