A Sen Gupta
email: a.sengupta@unsw.edu.au

A Ganachaud

S Mcgregor

J N Brown

L Muir

Drivers of the projected changes to the Pacific Ocean 2 equatorial circulation 3

Climate models participating in the third Coupled 6 Model Inter Comparison Project (CMIP3) suggest a signifi-7 cant increase in the transport of the New Guinea Coastal 8 Undercurrent (NGCU) and the Equatorial Undercurrent 9 (EUC, in the central and western Pacific) and a decrease in 10 the Mindanao current and the Indonesian Throughflow. 11 Most models also project a reduction in the strength of the 12 equatorial Trade winds. Typically, on ENSO time scales, a 13 weakening of the equatorial easterlies would lead to a reduc-14 tion in EUC strength in the central Pacific. The strengthening 15 of the EUC projected for longer timescales, can be explained 16 by a robust projected intensification of the south-easterly 17 trade winds and an associated off-equatorial wind-stress 18 curl change in the Southern Hemisphere. This drives the 19 intensification of the NGCU and greater water input to the 20 EUC in the west. A 1½-layer shallow water model, driven 21 by projected wind stress trends from the CMIP3 models 22 demonstrates that the projected circulation changes are 23 consistent with a purely wind driven response. While 24 the equatorial winds weaken for both El Niño events and 25 in the projections, the ocean response and the mechanisms 26 driving the projected wind changes are distinct from those 27 operating on interannual timescales.

bioavailable iron [e.g., [START_REF] Coale | Control of community growth and export production by upwelled iron in the equatorial Pacific Ocean[END_REF]. Both the CO 2rich water and the iron that maintains the high productivity are derived from upwelled water from the Equatorial Undercurrent (EUC). High concentrations of iron appear to be entrained into the New Guinea Coastal Undercurrent (NGCU) a feeder to the EUC, along the continental slope of Papua New Guinea [START_REF] Mackey | Iron in the western 481 Pacific: A riverine or hydrothermal source for iron in the Equatorial 482 Undercurrent?[END_REF]. Interannual variability in the strength of the NGUC (primarily related to ENSO) and the associated entrainment of iron has been linked to phytoplankton blooms in the equatorial Pacific that can increase equatorial chlorophyll levels by a factor of three to four [START_REF] Ryan | Western Pacific modulation of large phytoplankton blooms in 502 the central and eastern equatorial Pacific[END_REF]. Upwelling variability from the EUC in the eastern Pacific also dramatically alters the CO 2 air-sea flux [START_REF] Feely | Decadal variability of the airsea CO 2 fluxes in the equatorial Pacific Ocean[END_REF]. As such, any future changes in the equatorial circulation may significantly alter biological productivity and carbon cycling in the region.

[3] The EUC forms a remarkably long and narrow eastward ribbon of water that spans the Pacific basin, constrained by the Coriolis force to sit on the equator. The EUC is fed, at its initiation, by equatorward flowing low-latitude western boundary currents, in particular the NGCU and the Mindanao Current. It is strengthened by a thermocline convergence within the interior [START_REF] Johnson | Interior pycnocline flow from the subtropical to the equatorial Pacific Ocean[END_REF]. The equatorward transport constitutes the lower branches of the Subtropical Cells (STC) in which water subducted in the eastern extratropical Pacific, in both hemispheres, moves equatorward into the EUC [START_REF] Tsuchiya | 516 Source waters of the Pacific equatorial undercurrent[END_REF]]. This water is subsequently upwelled in the central and eastern equatorial Pacific and flows southward again in the surface Ekman layer.

[4] Linear theory suggests a relationship between the equatorial wind strength and the EUC strength [START_REF] Mcphaden | Trade wind fetch related variations in Equatorial 489[END_REF]. Using a reconstruction of EUC strength based on the TAO array, [START_REF] Izumo | The equatorial undercurrent, meridional overturning circulation, and their roles in mass and heat exchanges during El Niño events in the tropical Pacific Ocean[END_REF] shows that weakened equatorial winds in the western and central basin excite Kelvin waves that reduce the EUC strength to the east of the wind anomalies. We find a similar relationship also exists in the CMIP3 climate models (discussed below).

[5] Projections for ENSO behaviour, however, diverge considerably across the models [e.g., [START_REF] Collins | The impact of global warming on the tropical Pacific Ocean and El Niño[END_REF].

Despite this several aspects of background-state changes pertinent to tropical circulation, are quite robust. For example, theoretical arguments [e.g., [START_REF] Held | Robust responses of the hydrological cycle to global warming[END_REF], climate model projections and recent observations [e.g., [START_REF] Vecchi | Global warming and the weakening 528 of the tropical circulation[END_REF] suggest that the equatorial easterlies should weaken as the troposphere warms. There is also considerable agreement with regards to a projected intensification of SE Trade Winds and a weakening of the NE Trade Winds [START_REF] Ganachaud | Observed and expected changes to the tropical Pacific Ocean, in Vulnerability of Tropical Pacific Fisheries and Aquaculture to Climate Change[END_REF].

[6] The weakened projected equatorial winds directly drive a weakening of the westward surface flow. In contrast, a strengthening of the EUC in the western and central Pacific 92 is projected over the next century [START_REF] Ganachaud | Projected changes in the tropical Pacific Ocean of importance to tuna fisheries[END_REF] 93 [START_REF] Luo | Response of Pacific 478 subtropical-tropical thermocline water pathways and transports to global 479 warming[END_REF], apparently at odds with the observed 94 relationship between the equatorial Trades and EUC strength 95 evident on interannual timescales [START_REF] Izumo | The equatorial undercurrent, meridional overturning circulation, and their roles in mass and heat exchanges during El Niño events in the tropical Pacific Ocean[END_REF]. This study 96 examines the projected changes to the equatorial circulation 97 and the drivers of NGCU and EUC changes.

98 2. CMIP3 Simulations 99 [7] To examine changes in ocean and atmosphere 100 properties we use output from the third Coupled Model 101 Inter-comparison Project (CMIP3) [START_REF] Meehl | The WCRP CMIP3 multimodel 493 dataset[END_REF]. 102 Mean-state properties (based on the last 50 years of the 20th 103 century) are compared with changes over the full 21st cen-104 tury for the SRES A1B scenario. To minimise aliasing by 105 natural variability, we calculate linear trends in the proper-106 ties over the 21st century and present results as the change 107 per century. Model drift may affect the magnitude of the 108 projected changes [START_REF] Gupta | Projected changes to the Southern Hemisphere 506 ocean and sea ice in the IPCC AR4 climate models[END_REF], 2012] as such 109 trends in ocean properties for individual models have been 110 de-drifted, where possible, by subtracting any concurrent linear trends in the pre-industrial control simulation. For each scenario and model we use only a single ensemble member. For each property examined we use the maximum number of models available, except for the GISS ER model that was excluded for its inability to produce any ENSO-like variability [START_REF] Ganachaud | Observed and expected changes to the tropical Pacific Ocean, in Vulnerability of Tropical Pacific Fisheries and Aquaculture to Climate Change[END_REF][START_REF] Irving | Evaluating global climate models for climate change projections in the Pacific island region[END_REF].

Inconsistencies in output availability, mean that analyses of different properties are made using slightly different subsets of models (Figure 2). Using a smaller set of consistent models does not substantively change our results.

Projected Changes to the Equatorial Circulation

[8] All models show some degree of upward movement of the EUC core, with almost all models exhibiting greatest shoaling towards the west (Figure 1b). In the multi-model mean, the EUC core shoals by 25 m in the western basin decreasing to 5 m shoaling in the eastern basin. This shoaling manifests as an eastward flow anomaly above the mean EUC core depth and a westward anomaly below 130 (Figure 1b). However, the acceleration of the flow above the 131 core overwhelms the deceleration below in the western and 132 central basin, leading to an overall intensification of the 133 EUC, in most models. The region of strongest EUC trans-134 port in the western basin is enhanced by the largest amount 135 3 Sv or +10%, in the multi-model mean (Figure 2). While 136 there is a significant increase in EUC transport west of 137 160 W, there is a weak but significant reduction in trans-138 port east of 240 E (Figure 1d). This must result from 139 weaker meridional pycnocline convergence and/or weaker 140 upwelling in the eastern basin. 141 [9] In the multi-model-mean the NGCU, at 5 S, has a core 142 between 150 and 250 m, consistent with observations 143 [START_REF] Kuroda | Variability of currents off the northern coast of New 468 Guinea[END_REF], with a poleward flow extending from the 144 surface to 400 m (Figure 1a). The multi-model mean flow 145 (24 Sv) is within the range of observational estimates 146 [START_REF] Cravatte | Observed circulation in the Solomon Sea from SADCP data[END_REF] (13.5 Sv down to 300 m in the 147 Solomon straits [START_REF] Ueki | Observation of current variations off the New Guinea coast 519 including the 1997-1998 El Niño period and their relationship with 520[END_REF], 27 Sv down to 500 m). In 148 some models the NGCU does not abut the coastal margin leading to local maxima situated away from the western boundary in the model mean (and the projections). There is a robust projected intensification of the NGCU in the upper 250 m (with little change or a weak deceleration at greater depth) with almost unanimous model agreement at both 9 S and 5 S (Figure 2b). In the multi-model mean, there is a 4 Sv (+17%) increase in NGCU transport, although considerable model spread exists in the mean transport and the projected change. The enhanced input of water from the NGCU towards the equator is consistent with the large projected increase in EUC transport between 150 and 160 E.

[10] In the northern hemisphere there is no significant projected change in the southward western boundary transport at 5 N (Figure 2b), which in the mean state contributes to the EUC. There is however a significant decrease in the southward transport at 9 N and in the transport passing through the Indonesian Throughflow (ITF, of between 1 and 1.5 Sv, Figure 2b).

