Philippe Averty

DSNA Pascal Lezaud

Florence Nicol

Effects of aircraft trajectories geometrical features upon air traffic controllers' conflict judgments

This work is a twofold contribution to the analysis of conflict detection process in Air Traffic Controllers (ATCos). The first one addresses methodological aspects and proposes a way to get responses as close as possible to controllers' actual expertise without using artifacts such as rating scales or inferring judgments from verbal material. The second objective is to compare the influence of three geometrical features of aircraft encounters and their capacity to alter an accurate perception of conflicts. The proposed methodology appeared to be useful for collecting expertise as controllers quickly appropriated it, and led to get coherent data. Its use can be envisaged when a reliable representation of mental picture of ATCos is essential. Concerning the geometrical features of aircraft trajectories, aircraft attitudes i.e., the fact they are stable, climbing of descending, entailed significant differences on detection accuracy. To a lesser extent, catch-ups and segmented trajectories showed a capacity to make an accurate perception of conflicts more difficult. These results must be interpreted as tendencies more than precise or quantified results. As the objective of this experiment was to be a pre-experiment in preparation for future collecting in the framework of the European project SESAR, a few different choices concerning the trajectories to be used in the traffic scenarios will help to precise these results.

Introduction

Recent R&D developments in Air Traffic Management (ATM) already investigated some of the possible heuristic paths for simultaneously conciliating gain in capacity, enhanced safety and better services provision to users [START_REF] Nicol | Deliverable 3, The ATM Target Concept[END_REF][START_REF] Weber | ERASMUS: Concept of Operations & Initial Modeling Results, 7th R&D ATM Seminar[END_REF]. Among the enablers, the accurate trajectory prediction expected from the future FMS (Flight Management System) 4D stands in good place [START_REF] Weber | Analysis and improvement of ground and FMSgenerated trajectory predictions accuracy and integrity[END_REF]. Air and ground systems could inform each other of current and anticipated flight parameters and actions. But initiation of such a system will need a substantial period. Thus, a transitional phase will exist, during which man and more automation will have to share tasks in real time. Both keeping the first in the decision loop will still require -even more acutely -to pay off the problem of compatibility between human expertise and automated data processing while meeting all the necessary operational and safety requirements. Inasmuch as the gap between these two parties could have been reduced it would both keep a sufficient relevance of ensuing actions and reduce human workload, therefore founding conditions for capacity gain, just as the European project ERASMUS aimed at illustrating it [START_REF] Drogoul | ERASMUS Strategic Deconfliction to Benefit SESAR, 8th Air Traffic Management R&D Seminar[END_REF]. In particular, this would be the case for conflict risk assessment. Barring the appearance of new revolutionary equipments -which will precisely be the privilege of the future systemjudgments about aircraft encounters are the headstone in ATCos' operating modes. Actually, though this process is only responsible of a part of the workload, the whole task (situation awareness, plans, and actions) is dynamically and permanently (re-) structured in reference to such judgments and their revisions [START_REF] Hilburn | Cognitive Complexity In Air Traffic Control -A Literature Review[END_REF].

Extrapolation of Aircraft Positions

Regarding the compatibility problem, the major issue is that judgments are not the exact reflections of computed probable risks [START_REF] Kurchar | A Review of Conflict Detection and Resolution Modeling Methods[END_REF]. In ATC, human processing mainly brings into play visual abilities, heuristics, and conversely does a very moderate use of computing [START_REF] Bouju | Analyse de l'activité visuelle des contrôleurs d'approche[END_REF][START_REF] Bisseret | Une expérience sur le "choix des solutions" dans le contrôle du trafic aérien[END_REF]. In consequence, conflict judgments reflect the performance (and biases) of the visual system. If the latter is proved to be quick, holistic and resistant to disruption, it also has its own limits concerning extrapolation of current situations [START_REF] Law | Perceptual and cognitive factors governing performance in comparative arrival-time judgments[END_REF][START_REF] Remington | Visual Search in Complex Displays: Factors Affecting Conflict Detection by Air Traffic Controllers[END_REF]. Moreover, in ATC judgments integrate additional margins, in order to cope with data uncertainty and contingencies [START_REF] Leroux | Cognitive Aspects and Automation[END_REF]. These margins are related to idiosyncrasy and differences in individual experiences which induce a great variability among expert judgments. Nevertheless, a common and coherent cognitive processing caused by the major traffic configuration features has also 5.B.4-2 been shown, resulting in globally meaningful judgments [START_REF] Averty | Conflict perception by ATCS admits doubt but not inconsistency[END_REF]. Using the three main sources of variation in conflict judgment (minimum horizontal and vertical separation, time to conflict) the cited work developed a predictive model of conflict judgments from a experimental data collection (161 participants) in four ATC centers. A mathematical modeling was worked out from these results [START_REF] Averty | An Ordered Logit Model of Air Traffic Controllers' Conflict Risk Judgment[END_REF].

It must be noticed that currently available data for extrapolating positions by computation -and separations between aircraft consequently -lead to results at least as uncertain as the mere empirical ATCos' expertise. Actually, uncertainty margins commonly used for this computation are in the region of 5% for horizontal speed and 15% for vertical speed. As far as the extrapolation exceeds a few minutes, these margins bring about detection of an excessive number of conflicts compared to the one coming from empirical (perceptual) judgments from experts [START_REF] Alliot | A statistical analysis of the influence of vertical and ground speed errors on conflict probe[END_REF]. The use of VAFORIT (a medium term conflict detection device) in Germany confirms the previous considerations. This tool is at present used to simply make out a list of possible conflicts. From then on, controllers may check this list and possibly use it as a simple aid, although (or because) they clearly know at the onset that this list may be not complete and contains a significant number of 'false' conflicts i.e., encounters that themselves will not see as such. Ratifying the limits of this device -without renouncing to progressively make it more effectivemakes it accepted on working positions, as this tool is said to currently do controllers some appreciable turns.

Assessing Controllers Assessments

How could it be possible to assess controllers' thresholds between conflict and non conflicts? For long, experimental results as well as expert judgments gathering established that longitudinal distances around 7 to 15 Nm i.e., two or three times the norm represented the rough magnitude order of this threshold. Concerning the vertical dimension, margins differentiating conflict/non conflict judgments are more uneasy to assess. It was reputed to be more uncertain, generally needing more important margins than longitudinal distance (about 4000 to 6000 feet i.e., four to six times the norm) [START_REF] Michard | Analyse de la représentation des trajectoires d'évolution chez les Premiers Contrôleurs[END_REF][START_REF] Lafon | Observations en trafic réel de la résolution des conflits entre avions évolutifs[END_REF].

It would be interesting to explain a significant part of the variance about these thresholds. If idiosyncratic aspects seem to stay out of reach, the geometrical features in conflict configurations should be grasped when taking the relevant geometrical features into account. Identification of the geometrical characteristics in trajectories that take part in conflict detection processing has been made in several previous studies [START_REF] Rantanen | Hierarchical Conflict Detection in Air Traffic Control[END_REF][START_REF] Bouju | Analyse de la prévision de la séparation entre deux avions évolutifs convergents[END_REF][START_REF] Nunes | An Empirical Study of Calibration in Air Traffic Control Expert Judgment[END_REF][START_REF] Enard | Analyse de la prévision de séparation entre deux avions convergents sur l'écran radar[END_REF][START_REF] Boag | An analysis of relational complexity in air traffic control conflict detection task[END_REF][START_REF] Davison | Modeling the Air Traffic Controller's Cognitive Projection Process[END_REF][START_REF] Nunes | Interactions between Convergence Angle, Traffic Load, and Altitude Distribution in Air Traffic Control[END_REF]. Various cognitive strategies are likely to be used by controllers but their connections with traffic configurations to which they are applied failed to be clearly established [START_REF] Loft | Modeling and Predicting Mental Workload in En Route Air Traffic Control: Critical Review and Broader Implications[END_REF][START_REF] Xu | Conflict detection in air traffic control: a task analysis, a literature review, and a need for further research[END_REF]. Among others, a review of that question exists in [START_REF] Averty | An Ordered Logit Model of Air Traffic Controllers' Conflict Risk Judgment[END_REF].

Furthermore, the use of rating scales induces variability in responses insofar as participants do not appropriate these scales exactly in the same way. Ideally, a substantial training, using standardized (or standardizable afterwards) configurations, should be previously proposed to subjects in order to get properly calibrated judgments. Due to time constraints, it is generally not the case.

