Laurence Jolivet
email: laurence.jolivet@ign.fr

Daphné Bostancıoğlu

Catherine Dominguès
email: catherine.domingues@ign.fr

Éric Mermet
email: eric.mermet@ehess.fr

Sevil Seten
email: sevilseten@gmail.com

Panel of sensitive mapping experiments with respect to various sources of information

Keywords: sensitive mapping, source of information, experiment, information selection, map analysis

Sensitive mapping corresponds to a process of making maps by consciously integrating personal subjectivity about a space during observation and visualization. The approach is mobilized to express emotions, sentiments and opinions associated to a spatial environment as well as a mean to be attentive to this environment based on the five senses. The objective of the work is to explore the relations between sources of information about a space and resulted maps. Three sensitive mapping experiments implemented during the seminar in sensitive mapping in École des hautes études en sciences sociales (EHESS) are described. Different sources are used: direct observation, audio records and texts. The maps made by the participants were analyzed according to the criteria of the chosen material, the conceptualization of space, the scale and extent, the selection and display of information. Specificities and similarities between maps helped formulating hypotheses about the role of map-makers and the apprehension of space depending on the sources. Direct observation implied that the map-maker is physically in a space. Subjectivity can be seen on the maps through little completeness of the landscape features and display of emotions, sentiments and opinions. Audio records and texts implied that the map-makers did not go into the space. Maps contain relative completeness and details of information from the sources, mainly regarding landscape features. Interpretations by map-makers appeared more in the design than in the information selection. Sources of information can thus be considered complementary and sensitive mapping experiments can combine them to gather knowledge and perceptions about a space.

Introduction

1.1 From field to map: various sources of information Maps have taken various forms over time. They have fulfilled different needs and functions (e.g. historical Portolan charts for navigation). They correspond to different contents (e.g. shorelines, ports) and are dependent on the technics and tools (e.g. compass) and on the media and materials (e.g. vellum, printing). Each time, until today's digital technologies, has brought new opportunities and so new ways of exploring the space, collecting information and then displaying and disseminating this information [START_REF] Arnaud | La carte de France. Histoire et techniques[END_REF][START_REF] Hofmann | L'âge d'or des cartes marines[END_REF]. A research issue is about identifying the process from field to map and so to specify the relationship between the space as perceived and as described and an edited display [START_REF] Zwer | Cartographie radicale. Explorations[END_REF][START_REF] Arnaud | Cartes et cartographie des ressentis et représentations d'individus : état des lieux, questions sémantiques et méthodologiques[END_REF][START_REF] Gartner | Emotional response to space as an additional concept in cartography[END_REF][START_REF] Dewaele | Dessine-moi ta ville aujourd'hui et demain[END_REF]. Depending on how the field is observed, corresponding maps come out differently [START_REF] Carvalho Cardoso | Mapscapes: Applying Anachronic Techniques in Contemporary Maps as a Design Strategy for New Ways of Seeing[END_REF]. From field to map, there are intermediate processing steps that select, structure, interpret and conceptualize [START_REF] Béguin | La représentation des données géographiques. Statistiques et cartographie[END_REF]. First in the process, the step of observation and collection of information implies that one or several individuals, not necessarily the map-maker, travel in situ or remotely through a space. Second, information about the space is described using a medium and this description constitutes a source of information on its own. The medium can be memory, a text, a record, drawings, notes, photos or movies. Then the map is drawn. Analysing relationship between fields and maps may be based on the contents of the maps with respect to the successive steps of the mapping process. Existing approaches to analyze a corpus of maps depend on the characteristics of the maps including the material and the thematic. For maps in paper format, such as historical maps and contemporary drawn maps, a challenge is to be able to read information and to take it into account for qualitative interpretation or quantitative analyses. Information can be digitized and categorized into databases, then geolocalized. Considering map content can be done systematically by scanning and describing every map elements. List of landscape elements can be established, such as in the study of historical city maps by [START_REF] Dupont | Du texte à l'image. Les plans de Jacques de Deventer, un exemple d'appropriation cartographique de l'espace ? Penser les savoirs géographiques à l'époque moderne[END_REF] and in the study of the Cassini map by [START_REF] Dumenieu | Engraved footprints from the past. Retrieving cartographic geohistorical data from the Cassini Carte de France[END_REF]. Symbolization (graphics, colors) can be described. In [START_REF] Xie | Procedural Knowledge of Graphic Design for Analysing Graphic Elements in Historical Urban Maps[END_REF], detailing semiology enables to focus on important buildings and to witness urban evolution in old maps of London. In [START_REF] Kent | Stylistic Diversity in European State 1:50 000 Topographic Maps[END_REF], designs of European topographical maps are characterized and classified based on several criteria such as the hierarchy of mapped features, the symbols, the lettering and the scale. Locations of displayed features can be compared between maps and between maps and fields e.g. using regular grids such as in the analysis of drawn maps about perceived risk of mudslides in [START_REF] Heitz | Étude exploratoire des représentations de coulées d'eau boueuse en Alsace : Analyse d'enquêtes psychosociales et de dessins à main levée via un logiciel dédié[END_REF] and in the comparison of frontiers of Europe drawn according personal opinions in [START_REF] Didelon | Un monde d'interstices. Apport de la logique floue pour l'analyse des cartes interprétatives[END_REF]. To complete the means of systematic reading and analysis that are intended to be objective, user tests can be implemented to describe maps. [START_REF] Hagemeier-Klose | Evaluation of flood hazard maps in print and web mapping services as information tools in flood risk communication[END_REF] evaluated efficiency of different existing flood hazard maps. [START_REF] Harrie | Analytical Estimation of Map Readability[END_REF] defined readability measures and qualified, based on user tests, maps classified by their scale, their level of detail and their symbols.

From field to map: subjectivity in cartography, conventional and sensitive

In cartography, the goal is to display a part of land in a reduced plane or relief format. There are numbers of possibilities to observe the space to be mapped, and to map it. Perception of the space has changed over time and besides technical developments, maps translate these changes [START_REF] Dupont | Du texte à l'image. Les plans de Jacques de Deventer, un exemple d'appropriation cartographique de l'espace ? Penser les savoirs géographiques à l'époque moderne[END_REF]. One way to see the process of cartography is that a unique field may correspond to as many maps as there are map-makers. Differences between maps come from the field observation and from the specifications in content and in design of the maps as these aspects are under the influence of individual subjectivity. During the field observation, each person experiences the space according to previous experiments, to cerebral parameters such as emotions, sentiments, opinions, imagination and to physical parameters that are the five senses [START_REF] Tuan | Place: An Experiential Perspective[END_REF][START_REF] Wright | Terrae Incognitae": The Place of the Imagination in Geography[END_REF]. Concerns about subjectivity in the map-making process are due to the use and usability of the final map. In conventional cartography, rules and theories were developed to optimize objectivity in the map display, which consequently reduce the gap between the message shaped by the map-maker(s) and the message read by map user(s). Earth models, projections and scaling rules offer mathematical frameworks to downscale the field [START_REF] Béguin | La représentation des données géographiques. Statistiques et cartographie[END_REF][START_REF] Brunet | Les Mots de la géographie, dictionnaire critique, coll. Dynamiques du territoire[END_REF]. Semiology rules enable to associate graphic symbols to pieces of information. Visual variables have been formalized to display information structured regarding qualitative differences, orders or quantities [START_REF] Robinson | Elements of cartography[END_REF][START_REF] Bertin | Sémiologie graphique. Les diagrammes, les réseaux, les cartes[END_REF]. Readability capacities are taken into account, for instance the maximum number of distinct symbols in a key so that the map can be read. The final maps are assessed regarding readability, legibility and interpretation, e.g. implementing user tests which also integrate subjectivity [START_REF] Fabrikant | Emotional response to map design aesthetics[END_REF] studied how map contents are interpreted; Coltekin et al., 2009 used eye-tracking techniques to analyze how maps are physically browsed).