Mechanisms to Explain Projected Changes

[11] Figure 3a shows the projected multi-model change to the wind-stress. Most models project a strengthening of the southeast Trade winds and a weakening of the northeast and equatorial Trades. This leads to robust wind-stress curl anomalies: a strong negative anomaly is projected across much of the basin to the south of the equator at the boundary of the increasing south-easterly trades and decreasing equatorial trades with a less extensive negative curl anomaly at 10 N. The pattern of projected equatorial trade wind decrease is model dependent but is not systematically larger in the west, as is the case during El Niños. In fact, greatest model agreement is with respect to a decrease in the eastern basin, where there is typically little wind response during ENSO events (Figure 3b). Meanstate (1950Meanstate ( -2000) ) transport for major tropical currents (Indonesian Throughflow, ITF, South Equatorial Current, SEC, Equatorial Undercurrent, EUC; equatorial South Equatorial Current, SECeq, Mindanao Current at 5N and 9N, and New Guinea Coastal Undercurrent at 5S and 9S). Currents are calculated at locations shown in Figure 2a. Coloured markers show transport from individual models, horizontal black (red) lines represent multi-model mean (median) transport. (c) As Figure 2b for projected change in transport over the 21st century. Multi-model mean changes are significant at the 90% level, except for the poleward flow at 5N. Current locations can vary considerably between models. As a result, current definitions are model specific; model velocity fields were manually examined to determine mean-state boundaries (latitudes, longitudes and depths) of the different currents. Transports are then computed from the area integrated velocity flowing in the direction of the specific current, using annual averaged data. (Observational estimates from [START_REF] Butt | Currents off the east coast of New Ireland, Papua New Guinea, and their relevance to regional undercurrents in the western equatorial Pacific Ocean[END_REF], [START_REF] Gouriou | Mean circulation of the upper layers of the western equatorial Pacific Ocean[END_REF], [START_REF] Huang | Pacific subtropical-tropical thermocline water exchange in the National Centers for Environmental Prediction ocean model[END_REF], [START_REF] Izumo | The equatorial undercurrent, meridional overturning circulation, and their roles in mass and heat exchanges during El Niño events in the tropical Pacific Ocean[END_REF], [START_REF] Lukas | Observations of the Mindanao Current during 475 the western equatorial Pacific Ocean circulation study[END_REF], Wijffels [1993], [START_REF] Delcroix | Variation of the western equatorial Pacific Ocean, 1986-1988[END_REF], and [START_REF] Ueki | Observation of current variations off the New Guinea coast 519 including the 1997-1998 El Niño period and their relationship with 520[END_REF].) Notes: x, models used in Figures 2,3a, and 3b; *, models used in Figure 4; +, models used in Figure 3d.

183 [12] The projected equatorial wind-stress reduction is 184 small compared to a typical (one standard deviation) El Niño 185 event over most of the basin (Figure 3b). However the pro-186 jected wind-stress curl change in the southern hemisphere is 187 of a similar magnitude (and latitude) to a wind-stress curl 188 anomaly typical of a one-standard deviation El Niño, but 189 extends over a greater zonal extent (Figures 3a and3c). 190 In the northern hemisphere the projected change to the 191 curl is of the opposite sign (i.e., a negative change) to an 192 El Niño-related anomaly and is situated considerably 193 further north. 194 [13] For interannual timescales [START_REF] Lee | Interannual-to-decadal variations of tropi-470 cal-subtropical exchange in the Pacific Ocean: Boundary versus interior 471[END_REF] 195 separate the tropical circulation response onto a part driven 196 by changes to the equatorial zonal wind-stress and a part 197 related to the off-equatorial wind stress curl. These two 198 processes operate together to modulate the equatorial circu-199 lation response to ENSO or Pacific decadal variability. For 200 example, during an El Niño, the reduced equatorial easterlies 201 in the western basin, are associated with flanking positive 202 (negative) wind stress curl anomalies in the northern 203 (southern) hemispheres (Figure 3). Lee and Fukumori 204 [2003] show that the decreased equatorial wind-stress redu-205 ces the strength of STCs: the Ekman divergence, the com-206 pensating interior equatorward pycnocline convergence and the EUC that links the upper and lower STC branches. On the other hand, the flanking curl anomalies drive an increased equatorward boundary transport and a compensating reduced interior pycnocline convergence. The net effect is an increase in EUC transport in the far western basin (driven by enhanced boundary flow), but a more pervasive decrease in transport over the rest of the basin. Such a change is evident in the mean CMIP3 model response to ENSO (Figure 1d). Using an ocean model forced with historical winds [START_REF] Capotondi | Anatomy and decadal evolution of the Pacific subtropical-tropical cells (STCs)[END_REF] also demonstrate a strong compensation between interior and western boundary flow at both interannual and decadal timescales. They highlight how baroclinic Rossby wave adjustment to the wind stress changes act to set up the observed circulation changes.

[14] The projected EUC and NGCU changes can also be understood in terms of the on-and off-equatorial processes described above. The strong projected negative wind-stress curl anomaly in the Southern Hemisphere causes an intensification of the NGUC with a compensating reduction in the interior pycnocline convergence. This drives the projected EUC intensification in the west (Figure 1d). The weak projected reduction in the equatorial trades additionally forces a weak overall slowdown of the EUC. The relatively large

(d) As

Figure 3c for observations based on ECMWF [START_REF] Uppala | The ERA-40 re-analysis[END_REF], and HadISST [START_REF] Rayner | Global analyses of sea 497 surface temperature, sea ice, and night marine air temperature since the 498 late nineteenth century[END_REF], products. (Regression units, wind-stress: 10-3 Nm-2/standard deviation; wind-stress curl: 10-8 Nm-3/standard deviation.) influence of the off-equatorial compared to the on-equatorial process is consistent with the multi-model mean EUC projection whereby transport is enhanced over a considerably greater portion of the basin than typical during El Niño events.

[15] To summarise, it would appear that the EUC change is primarily related to an acceleration of the NGCU that feeds the EUC from the south, and a compensating reduction in the southern hemisphere interior pycnocline convergence. This is in turn related to the strong wind stress curl anomaly extending across much of the basin centred at 7 S. In the northern hemisphere the projected negative curl anomaly is consistent with the weakened southward boundary flow at 9 N. A direct link to changes in the boundary flow closer to the equator and thus to the EUC is complicated by complex circulation pathways that incorporate the ITF. These pathways are dependent on bathymetry that can vary considerably across models. It is plausible that the slowdown at 9 N may alter the potential vorticity and thus the pathways of flow feeding into the EUC. Here we have demonstrated that the projected changes are consistent with a purely wind driven response. We note however that there is a robust projected increase in the strength of upper ocean stratification over the tropical ocean [START_REF] Capotondi | Enhanced upper-ocean stratification with climate change in the CMIP3 models[END_REF]. Further experiments with more sophisticated ocean models would be required to identify the importance of buoyancy effects.

[20] While the wind-related processes described above can explain circulation changes associated with both interannual variability and multi-decadal trends, the causes for the wind changes are not the same. ENSO variability is intimately tied to the zonal equatorial SST gradient and the Bjerknes feedback. The causes for the projected wind changes appear to be very different. The strengthening of the southeast trades is fundamental in driving the projected circulation changes. It is associated with differences in projected warming between the equator and the southeastern Pacific Ocean [START_REF] Timmermann | Wind effects on past 513 and future regional sea level trends in the southern Indo-Pacific[END_REF]Xie et al., 2010]. Xie et al.

[2010], for example, use an atmospheric model forced (over 2000-2060) with (i) projected SST, with radiative forcing held fixed (ii) evolving radiative forcing, with SST held fixed and (iii) evolving SST and radiative forcing, to examine the mechanisms driving the intensification. Even in the absence of SST changes there is a projected intensification of the southeast trades south of 20S, suggesting that the wind intensification is triggered by changes in radiative forcing but is then amplified and extended equatorward by a windevaporation-SST feedback whereby stronger mean winds in the southeast Pacific slow the rate of ocean warming in this region [Xie et al., 2010]. Similar conclusions were used to explain historical changes [START_REF] Deser | Atmospheric circulation trends, 1950-2000: The relative roles of sea surface temperature forcing and direct atmospheric radiative forcing[END_REF]. This is a robust result from all climate models. Multiple processes also lead to an enhanced equatorial SST warming in many of the climate models [START_REF] Dinezio | Climate response of the equatorial Pacific to global warming[END_REF]. The strengthened meridional SST gradient helps to intensify the southeast Trade winds. In addition, the projected weakening of the equatorial winds appears to be related to a slowdown of the atmospheric overturning circulation, driven by the differential sensitivity of atmospheric water vapor increase and radiative cooling to a CO2-induced warming [START_REF] Held | Robust responses of the hydrological cycle to global warming[END_REF].

As such the drivers of the projected changes are fundamentally different to those that drive ENSO. Also, given the differences in the oceanic responses, describing the projected changes in the Tropical Pacific as 'EL-Niño-like' as is frequently done, is inappropriate. A number of previous studies that have examined different components of the tropical Pacific climate have similarly found that the projected change is not well described as being El Nino-or La Nina-like [e.g., van Oldenborgh et al., 2005;[START_REF] Collins | El Niño-or La Niña-like climate change?[END_REF][START_REF] Vecchi | Weakening of tropical Pacific atmospheric circulation due to Xie[END_REF][START_REF] Vecchi | Global warming and the weakening 528 of the tropical circulation[END_REF][START_REF] Dinezio | Reconciling differing views of tropical Pacific climate change[END_REF].