Another source of variation lies in assessment collecting when using a mere binary choice (conflict non-conflict) for ruling on a converging pair of aircraft. Then, it is not only the judgment about the actually perceived risk which is collected. It is more the behavior the controller is willing to adopt concerning the risk he/she perceives which is expressed in his/her response. This systematically leads to inflate the number of conflict judgments at the expense of non-conflict ones. Intuitively, rather than: "I can see these aircraft will probably (resp. will probably not) show a separation loss in the future", binary judgments from controllers mean: "I decide to deem the future separation to be insufficient, even if I can see some marginally sufficient separation value". This phenomenon has been attested for long among ATC experts [START_REF] Bisseret | Application of signal detection theory to decision making in supervisory control: the effect of the operator's experience[END_REF] and appeals for trying new paths for collecting expertise and appeals for trying new paths for collecting expertise.

Methods and Experimentation

Variables

As soon as the influence of geometrical features upon conflict detection (and resolution) is in question, the two relevant ones most often cited in the literature are the intersection angle between the 5.B.4-3 involved trajectories (we shall name it geometry) and the flight phase: climb, descent, level (hereafter named attitude). These are two independent (explanatory) variables we kept in our experimental plan.

Velocity vectors constitute a significant aid for directly extrapolating future 2-D positions on the radar screen and in real time. Even if these extrapolations do not take into account neither changes that will occur within the considered time interval (engines paramatering changes by crews, wind direction changes) nor curvature of trajectories, this system helps controllers to easily get a more accurate base idea of ensuing positions of aircraft. Consequently, they currently integrate its use into their current operating modes, as soon as it becomes available on their working position. Hence we added in our experimental plan a third variable we named segmentation, in order to explain variance coming from differences between straight trajectories (where relatively reliable extrapolations are provided at once by the device) and trajectories being composed of different legs (where additional perceptual inferences are needed to get the required future positions).

Obviously, other sources of variation exist. Empirical knowledge of controllers on airlines (engine parametering instructions) or on aircraft type behaviors, sometimes exist. Inferences from the verbal material with crew can also give information to controllers about the way the next portion of the trajectory will be managed, which may help to extrapolate more accurately future positions. But we assumed all these can be considered as minor, when compared to the variance magnitudes coming from either the three parameters already selected or the detection process itself (intra-and inter-individuals difference in processing) [START_REF] Averty | An Ordered Logit Model of Air Traffic Controllers' Conflict Risk Judgment[END_REF].

Hypotheses

The main hypothesis concerning these variables is that they make the difficulty of an accurate extrapolation vary, and consequently make more uncertain the identification of conflicts. In our experiment, this hypothesis comes in the three following propositions: Segmentation: as projection (mentally, or by use of the velocity vectors available on the radar display) of future positions is more difficult when the aircraft trajectory is not straight, it was assumed that conflicts should be easier to make when using one-leg trajectories than when using ones with 2 legs (or more). Geometry: as they develop on the same longitudinal axis, catch-ups and face-toface encounters should be easier to use for detecting conflicts than orthogonal trajectories. It is worth noting that we are not concerned with the 'resolution' aspect of the encounters.

Face-to-face contingencies are commonly considered among controllers as more risky than other configurations, for a given minimum separation distance. This will not be taken into account here as only the perception of norm was in the balance, but not the necessity to implement or not an action. Attitude: vertical speed meets more important variations than horizontal speed. Therefore, encounters only involving level-stable aircraft should be easier to recognize than those involving one aircraft climbing or descending, and yet more than those involving two evaluating aircraft.

Making Up the Traffic Scenarios

Our first concern was to supply participants with air traffic scenarios as close as possible to real situations. Using simulated traffic generally implies that horizontal and vertical speeds are kept constant all over the sequence, which is unsound (aeronautically speaking) and is also perceived by subjects, who then make artificially accurate decisions. The second concern was to fulfill the requirements for getting judgments as close as possible to the mental pictures relative to the configuration shown. Giving responses on a numerical scale introduces bias as scale values -in spite of sufficient instructions -are not always used in the same way (inter-individual differences) for expressing judgments.

In order to deal at best with these two concerns, we fulfilled the following requirements while making the traffic scenarios: Scenarios consisted of a traffic sequences composed of two converging aircraft. Clusters of more than two aircraft involve 5.B.4-4 more complicated processing and would be irrelevant in the context of this study. Aircraft trajectories were dynamically displayed, on the usual local radar map. Scenarios lasted about 40 seconds, as this duration appeared sufficient in a previous study [START_REF] Averty | Conflict perception by ATCS admits doubt but not inconsistency[END_REF] for controllers to make their decisions about conflict risk when only monitoring two aircraft. Aircraft trajectories had to be real, i.e., coming from traffic recordings in the considered control center. This means that horizontal and vertical speeds included variations that can be observed in real life. Both aircraft flew sometime in the presented paths but not concurrently: we managed to make them fly in the same space at the same time. They were selected because they had been flying on standard routes (known by all participants) which intersected in accordance with our explanatory variables. Then, a second sorting was carried out upon the targeted altitude, in order to build realistic conflict situations. This selection of valid trajectories could be made possible while using a specific device [START_REF] Hurter | FromDaDy: spreading data across views to support iterative exploration of aircraft trajectories[END_REF] which processed a two months traffic data base. No use of radio data during the test: aircraft were said to be flying on wellknown standard or direct routes. A paper strip including the main ATC data (callsign, aircraft type, route, departure/destination, cleared level) was provided for each of the two aircraft. Distance span was to be set to 15 to 20 Nm (representing approx. 4 to 5 minutes flight). Distance span is the distance between the position of aircraft when the scenario stopped moving i.e., when the participant had to provide his/her response, and its position at the closest point of approach (approx. the intersection point). The similar value that was chosen (15/20 Nm) comes from a previous study [START_REF] Averty | An Ordered Logit Model of Air Traffic Controllers' Conflict Risk Judgment[END_REF]. It globally corresponds to situations where controller's judgments are asked for, as the available delays remaining for making decision are calling for them.

Two scenarios (rectilinear and segmented/stablestable/face-to-face) confronted us to a problem since conflict conditions were always verified whatever the new 2-D location participants could give. In order to keep a complete combinatory from our variables, we decided to ask them, for these two scenarios, to make the null separation point at a given fix, located on the route of both. This amounted to agree on the specific point at which they had to be for being superposed. If this action did not make sense from the operational ATC viewpoint, it was a task equivalent to those of other scenarios, perceptively speaking, and we made previously sure this instruction was understood by controllers the way it should. So, 24 exact conflict configurations i.e., showing a quasi-null separation were initially built while combining the two appropriate trajectories in the same scenario file. At this stage, scenarios represented successes to the test. So it must not be presented as such to participants, and a proper version of scenarios had to be set. Hence, one of the two aircraft was moved along its trajectory so as to present a potential separation of 8 to 12 Nm with the other one, instead of the null one in the initial version. Then, this file was restricted to a 40 seconds sequence in such a way that the end of it corresponded to the distance span defined above.

For providing their judgments, participants would only have to directly interact with the mouse on the radar screen with a mere "drag-and-drop" of one of the two aircraft, thus named target-aircraft, as the other one was the reference-aircraft. So the difference between target and reference-aircraft laid in the fact that only the first could be moved by subjects during the test while none of other aircraft's parameters could be modified. This interaction consisted in a translation of the target-aircraft along the intended route i.e., from its last position at the end of the sequence to the position where it should be at this moment (in participant's mind) for getting further a final null separation with the referenceaircraft. Neither horizontal nor vertical speeds could be modified for none of the aircraft. Only the 2-D location and altitude of the target-aircraft -when it was in an evolution phase -had to be modified by subjects. When the aircraft was climbing or descending, controllers had to use the mouse wheel to scroll to altitude value they extrapolated at this new position. Participants had all the (reasonable) length 5.B.4-5 of time to provide their judgments. Actually, controllers were set in a situation where they had to create the most risky, or feared, configuration which could result from modifying the geometry of the encounter. We assumed this was intuitive enough to provide immediate access to the actual expertise in ATC, where perceptual processing of radar (and audio) data mainly impacts on separation assessments.

Quantification of Error Margins

Successes and failures would give global insight into conflicts identification. But interesting complementary information could also be found when differentiating between failures i.e., looking at their more or less important proximity to the 'good responses'. Actually, meaningful difference exists between those which would be close to the required positions and those which would show large separation distances.

Being twofold -horizontal and vertical minima -the conditions for setting conflicts pose problems for quantifying observed error margins in failures. First, a simple quantification (one-dimension) of conflict configuration proximity did not exist at the onset. Second, some scenarios could not be distinguished either in the vertical dimension e.g., the stable/stable attitude modality, or in the horizontal one e.g., the face-to-face geometry modality. This led us to design a variable for characterizing distances of each traffic configuration proposed by participants to the corresponding valid conflict one. This was made possible through the translation that had to be done to the trajectory of the target-aircraft, in the configuration provided by the participant. Actually, making afterwards the distance less than 3 Nm from the latter was possible when moving (forward or backward) the whole trajectory. The magnitude of that move could be expressed in Nm, this distance then representing the gap between response of participant and valid i.e., conflict, corresponding configuration. In cases where aircraft were also climbing or descending, their altitude generally did not show less than 1000 feet difference with the reference-aircraft. In these cases, an extra distance was added to the previous one corresponding to the distance flown while target-aircraft crossed the altitude in excess. We named this variable translatedistance (unit = Nm). Its purpose was to consistently arrange in order the different proximities to valid conflict situation for each 'failure' in that task. An example of this procedure is given in Appendix I. It was applied to all of the failure cases from the experiment.