In conventional or non-conventional cartography, when a map is intended to be used by other users than the mapmaker, questions arise on the gap between the cartographic message as shaped by the map-maker and the message as read by a map user. Conventional cartography aims at limiting subjectivity, whereas other approaches in cartography highlights this subjectivity. However, dichotomy between approaches with respect to subjectivity, or objectivity, is not strict [START_REF] Harley | Deconstructing the map[END_REF]. A gradient in the consideration of subjectivity exists among map-making approaches. The gradient spans from limiting and framing subjectivity to making it visible and explicit. In this article, we focus on the sensitive mapping which is an approach integrating explicit subjectivity. Sensitive cartography is close to other approaches, non-exhaustively: cognitive mapping, mental mapping and perceptive mapping. Each vocabulary corresponds to a rich literature and their definitions can overlap [START_REF] Olmedo | Mapping the Skin and the Guts of Stories -A Dialogue between Geolocated and Dislocated Cartographies[END_REF][START_REF] Gould | Cartes Mentales[END_REF][START_REF] Lynch | L'image de la cité[END_REF]. Sensitive cartography aims at displaying a spatial environment through subjectivity that can be of one individual or a group of people [START_REF] Pichon | Espace vécu, perceptions, cartes mentales : l'émergence d'un intérêt pour les représentations symboliques dans la géographie française (1966-1985)[END_REF][START_REF] Bailly | Les concepts de la géographie humaine. 1ère édition en 1984[END_REF]. Contents of the maps focus on how environmental features are perceived. Graphic display is about creating a down-scaled part of land as perceived. This display can benefit from evocative media and materials in order to help conveying information about perception.

Objective of comparing different sources of information in sensitive mapping experiments

Defining relevant experiments in sensitive mapping with adapted protocols, i.e. guidelines, is crucial to obtain targeted knowledge and increase the potentialities of created maps with respect of a part of space. Sensitive mapping stands as a method that can produce knowledge about a space as it focus on perception and on environmental features that may be rarely displayed. In this problematic, we are interested in the relationships between the observed field and the corresponding maps. Our general objective is to explore the relations between sources of information and the way information is mapped. The research hypothesis is that differences between sources of information that are part of the protocol (direct observation, audio and text in our study), imply differences between mapped information. Differences may concern the selection and the symbolization of sensitive and topographic information. There are numbers of parameters that influence a final map display, which are difficult to isolate from each other. Parameters may correspond to the context of the successive processing steps (perceiving, describing, and mapping) and to individual choices (knowledge, taste). Though, we assumed that differences due to sources of information still remain within the final displays of the maps because the source of information is a key aspect in the mapping process. We will present the corpus and our method to analyze this corpus, then we will synthetize the analysis results, at last we will discuss the potentialities of sensitive mapping experiments to better understand a space.

Map corpus and method

Map corpus

The studied corpus contains maps that were created during the teaching and research seminar Atelier de cartographie sensible. This seminar is held every year starting from 2016 in École des hautes études en sciences sociales (EHESS) in Paris, France (http://psig.humanum.fr/cartes-sensibles/). During the courses, sensitive mapping experiments are proposed to participants. The participants come from training programs and research laboratories mainly in sociology and in anthropology, psychology and geography. Protocols defined for the experiments are the set of instructions leading to maps. Three protocols (Table 1) have been selected in order to study potential differences in the maps due to the sources of information which are:

• In situ observation of the space. Observation is made by participants while walking. Filters of observation are used, for instance noise, building use, nature. The mapping was done on the moment of the walk (mainly note taking) and by memory while going back inside; • Audio records of bicycle itineraries with spoken comments of the rider and sounds from the environment; • Extract of written texts from novels. Texts are literacy classics with descriptions of a given site or along an itinerary, e.g. L'assommoir by Émile Zola and Une Traversée de Paris by Éric Hazan. Table 1. Three sensitive mapping experiments: description of the protocols including the different sources of information from which the maps where created.

Protocols provided two main types of sources. The first type was direct observations of the space by the mapmaker. The second one was given by intermediate media,

here audio records and texts. In the case of direct observation, spatial and sensitive information are collected and formatted by the map-maker. In the case of intermediate media, there is an additional formalization between the spatial environment and the map that is not set by the map-maker. Created maps thus correspond to a spatial environment which is perceived and lived by the map-maker, or which is first described as perceived and lived by an external author and then this description is interpreted and displayed by a map-maker. In all protocols, the spatial area is Paris, as a whole city including close suburbs, with focus on neighbourhoods.

Mapping was done during the courses by group sessions.

The maps were created after observation, partly based on note-taking and on memory. Instructions and explanations were given to all map-makers. The 105 map-makers were in great majority students, a few more women than men. The main media was paper and the material was free to choose e.g. drawing techniques, fabrics, stickers. Individual and collective maps were created, increasing the number of maps relative to the number of participants. In total, there are 127 maps from the three protocols, evenly distributed among the audio records and the in situ observation, and around a double more for the texts.

Method

The method to identify the relationship between protocols, especially information sources, and the resulted maps is to analyze the maps and the associated mapping processes which have led to the resulted maps. This is a bottom-up analysis in order to identify potential influence of sources on how environment is mapped. Thus the specificities encountered in maps of each protocol were looked at. We focus on what is specific to the sensitive mapping approach regarding selection of information: perceptive information (five senses), information related to the expression of subjectivity (emotions, sentiments and opinions) and also information as selected from field to display, and regarding geometrical display and symbolization: whether conventional or unconventional. The analysis of each map of the corpus is based on a list of criteria inspired by the generic steps in cartographical processes and corresponding to descriptors of a cartographical process and of the map content [START_REF] Dominguès | Connaissances opérationnelles pour la conception automatique de légendes de cartes[END_REF]. Criteria are defined as follows.

• Drawing of the map: medium (e.g. paper), materials (e.g. ink, fabrics), drawing of specific elements on the map such as title, key, frame, etc. • Conceptualization of the space: collection of information and its modelling. Collection can be by memory or by taking text notes and sketches. It may rely on external sources like existing maps or photos. Conceptualization of the spatial environment is interpreted based on the design, e.g. schematic shapes, different levels of detail between elements. It may reflect individual perception of the structure and the use of space.

• Spatial scale and extent: the interest is how reduction of space is implemented. Scaling rules are commonly used though in sensible maps, distances and shapes can be distorted and observed topological relations can be personal. • Selection of mapped information: specific elements in the map. It can be landmarks of landscape features and in sensible maps it can be perceptive information, emotions, opinions and individual hierarchy in the displayed elements. • Symbolization: it is the symbols defined for displaying elements such as semiology variables, place names, written words. The implementation of the analysis consisted in scanning paper maps. Each map was numerically identified and annotated following the defined criteria. Annotations could be associated to the whole map or to specific located elements. Description of maps from different sources of information were synthesized and compared.