[21] The projected increase in the NGCU and upper EUC has the potential to enhance entrainment and supply of bioavailable iron into the eastern Pacific. At the same time, however, there is an increase in the vertical stratification and a general decrease in the wind driven upwelling along the equator. As such further work is required to understand how these competing effects will affect the iron limited biological systems of the tropical Pacific. (CSIRO). This was also partially funded by ANR project ANR-09-BLAN-0233-01; it is a contribution to CLIVAR/SPICE. This project is supported by the Australian Research Council. We would like to thank Antonietta Capotondi and one anonymous reviewer for their valuable comments.

[23] The Editor thanks two anonymous reviewers for assisting with the evaluation of this paper.

Figure 1 .

 1 Figure 1. (a) Multi-model mean meridional velocity (lines) and change (shading) in meridional velocity at 5S off the coast of PNG (longitudes have been offset in individual models so that the coast of PNG lies at the same longitude). (b) Multimodel mean zonal velocity (lines) and change in zonal velocity averaged between 3S and 3N; dashed blue and red lines indicate the position of the EUC core in the 20th and 21st century, respectively (calculated as the zonal current weighted depth at each longitude). (c) Multi-model mean (continuous) and median (dashed) EUC transport. (d) Projected multi-model mean (continuous) and median (dashed) change in EUC transport (red) and 20th century EUC transport regressed onto ENSO index (black). Thickened line indicates longitudes where change is significant at 90% level.

Figure 2 .

 2 Figure 2. (a) Major tropical Pacific currents (red: surface, blue: sub-surface, black: mean surface winds). (b)Meanstate (1950Meanstate ( -2000) ) transport for major tropical currents (Indonesian Throughflow, ITF, South Equatorial Current, SEC, Equatorial Undercurrent, EUC; equatorial South Equatorial Current, SECeq, Mindanao Current at 5N and 9N, and New Guinea Coastal Undercurrent at 5S and 9S). Currents are calculated at locations shown in Figure2a. Coloured markers show transport from individual models, horizontal black (red) lines represent multi-model mean (median) transport. (c) As Figure2bfor projected change in transport over the 21st century. Multi-model mean changes are significant at the 90% level, except for the poleward flow at 5N. Current locations can vary considerably between models. As a result, current definitions are model specific; model velocity fields were manually examined to determine mean-state boundaries (latitudes, longitudes and depths) of the different currents. Transports are then computed from the area integrated velocity flowing in the direction of the specific current, using annual averaged data. (Observational estimates from[START_REF] Butt | Currents off the east coast of New Ireland, Papua New Guinea, and their relevance to regional undercurrents in the western equatorial Pacific Ocean[END_REF],[START_REF] Gouriou | Mean circulation of the upper layers of the western equatorial Pacific Ocean[END_REF],[START_REF] Huang | Pacific subtropical-tropical thermocline water exchange in the National Centers for Environmental Prediction ocean model[END_REF],[START_REF] Izumo | The equatorial undercurrent, meridional overturning circulation, and their roles in mass and heat exchanges during El Niño events in the tropical Pacific Ocean[END_REF],[START_REF] Lukas | Observations of the Mindanao Current during 475 the western equatorial Pacific Ocean circulation study[END_REF],Wijffels [1993],[START_REF] Delcroix | Variation of the western equatorial Pacific Ocean, 1986-1988[END_REF], and[START_REF] Ueki | Observation of current variations off the New Guinea coast 519 including the 1997-1998 El Niño period and their relationship with 520[END_REF].) Notes: x, models used in Figures 2, 3a, and 3b; *, models used in Figure4; +, models used in Figure3d.

Figure 3 .

 3 Figure 3. (a) Multi-model mean projected change. in zonal wind-stress (contours) and wind-stress curl (shading). (b) Multi-model mean zonally averaged (3S to 3N) projected wind stress change (solid red line) and regression of windstress onto ENSO index (solid black line). Thick red line indicates longitudes where the projected changes are significant at 95% level (t-test). Dashed lines show multi-model median results. Shaded regions indicate 1 standard deviation model spread about the multi-model means. (c) Multi-model mean regression of the mean zonal wind-stress (contours) and wind-stress curl (shading) on ENSO index (line contours; continuous-positive, dashed-negative, thickened-zero). (d) As Figure3cfor observations based on ECMWF[START_REF] Uppala | The ERA-40 re-analysis[END_REF], and HadISST[START_REF] Rayner | Global analyses of sea 497 surface temperature, sea ice, and night marine air temperature since the 498 late nineteenth century[END_REF], products. (Regression units, wind-stress: 10-3 Nm-2/standard deviation; wind-stress curl: 10-8 Nm-3/standard deviation.)

  249is connected with the ITF transport reduction and does not 250 have a large impact on the EUC changes. 251 5. Shallow Water Model (SWM) 252 [16] To test the qualitative arguments presented above we 253 use the projected 21st century wind-stress trends from indi-254 vidual models, to drive a 1½-layer SWM. The model 255 represents a dynamic upper ocean with a motionless deep 256 ocean separated by a thermocline that can vary in depth with 257 time [McGregor et al., 2007]. The model isolates the linear 258 wind-driven response of the upper ocean circulation, and 259 excludes possible buoyancy driven effects. 260 [17] Figure 4 compares the multi-model mean, depth 261 integrated (0-800 m), meridional velocity projections from 262 the CMIP3 model and the corresponding upper layer SWM 263 results. The SWM contains a relatively crude representation 264 of ocean dynamics. On long timescales it captures the 265 Sverdrup response to the wind field changes (Figure 4b) and

Figure 4 .

 4 Figure 4. Multi model mean change in (a) vertically integrated (0-800 m) meridional velocity for CMIP3 models, (b) Sverdrup transport and (b) meridional velocity from upper layer of shallow water model forced by wind-stress trends from individual models. Shaded areas indicate regions where the mean change is not significant (at 95% level). (Units m2/s.)

[ 22 ]

 22 Acknowledgments. This project was supported by the Pacific Australia Climate Change Science and Adaptation Program a program managed by the Department of Climate Change and Energy Efficiency in collaboration with AusAID, and delivered by the Bureau of Meteorology and the Commonwealth Scientific and Industrial Research Organisation

anthropogenic forcing, Nature, 441(7089), 73-76, doi:10.1038/

nature04744.

Wang, D., and M. A. Cane (2011), Pacific shallow meridional overturning

circulation in a warming climate, J. Clim., 24(24), 6424-6439,

doi:10.1175/2011JCLI4100.1.

Wijffels, S. E. (1993), Exchanges between hemispheres and gyres: A direct

approach to the mean circulation of the equatorial Pacific, PhD thesis,

Woods Hole Oceanogr. Inst., Woods Hole, Mass.

rainfall, J. Clim., 23(4), 966-986, doi:10.1175/2009JCLI3329.1. SEN GUPTA ET AL.: PACIFIC OCEAN CIRCULATION PROJECTIONS


Olivier Stasse

Adrien Escande

Nicolas Mansard

Sylvain Miossec

Paul Evrard

Abderrahmane Kheddar

Real-Time (Self)-Collision Avoidance Task on a HRP-2 Humanoid Robot

Keywords:

This paper proposes a real-time implementation of collision and self-collision avoidance for robots. On the basis of a new proximity distance computation method which ensures having continuous gradient, a new controller in the velocity domain is proposed. The gradient continuity encompasses no jump in the generated command. Included in a stack of tasks architecture, this controller has been implemented on the humanoid platform HRP-2 and experienced in a grasping task while walking and avoiding collisions with the environment and auto-collisions.

Index Terms-stack of tasks, proximity distance with continuous gradient,

I. INTRODUCTION

It is crucial for a robot to have, among others, the ability to (i) avoid undesirable collisions with both obstacles and own parts -for example undesirable auto-collisions for redundant robots such as humanoids-and (ii) detect desired collisions such as those necessary to perform contact-based tasks -for example haptic interaction with an environment or with own robot parts-. Collision detection and avoidance functions are needed either in simulation or in real implementation and can be used in off-line or on-line trajectory generation. Planning collision-free trajectories is an active area of research [START_REF] Lavalle | Planning Algorithms[END_REF]. Open-loop planning is generally made off-line and can make use of simple binary collision detection algorithms whereas closed-loop trajectory generation is on-line, mostly embedded with the controllers and makes use of proximity distance collision to predict and prevent collisions [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF]. In this paper we address the problem of on-line collision avoidance (including auto-collision avoidance) in the context of robotics and more particularly in humanoid robotics; although several closed-loop controllers have been proposed for various reactive task purpose full body motion, see for instance [START_REF] Neo | A switching command-based whole-body operation method for humanoid robots[END_REF] [START_REF] Sentis | A whole-body control framework for humanoids operating in human environments[END_REF], surprisingly none of them guarantee, in an explicit way, non desirable collisions or auto-collisions. We propose an efficient algorithm to compute fast proximity distances that can be efficiently integrated in a low-level reactive control. We used strict-convexity bounding volumes close to polyhedral convex hulls in order to guarantee the continuity of the proximity distance gradient [START_REF] Escande | Strictly convex hulls for computing continuous gradient proximity distances[END_REF] and in the same time satisfying real-time control requirement. In [START_REF] Patel | A collisionavoidance scheme for redundant manipulators: theory and experiments[END_REF] authors make use of cylinders and spheres to cover a redundant manipulator and compute in a efficient way proximity distance to be used as a secondary task in a kinematics task prioritization scheme and experimented on a 7dof redundant The authors are with the AIST/CNRS Joint Japanese-French Robotics Laboratory, JRL, Tsukuba, Japan.

olivier.stasse, adrien.escande, nicolas.mansard, sylvain.miossec, paul.evrard@aist.go.jp, kheddar@ieee.org manipulator. Instability that may occur from discontinuity of the witness points has been addressed in configurations where the cylinders are nearly parallel. Our algorithm makes use of patches of spheres and toruses to cover in a more precise way the convex hull of robot's part and get rid of this problem. Our algorithm description and its technical implementation issues are presented in the first section.