Experimentation

The experiment took place in Lyons, France. After being informed of the existence and content of the experiment, full-performance level voluntary controllers were invited to pass the "conflict making" test. A total of 18 participants (14 males and 4 females) completed the test. Each of them had the 24 traffic scenarios, representing the combinatory of the 3 variables. The latter were:

-Segmentation. Modalities will respectively be named hereafter: rectilinear or straight, segmented or 2-legs. The angle between the two legs in the latter was between 70° and 130°) -Geometry. Modalities are: face-to-face (trajectories intersection angle less than 160°), crossing (between 70° and 110°), catch-up (less than 20°).

-Attitude. Modalities are: stable/stable or S/S, stable/evolution or S/E, identical evolution or IE, opposite evolution or OE). 'Evolution' indiscriminately refers to a climbing or descending aircraft. For example, in 'IE' condition, both aircraft must be either climbing or descending.

The global objective of this study was to arrange these three variables in order from the perspective of the magnitude of their influence on conflict detection accuracy by ATCos.

Between 30 and 45 minutes (depending on subjects) were necessary to complete a 24-scenarios set.

Results

Global Success Rates

Comparing successes and failures, contingency tables account for the effect of each of the three variables upon controllers' responses. Success means that controllers moved the target-aircraft so that the future minimal distance would be less than 3 Nm and 1000 feet simultaneously.

A slight difference appears concerning the global performance to the test, showing that participants succeeded in finding conflict conditions in slightly more than half the cases. Now, one may 5.B.4-6 ask how each of the chosen variables divided successes and failures (see Table 1). A difference between the two modalities exists in our results. In accordance with the hypothesis we suggested, rectilinear trajectories allow a better identification of conflict configuration than segmented ones (see Table 2).

Table 2. Effects of Segmentation

Conflicts

Success Failure Straight 0.60 0.40 2-legs 0.47 0.53 Only minor differences exist between the three geometry modalities (Table 3). Face-to-face encounters are slightly easier to identify whereas crossings are the more difficult ones. The differences between the three values indicate only a tendency to validate the hypothesis on this variable.

Table 3. Effects of Geometry

Conflicts

Success Failure Face-to-face 0.56 0.44 Crossing 0.50 0.50 Catch-up 0.53 0.47 A significant effect is found for the stable/stable attitude (Table 4). This modality allows a really high rate of valid conflict recognition (81%). When referring to our hypothesis on that point (p. 5), stable/evolution configurations failed to be easier to combine than those implicating two evolving aircraft.

Estimation of Error Margins

In the tables above, failures are not differentiated according to their nearness to a valid conflict configuration. Examination of translate-distances in failure cases provided some supplementary information. Although this variable had a numerical unit, we used median rather than arithmetic mean as central value. In doing so, results were less sensitive to extreme values in each traffic scenario. Actually, even if the interaction used for giving responses was greatly intuitive to controllers, only a few trials could be run before the test for each participant. Therefore, existence of some excessive error values i.e., deviating from his/her real mental picture cannot be dismissed.

Translate-distances are represented by means of boxplots (cf. Appendix II). These diagrams give an idea of their repartition and show the aberrant values ("outliers"). The boxplots in Figure 1 are made from the 202 translate-distance values (corresponding to the failures in Table 1) and how they are spread over. Translate-distance values (in Nm) are on the abscissa. For each of the three explanatory variables, the different modalities used in the experiment are on the Y-axis.

Figure 1. Translate-Distance Values According to 'Segmentation'

Comparing the respective values of Q 0.75 and Max for the two modalities, translate-distances appear to be larger when using segmented trajectories (Figure 1). Nevertheless, the median values are not so different: about 5 Nm for rectilinear trajectories, about 6 for segmented.

Translate-distances are slightly lower when using opposite trajectories than using any of the two other modalities (Figure 2). The strongest effect -all of the three variables taken into account -is due to a stable/stable attitude of the two aircraft (median translate-distances value = 1.8 Nm). On the contrary, conflicts involving both climbing and descending aircraft appear to be the most difficult to identify, leading to possibly important error values. Aircraft configurations with stable/evolving or identical attitudes seem to lead to quite similar translate-distances values (Figure 3).

Discussion

As translate-distances were computable only for 'failure' scenario cases, it appeared difficult to simply confront and discuss the information stemming from success rates and translate-distances. An attempt for such a synthesis stands in Figure 4, both in terms of success rates and translate-distances, for two of the independent variables. Adding the third one would have made the interpretation of the graphics too uneasy. Each of the 24 scenarios presented to the participants is coded both through shapes (representing geometry modalities) and colors (aircraft attitude modalities). This figure evidences the scatter-plot (marked by the dotted envelope) between the global success rate and the mean translate-distance, all participants taken into account. This can be interpreted quite logically as follows: the conflict configurations that have a high success can be identified rather easily. Consequently, one may expect that in the few cases where valid response failed to be given relatively low translate-distances values must be found.

The wide range of catch-ups (circles) appears, as the eight of them are remarkably spread out from the best score to the worse score. As a result, this specific category of trajectories geometry can be held as a significant source of variation in conflict judgments.

On the top left of the graphics, the 6 stable/stable encounters confirm the high rates and low translate-distances they admitted to conflict recognition. This globally means that all conflicts involving aircraft stable in altitude are identified with a more or less comparable accuracy, whatever the two others trajectory characteristics (segmentation, attitude) are. Looking at the slight effect these two characteristics have (considering only the eight green elements) it can be noticed that crossings (squares) admit more successes and lower average translatedistances than face-to-face (stars). Although this result only applies to 8 items, it is noticeable that it refutes the global results shown Table 3 and Figure 3, where face-to-face encounters appeared to be easier than crossings ones. Our interpretation is that performance in face-to-face traffic scenarios was overvalued in the global results. There are two main reasons for that, which are developed in the two following paragraphs. The relatively poor performance related to scenarios integrating 'opposite evolution' attitudes (red color) appears quite clearly: most of them are located in the low performance area in the graphics both for success rates and translate-distances, aside from a unique scenario. Unlike the others, the latter (marked 'A') is situated on the top left of the graphics, meaning a high easiness for controllers to identify conflict from it. It corresponds to a combination segmented/face-to-face/oppositeevolution of the three explanatory variables. When asked on that point, controllers did cast doubt on such an easiness to extrapolate accurate separations between aircraft showing that particular combination. Furthermore, examination of this scenario showed that the presented locations of the two aircraft i.e., before participants had to interact with the targetaircraft and moved it to a suitable place, already put them in a quasi-situation of conflict. A mistake in the initial review of the experimental material is probably the cause of selection of an invalid version of the scenario. As a result, finding valid conflict conditions was much easier for this scenario than for others. Both for ethical reasons and to keep a complete combination of the different modalities in explanatory variables, we nevertheless decided to keep this scenario in the global results. The use of medians (instead of means) minimizes the effects of this mistake and keeps results globally relevant.

