Céline Villa

Roland Bremond

Enoch Saint

PhD, R Bremond PhD C Villa

Jacques Msc

Celine Villa
email: celine.villa@ifsttar.fr

Assessment of

come

Nomenclature

I 80 : luminous intensity at 80° from the vertical (in cd) I 88 : luminous intensity at 88° from the vertical (in cd) F : luminous surface of the luminaire seen at 80° from the vertical (in m²) h' : adjusted luminaire height (luminaire height -1.5m (observer's eye height)) (in m) p : number of poles per kilometre θ : eccentricity, i.e. the angle between the line of sight and the light source (in arc minute in Sch74, in degrees in the other models) L a : adaptation luminance (in cd/m²) L b : background luminance (in cd/m²) L l : source luminance (in cd/m²) E l : vertical illuminance due to the source (in lx) E s : vertical illuminance due to the immediate surround of the source (in lx) E a : vertical ambient illuminance (in lx) E b : vertical illuminance due to the background (in lx) ω : solid angle from the observer (in sr) E baffle : vertical illuminance measured when the illuminance meter is covered with a circular baffle to remove the direct illuminance from the source (in lx) E Lantern : vertical illuminance due to the lantern (in lx) E LED : vertical illuminance due to the LED module (in lx) L Lantern : average vertical luminance of the lantern (in cd/m²) L LED : average vertical luminance of the LED module (in cd/m²) L max : maximum luminance of the source (in cd/m²) L RZ : average luminance of the road zone (in cd/m²) L DZ : average luminance of the disc zone (30° circular zone) (in cd/m²) E RZ : vertical illuminance computed from L RZ (in lx) E DZ : vertical illuminance computed from L DZ (in lx) L black : average luminance of the whole image captured when all the lanterns are switched off (in cd/m²) E black : vertical illuminance computed from L black (in lx)

1.Introduction 1.1 Context

Urban lighting is designed for all road users, including pedestrians. As far as pedestrians are concerned, the main factors influencing lighting quality are feeling of personal security, facial recognition and visibility [START_REF] Raynham | An examination of the fundamentals of road lighting for pedestrians and drivers[END_REF] . However, the performance of a lighting installation must be balanced against its costs in terms of financial cost, energy consumption, light pollution and glare. Nowadays, pedestrian comfort has become a research topic [START_REF] Kostic | Subjective impressions under LED and metal halide lighting[END_REF][START_REF] Luo | Pedestrian way lighting: user preferences and eye fixation measurements[END_REF][START_REF] Miller | Pedestrian Friendly Outdoor Lighting[END_REF][START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] , especially with the increasing use of LED luminaires. Indeed, the small size of LED chips can lead to high luminances that may produce discomfort glare [START_REF] Behar-Cohen | Light-emitting diodes (LED) for domestic lighting: Any risks for the eye?[END_REF] . Kostic et al. conducted a field experiment to compare subjective judgments on LED and metal halide lighting with respect to various criteria about the light quality (illuminance, colour) and pedestrians' experience (security, comfort) [START_REF] Kostic | Subjective impressions under LED and metal halide lighting[END_REF] . Discomfort glare was evaluated on a 5-point scale while walking along the path, looking straight ahead. Luo et al. [START_REF] Luo | Pedestrian way lighting: user preferences and eye fixation measurements[END_REF] studied pedestrian zone lighting by collecting preference judgments and eye fixations from five participants, but no glare was reported by the participants in this experiment. Miller et al. [START_REF] Miller | Pedestrian Friendly Outdoor Lighting[END_REF][START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] investigated pedestrian-friendly outdoor lighting. To avoid pedestrian glare, the authors recommended limiting the maximum luminance, and avoiding strong luminous intensity / luminance variations with the viewing angle. They advised using frosted and diffusing optics to avoid a direct view of the LEDs. In addition, they raised methodological problems for discomfort glare assessment, including the photometric description of the scene (source size, background area definition). They also highlighted the need for new investigations on pedestrian discomfort glare, especially about the influence of the luminance distribution, the number of sources and the temporal changes occurring as the pedestrian walks along the path.