The very nature of reactive controllers is that they are local and not global such as in [START_REF] Lindemann | Simple and efficient algorithms for computing smooth, collision-free feedback laws[END_REF]. They are more suited to interactive task, and unstructured varying environments; they are also computationally lighter than planning. Our algorithm has been integrated as an additional task in the stack of the task sequencing architecture proposed in [START_REF] Mansard | Task sequencing for sensor-based control[END_REF] [START_REF] Mansard | Visually-guided grasping while walking on a humanoid robot[END_REF]. In humanoid robotics, a similar idea has been proposed in [START_REF] Sugiura | Real-time self collision avoidance for humanoids by means of nullspace criteria and task intervals[END_REF] where self-collision avoidance has been implemented on the simulator of ASIMO, their method makes use of an artificial force which changes the value of the desired posture in the gradient of a posture cost function projected in the null space of the main tasks; tasks are described in derivative of joints or Cartesian spaces (velocity). This virtual force penalizes a close proximity distance obtained from sphere swept lines [START_REF] Larsen | Fast proximity queries with swept sphere volumes[END_REF] bounding volume of the humanoid. Their approach is very elegant and simple to implement, yet they did not consider stability problems that may occur from discontinuous witness points and their formalism would not allow marking auto-collision avoidance with higher priority. This is possible by our method.

Our method has been ported and exemplified on an actual experiment involving the HRP-2 humanoid robot. The tasks consist in performing a ball-grasp guided by vision while at the same time walking stably and avoiding obstacles and auto-collisions. As a result of this experiment, open issues appear to be linked to task sequencing and prioritization and more generally the way to tackle tasks described through unilateral constraints... consisting in future work.

II. PROXIMITY DISTANCE HAVING CONTINUOUS GRADIENT

A. A new strictly convex bounding volume

Proximity distance and more generally collision avoidance have been widely studied, which results in numerous algorithms and schemes (the interested reader may refer to the recent, exhaustive and excellent review books [START_REF] Van Den Bergen | Collision detection in interactive 3D environments, ser[END_REF][13]). However, little attention has been paid to the continuity properties of the proximity distance. It has been pointed out however that in singular cases, the gradient of this distance is not continuous, generating oscillations or misbehaviours in the control scheme [START_REF] Patel | A collisionavoidance scheme for redundant manipulators: theory and experiments[END_REF]. For a complete discussion on the continuity problem as well as a method to regularize the proximity distance gradient, see [START_REF] Escande | Strictly convex hulls for computing continuous gradient proximity distances[END_REF]. The main idea is to build strictly convex hulls of the robot bodies in a way that can be seen as a slight blowing up of the usual convex hull. It is realized through patches of spheres and toruses. Such a volume is called Sphere-Torus-Patches Bounding Volume (STP-BV). Its advantages are (i) to ensure continuity of the gradient, and (ii) to accurately approximate the convex hull of the object (in typical cases we experienced, the volume increase from convex hull to STP-BV is 1-2%), while maintaining the number of collision pairs low (one volume per body) as well as the computation time for each of them.

One of the most interesting property of STP-BV main result presented is it is sufficient to have only one strictly convex body to have a continuous minimum distance between two witness points of two convex bodies. This means that the STP-BV construction is not mandatory for obstacles to hold the continuity. It is sufficient to build the patches only for the robot's bodies. The HRP-2's associated representation is depicted in figure 1. The computation of the gradient then from [START_REF] Escande | Strictly convex hulls for computing continuous gradient proximity distances[END_REF] of this distance is now detailed, as it is a key point to compute a control law to avoid self-collision.

B. Computing Proximity Distance's Gradients

Let us note δ the distance between two convex objects O 1 and O 2 . The relative position between two objects is parameterized by the actuated joints of the robot noted q. Assuming that the witness points of the STP-BV of objects O 1 and O 2 are respectively SP 1 min and SP 2 min then the gradient of the distance can be written:

∂δ ∂q = n ⊤ d ∂SP 1 min ∂q (q) - ∂SP 2 min ∂q (q) (1)
with n d the normal unit vector derived from the features. Intuitively the gradient is orthogonal to the vector defined by the two witness points.

For a point P of fixed coordinates (x, y, z) in the local frame of an object O at the configuration q, the gradient has the following expression:

∂P ∂q (q) = xJ 1 (q) + yJ 2 (q) + zJ 3 (q) + J 4 (2)
obtained by deriving

P (q) = R(q)(x, y, z) ⊤ + T (q) = xC 1 (q) + yC 2 (q) + zC 3 (q) + T (q) ( 3
)
where R is a rotation matrix, C i its columns and T is the translation vector. The J i are the gradient matrices of the C i and T . This matrices can be analytically computed beforehand and are called hereafter pregradient matrices.

III. STACK OF TASKS

The stack of tasks is a structure that orders the set of tasks that are currently active. Only the tasks in the stack are taken into account in the control law. The task at the bottom level has priority over all the others, and the priority decreases as the stack level increases. The control law is computed from the tasks in the stack, in accordance with three rules:

-any new task added in the stack does not disturb the tasks already in the stack. -the control law is continuous, even when a task is added or removed from the stack. The robot is controlled through the joint velocity q. A break of continuity would mean an infinite acceleration during a short period of time, which would imply that the control is not correctly applied. -if possible, the additional constraints should be added to the control law, but without disturbing the tasks in the stack. The control law is computed from the stack, using the redundancy formalism introduced in [START_REF] Siciliano | A general framework for managing multiple tasks in highly redundant robotic systems[END_REF]. The additional constraints are added at the very top of the stack, which means that they are taken into account only if some degrees of freedom (DOF) remain free after applying the active tasks. This priority order may seem illogical, considering that the constraints are obstacles that the robot should avoid above all. However, the positioning task has priority since it is the task we want to see completed, despite the presence of the obstacles. The high-level controller is then used to ensure that the constraints are respected when it is obvious that the robot will violate them.

1) Ensuring the priority: Let (e 1 , J 1 ) ... (e n , J n ) be n tasks. The control law computed from these n tasks should ensure the priority, that is the task e i should not disturb the task e j if i > j. A recursive computation of the joint velocity is proposed in [START_REF] Siciliano | A general framework for managing multiple tasks in highly redundant robotic systems[END_REF]:

q0 = 0 qi = qi-1 + (J i P A i-1 ) + ( ėi -J i qi-1 ), i = 1..n (4)
where P A i is the projector onto the null-space of the augmented Jacobian J A i = (J 1 , . . . J i ) and J i = J i P A i-1 is the limited Jacobian of the task i . The robot joint velocity realizing all the tasks in the stack is q = qn . The projector can be recursively computed by

P A i = P A i-1 -(J i P A i-1 ) + J i P A i-1
(5)

2) Ensuring the continuity: From (4), the control law is obtained by imposing a reference velocity ėi for each task in the stack. Generally, a exponential decrease is required by imposing the first order differential equation ėi = -λ i e i . However, this equation does not ensure the continuity of the robot velocity when the stack is changed. In [START_REF] Mansard | Tasks sequencing for visual servoing[END_REF], we proposed a solution to properly smooth the robot velocity at the transition, by imposing a specific second order equation:

ëi + (λ i + µ) ėi + (λ i µ) e i = 0 (6)
where λ i is the gain that tunes the convergence speed of task e i , and µ sets the transition smoothness of the global control law. The control law is obtained by introducing ( 6) in ( 4):

qi = qi-1 + (J i P A i-1 ) + (-λ i e i -J i qi-1 ) q = qn + G A e -µ(t-τ ) ė(τ ) + Λe(τ ) ( 7
)
where τ is the time of the last modification of the stack,

Λ = diag (λ i ) and G A is defined so that qn = G A    ė1 . . . ėn    in (4).
3) Adding the secondary constraints: The constraints are added using the Gradient Projection Method [START_REF] Liegeois | Automatic supervisory control of the configuration and behavior of multibody mechanisms[END_REF], [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF]. The constraints are described by a cost function V. The gradient g(q) of this cost function can be considered as an artificial force, pushing the robot away from the undesirable configurations. It is introduced as the last task of the stack. It has thus to be projected onto the null space of each task into the stack. Using (7), the complete control law is finally

q = qn + G A e -µ(t-τ ) ė(τ ) + Λe(τ ) -κP A n g (8)
The reader is invited to refer to [START_REF] Mansard | Tasks sequencing for visual servoing[END_REF], [START_REF] Mansard | Visual servoing sequencing able to avoid obstacles[END_REF] for more details.

IV. THE CONTROL LAW RELATED TO SELF-COLLISION A. Gradient Projection Method

We want now to find the cost function to be minimized in order to respect the constraint of self-collision avoidance. This problem is written

min V (q), q ∈ R n (9)
with n the number of DOFs of the robot. The classical iterative solution is then to move the robot along the gradient of the function:

q = -κg(q) = ∇ ⊤ q (10)
The task to avoid self-collision is straightforward and inspired from the joint limit avoidance scheme proposed by Khatib [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF].

Let us consider Φ a set of parameters to span the constraint space. The optimal force to satisfy this problem is then [START_REF] Mezouar | Path planning for robust image-based control[END_REF]:

g Φ (q) = ∂Φ ∂q ∇ ⊤ Φ V Φ (11)
For instance as proposed by [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF] we can set:

V (q) = 1 2 n i=1 α 2 i ∆q i (12)
with ∆q i = qmax i -qmin i the size of the joint space for joint i, and

α i =      q i -qmin li , if q i < qmin li q i -qmax li , if q i > qmax li 0, otherwise (13)
we would like to find a similar function to avoid the self collision.