5.B.4-8

Another point is that three types of encounters (on the right of the graphics, marked 'B', 'C', 'D') stand aloof from the dotted envelope, thus showing singular high success rates compared to their respective translate-distances values on abscissa. Examination of each of these three scenarios helped to find the most probable reasons for this discrepancy, inviting to some change to introduce for improving the experimental paradigm we used:

Combinatory of our variables included a scenario that is generally never processed in the same way than others, in real life. This scenario (marked 'B') represents a rectilinear/face-to-face/identical evolution encounter which, in real life, always appeals for an early and protective solution in terms of altitude but not for any accurate extrapolation at this stage. As a conflict identification is quite precise (less than 3 Nm and 1000 feet), our interpretation is that participants divided in two groups for processing this particular scenario. A first group did try to find the means to do it,

5.B.4-9

resorting to computing from available or inferable data. A significant part of them probably found the corresponding configuration, making the major part in the 67% success rate. But the other part of participants probably processed this scenario from their current operating modes (perceptual heuristics), ending in large error values since such a precise assessment is seldom accurately used for this configuration. This second bias adds to the previous one for favoring in excess face-to-face encounters (Table 3), as we already stated. The two others singular scenarios (marked 'C' and 'D') show both decent global success rates and the highest translatedistance values in the experiment. The cause seems to be the same for both, and appears to the involvement descending traffic, on initial then intermediate approach. During this last phase, aircraft speed greatly decreased -we used real traffic recordings. From then on, the freedom participants had for moving the target-aircraft at any (future) position of their own choosing appeared to be possibly excessive. When extrapolating the point of separation loss too far on the trajectories, the speed of descending aircraft varied so much than it did not only failed to find conflict conditions but also generated large translate-distance values. So, our interpretation for these two scenarios is that the global success rate is the reflection of expertise while the translate-distance, in case of failure, must be seen as artificially oversized, compared to the others scenarios. Last, even if the global effect of the rectilinear modality effect appears to be higher than the segmented one (Table 2), the more detailed effects i.e., upon the other variables, seems manifestly variable: significant differences sometimes point out segmented scenarios as substantially easier than their rectilinear homologues. This led us to wonder about our choice to use real recorded trajectories in the traffic scenarios. It is quite clear that great speed (horizontal and/or vertical) differences were present in some scenarios. This heterogeneousness could generate differences in identifying conflicts, preventing to find regular effects from the three independent variables. Similarly, the time spans between the end of scenarios (when participants were asked to respond) and the moment when aircraft could be in conflict probably lacked consistency (average: 4.5 min; minimum: 3.2 min; maximum: 6 min). This disparity was the price to pay for showing totally realistic configurations, and our results benefited from them. But on the other hand, it seems now that instead of real traffic, the use of aircraft flying by means of (computed but realistic) tabulated models of aircraft types would be more effective, allowing a higher consistency of experimental material without losing too much realism.

In summary, results show that:

For geometry, differences exist in conflict identification according as the involved aircraft are level or include at least one evolving aircraft. When the latter have opposite evolutions (climbing, descending) difficulty for conflict identification by controllers seems to be maximal. Consequently, only three different geometry categories will have to be kept for differentiating the effects on controllers' judgments: S/S ; (S/E, IE) ; OE. For segmentation, a significant effect tends to appear, as rectilinear trajectories are easier to identify. Consequently, the use of two modalities in this variable remains relevant: rectilinear; segmented. The use of traffic flying with more homogeneous speeds in a further experiment should lead to more reliable quantification of this effect. For geometry, our results failed to show any clear tendency about the effects of this variable. Though face-to-face initially tended to appear more helpful to identify conflicts, this must be counterbalanced since the existence of an invalid scenario favoring this result has been demonstrated. The methodology used for collecting controllers' expertise show interesting properties: participants quickly assimilated the requisite interactions and reported a rather pleasant and playful way of 5.B.4-10 providing their expertise. Yet substantial change will do better to be proceeded to, concerning some options initially retained: speeds coming from tabulated performance models (related to aircraft types), selection of homogeneous phases in flights, wide but limited range for aircraft positioning by participants. We aimed at developing an original way of collecting ATCos' expertise, and investigate the influence of geometrical features of aircraft trajectories in conflict judgments. Coherent results have been drawn from it, even if this first attempt is perfectible. Thus it could be expected that a larger scale collection using en-route traffic and integrating the improvements we mentioned above would provide more accurate data. These would allow the modeling of these judgments which would become greatly predictable, in a way similar to what we already did [START_REF] Averty | An Ordered Logit Model of Air Traffic Controllers' Conflict Risk Judgment[END_REF].

  Catch-ups can clearly lead to clearly larger translate-distances. Median values are approximately 5 Nm for face-to-face 5.B.4-7 encounters, and about 7 Nm for both catch-ups and orthogonal intersections.

Figure 2 .

 2 Figure 2. Translate-Distance Values According to 'Geometry'

Figure 3 .

 3 Figure 3. Translate-Distance Values According to 'Attitude'

Figure 4 .

 4 Figure 4. Scatter-Plot of Success Rates and Translate-Distances, for the 24 Types of Encounters

Table 1 . Global Results

 1

	Conflicts Success Failure Total
	Number	230	202	432
	Ratio	0.53	0.47	1

Table 4 . Effects of Attitude

 4

	Conflicts	Success Failure
	Stable/stable	0.81	0.19
	Stable/evolution	0.45	0.55
	Similar evolution	0.41	0.59
	Opposite evolution	0.45	0.55

Appendix I: Translate-Distance Definition

The mains steps for translate-distance value computation are intuitively given below by means of an example. A target-aircraft (CRL1584, descending) and a reference-aircraft (FBRSH, level) with their velocity vectors and flying on orthogonal trajectories are shown on the three next figures. Once participant had moved the target-aircraft, new minimal separation values (here 6.1 Nm longitudinally, on Figure 5) potentially existed between the two aircraft.

Figure 5. Checking the Conflict Conditions

In each failure case i.e., when the created separation did not fulfill the conflict conditions translate-distance was computed. This variable corresponds to an empirical expertise regarding the experimental task. Furthermore, it does not use the computation of the closest point of approach (CPA) as a rigorous approach would have required it. This could not have been done due to time constraints, but the uncertainty of the proposed method (hereafter) is largely compatible i.e., low compared to the magnitude of controllers' errors i.e., translatedistances, that was computed. Moreover, referring to the intersection point is probably not so inexact as in their judgments, controllers are likely to perceptually refer more to the intersection point of 'visible' trajectories than to the (computed) CPA.

So, in case of failure the next step was to identify the altitude of the referent-aircraft when it was at the place just sufficient for creating conflict, i.e., 2.9 Nm to or from the intersection point.

In the example (Figure 6), the reference-aircraft is from the intersection point, since it is the first to overfly it. The corresponding altitude is 11000 feet since this aircraft is level -but it could be otherwise, when taking into account the altitude at this location of a climbing or descending aircraft.

5.B.4-12

Figure 6. First Aircraft Altitude Computation

Once this altitude was known, the required altitudes of target-aircraft for creating conflict conditions were deductible when adding/subtracting 900 feet (conventionally representing the maximum margin to get conflict conditions). Here in our example, the altitudes between 10100 and 11900 feet satisfy this condition. Within this range, the altitude value to be chosen was the one allowing the minimization of participant's error. Here this value is 10100 feet, as it corresponds to the location of target-aircraft which is the closest to the intersection point i.e., where it should have been in order to fulfill just sufficient conflict conditions (approximately 2.9 Nm and 900 feet separations). Then, the last step consisted in determining the location of the target-aircraft when he flew at the chosen altitude (Figure 7). The distance between this last location and the intersection point gave the translate-distance value, representing the magnitude of error in controller's judgment.

Figure 7. Translate-Distance Computation

Let us notice that the interactions ('drag-anddrop') participants had to do on target-aircraft corresponded to a translation in time of the whole considered trajectory. This translation in time is equivalent to one in distance, as soon as the horizontal speed is known -what was the case. What we did while computing translate-distance was the analogous procedure, additionally integrating vertical errors -which are also translatable in time and consequently in distance, once the vertical speed is known.

Appendix II: Boxplots

Boxplots stem from the repartition of numerical values (translate-distances in this study) along the whole range of the sample values. This repartition can be grasped through the positioning of three quantiles: Q 0.25 , Q 0.5 and Q 0.75 (Figure 8).


Christophe Courtin
email: christophe.courtin@univ-savoie.fr

Stephane Talbot
email: stephane.talbot@univ-savoie.fr

Mathieu Mangeot
email: mathieu.mangeot@univ-savoie.fr

Activity regulation for building dictionaries on an on-line collaborative platform

This paper discusses automatic regulation in participative Web systems. We present a generic solution with an original trace-centered approach. We describe an experiment with a general trace-based system (TBS) called CARTE (Collection, activity Analysis and Regulation based on Traces Enriched) featuring a regulation mechanism and we couple this system with an on-line generic platform for managing lexical resources called Jibikipedia.

I. INTRODUCTION

Web2.0 is characterized by the Internet users' participative creation. Large-scale projects have highlighted the importance of the mode of participation which is extended to all Internet users, who are often anonymous, which thus allows the creation of consequent corpora of data (e.g. Wikipedia R in 2001, AgoraVox R in 2005 [START_REF] Nemec-Poncik | Wikipédia : à consommer avec discernement[END_REF]), where information validity is subordinated to the self-regulation principle. At the same time, this principle intrinsically demonstrates weaknesses that are due to the lack of systematic information control. The checking of sources' quality being a universal criterion, we have observed abuses such as self-proclamation as an expert in a domain (example of identity forgery with the following hoax: a main contributor was a 24-year-old student who pretended to be a professor of religion at a Faculty of political science [START_REF]Citizendium inaugure son alternative à wikipedia[END_REF]).