Analysis of resulted maps depending on information sources

In this section, analysis of the created maps is presented according to the three sensitive mapping protocols. It is structured according to the defined criteria in 2.2.

Mapping from field observation

In the protocol of field observation, the map-maker is the one who observes the spatial environment and displays it as perceived. Given instructions were to be attentive to space through one filter free of choice. Chosen filters were shops, metal plates, sky opening, vegetation and animals and more generally nature, density of people, sounds. An additional collective map was created by all participants of a same session in order to gather individual observations (extract in Figure 1). All final maps were drawn on paper, based on memory and written notes taken on the field mostly about the chosen filter. White paper sheets were provided as well as a whole set of black and colour pens, scotch tape, staples, stamps, fabrics, stickers. To locate information, mapmakers either used existing background maps (30% of the 26 maps) or white paper displaying a line corresponding to the followed itinerary (70%). Mapped information was displayed by symbols and text (key being written aside 25% of the maps). Conceptualization of the space corresponded to a spatial organization of two types, global (55%) or built step by step (45%). Space was drawn along the travel itinerary which was one central single route line with information on each side of the street or which was two lines corresponding to the borders (buildings, sidewalk). Some maps (n=2) were displayed in angle of view in perspective that could correspond to a global and distant personal insight of the mapped space. The shape of the route line was either similar to the itinerary (street turns and straight parts), or it could diverge (use of other landmark like street name for deviation instead of turns).

The extent of the maps could be adapted to one sheet of paper or extended progressively with new sheets of paper (25% of the maps). Maps are mainly high-scaled at the level of detail of the streets.

For the selection of mapped information, feedbacks of the participants were that it was difficult to select and synthetize information directly on the field and that memory in the selection is also crucial, focusing on salient observed information. The observation and interpretation of the space are dependent of personal knowledge. For instance regarding the filter about nature, knowledge about the history and configuration of the green spaces in the city of Paris has mattered in the selection of information. Participants were asked beforehand to name elements of nature. Answers were public green spaces (gardens, squares), trees and vegetation, evidences of animal presence (e.g. birds' nest and singing), absence of traffic sounds. More ambiguous elements are quoted such as human facilities for wildlife: insect houses, beehives that have been installed on rooftops. After field observation, green spaces have been consensually displayed. Some elements were added such as hydrography, e.g. the Seine River. Other elements were noticed but not displayed on maps due to scale and scarceness such as plants in the pavement interstices. In all maps, salient information is mainly about the filter, though landmarks have been displayed that can be used for relative location such as roads and specific buildings. Conventional symbolization including rules about visual variables was mobilized, mainly for features commonly displayed in topographical maps: vegetation (in green colour), roads (in black) and hydrography (in blue) (Figure 1). Concerning sensitive and perceptive information, some figurative symbols were used, e.g. traffic sign for cars, ear for sounds, or evocative symbols e.g. hatches for sounds. Colours were chosen to highlight personal positive or negative assessment on features or to highlight well-known features.

Mapping audio records

The second protocol is based on audio records during a bike ride. Map-makers were asked to display the travelled space as being described by the rider and speaker. The records stand as third-party sources for the map-makers. For the drawing of the maps, white paper sheets and the same materials as for the protocol of field observation were provided. Most formats of the final proposed map were adapted to the linearity of the movement of the rider describing and perceiving the spatial environment. No existing background map with streets layout and names was supplied, though some map-makers printed one in order to support the location of mapped elements and especially of sensitive and perceptive information. Those background maps were integrated into the final map or only used as an external resource so that to visualize the spatial environment and to help locate the spatial features. All map-makers produced intermediate materials: notetaking or sketch maps. As for the protocol based on texts, map-makers had full access to the source, meaning that they could listen several times the records, press pause or browse. The conceptualization of space is related to the layout of the cycling itinerary explicitly displayed by a line or not. In the same way that in the audio, the space is described from one place to another successive place, the produced maps contains elements that were located and designed related to each other successively, e.g. a store located near a crossroad on the map, as both elements are mentioned successively in the record. Among the produced maps, the spatial extent was defined according to the itinerary. One approach by the mapmakers was that the layout of the route was defined in advance within a format (one or several sheets of paper). Another approach was to adapt the format as the drawing proceeds (by assembling the sheets). Maps were of high spatial scales, due to the relatively low movement speed of a bicycle within the city streets and to the precise description of the space that could be given by the rider. Though, levels of details differ according to record segments: when the rider is describing a temporary event (e.g. someone is crossing the road), the description of physical spatial environment is let aside. Contrary to a written text, there is no overlay of formulated information at the same place and time in the live audio records. The selection of information was explicitly made by the map-maker. During note-taking or sketch map while listening to the records, there were a selection as not all information given could be listed. Some map-makers listened to the audio record in a raw, taking the most exhaustive notes as possible, and then made a selection afterwards. Other map-makers navigated through the record and organized their notes progressively while stopping the record. Maps contain: the layout of the itinerary, the road network displayed explicitly or implicitly by buildings or elements on both sides of the roads, elements of the environment perceived and described by the rider e.g. public works, salient architecture features and the sounds captured by the recorder e.g. car traffic, horns. In the final displays of the maps, there is a will to describe the space as used by a bicycle rider, in particular relevant elements for cycling such as bike paths, traffic signs, temporary public works and other users in the streets such as pedestrians. The selection of some items has induced the selection of other items, e.g. the selection of mentioned pedestrians has induced the selection of mentioned pedestrian crossing. No drawing of the rider was done, only the rider's comments and the surrounded sounds. Symbolization related to the displayed elements corresponds mostly to punctual symbols for specific features, e.g. buildings (estimated date of construction, style, colour, height) and urban furnishing, and to a line for the road textured depending on the covering (Figure 2). Elements were either displayed in perspective or by flat polygons. The background sounds in the audio (other than the rider's voice) contributed to the general atmosphere perceived by the map-maker though were said to be quite difficult to display: voice from other people, cars, noise from public works. Some unusual materials for maps were used to convey information and to help the display of unusual mapped elements, e.g. metal staples for barriers. For most maps, a key was displayed. When no key were provided, symbolization was mostly designed as evocative, e.g. a more or less high sinusoid for the varying intensity of noise.

Mapping texts

In the third protocol, information sources are texts from novels corresponding to descriptions of existing places as observed, interpreted and imagined by the writer. The map-makers were asked to display the spatial environment as described in the texts, taking into account physical elements as well as described perception (senses, emotions, sentiments, opinions). As well as for the audio records, these texts are a third party point of view of a perceived space for the map-maker. Created maps were drawn on sheets of paper that were supplied, containing the text and a white space for mapping, and with a set of black and colour pens. Some explicit links (drawn arrows) have been made between segments of text and the parts of the maps. Drafts were sometimes produced before a final version. Several displays mix 2D and 3D displays. Some maps correspond to perspective views, e.g. buildings and roads from an elevated angle of view and perspective line. Some maps contain a displayed line explicating the limit between the ground (and the elements shortly above) and the sky. 3D displays of buildings and landscape features (roads, bridges) are present in half of the produced maps (Figure 3). Other landscape elements are not that obvious to be displayed in 3D and 2D was used partly due to drawing limitation. The space travelled along an itinerary is displayed thanks to a line or to successive arrows. In the narration of the different texts, disorientation or interrogation about the location of places are described though have not been displayed in the maps.