B. A cost function to avoid self-collision

As we want to keep distance between two bodies of the robot to be above a certain threshold a, we propose the following cost function:

V (q) = i∈Cp g i (q) g i (q) = (δ i (q) -a i ) 2 if δ i (q) < a i 0 otherwise (14)
with C p = {C j , ∀g j (q) < αa j }, 1 < α ∈ N. and C = {C 0 , ..., C m } is the set of m pairs of bodies which are checked for collision. a i represents the activation distance between the two bodies of pair C i .

C. Gradient of the cost function

The gradient of the cost function is obtained by simple derivation:

∂V i (q) ∂q = 2(δ i (q) -a i ) ∂δ i (q) ∂q (15)
if δ i (q) < a i , ∂Vi(q) ∂q = 0 otherwise. The final Jacobian for the cost function is:

∂V (q) ∂q = i∈Cp J i (q) ( 16
)
which size is 1 × n. It is also possible to have a weighted function on all the pair of bodies formulate as:

g i (q) = w i (δ i (q) -a i ) (17)
But this will imply to compute the gradient on each pair.

D. Exponential decay

As self-collision avoidance (SCA) is of prime interest for safety reason, we would like to put it as one of the first task to be realized. In order to insert the SCA task inside the stack of tasks, we need to create a projector to constraint the lower priority tasks inside the null space of SCA's task. Integrating the Jacobian of the SCA task directly and its related nullspace as proposed in 4, is not a good idea. Indeed there is no constraint regarding the evolution of the function with respect to time. Therefore we finally introduce the following task: e = V (q), ė * = -λe. The second equation means that the desired task velocity is an exponential decay.

E. A multi-dimensional task to avoid self-collision

In case of simultaneous collisions, it appears that task [START_REF] Siciliano | A general framework for managing multiple tasks in highly redundant robotic systems[END_REF] can cause some problems. The null space of the task ( 14) allows collisions to occur, because the avoidance of potential collision is considered as a one-dimension task; the gradients of all the collision distances are summed. The null space of this task will thus be of higher dimension than it would have been if we had considered each collision separately. This is illustrated on figure 2. Let us suppose the operational space is a plane with two collisions detected. The figure represents the velocity plane. G 1 and G 2 represent the gradients of the collision distances. The hatched area represent the locus of velocities for which a collision will occur. C 1 and C 2 represent the collision constraints. In the framework of the stack of tasks, no motion is possible in such a case because the velocity along both G 1 and G 2 will be constrained to be zero and since G 1 and G 2 are independant, no more degree of freedom is available. However, if we use task [START_REF] Siciliano | A general framework for managing multiple tasks in highly redundant robotic systems[END_REF], lower priority tasks will be projected onto the null space of the sum of G 1 and G 2 . This null space is one-dimensional and thus allows motion along the dashed line which cause the violation of the collision constraints. In order to avoid this behavior, we replaced task [START_REF] Siciliano | A general framework for managing multiple tasks in highly redundant robotic systems[END_REF] with the following:

V (q) =     . . . g i (q) . . .     i ∈ C p g i (q) = (δ i (q) -a i ) 2 if δ i (q) < a i 0 otherwise (18)
The dimension of ( 18) can change depending on the number of potential collisions. To avoid implementing dimensionvarying tasks, we fixed the dimension of ( 18) to a constant N c , so that it is possible to handle up to N c collisions. We tested the case where N c = 5. Fig. 3. Distance of the head and the gripper for V (q) = (δ 0 (q) -a 0 ) 2

F. Problem of remaining stuck in collision

In some other experiments of the collision avoidance control, we observed that the robot was stuck at distance a 0 to contact, after it occurred. This behavior was observed even if another task with a lower priority was pushing the robot away from the collision. Such a behavior is due to the collision-avoidance task that exponentially decreases the distance between two bodies to the minimum distance. The minimum distance is thus asymptotically reached after a long time. The collision task is deactivated only when this minimum distance is reached. While the collision task is converging, no other task with a lower priority can act in its space to quit the collision. For the experiments presented in this paper, we believe this problem was not observed because collision constraints are strictly convex and that it is possible to quit a collision in the null-space of a collision task thanks to the high-redundancy of HRP-2. Solving such a problem requires to develop a new theoretical framework to deal with collision constraints, that are inequality constraints rather than equality constraints.

V. EXPERIMENTS

A. Control the distance between two objects.

In order to have a better understanding of the collision distance behavior and its jacobian inside the stack of tasks, let us consider a simpler version of the collision avoidance control law proposed previously. The cost function is set to:

V (q) = (δ 0 (q) -a 0 ) 2 (19)
where δ 0 (q) is the distance between the head and the right gripper, and a 0 is set to 0.01 m. Here the test δ 0 (q)-a 0 > 0 is removed. This task is interesting because as there are eight articulations from the gripper to the head it is redundant, so an infinite number of solutions is possible. Thus face crossings triggering discontinuities are very likely to occur. The evolution of the distances between the two bodies return by V-Clip and STP-BV are given in figure 3. Note that the graph's is very close to an exponential decrease. The evolution of the Jacobian's relevant components are depicted in figure 4. As expected, the legs were equal to zero, as well Fig. 4. Right arm's Jacobian components for the distance between the head and the gripper with V (q) = (δ 0 (q) -a 0 ) 2 as the chest, the head's tilt, the free-flyer and the left arm.

The only moving parts of the robot are the right arm and the head's pan. Between iterations 50 and 60 a discontinuity seems to have occur (figure 4 up), but a careful examination shows that this is only a quick continuous change (figure 4 bottom). This especially appears when two faces are parallel during which the witness points thus move very quickly along the STB-BV geometric shapes.

B. Avoiding known obstacle

In this section, the experiment fully exploits the redundancy of the HRP-2 humanoid robot by combining several tasks. The robot has to grasp a ball while walking. An image centering task ensures that the robot is always seeing the ball. An arm-orientation task makes sure that the gripper is ready to grasp. When the gripper is close enough the ball is catched. If the gripper misses, it is detected by monitoring the torque. A detailed description of the control laws can be found in [START_REF] Mansard | Visually-guided grasping while walking on a humanoid robot[END_REF]. The priorities of the tasks are the same, with the collision avoidance task having the second priority just after walking. Two original modifications have been realized to implement obstacle avoidance in the stack of tasks. Firstly a set of 116 pairs are chosen to track auto-collision. Bodies linked to each other are not included because they are treated by the joint limits constraints. The second originality is done through the inclusion of a 25 cm diameter ball in the collision pairs. The ball position is put in such way that the robot's hand comes into collision, see figure 5. The value starting the inclusion of the distance inside the control law is set to a i = 0.1 m.

The robot avoids the ball in two occasions. First by holding the hand when moving forward. Then the avoidance stops while the robot is moving away. In second when the robot swing back to the left for the next step the hand and the arm moves to the right to avoid collision.

As in [START_REF] Mansard | Visually-guided grasping while walking on a humanoid robot[END_REF]the high-level controller removes the orientation and grasp tasks right after grasping, and a task extending the right arm is put inside the stack. The CoM task then uses the left arm to maintain the CoM given by the pattern generator. However this motion makes the robot reach its joint limits. The left arm then moves toward the left leg, and avoid it thanks to self-collision pairs in the controller, see figure 6. This behavior do not appear when using CoM or Collisionavoidance alone. The described experiment can be watch in the companion video, and is depicted in figure 7.

VI. CONCLUSION

We have presented a new controller which can be used to avoid self-collision and collision with an external object. This new controller is based on a proximity distance which has a continuous gradient. A new geometric representation of the robot bodies bouding volume is at the heart of this new result. This controller has been implemented and tested on a real full-size humanoid robot.

The main limitation of the current system is that the Jacobian components related to the free flyer's humanoid are not considered. Indeed this might involve to change in real-time the CoM trajectory [START_REF] Kajita | Resolved momentum control: Humanoid motion planning based on the linear and angular momentum[END_REF] and in some cases the foot position [START_REF] Nishiwaki | Short cycle pattern generation for online walking control system of humanoids[END_REF]. A new challenge is to include obstacle avoidance in real-time biped walking engine.

Fig. 1 .

 1 Fig. 1. STP-BV representation of HRP-2.

Fig. 2 .

 2 Fig. 2. Using a one-dimensional task for collision avoidance allows the violation of constraints.

  distance between the head and the gripper STP-BV Vclip

Fig. 5 .Fig. 6 .

 56 Fig. 5. Initial motion with collision

Fig. 7 .

 7 Fig. 7. HRP-2 reactively avoids the biggest ball.

ACKNOWLEDGMENT

This work is partially supported by grants from the ROBOT@CWE EU CEC project, Contract No. 34002 under the 6th Research program www.robot-at-cwe.eu.


Pascal Lièvre
email: pascallievre@orange.fr

Michel Récopé
email: michel.recope@univ-bpclermont.fr

Géraldine Rix-Lièvre
email: geraldine.rix@univ-bpclermont.fr

Based on real cases, this communication aims to answer to the following research question: what can be the impact of stress on the decision taken by an expert? We assess that in our specific context, experience determines the level of stress. And due to the fact that our actors are driven by well-being, this stress will be positive.

INTRODUCTION

Switzerland is a very nice country with plenty of wonderful mountain. Nevertheless, more than 100 alpinists die every year and nearly 2500 are rescued. 2010, December 12 th , a free-rider on a snowboard -searching for sensations -has fallen from 30min off-piste skiing in the Canton of Glaris. He was 33 years old and he has not survived. He was performing an extreme ride and he had surely taken a bad decision. Was he under stress because he could not commit the raid as he wanted? Or was it rather a state of intense excitement, pleasure, in this exercise which is his passion? What role did or could have played the stress in the process? This is the context of this communication.