The consideration of these abuses led to the emergence of new projects (Citizendium R [START_REF]Citizendium inaugure son alternative à wikipedia[END_REF] and Knol TM in 2007 [START_REF]Encyclopedia knol[END_REF]), where Internet users must be identified and where thematic roles (e.g. author, collaborator) must be allocated to them. Actancial roles must be associated to these thematic roles, i.e. a set of predefined authorized actions (e.g. publish, modify with validation levels). This hierarchical organization of the roles led to the emergence of various groups of participants, who were more or less expert, and had greater or lesser power. Role allotment is based on activity and on notation of articles produced.

In the Knol TM project of Google TM , the validation of articles is carried out by contributors given the role of "questionable" (an expert's role). It is worth noting that the workload relative to the task of the role allocation can become very heavy (or time-consuming) given the sizeable increase in the number of participants (e.g. 800 authors in 2007 at Citizendium R , 1 million visitors a month and 5 to 10,000 regular writers a month in 2008 at AgoraVox R [START_REF] Colombain | Agoravox devient une fondation, 21st[END_REF]).

This article is divided into three main sections. The basics of our original approach to answer the regulation problem in the participative systems is presented in the first section. An experiment with an existing participative system is described and the regulation mechanism is detailled with concrete examples in the second section. The expected results are covered in the third section. Several avenues of research will be discussed before concluding.

II. TRACE-BASED APPROACH

The approach we propose would not be original if it was only a matter of making the same report about regulation. Most of the time, a regulation mechanism is specific to a system and takes into account events which are generated inside it only. The originality of our system consists in using an external regulation mechanism which works with a tracecentered approach. The main advantages of such an approach are the possibility of linking events stemming from several software applications to be regulated (e.g. a chat room and a collaborative text editor) and that of changing a tool for another one that has similar functionalities with few modifications of the regulation mechanism (at the lowest level of abstraction, but not at the higher levels).

The coupling of the on-line generic platform for managing lexical resources (Jibikipedia) and the system based on trace interaction (CARTE) enables one to take into account automatically and dynamically the increase in the Internet users' participation. The activity trace analysis in the Jibiki platform [START_REF] Mangeot | Dictionary building with the jibiki platform: the gdef case[END_REF] by the observation station CARTE allows retroaction operations to be performed automatically in order to allot roles.

The participative Web enables the production of very large data banks in a short period of time. This method of production of contents is very useful, and even indispensable, for underresourced domains because of the lesser impact of the related systems.

The final research question that we are going to deal with in this article is: "How to take into account in the most automatic way the increase in the Internet users' participation?" The evolution of this research work consists in estimating the relevance of the regulation for the development of participative applications.

Unlike encyclopaedias, where contributors may describe very complex and detailed entries, it is more frustrating to contribute to dictionaries because of their restricted structure. Therefore, we consider the postulate that the participants' involvement in such a system is subordinated, among other factors, to the participants' consideration. From this, it follows that the participants' activity must be analyzed in order to calculate indicators about the participation's quality. Generally, these indicators are not intrinsically provided by the software applications themselves. Indeed, generated traces (e.g. log files) represent low level traces (e.g. "edit" event), which are not elaborate enough to recognize complex situations (e.g. the event "many contributions without correction in a limited amount of time").

III. EXPERIMENT

A. Description of the experiment

First and foremost, it is essential to begin by describing the observation objectives from which we built our experiment. Considering that some researchers would like to know if the activity regulation modifies the Internet users' perception of the IT tools, and if this new perception modifies their involvement in the activity, our main objective is to define how it is possible to take this participation into account automatically and dynamically.

In this experiment, the observers are researchers in computer science and in linguistics and also participants in the collaborative activity themselves. Therefore, observations have been made from activity traces having an abstraction level close to that of the observers. We designate as indicators the traces which may be directly interpreted by the observers. Generally, the software tools do not produce traces with a high enough abstraction level to build these indicators directly. In this experiment, we use two types of traces in a trace-based system (TBS) called CARTE (Collection, activity Analysis and Regulation based on Traces Enriched) [START_REF] Courtin | Carte: an observation station to regulate activity in a learning context[END_REF] [6]:

1) interaction traces stemming from software tools which are used for the collaborative activities; 2) enriched traces, i.e. those originating from transformations of interaction traces or already enriched by means of use models of the software tools from which they arise. In the following part, we will present the software tools of the experiment (see Figure 1) and then the indicators we wish to observe. Some of these indicators stem from the tools themselves and the others are generated by means of the observation station CARTE. This means that the indicators description must be defined by the observers before starting the collaborative activity. These indicators are integrated into the collaborative software tools and are activated via the retroaction mechanism of the observation station CARTE.

From our point of view as researchers in computer science, we have set up this experiment to test the mechanism of activity regulation in a context of participative production (Web 2.0). A first result will therefore be the expressiveness of the underlying models of the TBS (models of trace collection, use of tools and regulation of the activity) [START_REF] Laflaquière | A tracebased system framework for experience management and engineering[END_REF] [START_REF] Settouti | A trace-based systems framework : Models, languages and semantics[END_REF]. Another result will consist in estimating the effects of the regulation [START_REF] Talbot | Helping in collaborative activity regulation: modeling regulation scenarii[END_REF] on the participants' perception of the collaborative software tools, which thus have augmented functionalities.

B. Description of the equiped platform

Our experiment takes place in a research project called MotMot [START_REF] Mangeot | Building lexical resources: towards programmable contributive platforms[END_REF] built on the Jibiki platform. In this project, there are two main challenges: to gather a community to produce dictionaries and to ensure the quality of the content.

In the first challenge, it is a matter of providing online generic tools to co-produce dictionaries. As far as the second challenge is concerned, famous projects such as Wikipedia R or AgoraVox R have tested the limits of self-regulation (e.g. hoax, identity forgery, relative errors, etc.). Conversely, the static definition of a committee of experts raises questions about the level of participation or about the variation of level of expertise over time. A dynamic definition would consist in setting different profiles in real time by considering several predefined criteria. This operation may become complicated (too many criteria) and time-consuming for a human team with a large set of participants.

In this context, we have developed a prototype called Jibikipedia in the Jibiki platform [START_REF] Sérasset | Papillon lexical database project: Monolingual dictionaries and interlingual links[END_REF] implementing an automatic profiling process for participants. The participants receive thematic roles (contributor, reviewer, validator) in the editing interface of the Jibikipedia prototype according to their involvement and the quality of their production: a contribution consists in creating and editing an entry of a dictionary; a reviewing activity consists in verifying the exactness of an entry; a validation consists in storing a correct(ed) entry in a dictionary. In order to have a role attributed to them, the participants have to be registered in the Jibiki platform, i.e. they are not anonymous. Therefore, the various participants share the entries by modifying their status. During the contribution, the entry's status changes from "not finished" (editing) to "finished" (save). In the reviewing process, the entry may again be edited and saved to be corrected. At the end of the validation stage, the entry's status becomes "validated" and the entry will be effectively stored in the dictionary.

Figure 2 shows a French entry in the MotMot dictionary on the Jibiki platform. This entry has been reviewed by a level 3 user, thus the entry level has gone up to 3 stars.

C. Description of the indicators

According to the way a contribution has been accepted, i.e. with or without correction, the contributor's level of expertise may be respectively downgraded or upgraded. For example, each participant will be allocated a set of stars, the number of which corresponds to the level of expertise. When the contributor obtains three stars, s/he gets a second role: reviewer. Ditto with a third role from reviewer to validator. Conversely, s/he may lose stars and hence roles, back down to contributor. From the participants' point of view, these indicators are elements of awareness which are integrated We present below the list of the indicators implemented in the Jibikipedia system:

1) creation of n entries by X during m days: this indicator corresponds to the number of word creations that a contributor X has made in a limited period of time m (e.g. in days); 2) n proofreadings of A: this indicator means that the definition A has been read n times; 3) n proofreadings of A by X: this indicator means that the participant X has read the definition A n times, but s/he has not necessarily modified it; 4) n corrections of A: this indicator specifies that definition A has been modified n times; 5) n corrections of A by X: this indicator specifies that the participant X has modified the definition A n times; 6) creation of n entries in the domain D by X: this indicator specifies that the participant X has contributed n times in a particular domain D. These indicators are represented by sequences and may be combined again, together or with other trace elements, in order to make more complex requests. For example, in the experiment, we consider that if a contributor produces three entries in a month, which are validated without modification, then her/his level of expertise is upgraded by one star, and at the end of three stars, s/he becomes a reviewer (or proofreader). In the following part, we will present a rule description with our CARTE analyser which enables one to recognize certain situations of regulation.