There is no consensus in previous work about the effect of the number of sources on discomfort glare. Schmidt Clausen and Bindels 7 tested multiple glare sources very close to each other at low eccentricities (i.e. small angle between the line of sight of the driver and the light sources) and predicted that discomfort glare increases with the number of sources (additivity). In assessing road lighting installations, de Boer and Schreuder 8 found an increase of +0.5 on the de Boer scale when the number of visible light sources was about halved (from 11 to 6 luminaires) for a driver point of view. Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] addressed outdoor lighting independently of the participant's status (driver or pedestrian) and found no effect of a second distant source, when this source is at least 9 degrees away from the line of sight. Zhu et al. [START_REF] Zhu | The luminaire beam-shape influence on discomfort glare for led road lighting[END_REF] found no effect of the number of sources on discomfort glare either; they used a vertical panel of LEDs to simulate road lighting in the laboratory. Pedestrian studies also suggest that observers feel the discomfort glare due to one luminaire at a time [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] , and judge the lighting quality with respect to the luminaire closest to them [START_REF] Viliunas | Subjective evaluation of luminance distribution for intelligent outdoor lighting[END_REF] .

In order to quantify the quality of a lighting installation in terms of comfort, one would like to predict the discomfort glare level. For that purpose, various models [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF][START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF][START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] have been developed mostly in laboratories (i.e. with simplified and controlled visual scene photometry) to predict discomfort glare from automotive [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF] and/or outdoor lighting [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF][START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] . These models predict the discomfort glare level on the de Boer scale [START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF] from the photometric and geometric characteristics of the visual scene. These models estimate the discomfort glare experienced by a static observer, with a fixed gaze direction.

As pointed out by Miller et al. [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] , discomfort glare is somehow different for pedestrians compared to drivers. Although pedestrians and drivers share the same visual system, their visual experience (including glare) differ in some respect. Firstly, they do not perform the same visual tasks, which is known to impact visual performance [START_REF] Mayeur | Effect of task and eccentricity of the target on detection thresholds in mesopic vision: implications for road lighting[END_REF] as well as discomfort glare [START_REF] Sivak | Discomfort Glare is Task Dependent[END_REF] . Secondly, their regions of interest (in which information to perform the task is collected) are different; Driver gaze has been studied intensively in the last 20 years [START_REF] Land | Where do we look when we steer[END_REF][START_REF] Lappi | Future path and tangent point models in the visual control of locomotion in curve driving[END_REF] , while pedestrian gaze allocation still is in its infancy [START_REF] Tom | Gender differences in pedestrian rule compliance and visual search at signalized and unsignalized crossroads[END_REF] . This impacts both the source eccentricity (which in turn impacts glare) and the adaptation luminance, which is a proxy for the luminance in the area where people stare, that is, the Area of Interest (AoI). Also, a typical driver gaze is much more constrained to look towards specific AoI (tangent point, vanishing point, other road users, etc.) than a pedestrian's gaze, which is expected to increase the discomfort glare [START_REF] Bullough | Discomfort glare from headlamps: Interactions among spectrum, control of gaze and background light level[END_REF] . Another issue is that some level of overhead glare is experienced by pedestrians, not by drivers, because of the cut-off of the car roof. Finally, the speed of movement is different, and dynamic effects on glare may be different.

The models for predicting discomfort glare level have each been developed using data for a given range of variables (see Table 1). Many of these, especially the range of tested eccentricities, do not cover all the values appropriate for a pedestrian situation. In addition, these models have not been used so far for outdoor lighting from a pedestrian point of view, and therefore deserve to be assessed in such a scenario.