We aim to highlight relations between the stress and the performance of team leaders facing an extreme situation such as polar or high mountain expeditions. We base our work on two conceptual frameworks. __________________________ Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies bear this notice and the full citation on the first page. Authors retain copyright of their work. (NDM 2011). May 31 st to June 3 rd , 2011, Orlando, FL, USA. S. M. Fiore & M. Harper-Sciarini (Eds.). Orlando, FL: University of Central Florida.

Proceedings of the 10 th International Conference on Naturalistic Decision Making

First, appraisal theory from Lazarus [START_REF] Lazarus | Toward Better Research on Stress and Coping[END_REF][START_REF] Lazarus | Emotions and Interpersonal Relationships: Toward a Person-Centered Conceptualization of Emotions and Coping[END_REF][START_REF] Lazarus | Does the Positive Psychology Movement Have Legs?[END_REF][START_REF] Lazarus | Relationnel Meaning and Discrete Emotions: Theory, methods, research[END_REF][START_REF] Lazarus | Stress, appraisal, and coping[END_REF][START_REF] Lazarus | Knowledge and appraisal in the cognition-emotion relationship[END_REF] provides us to better understand how to handle the concept of stress. Second, Naturalistic Decision Making [START_REF] Kahneman | Conditions for intuitive expertise: A failure to disagree[END_REF][START_REF] Klein | Sources of Power How People Make Decisions[END_REF] help us to deal with decision making processes followed by expert in natural settings. More precisely, we will try to answer to the following research question: what can be the impact of stress on the decision taken by an expert? This question is of managerial and academic interest. First, the goal is to provide real advices for people who could be confronted with high stakes situation. Second, we want to see how two streams of research can be mutually enriched.

Firstly, we describe what we consider as an extreme situation. Traditional management situation can be defined as follow: "when participants join together and have to accomplish in a determined period a collective action leading to a result which going to be assessed by an external person." J. Girin (1990: 142). A management situation is extreme when it presents three characteristics: time sensitivity, uncertainty and risky [START_REF] Lièvre | Les registres de la logistique des situations extrêmes : des expéditions polaires aux services d'incendie et de secours[END_REF]. Time sensitivity means that such a situation is disruptive. Uncertainty is a very well-known concept but here, we are facing a radical uncertainty because it is impossible to be ready for unforeseeable events. In this way, teams have to develop high resiliency capacities [START_REF] Weick | The collapse of sensemaking in organizations: The Mann Gulch disaster[END_REF][START_REF] Weick | Managing the unexpected : resilient performance in an age of uncertainty[END_REF]. The level of risks is high and their effects are often dramatic.

Regarding our methodology, we are performing case studies [START_REF] Yin | Case study research : design and methods[END_REF]. For the polar expedition, data was collected concurrently with the course of the expedition as part of a participating observation [START_REF] Rix-Lièvre | An innovative observatory of project of polar expeditions: the organizing's question[END_REF]. It can be classified according to two categories: 1) a researcher's on board logbook, 2) simulated recall interviews on the personal experience of each team member [START_REF] Rix-Lièvre | Towards a codification of practical knowledge[END_REF]. For the high mountain expedition, we have based our analysis on a film produced by a high specialized guide and on a long interviewdebriefing-with the team leader of this expedition [START_REF] Rix-Lièvre | Self-Confrontation Method[END_REF].

THEORETICAL FRAMEWORK

We based our work on two theoretical streams that appear to be compatible [START_REF] Hannah | A framework for examining leadership in extreme contexts[END_REF] but that are rarely used together in academic articles. The first approach focuses on the characterization of stress from appraisal on human behavior while the second explains how decision makers act in a real situation.

2.1

Appraisal and stress We base our work on the approach of Lazarus and his concept of appraisal. The concept of appraisal was explained in the Lazarus's framework cognitivemotivational-relational theory (2001). It refers to an appraisal of the significance of the environment (objects and/or events) for personal well-being. Appraising is an intuitive, instantaneous, largely unconscious process, inseparable from the aspects perceived here and now in situation, operating on tacit knowledge basis about ourselves and our environment. The perspective is clearly relational: the appraisal of the events is what directs behavior-not the events themselves. The essential point, for Lazarus, is whether or not circumstances are relevant to personal values and to the existential impact of the goals he pursues (primary appraising), and on the other he (re)acts in conformity with this appraisal (secondary appraising).

He affirms the relational nature of the two forms of appraisal: the relevance of a situation and adaptive activity in situation. The goal or project commitment determines, according to Lazarus, the extent of personal mobilization for a gain or loss: what is at stake for the person? This commitment is the main criterion of appraisal. Commitment determines, for instance, what a loss is, what importance it has, and what must be done to prevent it [START_REF] Lazarus | Knowledge and appraisal in the cognition-emotion relationship[END_REF]. This perspective is useful for clarifying the issue of the appetitive or aversive values conferred on the elements in the environment on which the action takes effect [START_REF] Coquery | Grand dictionnaire de la psychologie[END_REF](Coquery, ). (1985)):"Certain forms of contact and interactions are preferred to others, certain are sought for and even required (…), others are avoided and apparently harmful" (Nuttin, 1985,p.15). Consequently, the subject and the world do not form two autonomous pre-existing entities subsequently coming together: "the basic unit, from the beginning, is the functional network of the relations themselves (…). Outside this functional unit neither individual nor world exists" (Ibid, 103).

Our analysis suggests that: the individual and the world should be thought of in relational terms; within this relational framework permanent appraisal is at work-it is activated not by the events themselves, but depends on their significance for the individual in the light of his well-being. Appraisal must be referred to preferential relations individual has established. These relations are established with the world from which action is not separable. The action is characterized by a behavioral dynamic and direction towards certain events evaluated as favorable and away from certain others appearing as harmful.

Therefore, the stress cannot be conceived as intrinsic to a type of environment and/or activity. It is not an aggression from outside. We can define the concept of stress as a negative emotional state resulting from the appraisal process, the latter establishing the inability to cope with the situation in spite of a stake and a significant commitment. As Lazarus mentions, stress has an impact on decision processes [START_REF] Lazarus | Toward Better Research on Stress and Coping[END_REF]. However, the perception of a gap in a situation marked by a strong personal stake impulses action by orienting the commitment to the achievement of performance essential to the actor's wellbeing. The latter is driving.

2.2

Naturalistic decision making Decision making is a process containing at least two steps: problem finding and problem solving. Two main approaches to decision making can be found. The first one is focused on the entire process and tries to conceptualize this process. The decision is the result of a rational choice between alternatives although this rationality can be bounded [START_REF] Simon | Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations[END_REF]. This approach is useful to explain problem resolution and results in building guidelines that can help novice decision makers. At the end of the 80's, a team of researchers led by G. Klein decided to follow an original path to study decision maker [START_REF] Klein | Sources of Power How People Make Decisions[END_REF][START_REF] Klein | Decision Making in Action[END_REF][START_REF] Lipshitz | Introduction to the Special Issue. Naturalistic Decision Making and Organizational Decision Making: Exploring the Intersections[END_REF][START_REF] Zsambok | Naturalistic Decision Making[END_REF]. They just observed the way decision makers behave in natural settings. That is what we do with leaders facing an extreme situation such as polar or high mountain expeditions. Such situation has all the characteristics of the environment in which the NDM movement is interested in (Orasanu and Connolly, 1993). This naturalistic or observational methodology, which contrasts with experimental and quasi-experimental methodologies [START_REF] Lipshitz | There is more to seeing than meets the eyeball: The art and science of observation[END_REF], has led to a relevant result: in context, an expert decision maker facing a complex, urgent and risky situation does not choose between options to decide. His decision is the result of a recognition primed process. This new result appears to be very important to decision support, since it means that support is more effective at the very beginning of a decision process rather than at the end by proposing many options [START_REF] Lebraty | Biais cognitifs : quel statut dans la prise de décision assitée[END_REF]. Therefore, in __________________________ Proceedings of the 10 th International Conference on Naturalistic Decision Making (NDM 2011). May 31 st to June 3 rd , 2011, Orlando, FL, USA. S. M. Fiore & M. Harper-Sciarini (Eds.). Orlando, FL: University of Central Florida.

the way the individual builds his situation with regard to what matters to him, the process of appraisal may appear discriminatory in the recognition primed process.

CONCRETE CASE STUDIES

We want to display two cases which contain paradox on the subject of the report stress and performance in the field of polar expeditions and mountaineering, as framework of a research program management in extreme situations (Aubry, Lievre, Hobbs, 2010). First paradox, two individuals placed in the same context may behave differently. Second paradox, two people living the same pleasure from a situation may assess the risk differently. We think that we can use the work of Lazarus mentioned previously to give an interpretation in terms of sensitivity and to explain these paradox.

3.1

One Tent: Two approaches When the issue of the type of tent to be used on the Greenland has appeared, the team member with polar experience listed those features essential for a good tent: a four-season dome tent, with two apses1 . He had one 2-place tent and Gerard borrowed a 3-place one. The solution was not ideal, but one that everyone could accept. In Greenland, the team began to pitch their first camp. Gerard joked, "So, how does this tent go up, then!" He unfolded it while two teammates dug in a snowdrift to find a place for the tent. He called on the 4 th team member to ask for advice with the pitching. They then realized the tent was a three-season tent with two doors but only one apse. Gerard admitted he had not had the time to try putting up the borrowed tent ahead of time. With the help of a teammate, he put the tent up next to its definitive place while another went on digging in the drift, then went to the crest to find the route for the next day, while the others finished pitching camp.