D. Description of the rules

In this part, we will explain how to build indicators from generated and/or enriched traces of interaction. The first stage consists in defining the trace-based specification of the observation. As is explained above, the observation concerns the effects of the regulation of the activity in participative software tools. Regulation is a mechanism which transforms a system from an initial situation (or precondition) to a final one (postcondition or goal). The initial situation is represented by means of activity traces stemming from tools instrumentation [START_REF] Courtin | an architecture to record traces in instrumented collaborative learning environments[END_REF] and traces enriched by the CARTE system. In this system, these traces are called signals and sequences, presented in Figure 3. The final situation is obtained automatically by means of the action part (or retro-action) in the rules of the observation station analyser.

The first and the last indicators can be broken down using the basic signals "create", "edit" and "save". The other indicators stem from the CARTE analyser.

In the experiment we used three sets of rules. The first one is used to interpret the actions of the users. Indeed the events collected from the collaborative entry editor, the Jibiki, at the first stage are quite basic:

• A user has created a new entry.

• S/He has started to edit an entry.

• S/He has saved some modifications to an entry.

• S/He has changed the status of the entry (for example from "not finished" to "finished") and so on. However the actions, which really interest us are a little bit more complex. For example the editing of an entry should be associated with a set of related events (the user loads the entry, starts editing it, then saves the modifications). The proposal of a new entry implies its initial creation, then a sequence of edits that conclude with the modification of the entry status (the entry is considered as proposed when its status is changed from "not finished" to "finished"). In the same way we must distinguish entries reviewed and validated without further modification from the others. The first set of rules is used to identify those relevant sequences of events : first the edits, then the entry proposals, which are reviewed and validated with or without further modifications.

The second set of rules (see Figure 7) is used to compute the indicators, in our case the star numbers awarded to each element : the entries and the users. Since this process depends on the number of entries contributed, modified and validated by each user in the previous periods, it implies using the sequences identified via the first set of rules. It also depends on itself: highly-rated users are supposed, without further evidence to the contrary, to produce high quality entries, and users who produce highly-rated entries should get good evaluations.

Finally the third and last group of rules is used to modify the statuses of users. Highly-rated users will be able to review, validate or invalidate the entries contributed by the other users.

In contrast, new or poorly-rated users will have to work with the "expert" ones and improve their skill before being able to contribute new entries without supervision.

All the rules are built from the traces with an ad-hoc editor, see Figure 4.

IV. RESULTS

We have highlighted above the difficulty in obtaining Internet users' participation in under-resourced domains because of the lesser impact of the related systems. We postulate that if there is a regulation mechanism which provides the possibility of adapting the users' profile to their own activity, we expect that these users will have the feeling that their activity will be more highly thought-of by the community of participants. We thus consider that regulation improves interactions with the computing environment and can have an influence on the users' participation.

However, a computer-based study alone does not allow us to evaluate regulation's effects on participation quality. Therefore, the main research objectives of this article consist in transforming information which derives from computing traces of collaborative activities in order for it to be used for the regulation mechanism, and in testing our trace-centered model's strength. The experiment has revealed the regulation model's capacity for specifying the authorized actions of the asynchronous collaborative editing session in progress. In order to present the results, we propose to describe the regulation mechanism and to present the indicators generated.

In this part, we present an instrumentation technique which takes place at the level of the collaborative software tools themselves and then close to their use model. The definition of the indicators is facilitated by the structuring and the explicitation of the collected elements and their interpretation requires the definition of a use model of the software tools which make up the participative work area. The collect instrumentation enables the gathering of trace elements in order for them to be analyzed by an observation station (see Figure 6). The latter is an external system which transforms the traces and re-injects actions (postcondition) in the Jibikipedia prototype, by means of retroaction instrumentation, in order to modify participants' roles for example (see Figure 1).

It should be recalled that the use model enables the analysis of collected traces and is based on how the concerned software tools are supposed to be used. The analyser is composed of a set of rules of transformation (see Figure 4) with logical operators (AND, OR, NOT), a temporal relation (THEN) and priority relations (brackets). We present partially in Figure 5, with the XML format (DTD), the rule description of the experiment.

In Figure 7, we present an instance of a rule based on the previous DTD. This rule specifies the following indicator: "5 entries have been created by a contributor in 1 month".

V. CONCLUSION AND PERSPECTIVES

In this article, we have presented how to adapt the users' profile and then the functionalities of a Web-based participative system called Jibikipedia [START_REF] Mangeot | Dictionary building with the jibiki platform: the gdef case[END_REF], by means of an external Fig. 3. trace format trace-based system called CARTE [START_REF] Courtin | Carte: an observation station to regulate activity in a learning context[END_REF]. We have postulated that this activity regulation could have an influence on the users' participation. Therefore, we have worked on how to operationalize our regulation mechanism in the project about multilingual dictionary asynchronous co-construction. Our main objectives have consisted in testing both the relevance of the coupling of the two systems and the corresponding models' strength. In particular, we have described an example to take into account in the most automatic way the increase in the Internet users' participation. An important first stage of this work has consisted in defining relevant indicators.

The perspectives of such research work consist in plugging our regulation mechanism into other participative systems and in measuring the effective impact of regulation on the Internet users' participation, for example, in multilingual dictionaries and especially for under-resourced domains.

<?xml version="1.0" encoding="UTF-8"?> <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" version="1.0"> <xs:element name="rules" type="listOfRules"/> <xs:complexType name="listOfRules"/> <xs:sequence> <xs:element minOccurs="0" name="rule" type="rule"/> </xs:sequence> </xs:complexType> <xs:complexType name="rule"> <xs:sequence> <xs:element minOccurs="0" name="description" type="xs:string"/> <xs:element minOccurs="0" name="conditions" type="listOfConditions"/> <xs:element minOccurs="0" name="retroActions" type="listOfRetroactions"/> </xs:sequence> </xs:complexType> <xs:complexType name="listOfConditions"> <xs:sequence> <xs:element minOccurs="0" name="condition" type="condition"/> </xs:sequence> </xs:complexType> <xs:complexType name="condition"> <xs:sequence> <xs:element maxOccurs="1" minOccurs="1" name="action" type="action"/> <xs:element maxOccurs="1" minOccurs="1" name="numberOfResults" type="xs:int"/> <xs:element maxOccurs="1" minOccurs="1" name="numberOfResultsSemantic" type="xs:string"/> <xs:element maxOccurs="1" minOccurs="1" name="subCondition" type="listOfConditions"/> <xs:element maxOccurs="1" minOccurs="1" name="parameters" type="listOfParameters"/> </xs:sequence> </xs:complexType> <xs:complexType name="action"> <xs:sequence> ... </xs:sequence> </xs:complexType> <xs:complexType name="listOfParameters"> <xs:sequence> ... </xs:sequence> </xs:complexType> ...

Fig. 1 .

 1 Fig. 1. Schema describing experiment

Fig. 5 .Fig. 6 .

 56 Fig. 5. Rules description

Fig. 7 .

 7 Fig. 7. Example of rule


Mehdi Zaamoune
email: mehdi.zaamoune@irstea.fr

Sandro Bimonte
email: sandro.bimonte@irstea.fr

François Pinet
email: francois.pinet@irstea.fr

Philippe Beaune
email: pbeaune@agaetis.fr

A New Relational Spatial OLAP Approach For Multi-resolution and Spatio-multidimensional Analysis of Incomplete Field Data

Keywords: Spatial OLAP, incomplete continuous field, multi-resolution geographic data

Integrating continuous spatial data into SOLAP systems is a new research challenge. Moreover, representation of field data at different scales or resolutions is often mandatory for an effective analysis. Thus, in this paper, we propose a logical model to integrate spatial dimensions representing incomplete field data at different resolutions in a classical SOLAP architecture.

INTRODUCTION

Spatial Data Warehouse (SDW) and Spatial OLAP (SOLAP) systems play an important role in helping decision-makers obtain the maximum benefits of these large amounts of geographic data [START_REF] Bédard | Fundamentals of Spatial Data Warehousing for Geographic Knowledge Discovery[END_REF]). These technologies extend Data Warehouse (DW) and OLAP systems to integrate spatial data with warehoused classical data to achieve the on-line analysis of large georeferenced data sets. SOLAP systems integrate advanced OLAP and Geographic Information Systems (GIS) in a unique framework usually based on the relational storage (i.e. Oracle, etc.) of spatial data according to the vector model, and their analysis through SOLAP operators (Spatial Roll-Up, Spatial Slice, etc.) implemented by the SOLAP server (e.g. Map4Decision, etc.) and visualized by means of tabular, graphical and cartographic displays [START_REF] Gomez | A Generic Data Model and Query Language for Spatiotemporal OLAP Cube Analysis[END_REF]. SDW are modeled according to the spatio-multidimensional model that extends the traditional multidimensional model to define spatial dimensions (i.e. analysis axes with spatial attributes) and spatial measures (i.e. analysis subjects) that integrate geographic information using the vector model [START_REF] Bédard | Spatial On-Line Analytical Processing (SOLAP): Concepts, Architectures and Solutions from a Geomatics Engineering Perspective[END_REF]. SOLAP technology can be applied in different domains (e.g. archeology, public health, etc.).