Figure 3. Figurative symbols and drawings: display in 3D of buildings and of a bridge.

Multi-scaling is found within several maps. Scaling variations are related to the different levels of details described in a same text and to the importance given to the described elements by the map-makers. Selection of mapped information corresponds to spatial landmarks, e.g. the layouts of the streets. Most produced maps contain a topographic background including topographical elements: roads, buildings, vegetation, water features. Aside from the topographic background, selection of information is different between map-makers. Shared pieces of information can be encountered among the maps, especially if highlighted in the text. Highlights can be about unusual elements (e.g. spotted colour lights) and elements described or mentioned several times (a balcony). Extracts from the novels contain rare phenomenon, that are displayed or not depending on the map-maker, for instance cars that rarely pass by a street or a place with a few stores. In general, absence is not displayed or can be displayed by a proxy, e.g. when it is written that few people risk walking in a street, one map displays a succession of inhospitable buildings. Symbolization mainly correspond to figurative drawings and so the visual variables shape, texture and intensity. A key is present in most maps. In a few maps with no key, some symbolization choices, e.g. colour codes, are difficult to interpret and left to interpretation of the map readers. Words are largely used in order to display information such as place names, landscape elements types, and mentioned absence in the text and so not symbolized but written, e.g. the words "no dogs barking" is taken from the novel and placed in the map.

Discussion: differences and shared map characteristics regarding information sources

Analysis of maps created from the three sensitive mapping protocols highlights some differences as well as common characteristics, regarding the selection and display of the spatial environment as perceived.

Information selection

The list of criteria for analysing the maps was not an evaluation grid as in sensible maps, there is no correct or incorrect designs concerning readability and good understanding by a map user. Those criteria remain entries to describe the maps and to structure comparison according to protocols with various information sources. In the implemented sensitive mapping experiments, several interpretation layers stand between the field and the analysis of the resulted maps: the interpretation of the collector of the sources of information (in the case of the audio records and the text), the interpretation of the mapmaker when making the maps and the interpretation of the map reader and analyst. The defined protocols were the same for all participants, however there are always degrees of freedom in the implementation. Individual interpretation of instructions comes into play in addition to individual interpretation of sources, knowledge in cartography and abilities to drawing. In the sensitive mapping approach, information may not have been displayed in such a way as to be easily read and understood. Though, all maps have somehow the capacity to store and to pass on an observed reality or a message. Besides, discussions between map-makers regarding their cartographical choices were held after the experiments. Analysis of the maps enabled to highlight specificities of the protocols and shared features. During the part of information selection from the different sources, there were a balance between live selection and selection based on memory. Taking notes was possible during the handling of the source information in the three experiments. These notes are intermediate productions helping the map-maker appropriating the given information by listing observed, heard and formulated elements and by organizing them. Participants expressed the difficulty to synthetize their observations directly and to display them while on the field, while listening or while reading. In the protocol in situ, chosen filters induced explicit selection while observing in the field and taking some notes and memory acted as an additional filter back inside where the maps were created. Based on notes and memory, mainly salient information was selected. The distance between the observed space (outside) and the space where the maps were created (room inside) may change the selection of information, compared as if the maps had been created entirely on the field. The appropriation of the space was generally strong as observation involved the whole body including the five senses. Subjective comments were integrated to the maps. In the protocols based on audio records and texts, mapmakers were not the observers of the space. Access to the sources and map creation were proceeded inside with possible replays and several readings. Memory was less mobilized and the information given in the records and texts was more exhaustively selected. In that sense, mapmakers have taken on the role of preserving the perceived space as formulated by the bike rider and by the writer by keeping many details. This understanding should be completed by other experiments and in particular in the light of map-makers' profiles and familiarity in the mapped area.

Information display

In the map displays, scaling factor between field and map varies, possibly within a same map. Cases that are encountered are: 1. a general score of the space (e.g. road network, limits of the mentioned space in the text) filled with located features, 2. one or several zoom centred on parts of space and detailed with landscape features (e.g. buildings) or aspect of the living space (e.g. people), 3. non-precisely located information and so displayed elements distributed in the map according to existing spatial relations or not. The extent of some displayed elements can be constrained by the format of the given sheet of paper in the protocol. The information content is relatively complete and detailed compared to the sources in the protocols based on audio records and texts. It is made of landmarks such as buildings, roads and trees, of services such as store brands, of people. The lack and the absence are rarely displayed, except in the protocol based on texts where absence of some facts or elements is written. For all the three protocols, temporary information, e.g. people walking in the street, weather conditions, are more likely to be displayed as the maps are about a spatial environment at a certain date. Not only permanent elements are noticed but also ephemeral ones that correspond to a certain atmosphere that may change at another time. Movement is a central part of the three sources: map-makers walk, listen to a biker that rides, read texts describing different parts of a space or following an itinerary. Movement is not obvious to display on paper maps, though symbols of walking person and moving bicycle were displayed and the layout of the route or an itinerary were associated with arrows. It can be noticed that little information about emotions, sentiments and opinions were displayed. Symbolization and graphical display mix personal and unusual choices with conventional and common ones. Personal symbols can be used for describing information that is generally not on topographical maps, e.g. density of people, weather. Perception information from senses is displayed with personal symbols inspired by abstract symbols like points or hatches, or by figurative symbols. A number of words are written on the maps, sometimes for place names as in conventional maps, though mainly for perceptive information about emotions, sentiments and opinions. That last type of information is not obvious to associate to a symbol, as no conventions are defined and creating evocative symbols are not easy. The use of conventional symbols has been made for information generally present on maps, e.g. the symbol of a red cross for a hospital, the uppercase letter M for the subway in Paris. In the protocols based on audio records and texts, formulated words can be interpreted to display some information, e.g. when a round lake is mentioned, symbolization will correspond. When the non-travelled space is mentioned, there can be explicit symbols like a crossed out line or place. Unusual materials (fabrics, stickers, wires) helped displaying a spatial environment in a tangible way and conveying an atmosphere, which is said among mapmakers as difficult to display apart from context elements (e.g. landscape features, works in the streets) and specific elements (e.g. sounds, smells). In the audio records and texts protocols, interpretations by map-makers can be seen more on the display of information, for instance creative, original and figurative, than on its selection which is quite complete. Keys have been associated to the some map displays. They were decided before or after the drawing of the map. Defining a key before drawing was associated to explicit modelling of the information along the different steps of the cartographical process: browsing through the field, record or text, taking notes, selecting and organizing pieces of information within the notes, defining symbolization for each pieces of information. Defining a key after drawing corresponded to an on-thefly process and designing the map was intertwined with the drawing. Producing a key is also a way to communicate with the reader of the map, a will to guide the interpretation of the map as close as possible to the intentions of the map-maker.

Conclusion

Sensitive cartography focuses and emphasizes the subjectivity of map-makers and of users of a spatial environment. Map-makers are likely to map space as they perceive it, for instance so that to question their own perception of space. They are also likely to map the space based on the experiences of others. Based on implemented protocols during the seminar Atelier de cartographie sensible, insights about interactions between sources of information and resulted maps concerned the role in which the cartographers put themselves. When map-makers draw their own observations, mapping is oriented as an introspective work. When they draw observations that were formulated by others, mapping is more focused on reporting and communicating. Completeness of formulated information in the sources audio records and written texts that were displayed in the maps was high. Sensitive information (from the five senses, emotions, sentiments, opinions) comparatively to landscape features was more displayed in the maps from direct observation than in the maps based on audio and text. Description of sensitive information and description of landscape feature, their physical aspects and their configuration both contribute to personal interpretation of a spatial environment and to its uses. Adapting experiments and associated protocols for sensitive mapping are interested to explore potentialities regarding collecting knowledge about parts of space and designing land planning projects. Various possible sources of information can supply the maps and can be used separately or combined.