Discomfort glare models

Previous work on lighting design investigated the link between geometric and photometric characteristics of the illuminated scene and discomfort glare. The main photometric/geometric factors identified in the literature are the source luminance, the background or adaptation luminance [START_REF] Hickcox | Effect of different coloured luminous surrounds on LED discomfort glare perception[END_REF] , the vertical illuminance at the eye of the observer [START_REF] Bullough | Discomfort and disability glare from halogen and HID headlamp systems[END_REF] , the source eccentricity (angle between the observer's gaze direction and the source) and the solid angle of the source from the observer point of view. Based on these factors, various models have been proposed [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF][START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF][START_REF] Clear | Discomfort glare: What do actually know?[END_REF] . In outdoor lighting, most of them predict a level of discomfort glare on a subjective scale, such as the de Boer scale [START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF] . The de Boer scale has been the most widely used scale in previous outdoor lighting studies [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF][START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Zhu | The luminaire beam-shape influence on discomfort glare for led road lighting[END_REF][START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF][START_REF] Hickcox | Effect of different coloured luminous surrounds on LED discomfort glare perception[END_REF][START_REF] Bullough | Discomfort and disability glare from halogen and HID headlamp systems[END_REF][START_REF] Niedling | Influence of a glare sources spectrum on discomfort and disability glare under mesopic conditions[END_REF][START_REF] Sivak | The influence of stimulus duration on discomfort glare for persons with and without visual correction[END_REF][START_REF] Theeuwes | Relation between glare and driving performance[END_REF] and therefore was implemented in our experiment in order to compare predictions from different models to our experimental data. This is why our overview below only focuses on the models predicting a de Boer rating. The ranges of values of the variables employed in the original papers to fit each of these models are shown in Table 1. A more comprehensive review of discomfort glare models was conducted by Gibbons and Edwards [START_REF] Gibbons | A review of disability and discomfort glare research and future direction[END_REF] .

De Boer and Schreuder 8 introduced a model to determine the level of discomfort glare in road lighting installations using the de Boer scale: the Glare Control Mark (GCM) index [START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF][START_REF]Commission Internationale de l'Eclairage. Glare and Uniformity in Road Lighting Installations[END_REF] . The model was developed with data collected from participants who judged the discomfort glare from a driver's point of view moving along a 300 m lighting installation, simulated on a 1:50 scale dynamic mock-up. It accounts for the light distribution (cut-off) by means of luminous intensity levels in two directions (80° and 88° from the vertical), the luminous surface, the average road luminance, and the number of sources (height and pole spacing), see Equation 1. In this experiment, the authors found no impact of the nonuniformity of the road luminance on discomfort glare.

(1) Schmidt-Clausen and Bindels 7 introduced a model to predict the discomfort glare on the de Boer scale due to automotive lighting (the model is hereafter referred to as Sch74). It takes as input the source vertical illuminance at the observer's eye and the adaptation luminance (which is taken as the average luminance of the road surface); see Equation 2. As in the GCM model, the adaptation luminance is not easy to estimate. Moreover, as in all models with source eccentricity, glare is undefined when looking directly towards the light source (-∞ on the de Boer scale).

(2)

In order to overcome these limitations, Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] introduced an index for outdoor lighting, predicting the discomfort glare on the de Boer scale from three vertical illuminance levels at the observer's eye (the model is hereafter referred to as Bul08), when looking directly at the source. These illuminance levels are respectively associated to the observed light source (E l ), the surround (E s ), and the ambient term (E a ), (see DG in Equation 3); the total vertical illuminance E tot at the observer's eye is the sum of E l , E s and E a . To develop their model, Bullough et al. carried out a set of experiments in the laboratory and outdoor with metal halide or mercury vapour lamps in front of the observers. Later, Bullough et al. [START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF] highlighted the limits of their previous model and proposed a model extension (Bul11 in Equation 3), which includes as input the source luminance L l when the source subtends more than 0.3° of visual angle (the model is hereafter referred to as Bul11).