For Gerard, the tent did not have the features required at the start, but it did have two entrances. The weather was fine and not very cold, so it would do. Having helped put up the tent, he allowed the others to pitch camp, dig in the drift, make a snow wall, and get water, while he climbed up the crest so as not to lose time and explore the next day's route. When interviewed about this event, he explained that he had a bad back, and for this reason could not pitch the tent or dig, so he decided to best use his time to explore and plan the route for the following day. For Dominique, putting the tent up for the first time in the expedition was important. The test had to be pitched well. Gerard had made a mistake about the tent as it only had one apse: it was a pity to let the snow into the tent-a consequence of having no second apse.. At the debriefing interview, Dominique explained this episode as an accumulation of errors: pitching the tent in a snowdrift exposed to the wind, having a tent without an apse to stop the snow from getting in, not knowing how to get organized collectively to pitch camp (i.e., not knowing who is responsible for what), etc. Thus, certain elements seemed to be requirements for Dominique: the time and energy spent digging, protecting the tent, and pitching the camp were activities that tended to avert an undesired state of things, to satisfy his wellbeing. Gerard, for his part, was preoccupied by progression. Pitching the camp was not very important for Gerard as his attention was directed towards the following day's journey and his energy was spent on going forward. The concept of appraisal is essential to understand the actions of individuals and seize what they tend towards a particular performance in terms of what matters to the individual. Even if it wasn't the good tent, Gérard felt no stress: it is not so important. For Dominique, there is something to lose: his well-being. He perceived a gap between the situation and his expectancies. He mobilized himself in order to protect the tent and well pitch the camp. We can make the hypothesis that if the weather had been worst, his actions had not been sufficient to deal with this tent problem and he would have been stressed.

3.2

One situation: Two perceptions Spring 2009, a team of alpinist tries to reach 8000m Manaslu summit in the Himalaya chain.

The guide, Joel, is highly experienced particularly of the Himalaya and develops a double ascent and progress technique. This technique aims to develop exploration rather than realizing an exploit. The idea is to live a human collective experience. On the last day, 7 remain from the beginning of this venture. They are at a high of 7500m. They fell in perfect shape and they are sure that is going to be a success. At 400m from the top, the guide decides to go back without any advance notice. He has assessed that weather situation may degenerate. During the descent, team members are totally disappointed like Luc. He was dreaming for this ascent since many years. He thought that he was so close…400m… He wants to reach the top and can't do so since the guide ordered to return: he is unable to achieve his goal and that generates stress. Luc had a lot of experiences in Europe, but none in Himalaya. In that way he can be considered as a novice. Otherwise, the guide is an expert. Thus, the assessment of a gap also depends on the expertise of the actor. Luc did not perceive the situation as dangerous. We can say that a person perceives a gap if he is in a situation he has experienced. The gap is not seen by a novice. Thus it could lead to non-adapted and can generate stress because novice does not understand the decision that has been taken.

DISCUSSION CONCLUSION

Stress results from the perception of a gap between the situation and the decision maker expectancies and capabilities. Several cases have been studied: 1) Gérard: nothing is at stake and there is no stress. But we have studied a specific situation: polar expedition or high mountains hiking. People involved participate freely to these projects and can choose their responsibilities. It could different for a mandatory job. This could be a stress factor because he/she can't achieve himself/herself in his work.

2) Dominique: what is at stake is his well-being, there is a gap between his perception and his expectancies but he can cope to the situation, deal with the problem and reduce the gap between his perception and his expectancies. Back to classical model, it could be identified to a positive stress;

3) Luc: what is important is to reach the top. He is unable to achieve it without the guide. That generates stress. This stress is even more important because he has not enough experience to perceive a gap and a danger.

To conclude, we can propose that an extreme situation is not necessarily a stressful one. However, a perception of a gap between situation and expectancies which could lead to a positive stress, is very important because it is necessary to begin an adaptation process. At least, stress is an important indicator of a lack of capacities to cope with the situation. In this way, we consider as [START_REF] Kahneman | Conditions for intuitive expertise: A failure to disagree[END_REF] that expertise is determinant.

The apses are projections of the double roof forming a sort of lock between the exterior and the interior of the tent; a lock where equipment can be stowed and protected from bad weather.

Stress and decision: The role of experience

Jean-Fabrice Lebraty


Simon Boyer
email: simon.boyer@univ-bpclermont.fr

Michel Récopé
email: michel.recope@univ-bpclermont.fr

Keywords: Perception/action coupling, head mounted video recording, naturalistic approach, intuitive judgment, rugby referee cognition

Referee decision making is an emblematic example of complex cognition. We study it as it occurs during rugby matches. Using a head-mounted video, we help the referee during an interview to articulate what makes sense. This allows proposing an alternative perspective to classic decision making theory to describe referee activity.

INTRODUCTION

Referee decision making is an emblematic example of complex cognition occurring in real-world context; this context has all the characteristics of the environment in which the NDM movement is interested in [START_REF] Kahneman | Conditions for intuitive expertise[END_REF]Orasanu & Connolly, 1993). A referee has to cope with ill-structured problems, uncertain dynamic environments, ill-defined and competing goals, shifting conditions, time pressure, high stakes, multiple players and organizational constraints. So, refereeing is a case of NDM [START_REF] Mascarenhas | A Naturalistic Approach to Training Accurate and Coherent Decision Making in Rugby Union Referees[END_REF], but it seems to be an extreme case for different reasons, some evoked by Mascarenhas et al., and others at least as much important:

(1) the referee makes decisions under intense scrutiny;

(2) referee physical demands are intensive;

(3) referee decision making occurs in an antagonistic environment -teams confront each others in order to win a match-: what is right for one team would be wrong for the other and players provide irrelevant cues such as feigning; (4) the referee has to react instantaneously: if he/she doesn't, it would be too late as play keeps running;

(5) it is difficult to identify a decision moment for two reasons: first, not all decisions are visible, second, overall referee activity is deciding;

(6) the referee is not called upon to solve a problem or to cope with a prior and external event, he/she participates in the event content to be assessed.

Although NDM provides a relevant frame in order to study referee decision making, very few studies are involved into this movement [START_REF] Mascarenhas | Physical performance and decision making in association football referees: A naturalistic study[END_REF][START_REF] Mascarenhas | A Naturalistic Approach to Training Accurate and Coherent Decision Making in Rugby Union Referees[END_REF]. Most researches focus on heuristics and biases: visual input distorted perception, influence of uniforms' color or stereotypes, reputation bias, home bias, sequential effect [START_REF] Mascarenhas | The Psychological and Performance Demands of Association Football Refereeing[END_REF][START_REF] Plessner | Sports performance judgments from social cognitive perspective[END_REF])… However, some research studies try to take into account the complexity of referee activity. [START_REF] Plessner | A multiple-cue learning approach as the basis for understanding and improving soccer referee's decision making[END_REF] highlight that refereeing studies suppose embodied cognition perspective and focus on referee's ability to make decisions by assessing multiple features of the situation. In this way, what is usually considered as bias -for example crowd noise-could be used as an additional cue. The NDM movement radicalizes this orientation: "members of NDM community have an aversion to the word bias" (Kahneman & Klein, 2009, p 525) and do not compare human judgments between algorithm outcomes. They describe expert performance: "how people actually make decisions in real-world setting" (Klein, 2008, p456). In this way, there is a shift in the perspective to study refereeing: Referees do not only apply the rules; their judgments are active decision making processings; they have to sell the resulting decision to the players; they account for the context of the game [START_REF] Mascarenhas | Physical performance and decision making in association football referees: A naturalistic study[END_REF][START_REF] Mascarenhas | The Art of Reason versus the Exactness of Science in Elite Refeering: Comments on Plessner and Betsch (2001)[END_REF][START_REF] Mascarenhas | A Naturalistic Approach to Training Accurate and Coherent Decision Making in Rugby Union Referees[END_REF][START_REF] Mascarenhas | The Psychological and Performance Demands of Association Football Refereeing[END_REF].

Although research on referee performance should consider a naturalistic environment [START_REF] Mascarenhas | The Art of Reason versus the Exactness of Science in Elite Refeering: Comments on Plessner and Betsch (2001)[END_REF], most of the investigations fail for two main reasons. Firstly, even if there isn't solely a reference to an application of the rules to a reality, the methodology is still normative: referee decision making processing is always evaluated according to judgment accuracy [START_REF] Mascarenhas | Physical performance and decision making in association football referees: A naturalistic study[END_REF]. Therefore, the research does not focus on referee decision making as it occurs, but refers to what it should be. Secondly, methodological procedures are based on decision making tasks about critical incidents in which referees have to decide if there is a foul or not and to award an appropriate sanction. These incidents are presented in brief __________________________ Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies bear this notice and the full citation on the first page. Authors retain copyright of their work. (NDM 2011). May 31 st to June 3 rd , 2011, Orlando, FL, USA. S. M. Fiore & M. Harper-Sciarini (Eds.). Orlando, FL: University of Central Florida.

Proceedings of the 10 th International Conference on Naturalistic Decision Making

video sequences (few seconds) which already circumscribe particular events. Thus, the situation which has to be judged is a priori defined in time, space and perspective. The referee's attention is already focused on an event, while on the pitch -rather than with a succession or sequence of events -he has to cope with the game's continuous play. Consequently, part of the complexity of referee cognition is perhaps to construct what has to be judged. After all, as Mascarenhas does -but for different reasons from ours- [START_REF] Mascarenhas | The Psychological and Performance Demands of Association Football Refereeing[END_REF], we can say that referee cognition in real-world context has not ever been described.