Figure 1 .

 1 Figure 1. Extract from a collective map displaying individual observation filters: mix between conventional and personal symbolization. Vegetation display uses conventional green colors; observed animals are displayed using figurative symbols (bone, feather).

Figure 2 .

 2 Figure 2. Formulated information (buildings, trees) and background sounds from the audio records (displayed with three colors corresponded to calm, intermediate and noisy).

Proceedings of the International Cartographic Association, 5, 7, 2023. 31st International Cartographic Conference (ICC 2023), 13-18 August 2023, Cape Town, South Africa. This contribution underwent single-blind peer review based on submitted abstracts. https://doi.org/10.5194/ica-proc-5-7-2023 | © Author(s) 2023. CC BY 4.0 License.

Acknowledgments

The authors thank all the participants of the seminar Atelier de cartographie sensible along the years, EHESS for hosting the seminar and IGN for resources.


Gaétan Berthe

Yoann Coudert-Osmont

Alexander Dobler

Laure Morelle

Amadeus Reinald

Mathis Rocton

PACE Solver Description: Touiouidth

Keywords: 2012 ACM Subject Classification Theory of computation → Graph algorithms analysis; Theory Twinwidth, Pace Challenge Digital Object Identifier 10, 4230/LIPIcs, IPEC, 2023, 38

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Twin-width is a graph parameter introduced in 2020 by Bonnet,Kim,Thomassé and Watrigant [3]. The PACE 2023 Exact Challenge asks to compute the exact twin-width of a dataset of 200 graphs. It is known that deciding whether a graph has twin-width 4 is NP-complete [1], and no approximation algorithms are known. On the exact front, there exists a polynomial-time algorithm for deciding whether a given graph has twin-width 1 [2], and the complexity remains open for twin-width 2 and 3. The exact computation of twin-width has already been tackled using SAT solver methods in [4].

38:2 PACE Solver Description: Touiouidth

A trigraph G = (V, E b , E r ) consists of a vertex set V , a set of black edges E b , and a set of red edges E r . All trigraphs considered in this paper are undirected, finite, and without loops or multiple edges (red or black). Let

N G b (v) = {x | {v, x} ∈ E b } be the open black neighbourhood of v in G, and N G r (v) = {x | {v, x} ∈ E r } be its open red neighbourhood. The red degree of v ∈ V is δ r (v) = |{e ∈ E r | v ∈ e}|. The red degree of G is max v∈V δ r (v).
A contraction in a trigraph G consists of merging any two vertices u and v into a single vertex w, and updating the edges of G as follows. Every vertex

x ∈ N G r (u) ∪ N G r (v) ∪ (N G b (u)∆N G b (v)
) is linked to w by a red edge, and every vertex x ∈ N b (u) ∩ N b (v) is linked to w by a black edge. All other edges in the graph (those not incident to u or v) remain unchanged. A contraction sequence (G 1 , . . . , G |V | ) for G is a sequence of contractions starting from G 1 = G with no red edge and ending in G |V | consisting of a single vertex, where G i+1 is obtained from G i by performing a contraction. A k-contraction sequence is such a sequence in which all graphs G i have red degree at most k. Then, the twin-width of the graph is the minimal k for which there exists a k-contraction sequence.

In the following sections we describe our algorithm finding such an optimal contraction sequence. Section 2 describes a simple reduction rule. Section 3 describes the branch and bound algorithm that is used in several parts of our final algorithm, which is described in Section 5.

Reduction Rule

The following reduction rule is a generalisation of twins for trigraphs and is applied in all parts of our algorithms.

▶ Reduction Rule 1. If there exist two vertices u, v ∈ V such that

N G b (u) ⊆ N G b (v), and
(N G r (v) ∪ N G b (v)) ⊆ (N G r (u) ∪ {u, v}), then contract u and v.
The correctness of this reduction rule is immediate: Let G ′ be the graph after contracting u and v. Then G ′ = G[V \ {v}] and the twin-width of induced trigraphs can only decrease [3]. Note that u and v are not symmetric in the above description of the reduction rule. But the rule as it is presented above is easier to implement.

Main Branch and Bound Algorithm

The main building block of our algorithm is a branch and bound algorithm that tries all pairs of possible contractions in each search tree node. In the following, we present a few optimizations made in our solver.

Search space reduction. Consider a search tree node x of our branch and bound algorithm. Assume we contract vertices u and v in G, and recurse into child node y of the search tree. We do not have to try contracting u and v in the search trees rooted at sibling nodes of y until some contraction "touches" N 2 G (u) or N 2 G (v) where N 2 G is the closed radius-two neighbourhood in G (considering black and red edges) (see Algorithm 1). We store these so-called forbidden contractions (set S in Algorithm 1) using a global vector of sets.

Funding Gaétan Berthe: Supported by the ANR project ELIT (ANR-20-CE48-0008-01). Alexander Dobler: Supported by the Vienna Science and Technology Fund (WWTF) under grant [10.47379/ICT19035]. Laure Morelle: Supported by the ANR project ELIT (ANR-20-CE48-0008-01) and the French-German Collaboration ANR/DFG Project UTMA (ANR-20-CE92-0027). Amadeus Reinald: Supported by the ANR project DIGRAPHS (ANR-19-CE48-0013). Mathis Rocton: Supported by the European Union's Horizon 2020 research and innovation COFUND programme (LogiCS@TUWien, grant agreement No 101034440), and the FWF Science Fund (FWF project Y1329).

://doi.org/10.5281/zenodo.8027195

Algorithm 1 A sketch of the recursive branch and bound algorithm that avoids symmetries. The input is a trigraph G and a set S of forbidden contractions. Both are updated during the search tree.

1 SearchTree(G, S):

SearchTree(contract(G, u, v), S ′ );

Branching order. To guide the order in which we explore the search tree induced by our branch and bound algorithm, we consider all possible contractions in a search tree node in a given order. Namely, for

We sort all pairs using bucket sort, using one bucket for each k = ∆(u 1 , v 1 ). This is faster than sorting all pairs using standard sorting algorithms when k is small. We observed that our initial upper bounds are small for most instances, so this improved the overall runtime of our algorithm.

Optimisations. We list further optimisations that we apply during the branch and bound process.

If the current trigraph has at most 64 vertices then a vector of unsigned long long is used to store the current adjacency lists (for red and black edges). If bit j for index i in this data structure is one then this indicates the presence of an edge. This allows for faster set operations on neighbourhoods of vertices.

At each search tree node, contract twins based on Reduction Rule 1. To find these twins, we do not have to try all pairs of vertices, but only those that are in the neighbourhood of contractions.

We use a global upper bound and local/global lower bounds to leave infeasible parts of the search tree as early as possible.