(3) More recently, Lin et al. [START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF] introduced a model derived from laboratory data obtained with a 3000 K LED source located 2 m ahead of the observers (the model is hereafter referred to as Lin14, see Equation 4). The model was also tested in the laboratory with a 6500 K LED source and outdoors with a 5000 K LED source. The authors found an offset in average judgments related to the correlated colour temperature, the discomfort glare being higher for higher correlated colour temperatures, but they did not introduce this factor in their model.

(4) Lin et al. [START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] proposed another model in 2015 (the model is hereafter referred to as Lin15, see Equation 5). The Lin15 model is based on the illuminance due to the source and background illuminance. Unlike Lin14, the luminance and the solid angle of the source are not needed.

Moreover, the Lin15 model was based on data collected with a larger range of background photometry (0, 10 and 200lx) than the Lin14 model (around 1-10 cd/m²), see Table 1. The main difference between these models is the value of the constant which allows for rescaling the log magnitude to the de Boer scale (3.45 in Lin14 vs 7.09 in Lin15): Lin14 predicts higher discomfort glare than Lin15.

(5)

Model implementation: State of the art

These models were mostly developed in laboratory conditions with uniform backgrounds and light sources. In heterogeneous real-world scenes, evaluating luminance values requires some choices. Previous work assessing these models [START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Sammarco | Discomfort glare comparison for various LED cap lamps[END_REF] has been done by laboratory experiments and followed the method described in the original papers. Very few studies have implemented these models outdoors [START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF][START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] .

Background luminance

When the visual scene is complex, the background luminance depends on the geometric definition of the background area and on the computational method employed to reduce a luminance distribution into a single luminance value. In previous work [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] Bommel | Road Lighting, Fundamentals, Technology and Application[END_REF] , the background luminance is often defined as the average luminance of the road surface.

However, drivers and pedestrians look at specific and different AoI. The adaptation luminance roughly reflects the luminance in these areas of interest, and thus they are expected to be different. More specifically, the AoI of pedestrians is expected to be larger, and farther away from the light sources and their gaze is expected to be less constrained [START_REF] Bullough | Discomfort glare from headlamps: Interactions among spectrum, control of gaze and background light level[END_REF] . Researches are in progress [START_REF] Luo | Pedestrian way lighting: user preferences and eye fixation measurements[END_REF][START_REF] Davoudian | What do pedestrians look at night?[END_REF] to understand the shape, size and location of each road user's adaptation area [START_REF] Cengiz | Combined eye-tracking and luminance measurements while driving on a rural road: Towards determining mesopic adaptation luminance[END_REF][START_REF] Uchida | Adaptation luminance simulation for CIE mesopic photometry system implementation[END_REF][START_REF] Maksimainen | Veiling luminance and visual adaptation field in mesopic photometry[END_REF][START_REF] Foulsham | The where, what and when of gaze allocation in the lab and the natural environment[END_REF] , and some researches focus on pedestrians, investigating pedestrians gaze patterns with eye-trackers [START_REF] Luo | Pedestrian way lighting: user preferences and eye fixation measurements[END_REF][START_REF] Cengiz | Combined eye-tracking and luminance measurements while driving on a rural road: Towards determining mesopic adaptation luminance[END_REF][START_REF] Davoudian | What do pedestrians look at night?[END_REF][START_REF] Foulsham | The where, what and when of gaze allocation in the lab and the natural environment[END_REF] . Davoudian et al. found that pedestrians spend 40-50% of the time looking at the footpaths [START_REF] Davoudian | What do pedestrians look at night?[END_REF] . Recently, Uchida et al. introduced a simulation method to compute peripheral adaptation luminance in an area of measurement (AOM) in mesopic outdoor scenes, from a static luminance distribution and an eye movement distribution [START_REF] Uchida | Adaptation luminance simulation for CIE mesopic photometry system implementation[END_REF] . The authors tested various AOM sizes on the road surface with drivers' or pedestrians' eye movement distributions, and they compared the simulation with simpler proxies, such as the average luminance in the AOM and the average luminance in the whole image. They found that the adaptation luminance could be predicted with the average luminance in the AOM, especially when eye movements are not large. For pedestrians, the footpath surface average luminance is a fair predictor of the adaptation luminance, except when many high luminance sources are in the surroundings. Cengiz et al. assumed a disc-shaped visual adaptation field, centred on the mean gaze direction [START_REF] Cengiz | Combined eye-tracking and luminance measurements while driving on a rural road: Towards determining mesopic adaptation luminance[END_REF] . They computed the average luminance in circular fields extending 1° to 20° from the line of sight of drivers. Maksimainen et al. compared average mesopic luminance values in the AOM, with various sizes and shapes (road surface, circular, elliptical). For each street illustrations employed in this work, they obtained a standard deviation of the average luminances computed in various AOM around 21% [START_REF] Maksimainen | Veiling luminance and visual adaptation field in mesopic photometry[END_REF] . To implement discomfort glare models for pedestrian applications, Kohko et al. tested averaging the luminance on the road surface and in a circular visual field (20° or 40°), "but none of them showed acceptable fitting" [START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] . Finally, they used a constant background luminance for all stimuli.