Geographic information can be represented by two models, depending on the nature of data: discrete (vector) and continuous field [START_REF] Mennis | Cubic Map Algebra functions for spatio-temporal analysis[END_REF]. Continuous fields (also called continuous spatial data) represent physical phenomena that continuously change in space [START_REF] Paolino | Integrating Discrete and Continuous Data in an OpenGeospatial-Compliant Specification[END_REF], for example the temperature, population, etc. Two representations of field data have been proposed: incomplete and complete [START_REF] Paolino | Integrating Discrete and Continuous Data in an OpenGeospatial-Compliant Specification[END_REF]. Incomplete representations store a sample of points and need additional functions to calculate the field in nonsampled areas (e.g. grid of points, TIN, etc.) (e.g. Figure 2). Complete representations associate estimated values to regions and assume that these values are valid for each point in the regions (e.g. raster). For those representations some ad-hoc analysis operators have been defined that allow a point by point analysis (i.e. map algebra [START_REF] Mennis | Cubic Map Algebra functions for spatio-temporal analysis[END_REF]). Representation of geographic data at different scales or resolutions (e.g. Figure 2b) is mandatory for an effective analysis of spatial complex phenomena since it represents a geovisualization method [START_REF] Camossi | Adaptive Management of Multigranular Spatio-Temporal Object Attributes[END_REF]. Consequently, these resolutions or scales represent decision-makers analysis needs that should be explicitly represented in any data and query model. Indeed, in the context of Geographic Information Systems and Spatial Databases Management Systems (SDBSM), several works addresses this issue by proposing conceptual, logical and physical data models and analysis techniques [START_REF] Parent | Conceptual Modelling for Traditional and Spatio-temporal Applications[END_REF].

Motivated by the important analysis capabilities offered by the continuous field representation of geographic data when integrated in SOLAP systems (visualization, querying, etc.) recently some works investigated the extension of the spatiomultidimensional model and SOLAP operators with complete and incomplete field data (cf. Section 6). In the same way, handling multi-resolutions of spatial data into spatial multidimensional models has been proposed in few works [START_REF] Yvan | Modeling multirepresentations into spatial data warehouses : A UML-Based approach[END_REF] [START_REF] Gascueña | A MULTIDIMENSIONAL METHODOLOGY WITH SUPPORT FOR SPATIO-TEMPORAL MULTIGRANULARITY IN THE CONCEPTUAL AND LOGICAL PHASES[END_REF] that propose conceptual models to represent SDW with several representations (scales, resolutions, etc.) of spatial dimensions and measures.

However, to best of our knowledge existing works concerning field data and multi-resolutions lack of a complete implementation in a full-featured SOLAP architecture, or in other terms they do not propose a coupled relational and SOLAP server model for a generic SOLAP architecture allowing (i) the map algebra operators, (ii) the multi-resolution, and (iii) a continuous view of the field.

In order to handle the spatio-multidimensional analysis of incomplete regular grid field data at different resolutions, we propose in this paper: (i) a specific logical model, extending the well-know relational star schema; (ii) and some new MDXbased defined functions. We validate our proposal using a real case study concerning the odor monitoring, and we provide some experiments showing the feasibility also in terms of storage and computation performances.

MODELING AND ANALYSIS REQUIREMENTS

In order to show our proposal, we present a case study based on data issued from the monitoring of urban odor. proportion the value of a neighbour impact on the value of the point to be estimated (Figure 1). Finally, as stated in the previous section, since visualization of spatial data at different resolutions is mandatory for the exploration/analysis process, decision-makers should be able querying spatial warehoused data at different resolutions. It is very important to note that for each spatial phenomenon a set of useful known resolutions exist, so they could be predefined according to data and users needs. Moreover, in order to calculate values at finer resolutions spatial interpolation functions as previously described can be used.

To summarize, spatio-multidimensional analysis of field data implies: supporting (i) OLAP classical operators as Map Algebra, (ii) continuous view of spatial data, (iii) spatial slice operators using field data, and (iv) visualizing and querying data at different predefined resolutions.

Spatio-multidimensional model for incomplete field data

In this section we describe our spatiomultidimensional model for handling incomplete fields at different resolutions. Our model extends the classical spatio-multidimensional models to generate the continuity of the phenomena over the studied area, and represents pre-defined levels of resolution.

In particular, a "Cube" is composed of "Facts" and "Dimensions". A "Dimension" is composed of "Hierarchies", which are composed of "Levels". A "Level" can be spatial or conventional. This means that it can contain "Spatial attributes" (e.g. points, etc.), or contain only alphanumerical attributes respectively. "Facts" is composed of "Spatial Measures" or "Conventional Measures". Moreover, our extension defines a "Field level" as a special type of spatial level where each member has a geometric attribute (e.g. point), a "neighbourhood relationship" association, and a re which it belongs.

(a)

(b) (c) (d)
Figure 2: a) local map algebra incomplete field. b) multiresolution r incomplete field c) querying an un querying an unsampled zone Indeed, as described in the pr spatial interpolation function uses which depend on the function (e.g. uses a 2*2 grid), to estimate the Thus, in our approach values are measures, the "Neighbourhood rela detailed "Field level" to its neighb detailed level. As soon as the v resolution "Field level" is required i found through the "Neighbour However, this type of relatio implemented in different ways, de intended purpose as shown in the our case, we want to estimate the v (x, y) of a Field level, so neighbou the fly by the relation "Neighbourh the case of a change in the level o members of a high resolution (e.g predefined and therefore, th neighbours, which belongs to 100*100, can be pre-stored as attrib

As described in the model, contain several field levels r phenomena at different resolutions.

Incomplete field

In order to implement field levels we have defined a GeoMDX user-defined function that represents a spatial interpolation as:

NumericType InterpolatePoint(Geometry)

This function takes as input a geometry (point) and returns a numerical value, which is a derived measure in the OLAP model, representing an estimated value calculated using the neighbourhood values of the point given in input. Thus, let us suppose that we want to retrieve a value of the field in a location whose geometric property is set to the geometric coordinates POINT (-72.1235 42.3521). Then in order to answer to that need using the Bilinear interpolation function, decision-makers have to simply use a GeoMDX function in the following way: InterpolatePoint(POINT(-72.1235 42.3521)).

Thus, the function will look for the neighbours of the point given as a parameter, in the field level ([Field].[res100]), on the basis of the distance, and then find neighbours' respective values in the fact table, evaluate the value of the point to estimate using these values, and then return an estimated derived measure. Here is an example query that uses the "InterpolatePoint" function:

Query 2: select a field member's value at coordinates (721148 3140020) for the year 2012.

With member [Measures].[value] as' InterpolatePoint(ST_GeomFromText(" POINT (721148 3140020)"))' SELECT [Measures].[value]ON ROWS, [time].[2012] ON COLUMNS FROM [odorCube]

Figure 4: Classical star schema integrating regular grid of points Note that generally MDX allows defining userdefined functions in several programming languages (i.e. Java, .NET, etc.) depending of the OLAP Server used. In this work we have used a Java-based implementation in GeoMondrian (see Sec. 5). In particular, the interpolation is done using an existing interpolation Java API "javax.media.jai api" (JAI).

In this way we achieve the continuous view of field data using incomplete fields as stated in Section 2.

Multiresolution

Theoretically, we can measure a value of a field at every position inside a geographic space. However, not all resolutions are necessarily relevant. Indeed, according to the type of analysis performed by the user, a more or less detailed resolution can be requested. The multiresolution is an approach that consists in defining resolution levels likely to improve the rendering of the requests made by the user. To model an incomplete field at several resolutions in a multi-dimensional model, we propose two Approaches based on the "Classical Star Schema": The "field aggregation star-schema" approach and the "field interpolation star schema" approach.

Field Aggregation Star-Schema Approach

Based on the star schema model previously described, we propose a logical schema where the spatial dimension presents different field levels at different resolutions (fig. 5-a). This model extends the spatial dimension of figure 4 Each level of the field dimension is composed of an identifier and a geometry representing a point. The fact table is associated, classically, to the most detailed level of the field dimension.