Upper Bounds

We apply two heuristics that compute contraction sequences yielding us upper bounds. The first, called Heuristic1, iteratively contracts two vertices u, v such that ∆(u, v) is minimal among all pairs of vertices of the current graph. The second heuristic, called Heuristic2, uses randomness and can be executed several times. Given the current graph and an upper bound T , it contracts a random pair of vertices among all pairs u, v such that, after the contraction of u and v, the red degree of the trigraph does not exceed T -1. If Heuristic2 is able to find a contraction sequence with twin-width less than T then this twin-width can be used as new upper bound for the next iteration.

The Complete Algorithm

The complete algorithm consists of three phases: computing a lower bound, computing an upper bound, and then using the branch and bound algorithm. It is run on each connected component of the graph, and each phase is given a time limit as indicated below.

I P E


Thibault Boulant

Matthieu Valla

Jean-François Mariscal

Nicolas Rouanet

David Tomline Michel

Robust molecular wind lidar with Quadri Mach-Zehnder interferometer and UV fiber laser for calibration/validation and future generation of Aeolus

Keywords: molecular wind lidar, Quadri Mach-Zehnder, fiber laser

Wind speed measurement with on-board system has many applications in aeronautics (Gust Load alleviation, Haps, etc.) and space (Weather forecast). The molecular wind lidar is developed for those purposes as it sent laser pulses into the atmosphere to determine, with a spectral analyzer, the wind speed from the Doppler shift induced by the molecules of the atmosphere. In this paper we present the lidar architecture developed at ONERA, that uses a Quadri Mach-Zehnder (QMZ) as a spectral analyzer and a UV fiber laser, designed for gust load alleviation application. We discuss about the advantages of such architecture for wind measurement from space. Simulations of the performances have been performed in the case of Calibration/Validation (Cal/Val) of Aeolus, showing standard deviation on wind speed measurement less than 2 m/s up to 17 km of altitude for the optimized hybrid fiber laser of 10 W laser average power and a pulse repetition frequency (PRF) of 5 kHz. Simulations that evaluates the performances for Aeolus measurement with minor changes in the lidar architecture have been computed, with results showing that requirements are fulfilled up to 22.5 km of altitude with the optimized hybrid fiber laser of 10 W and 3 kHz PRF.

INTRODUCTION

The wind measurement with embedded atmospheric lidar have many applications such as gust load alleviation, [START_REF] Soreide | Coherent lidar turbulence for gust load alleviation[END_REF][START_REF] Fournier | Robust gust load alleviation of flexible aircraft equipped with lidar[END_REF][START_REF] Cavaliere | Gust load control design challenge including lidar wind measurements and based on the common research model[END_REF][START_REF] De Souza | Observer-based gust load alleviation via reduced-order models[END_REF] navigation aid for aircraft navigation [START_REF] Augere | 1.5 µm lidar anemometer for true air speed, angle of sideslip, and angle of attack measurements on-board piaggio p180 aircraft[END_REF] or high-altitude platform system, [START_REF] Strganac | Wind study for high altitude platform design[END_REF] weather forecasting improvement using wind measurements from spaceborne lidar. [START_REF] Bruneau | A new lidar design for operational atmospheric wind and cloud/aerosol survey from space[END_REF] The latter was realized during the ADM-Aeolus mission, launched in 2018, providing the first global wind profiles from space across the entire troposphere and lower stratosphere which led to a significant improvement in the weather forecast score. [START_REF] Rennie | Demonstrated aeolus benefits in atmospheric sciences[END_REF] To achieve the 2 m/s velocity measurement precision required for Aeolus up to 16 km, [START_REF] Adm-Aeolus | Mission Requirements Document[END_REF] the mission places high demands on instrument characteristics such as alignment stability, compactness, fringe contrast, sensitivity to the spectral shift, resistance to vibrations and thermal gradient. In order to verify the overall performance, comparative measurements should be performed, especially with other wind lidar. In this respect, the use of onboard lidar makes it possible to follow the measurements made by the satellite and to bring the lidar to high altitude in order to improve the precision of the measurement. On the other hand, optimizing the technologies used to design Aeolus could lead to better performance, in particular better precision, greater longevity or lower weight, which would lead to a reduction in the overall cost of the mission and/or further improve the weather forecast score. For these two reasons, the exploration of new lidar technologies is very important for the mission and the continuation of Aeolus.

Wind lidars are instruments that measure wind speed remotely. A laser emits pulses into the atmosphere and the velocity is deduced from the Doppler frequency shift induced by the speed of molecules and particles Further information : The project 101101974 -UP Wing is supported by the Clean Aviation Joint Undertaking and its members. Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or Clean Aviation Joint Undertaking. Neither the European Union nor the granting authority can be held responsible for them. on backscattered light using a spectrum analyzer. For wind measurements at all altitudes, molecular lidar are used as molecules are present in the entire atmosphere. For such measurement, UV laser is preferred to improve the backscattered light intensity (∝ 1/λ 4 ). To determine the spectral shift of the backscattered light, an interferometer is typically used [START_REF] Flesia | Theory of the double-edge molecular technique for doppler lidar wind measurement[END_REF][START_REF] Bruneau | Mach-zehnder interferometer as a spectral analyzer for molecular doppler wind lidar[END_REF][START_REF] Bruneau | Fringe-imaging mach-zehnder interferometer as a spectral analyzer for molecular doppler wind lidar[END_REF][START_REF] Herbst | Design of a monolithic michelson interferometer for fringe imaging in a near-field, uv, direct-detection doppler wind lidar[END_REF] to obtain an interference figure that depends on the optical frequency of the input light. By comparing the interference figure obtained for the backscattered light with the one obtained for the laser, the Doppler frequency shift is measured, and then the wind velocity.