In some models [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] , the background photometry is measured by switching off the light source. However, in a pedestrian case study, urban lighting contributes to both glare and adaptation (indirect lighting). Therefore, in such a case study, the indirect component of the sources needs to be taken into account in the background term estimation.

Light source photometry

Some models use the source vertical illuminance as input. In this approach, the whole lantern defines the light source. The larger the source region, the higher the illuminance and therefore the discomfort glare.

Other models use the product of the source luminance and its solid angle as input, but they do not specify the region which should be considered and how to compute luminance and solid angle of a LED source. Indeed, LED light sources can be non-uniform compared to other common sources (e.g. High Pressure Sodium, Metal-Halide, Incandescent, Fluorescent) because they associate many very small sources (LED chips) on a LED module, fitted with optical components. The non-uniformity of LED luminaires may contribute to discomfort glare [START_REF] Behar-Cohen | Light-emitting diodes (LED) for domestic lighting: Any risks for the eye?[END_REF][START_REF] Ayama | Discomfort glare of white led sources of different spatial arrangements[END_REF][START_REF] Higashi | The development of evaluation for discomfort glare in led lighting of indoor work place: the effect of the luminance distribution of luminous parts on subjective evaluation[END_REF][START_REF] Tashiro | Discomfort glare for white LED light sources with different spatial arrangements[END_REF] . From a luminance map, a computational method has to be chosen to provide a single value as input to the models. In most previous work, the average luminance is used as the input value for the source luminance. The average may not be the most relevant way to estimate the luminance of a non-uniform source; other estimates may also be considered, such as the maximum luminance or a weighted sum [START_REF] Tashiro | Discomfort glare for white LED light sources with different spatial arrangements[END_REF] . In addition, whatever the model, the predicted discomfort glare increases with the source luminance as well as with the source solid angle. Therefore, in some cases, model predictions are sensitive to the geometric definition of the light source in an unpredictable way. For example, in urban LED lanterns, the LED module is usually surrounded by optical components (e.g. clear glass, frosted glass).

In this case, the source area may be described in at least two ways: either the whole lantern or restricted to the LED module (see Figure 3(b)). The average luminance is higher in the LED module area than in the Lantern area, whereas the solid angle of the LED module area is lower than the solid angle of the lantern area.

Implementation of Bullough's model

This model addresses the discomfort glare from each light source in the lighting installation. Bullough's model needs as inputs the direct source illuminance E l , the illuminance from the area surrounding the source E s and the ambient illuminance E a . E a is the vertical illuminance measured when the sources are switched off. E l cannot be measured directly. Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] proposed to deduce E l from the total vertical illuminance and the vertical illuminance measured when the direct component of the source is hidden from the illuminance meter. It is not possible to "cover" the light source up a 4 m high pole as proposed by Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] in a laboratory setup. This is why, Brons et al. [START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] proposed to shield the illuminance meter with a circular baffle, to remove the direct illuminance of the source E l from the measurement and deduce it by computation: E l =E tot -E baffle .