In this way, decision-maker can explore warehoused field data at different resolutions during the same analysis MDX-based session. Only need to change the level of resolution in the query to change the level of details of the result. Using this approach, we use in an MDX query, the appropriate level of resolution of the field dimension as in the following where the Query 1 becomes:

Query 3: select average odor for each field member at the 400*400 resolution during 2012

SELECT [Field].[res400]. Members ON ROWS, {[time].[2012]} ON COLUMNSFROM [odorCube] WHERE [Measures].[value]

Field Interpolation Star-Schema Approach

As stated in Section 2, in order to provide field data at finer resolutions, spatial interpolation methods can be used. Then, here we propose a variation of the previously proposed schema for handling multiple field resolution levels, by associating the fact table to the field at less detailed resolution as shown on figure 5-b. In our approach moving from fact table values to finer spatial members' values implies applying spatial interpolation functions. Note that this approach is possible only when dealing with spatial data, because according to the Tobler law geographical position of data can be used for estimating missing values. We have implemented a GeoMDX function in the same way of the function defined in Section 4.1:

Numeric-type InterpolateBilinear (Field Member)

However, this function, named "InterpolateBilinear" is prepared to receive as input a field level member instead of geometry and return an interpolated value of this member. We can also see that in this case, the neighbors of each member of a higher resolution than the original one are also stored in the "Field" (Neighbours2, Neighbours3), since members of each resolution are pre-defined in advance, but their values are not since they depend on other dimensions. Calling this function as follows:

InterpolateBilinear ([Field].[res400].CurrentMember) in the formula of a derived measure, allows to find the values of all the members of the level "res400" (incomplete field at a 400*400 resolution) using their neighbors "Neighbors3" . Thus, the query 3 can be performed as follows:

SELECT {[Field].[res400].Members} ON ROWS, {[time].[2012]} ON COLUMNS FROM [odorCube] Where [Measures].[EstimatedValue]
While in the multidimensional SOLAP schema, the "InterpolateBilinear" function is called in the "EstimatedValue" calculated measure formula as:

formula="InterpolateBilinear([Field].[ res400].CurrentMember)"

As we can see in the previous query, the call of the calculated measure enables to find the values at a given scale transparently to the decision maker as a classical aggregation (SQL). This approach is motivated by performance issues as described in the next section.

Experimentations

In this section we detail the performances of the two approaches proposed in Section 4.2 (FASS and FISS) in terms of storage and time computation. The computer used for the following tests has the following configuration: processor Intel® core ™ i3 2,20 GHz, RAM 4 Go, Operating system Windows 7 professional, System OS 64 bits.

In particular, spatial data is stored in PostGIS Spatial DBMS. PostGIS is an open source software that adds support for geographic objects to the PostgreSQL object-relational database. PostGIS follows the Simple Features for SQL specification from the Open Geospatial Consortium (OGC); we use GeoMondrian as a SOLAP server; and JPivot as a client. GeoMondrian is an Open Source Spatial Online Analytical Processing Server.

In order to test our proposal we define different cases where the spatial dimension presents: one field level at the 100*100 resolution; two levels at the resolutions 100*100 and 200*200; and finally three levels at the resolutions 100*100, 200*200 and 400*400. We also vary the size of the temporal dimension in order to understand impact of the spatial and non spatial dimension on performances.

Figure 6-a shows the size of the fact table measured in function of the number of spatial and temporal members (spatial finest resolution / temporal finest granularity) using the two approaches. We can easily see two important differences: i) the field aggregation approach is expensive in terms of storage than the field interpolation one since the latter stores only facts values at a less detailed spatial granularity, ii) in the field interpolation approach the size of the fact table only varies depending on the size of the non spatial dimensions. Thus, even increasing the size of the spatial dimension, the fact table does not change since it contains only measures related to the first level of resolution.

In order to evaluate computation performance we execute the queries previously cited, where we combine roll-up operation on non spatial dimensions, and spatial slice operators over different field resolutions. Figure 6-b represents the execution time of the query 3, which consists in generating values of the members at different resolutions taking into account different sizes of the time dimension. This figure shows a certain degree of approximation in execution time between the two approaches to a certain level. Beyond this level, we note that the gap widens considerably. Thus, minimizing storage and relations has allowed the field interpolation approach we propose to have better execution time than the field aggregation approach at all resolution levels (100*100, 200*200 and 400*400). Figure 9 shows that the execution time in the "field aggregation approach" increases depending on the number of spatial and temporal members, whereas in the "field interpolation approach", it increases mainly depending on the number of temporal members. Indeed the size of the spatial dimension does not influence much on performance, since there is no relationship between the fact table and the members who belong to high resolutions. a) Figure 6: a) Fact table size with time for Query 3 for the Field aggre 6

Related work

In order to integrate fields da model, (Ahmed and Miquel 20 multidimensional model for hand discrete fields, storing a sample of members, to create a discrete interpolated in the client-side continuity. [START_REF] Mchugh | Intégration de la structure matricielle dans les cubes spatiaux[END_REF] define dimensions handling fields as a squares (raster): "hybrid dimension dimension", "mixed matrix d "geometric matrix dimension". She "matrix cube" where facts are cel grid. The "field aggregation approa section 4.2.1 is based on this wor "field interpolation approach" we p it gives the same result, it is more e of storage and execution time. (Gom 2012) presents a discrete data mode continuous fields and an algebra th OLAP operators (e.g. Dice, Slice down …). However, the discrete m propose does not support the cont the field, which consists to retrieve point with coordinates x and y [START_REF] Gomez | Physical Design and Implementation of Spatial Data Warehouses Supporting Continuous Fields[END_REF], the a multidimensional model handlin define two types of fields, "field" (spatial field and temporal field), a the operators associated to these d include the notion of field dimen measures. They define the "field dimension containing at least one le (temperature, precipitation…), the as a measure represented by a fiel Finally, (McGuire, Gangopadhyay et al. 2008)define a snowflake schema for an environmental application where three dimensions represent the same spatial members at different resolutions.

Conclusion and future work

In this paper we present a multidimensional model for incomplete fields at several resolutions and its implementation in a SOLAP architecture based on standards (e.g. SQL and MDX). We are working on using spatial data mining to speed-up map algebra operations and implement a SOLAP visualization client. We also work in integrating other interpolation functions to generalize the proposed approach.

  Figure 3: Odor SDW multi-dimensional model Query 1: select average odor for each field member during 2012 SELECT [Field].[res100]. Members ON ROWS, {[time].[2012]} ON COLUMNS FROM [odorCube] WHERE [Measures].[value]

  with 2 other levels each representing a different level of resolution ([Field].[res200] and [Field].[res400]).

Figure 5 :

 5 Figure 5: (a) Field Aggregation Star Schema (FASS), (b) Field Interpolation Star Schema (FISS)

  They also propose a physical schema, but any implementation into a classical ROLAP architecture is presented.

		b)
	ith the field aggregation and the field interpolation app approaches b) Execution
	regation Star Schema and the Field Interpolation Star Sc Schema approaches
		hierarchy" as a set of relate ted field levels, which
		allows a field to be seen a at different levels of
		granularity . They also propose ose a physical model for
	data in a SOLAP	data warehouses with continu inuous fields. However,
	2005) propose a	no implementation has been een proposed and the
	andling continuous	hierarchical relationship betwe ween field levels has not
	of points as spatial	been brought to light. (Bimon onte and Myoung 2011)
	e cube which is	provide a multidimensional m l model that integrates
	e to simulate a	field data independently from m their implementation,
	ines new types of	as measures and dimensions. ns. They also present a
	a regular grid of	formal representation of the sp spatio-multidimensional
	on", "mixed hybrid	model schema where they de define the concepts of
	dimension" and	field dimensions, field measure ures, and field views. To
	e also defines the	our knowledge, no implemen entation including the
	cells of the matrix	continuous appearance of inc incomplete field or the
	roach" presented in	multiresolution over incompl plete fields has been
	ork. However, the	proposed.
	e propose, although	Representation of multidim idimensional data under
	re efficient in terms	different resolution levels s or scales may be
	omez, Gomez et al.	considered as multirepresentat tation. (Bernier, Bédard
	del for representing	et al. 2005) proposes an app pproach to provide on-
	that makes use of	Demand multi-scale maps. Al Although this approach
	ice, Roll-up, Drill-	models maps features at diffe ifferent scales by using
	model the authors	spatial hierarchies, but it does es not contain measures.
	ntinuous aspect of	(Yvan, Proulx et al. 2002) d defines a UML-based
	ve a value for each	conceptual model that integrat rates multiple geometric
	y in the map. In	and semantic representations ns properties of spatial
	e authors propose a	levels. However, this work rk does not present a
	ling fields. They	complete multidimensional m model with facts and
	d" and "tempfield"	hierarchies.
	, and semantics for	Moreover, (Bédard et al., 200 2002) suggests (without
	e data types. They	providing details) using a d different spatial data
	ensions and field	warehouse for each repres resentation. Therefore,
	ld dimension" as a	changing the representation co corresponds to move to
	level that is a field	another spatial data wareho house. (Gascueña and
	he "field measure"	Guadalupe 2009) propose a co conceptual model with a
	field and the "field	multi-representation of spatial ial members.

Acknowledgements

The authors wish to thank the FEDER and the region for funding this project and project partners who provide us the data.