Several molecular wind lidar architectures have been developed and used for Aeolus calibration/validation and for Aeolus measurements. A first set-up consists in using a double-edge Fabry-Perot interferometer as a spectral analyzer. This set-up is used for ground based lidars of the Observatoire de Haute Provence and Observatoire de Physique de l'Atmosphère de la Réunion observations sites, [START_REF] Ratynski | Validation of aeolus wind profiles using ground-based lidar and radiosonde observations at réunion island and the observatoire de haute-provence[END_REF] the lidar embedded in Aeolus named ALADIN and the ALADIN Airborne Demonstrator (A2D). [START_REF] Lux | Intercomparison of wind observations from the european space agency's aeolus satellite mission and the aladin airborne demonstrator[END_REF] This spectral analyzer consists of two coupled Fabry-Perot interferometers, placed on either side of the Rayleigh spectrum: when the spectrum is shifted in frequency the light ratio between the two channel varies. The main disadvantage of this technique comes from the dependence on the shape of the spectrum, which depends on the atmospheric temperature and pressure, [START_REF] Zhai | Rayleigh wind retrieval for the aladin airborne demonstrator of the aeolus mission using simulated response calibration[END_REF] and also depends on the amount of scattering from particles in the collected signal. [START_REF] Witschas | First validation of aeolus wind observations by airborne doppler wind lidar measurements[END_REF] Indeed, a change in the shape of the spectrum induces a modification of the ratio of light passing through each filter. For ALADIN and A2D, a Mie channel using a Fizeau interferometer has been added. This channel is used to retrieve the backscattering ratio and correct the bias induced by Mie scattering on the Rayleigh channel measurement. A second type of spectral analyzer is the Michelson interferometer, that first has been studied at ONERA [START_REF] Cezard | Etude de faisabilité d'un lidar Rayleigh-Mie pour des mesures à courte portée de la vitesse de l'air, de sa température et de sa densité[END_REF] and developed in a monolithic design for on-board application by the DLR. [START_REF] Herbst | Design of a monolithic michelson interferometer for fringe imaging in a near-field, uv, direct-detection doppler wind lidar[END_REF] This interferometer is set to give linear interference fringes on a multi-pixel detector of the incident ligth, where the position of the fringes depends on the optical frequency. This technique has several disadvantages including the difficulty of accessing the second output of the interferometer which goes in the backward direction with a very small angle (almost superposed to the input beam). Not analyzing the second output reduce the total intensity of the analyzed signal by a factor of 2 which lead to a decrease of the signal-to-noise ratio (SNR) by a factor of √ 2. Also the use of the imaging detector often requires adapting the circular pupil of the beam to the square shape of the detector and some signal is lost due to the spacing between the pixels. All these effects reduce the SNR resulting in an increase of the error on the estimation of the wind speed. The third type of spectral analyzer is the QMZ interferometer [START_REF] Tucker | Oawl: A high-heritage us doppler wind lidar for next-generation space-based wind and aerosol observations[END_REF][START_REF] Tucker | Quadrature mach zehnder interferometers for lidar remote sensing of winds and aerosols in the planetary boundary layer through the lower stratosphere[END_REF] that have been developed for airborne wind measurement and have also been tested for Cal/Val campaigns of Aeolus. The cat-eye design allows to field widened the interferometer which reduces sensitivity to beam divergence. However, the number of optics increase the alignment complexity and the risk of having optics disrupt by vibrations in flight. All those lidar use 1 µm solid states laser where a laser diode is injected in the optical cavity to maintain a narrow spectrum and stabilize the wavelength value. However, this requires to keep the cavity length adapted to the wavelength of the laser diode which requires to control the cavity length within less than 1 µm with a feedback loop. In addition such design is expensive, heavy and difficult to use in space because they cannot operate in vacuum environment. For Aeolus a continuous injection of oxygen is required to avoid damages optical surfaces which further increase the difficulty to operate such laser in space.

In this paper, we present a molecular wind lidar developed at ONERA that use a monolithic QMZ spectral analyzer and a UV fiber for airborne wind speed measurement. The combination of these two bricks allows to increase robustness to vibrations, to have a strong signal at the output of the detector and to have a large angular acceptance of the spectral analyzer. This lidar is currently developed to measure turbulence in front of an aircraft. We investigate with simulations the possibility to use this lidar for Cal/Val applications with minor changes. Then, we study with simulations how it should be modified to be used for the future Aeolus mission and the advantages of such architecture.

UV LIDAR ARCHITECTURE

In the frame of the clean aviation project we develop a UV lidar for future aircraft with larger wings designed to reduce aircraft consumption. The lidar will be used to measure turbulences in front of the aircraft to modify the wing shape to reduce the load of the air on the wings using actuators that modify the aircraft aerodynamic profile according to the direction and strength of the wind. Indeed, larger wings are more sensitive to turbulence and requires such technique (called gust load alleviation). The lidar is configured to measure the wind between 100 m and 300 m ahead of the aircraft, with a spatial resolution of 10 m, a precision of 1 m/s with an integration of 100 ms. The schematic of the UV molecular wind lidar developed at ONERA is presented in Fig. 1a. The system is separated in three main part: the laser system, the emission/reception telescope and the QMZ interferometer. The laser system emits about 10 ns UV pulses that pass through a beam expander to have a beam diameter of about 4 cm and are sent out into the atmosphere. Backscattered light from molecules and particles is collected by a 6 inch Newton telescope with a geometrical aperture of 4 which focuses the light into an optical fiber of 400 µm-core diameter. An interference filter of 1 nm bandwidth makes it possible to reject the part of the broad spectrum coming from the scene captured by the telescope. The collected signal is sent to the QMZ and followed temporally by a sample of the laser taken just after the laser output. The QMZ interferometer splits the incident beam into two beams of equal intensity using a 50/50 beam splitter. The two beams pass through two arms with different optical paths and are recombined on a second beam splitter. A quarter-wave plate on an arm increases the optical path of a vertical polarization state relative to the horizontal polarization state. The two polarization states are separated at the two outputs with polarization separator cubes and four interference states out of phase by π/2 are obtained (i.e. separated by 0,π/2,π,3π/2). The intensity of the four interferences is a function of the optical frequency of the incident light. The difference in intensity between the collected signal and the laser gives the frequency offset and therefore the wind speed. [START_REF] Bruneau | Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a mach-zehnder interferometer: principle of operation and performance assessment[END_REF] In order to obtain a robust design insensitive to misalignment caused by flight vibrations, a monolithic QMZ interferometer [Fig. 1b] is currently under development in collaboration with the LATMOS Laboratory. The interferometer consists of four prisms held together by molecular adhesion or glue to form a monolithic interferometer. Some faces are coated to achieve equal intensity separation of light and to maximize the overall transmission of the interferometer. A mechanical structure is also developed to minimize thermal gradient and to further increase robustness to vibration in typical aircraft environment.

To further improves robustness of the system, a fiber laser is currently studied and developed according to the architecture shown in Fig. 1c. A distributed feedback (DFB) laser diode emits 1 µm continuous beam, that is amplified by a pumped doped fiber. Pulses are generated with an acousto optic modulator and are amplified by another pumped doped fiber. The third harmonic generation crystal is used to have a 0,34 µm pulse beam. A free space amplification crystal may be added to the architecture to increase the energy of the laser (hybrid fiber laser). We can note that this instruments had additional advantages including efficiency, cheaper components and the ability to shape temporally the pulses to optimize them for the lidar measurements. We can also notice that a free-space amplifying crystal is quite robust to misalignment. [START_REF] Pouillaude | Amplification d'impulsions monofrequences et nanosecondes dans des fibres dopées yb courtes: 1030 nm ou 1064 nm ?[END_REF] For the current study three different laser are planned : a commercial solid states laser, the MerionC from Quantel with energy per pulse of 22.5 mJ and a PRF of 400 Hz, a fiber laser of 40 kHz and 250 µJ, and a hybrid fiber laser with free-space amplification stage of 40 kHz and 750 µJ.

CALIBRATION/VALIDATION APPLICATION

In this part, we evaluate the performance of the UV lidar for Calibration/Validation of Aeolus with minimum changes in the architecture. The lidar performances are evaluated using simulations. To evaluate the performances, we estimate the precision of the wind speed measurement. The simulator include three parts:

-the first part calculates the molecular backscatter coefficient and atmospheric transmission along the lineof-sight of the lidar. In this purpose, the molecular backscatter and extinction coefficients are evaluated at each altitude using the temperature and pressure given by the 1976 Standard Atmosphere Model [START_REF] Oceanic | Us standard atmosphere[END_REF] -the second part determines the flow of photons collected as a function of distance (deduce from the time accounting for the speed of light). At each distance, the lidar signal is average over a spacial distance, called range gate, to improve the SNR but reduce the spatial resolution.