The illuminance from the area surrounding the source E s is not easy to define in a complex scene. It is defined by Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] as the remainder found when subtracting (E l + E a ) from E tot . For pedestrian applications, the same authors 31 defined the surrounding illuminance E s as the difference between the illuminance measured when the lighting installation is switched on except the tested luminaire, and the sum of the direct illuminance levels from all other luminaires (E s includes the ambient illuminance, unlike Bullough's (2008) definition [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] ).

Whatever the computational definition, we understand that the surrounding illuminance is introduced in the model to quantify the adaptation illuminance due to the indirect component of the lighting installation.

Decomposition of direct and indirect contributions from the light source

We have seen above that models based on illuminance (i.e. Sch74, Bul08, Lin15) [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF][START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] require the estimation of the direct illuminance from the light source, as well as the indirect illuminance due to light reflections in the environment. Unfortunately, measuring the vertical illuminance at the observer's eye merges these variables. The measurement can be split into two parts, for example using a baffle on the illuminance meter [START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] .

The two components of the vertical illuminance may also be computed from luminance values. Indeed, the direct illuminance due to any region of a luminance map, captured with an imaging luminance measurement device (ILMD), can be calculated from pixel luminance, solid angle and eccentricity, assuming that the gaze is at the centre of the map.

Finally, the background vertical illuminance from a given region may also be estimated from the average luminance over this region assuming the reflecting surfaces to be Lambertian. This assumption is supported by de Boer, who found no influence of the road luminance non-uniformity [START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF] and a direct correlation between the average illuminance and average luminance of a lighting installation [START_REF] De Boer | Lighting of traffic routes[END_REF] .

Objectives

A pilot outdoor study was conducted to investigate pedestrian discomfort glare in complex visual scenes (as opposed to controlled laboratory experiments with uniform background and source luminance). The objectives of this work were twofold:

1) To investigate a protocol for assessing the pedestrian discomfort glare from LED urban lighting;

2) To implement and test the relevance of previously developed models for predicting the pedestrian discomfort glare from LED urban lighting.

The second objective was limited to those models which predict a score on the de Boer scale.

Two experimental protocols were tested. The "Static" protocol involved collecting judgments under various lighting installations, from specific positions and gaze directions.

The "Dynamic" protocol involved collecting a global judgment of discomfort glare after walking under the poles. This protocol integrates temporal variations in the glare experience during the walk. Installations were judged with one or two luminaires switched on in order to study the influence of the number of sources. In order to collect robust data, some variability was introduced in the visual environment by using four different lanterns. Viewpoints and gaze directions were also varied.

Mean glare ratings were compared to various model predictions in order to evaluate their relevance for a pedestrian application. This comparison was based on the Root Mean Square Error (RMSE) and on the Spearman correlation (R²). RMSE quantifies a global error between the participants' mean ratings and the model predictions. R² quantifies the ability of the model to predict ordinal results (ranking).

The remainder of the paper is organized as follows. Section 2 is dedicated to the material and methods of our experiment and to the implementation issues of the various models. Section 3 presents the psychovisual results. Section 4 presents the evaluation of each predictive model for a pedestrian application. Findings are discussed in Section 5 while conclusions and future work are presented in Section 6.

Material and methods

A psychovisual experiment was carried out on a test track in Les Andelys, France (see Figure 1) in order to collect discomfort glare ratings (on the de Boer scale) under different LED urban lighting installations. The street section was approximately 100 m long and 5.5 m wide.