PROPOSITION TO STUDY REFEREE COGNITION IN REAL-WORLD CONTEXT

Our purpose is precisely to study rugby referee cognition as it occurs. Like Klein (2008, p456), we conduct field research "to find out how people were able to make tough decisions" in their own real-world context. Refereeing should not be considered as a cold mental process, but as a complex practice. As firefighters who "saw themselves as acting and reacting" (Klein, 1993, p 139), referees do not only judge but act on the pitch. In order to understand what a referee really does during a match, we propose a novel perspective which does not distinguish acts from judgments. This perspective highlights perception-action coupling [START_REF] Gibson | The theory of affordances In[END_REF]. What makes instantaneously sense for the actor in situation depends on certain orientations in which cognitive, affective, motor spheres are inextricably linked [START_REF] References Canguilhem | Knowledge of life[END_REF][START_REF] Récopé | The commitment of polar expedition members to a project: declared motivation or in situ mobilization[END_REF]. Therefore, action and perceptive knowing cannot be separate: acts are embodied and spontaneous meanings [START_REF] Merleau-Ponty | La structure du comportement[END_REF]. Like Klein, we consider that expert decision-making is based on tacit knowledge [START_REF] Kahneman | Conditions for intuitive expertise[END_REF]; we propose that it is as much a perceptive as an acting knowledge. In a pragmatic perspective, we have no more hypotheses on referee cognition, but start from what referee cognition and action produce. According to different propositions concerning a judge's activity [START_REF] Perelman | Ethique et Droit[END_REF][START_REF] Ricoeur | Le Juste[END_REF], we focus on judgment acts which are defined as bodily or linguistic manifestations which show to players and impose upon them what is possible and conversely what is unacceptable during a match. Therefore, our purpose is to study what and how players' activities are making sense for the referee in order to understand what and how he shows something and imposes it.

In order to study how he spontaneously constructs, shows and imposes what is possible, three main points have to be taken into account. Firstly, as what makes sense is for the most part implicit, we have to help the referee to articulate it. Although, "the power the subject has to set sights on himself" (Merleau-Ponty, 1988, p408) establishes the possibilities the actor has to explicate his experience, the actor is not spontaneously able to bring it to light. "If the subject wants to be able to produce a description he first has to presentify the lived experience […] to suspend his usual way of doing things in order that what previously only existed "in act" now appears as object" (Vermersch, 1999, p36). If any actor is capable of reflection, it is not a position that is spontaneously adopted towards his/her own action; it must be encouraged by a method. This presupposes that each referee must be assisted in rendering explicit what makes sense for him during the course of the match. Secondly, the activity of a referee is a public one. It is impossible, therefore, to ask him about what is making sense during the match: we have to wait to the end. In this way, some methodologies use video "to assist the subject to recall important mental events" (Omodei & McLennan, 1994, p1412). During an interview, video recording allows the actor to relate to a particular lived-experience and to invite him to render explicit what is making sense for him throughout. It is important because practice and its knowledge are embedded in context. Thirdly, video is usually used by referees for auto-appraisings or external evaluations. Therefore, when watching the video, most of their discourse is about justification: they watch the match as a spectator or a supervisor. In order to overcome this problem, we propose like [START_REF] Omodei | Studying complex decision making in natural settings : using a headmounted video camera to study competitive orienteering[END_REF], another kind of video recording, a perspective closest to the referee's one during the match. Using this perspective during a video-stimulated recall enables "the subject to become psychologically re-immersed in the orignal situation" (Omodei, Wearing, & McLennan, 1997, p142). In order to distinguish this kind of self-confrontation interviews, we called it subjective re situ interviews [START_REF] Rix-Lièvre | Différents modes de confrontation à des traces de sa propre activité. Entre convergences et spécificités[END_REF][START_REF] Rix | Enregistrement en perspective subjective située et entretien en re situ subjectif : une méthodologie de constitution de l'expérience[END_REF][START_REF] Rix | Towards a codification of practical knowledge[END_REF].

METHOD

We have worked with seven experienced rugby referees. The investigations took place during official matches of French "Federal 1", a semi-professional Rugby championship (third French high-level Championship).

For each investigation, (1) the match was filmed from the stands, (2) the referee was eqquipped with a head-mounted camera to record a perspective close to his own subjective one in the situation (see Figure 1); this perspective was audio and video-recorded all along the match, (3) after the match, a subjective re situ interview was realised in which the referee was asked to describe his activity, to tell the researcher what was important for him during his action. In doing this, we used the head-mounted video from the beginning of the match to foster "an experiential immersion" (Omodei, et al., 1997, p 142); there isn't any sequence which points to a particular event but the aim is to return to what was salient for the referee all along the match.

Observational data and the referee's verbalisations were then examined together in order to relate judgment act processings with both subjective and objective approaches.

FINDINGS AND DISCUSSION

These investigations have produced data enabling the researcher to understand the cognitive dimensions of referee's activity as it occurs in situ. From this material, three kinds of judgment acts were distinguished [START_REF] Rix | Typologie des actes de jugement de l'arbitre de rugby expérimenté[END_REF]: act-judgment, fact-judgment, deliberate judgment. These are three different relations between the referee and the players' actions, three manners to construct, to show, to impose what is possible and conversely what is unacceptable, and three kinds of 'things' imposed. A factjudgment instantaneously shows a precise point of context in its relation to a rule, which appears perceptually evident. "Knock-on" tells the referee; he explicates ex post during the interview that there is knock-on, it is a pity, it was a good action, but there is knock-on. Fact and rule exist at the same time for the referee during the match. An actjudgment is a judicatory moment insofar as it builds itself progressively in the referee's dynamic relation to the players' acts. What the referee imposes does not exist autonomously in the game context, but results from referee and player interaction throughout a game moment. Referee, for example, tells one player "Move back, move back, move back", the player doesn't, the referee whistles and says: "I tell you, three times". There is an offside position but it is not referred to as a fact, but to players activities flux. In these two cases, there isn't any alternative evaluation, nor mental simulation: the referee hasn't enough time to imagine the accuracy of his judgment act. These judgment acts are "intuitive judgment" (Kahneman & Klein, 2009, p519): there are spontaneous acts; what is imposed is necessary or evident for the referee. Unlike actjudgment and fact-judgment, the referee develops deliberate judgment when the game is stopped. In problematic contexts, the referee takes time to examine the events with more information. After a scrum, a little fighting begins but the referee had followed the ball; he perceives a problem and stops the play in order to ask his assistants what happens. His judgment act results, in this case, in the conscious reconstruction of a finished event. This decision making processing is close to the one describe by Pennington and Hastie: like a juror, the referee construts "a coherent story of what apparently has happened" (Lipshitz, 1993, p110).

The research assumes there is not only one recognition processing. Indeed, three kinds emerge, each corresponding to a kind of judgment act. The referee situation is constructed: -instaneously during continuing play as a precise fact which appears as a shared evidence; -throughtout player activities flux during continuing play , as a necessity according to what is possible and conversely what is unacceptable for the referee; -as a critical event whose logic is reconstructed ex post Although this research informs what is recognized by the referee, it mainly highlights the way in which the referee constructs his own situation.

Even if we distinguish different judgment acts, they have some generic characteristics. These are neither passive reactions to an environmental configuration, nor a decisiontree framework. Every judgment act is descriptive and performative: descriptive insofar as a game moment is displayed in a particular manner; performative insofar as what he decribes happens. Consequently, his description gives a direction to the game. Thus, every judgment act has several relations to game rules which is not a simple application. The referee's activity could not still be considered as passive rule application to a peculiar context, but the referee co-constructs, with players, the match's course, and the rules of the game establish this possibility.

Studying referee decision making activity in a real environment shows (1) it's impossible to conceptually dissociate foul judgment from control of the game procedures; (2) referee NDM is not just decision processing, but an interactive activity.

Therefore, to understand referee cognition activity, the research in refereeing NDM has to focus on designing dynamic descriptive concepts which include together these different dimensions, as "judgment acts" do. But we have to notice that the referee's NDM is not only characterized by judgment acts which are bodily observable displays. Indeed, as [START_REF] Helsen | Physical and perceptual-cognitive demands of top-class refereeing in association football[END_REF] highlight, numerous referee decisions are non-observable. So, in order to study referee's NDM, future research will also have to investigate the referee's non-observable judgment activity.

CONCLUSION

However, our research allows us to suggest some directions to referee training programs. Firstly, using head-mounted video recording during an ex post interview is a powerful tool of experience recall [START_REF] Omodei | Studying complex decision making in natural settings : using a headmounted video camera to study competitive orienteering[END_REF][START_REF] Omodei | Headmounted video recording: a methodology for studying naturalistic decision making[END_REF][START_REF] Omodei | Using a head-mounted video camera and two-stage replay to enhance orienteering performance[END_REF]. Most of referees who have participated to this research highlight that the re situ subjective interview arouses reflective learning. Therefore, the methodology developped could be a first stage of a coaching method. Secondly, training programs have to be worked out in order to enhance referee deliberate practice [START_REF] Mascarenhas | A Naturalistic Approach to Training Accurate and Coherent Decision Making in Rugby Union Referees[END_REF]. The most important seems to train referees to construct what has to be imposed. For example, according to his position, what makes sense for the referee is different, and the possiblity and the way to impose it, is also different. Consequently, training programs should propose to the referee not only to judge, but especially to step in the play. In this way, simulation and virtual training environments have to be conceived.

Figure 1 :

 1 Figure 1: Perspective recorded by referee head-mounted camera

ACKNOWLEDGMENTS

We acknowledge the Rugby French Federation (Fédération Française de Rugby, F.F.R.), the Firm La Poste and the Auvergne regional council (Conseil Régional d'Auvergne), for its support. We thank the referees of F.F.R for their contribution which permits this study to be conducted.