-the last part firstly computes the contribution of each noise sources on the SNR. The total noise includes the shot noise of the backscattered signal, the shot noise of the background signal, the Speckle noise and the detection noise, that include dark noise from the detector and electronic noise. The detection noise is negligible because of the use of Photo-multiplier tube that amplified the collected signal. The Speckle noise from the signal is also negligible because the beam size and the coherence length (compared to the range gate) lead to a strong averaging of the Speckles. Then the SNR is calculated at each range by dividing the number of photons per the quadratic summation of the two shot noises. To evaluate the precision of the retrieved wind speed, we use the formula that gives the standard deviation presented in the paper of Bruneau and Pelon part 2.B.. [START_REF] Bruneau | Simultaneous measurements of particle backscattering and extinction coefficients and wind velocity by lidar with a mach-zehnder interferometer: principle of operation and performance assessment[END_REF] We can note that this formula is calculated for a specific signal processing method. However, we did comparison with the Cramer-Rao boundary and excellent agreement were obtained.

To evaluate the performance of the lidar for Cal/Val application, we have performed simulations using the same lidar optics as presented previously. We consider that the lidar is located on the ground and its line-ofsight goes toward the zenith, the range gate is equal to 200 m and the measurement is integrated over 2 s. The background radiation power was taken equal to 0.001W/m 2 /str/nm which is similar to the one taken in ref. [START_REF] Bruneau | A new lidar design for operational atmospheric wind and cloud/aerosol survey from space[END_REF] The PRF of the laser had to be decreased to avoid pulse overlapping between the one reflected at the end and the following one reflected at the beginning of the atmosphere (called range ambiguity). As the measurement have to be made up to 20 km, the corresponding PRF limit is c/(2 * d max )=5000 Hz where c is the light celerity and d max =20 km. The PRF of the two fiber laser, chosen for on-board application, are too high and so they are not adapted to the study. However, it is possible to decrease the PRF down to 5 kHz using pulse picking that consist of taking one pulse over a certain number of pulses, while maintaining the same energy per pulse. The final mean power would be around 1.25 W for the fiber laser and 3.75 W for the hybrid fiber laser.

Simulations of the evolution of the standard deviation as a function of the PRF and laser average power have been performed for an altitude of 15 km and the result is shown in Fig. 2a. As the precision decrease with altitude, fulfilling the requirement of Aeolus is equivalent to have a lidar that have a standard deviation below 2 m/s at this altitude. This simulation evaluate the optimization of the laser for wind speed measurement. The parameter of the three laser used for the project of the ONERA UV wind lidar have been placed on the figure. We also represent the two fiber laser with lower PRF. The result shows that only the MerionC fulfill the requirements at 15 km. However, we decrease here the PRF of the fiber laser considering that we only use pulse picking. However, previous experiment suggest that it is also possible to decrease the laser PRF at constant average power down to about 15 kHz by reducing the PRF of the initial laser diode but keeping the same diode pump power. If we consider that pulse picking is used in a second time to reduce the PRF down to 5 kHz, we obtain an average power of 10 W for the hybrid fiber laser (square on the figure) and the laser fulfills Aeolus requirements at 15 km. Another possibility is to increase the integration time to increase the SNR.

To verify if the requirements of Aeolus are met, simulations were performed to determine the wind speed standard deviation as a function of altitude for the three laser [fig. 2b]. The results show that the MerionC meets the requirements up to 17.5 km, the fiber laser up to 10 km and the hybrid fiber laser up to 12.5 km. If we assume a 10 W average power hybrid fiber laser (optimized on the figure), the requirements are fulfilled up to 17 km of altitude.

AEOLUS TYPE MEASUREMENTS ASSESS BY SIMULATION

In this part, we evaluate the performance of the UV lidar for Aeolus wind measurement with minimum changes in the architecture. We assume the initial Aeolus requirements as mentioned in the Aeolus Mission Requirements Document 9 (that differ from the last Aeolus design). Fig. 3a presents the geometry of Aeolus measurement. The satellite is located at 400 km of altitude and the angle of the line-of-sight of the lidar is 45°from nadir. The measurement has a range gate equal to 707 m to give a vertical resolution of 500 m. The satellite speed (7.2km.s -1 ) and the integration time of 7 s give a horizontal resolution of 50 km. Simulation have been performed with the same parameters as the one presented in the paper of Bruneau and Pelon: 7 the telescope is a 1.5 m mirror, with a 0.1 mrad field of view, the interferential filter bandwidth is 0.1 nm. For the laser parameter, we adopted the same strategy as for the previous Cal/val simulation, except that the range ambiguity of 40 km is assumed and we only consider the hybrid fiber laser. The PRF of the hybrid fiber laser of 3 kHz is chosen to be below the PRF limit imposed by the range ambiguity. We only consider pulse picking that give an average power of 2.25 W.

Simulation of the evolution of standard deviation as a function of PRF and laser average power have been performed for an altitude of 15 km and the result is shown in Fig. 3b. The results show that the MerionC fulfill the requirements at 15 km but not the hybrid fiber laser. To meet the requirements with the hybrid fiber laser, it is possible to decrease the laser PRF at constant average power down to about 15 kHz and then do pulse picking at 3 kHz to reach average power of 6 W . Moreover, free space amplifier could be added to reach an average power of 10 W (magenta cross) to fulfill the Aeolus requirements at 15 km. To evaluate the performances of the two laser, standard deviation as a function of the altitude have been computed and the results are presented in Fig. 3c. The results show that the MerionC fulfill the requirements up to 25 km and the hybrid fiber laser gives a standard deviation above the requirements at all altitude. Then it is necessary to use the optimized hybrid fiber laser of 10 W that reach the requirements up to 22.5 km of altitude. Note that it is also possible to increase the integration time by a factor 2 as it is the case for Aeolus to improve the precision by a factor √ 2.

CONCLUSION

A robust lidar architecture comprising a monolithic QMZ interferometer and a hybrid fiber laser was presented. Simulations were performed to evaluate the performances of such architecture for Cal/Val of Aeolus and for future Aeolus generations. For Cal/Val, simulations show that Aeolus requirements of 2 m/s are fulfilled at all altitude below 16 km with the MerionC and the hybrid fiber laser of 5 kHz and 10 W average power. For future Aeolus generation, the requirements are met up to 25 km of altitude for the MerionC and up to 22.5 km of altitude for the hybrid fiber laser of 10 W and 3 kHz.

Figure 1 :

 1 Figure 1: (a) schematic of the UV molecular wind lidar (b) The monolithique Quadri Mach-Zehnder (c) schematic of the hybrid fiber laser

Figure 2 :

 2 Figure 2: (a) wind speed standard deviation as a function of the laser mean power and the pulse repetition at 15 km altitude. Blue cross: MerionC; red cross: fiber laser; black cross: hybrid fiber laser; black square: optimized hybrid fiber laser of 10 W. The blue line represent the PRF limit that correspond to the range ambiguity of 20 km. The white line represent 2 m/s limit (b) wind speed standard deviation as function of altitude for the three laser. Green rectangles indicate the Aeolus requirements according to the Mission Requirements Document 9

Figure 3 :

 3 Figure 3: (a) Schematic of the Aeolus measurement with the new parameters 7 (b) Standard deviation on wind speed measurement with Aeolus at 15 km altitude. The blue line represent the PRF limit that correspond to the range ambiguity of 20 km, The white line represent 2 m/s limit. Blue cross: MerionC; black cross: hybrid fiber laser; magenta cross: optimized hybrid fiber laser. (c) Standard deviation on wind speed as a function of altitude. Green rectangles indicate the Aeolus requirements according to the Mission Requirements Document 9

ACKNOWLEDGMENTS

Our thanks to Pierre Pichon, Jonathan Pouillaude and Laurent Lombard for the valuable discussion on the fiber laser.