The road surface reflection properties was classified according to the CIE standards [START_REF]Commission Internationale de l'Eclairage. Road Surfaces and Lighting[END_REF] : the road surface was class R3 (with a lightness of Q 0 =0.07) [START_REF]Commission Internationale de l'Eclairage. Road Surfaces and Lighting[END_REF] and W3 (Q 0 =0.02) for a wet road. The main photometric and geometric characteristics of the lighting installations are provided in Table 2. The spacing between the poles was 13.3 m and the height of the luminaires was 4 m, which is consistent with the European standard NF-EN13201 43 (type S2) (according to DIALUX a computations). Urban lighting poles are usually 3 to 8 m in height, and the spacing is defined in order to ensure an average illuminance of between 10 and 15 lx and a uniformity level U 0 (i.e. Minimum/Average) higher than 0.4 on the road. Four lanterns were tested (A, B, C and D in the following). The correlated colour temperature was 4000 K and the CRI Ra = 70 for all lanterns. The luminous flux was chosen so as to ensure similar average horizontal illuminance under each installation.

Description of the urban lighting installations

Panel

Thirty-three participants were involved in this study (14 men, 19 women), with ages between 21 and 60 years (M=42.2, SD=13.7). Their vision was tested with an ErgoVision device (Essilor) prior to the experiments to check binocular visual acuity in photopic and mesopic conditions, contrast sensitivity and time of recovery after glare. Table 3 provides the characteristics of the panel. Participants read and signed an informed consent form; they received a financial compensation after the experiment.

Experimental setting and protocol

Static protocol

In order to investigate urban lighting, the experiment was based on common use conditions, rather than on a factorial plan with photometric/geometric variables (e.g. a https://www.dial.de/en/dialux/ eccentricity, luminance, etc). Participants were asked to rate the discomfort glare on the de Boer scale [START_REF] De Boer | Glare as a criterion for quality in street lighting[END_REF] from four positions illustrated in Figure 1: 8.5 m (circle), 6.5 m (square), 4.5 m (triangle) and 2.5 m (star) ahead of the first pole (the closest to the observers). The de Boer scale as follows was translated into French:

 1 Unbearable (Insupportable)  2  3 Disturbing (Dérangeant)  4  5 Just admissible (Supportable)  6  7 Satisfactory (Acceptable)  8  9 Unnoticeable (Négligeable)
They were asked to look at one of two targets (see Figure 1). The first target was straight ahead 14 m away from the first luminaire (Lum1 in Figure 1); the second target was also 14 m away from Lum1 but 10° to the left (one for each of the four positions).

In order to study the impact of the number of luminaires on discomfort glare, each lantern was judged with one (1S) or two luminaires (2S) switched on. In condition 1S, the luminaire closest to the observer (Lum1) was switched on; in the condition 2S, both luminaires were switched on. Sixty-four ratings (4 lanterns x 4 positions x 2 gaze directions x 2 numbers of luminaires) were collected in the Static protocol for each participant.

Dynamic protocol

In the dynamic, more realistic condition, participants were asked to walk from the first static position (8.5 m from Lum1) to the target ahead, in front of them (target 0° in Figure 1), looking continuously at this target. The gaze direction was thus parallel to the road axis. Then, they were asked to rate on the de Boer scale the global discomfort glare they felt during the walk. Each participant made eight such ratings (4 lanterns*2 numbers of luminaires).

Experimental design, procedure and statistical analysis

In the "Static" protocol, the four experimental factors are the lantern (A, B, C or D), the viewpoint (8.5 m, 6.5 m, 4.5 m or 2.5 m from Lum1), the gaze direction (0°, 10° from the street axis) and the number of luminaires (one or two). In the "Dynamic" protocol, the two experimental factors are the lantern and the number of luminaires.

Participants came two by two. Each participant was handed a booklet where the individual order of the experimental conditions was specified. Lanterns and conditions 1S/2S were presented in a balanced random order. For each lantern, the order of the Static and the Dynamic tasks was reversed between condition 1S and 2S for each participant. For the Static Protocol, based on a balanced random experimental plan, positions and directions were presented in a different order to each participant. The experimental sessions lasted about 1 hour. A short practice was carried out at the start of the session to familiarize the participants with the experimental protocol and the de Boer scale.

For data analysis, repeated measures ANOVAs [START_REF] Howell | Statistical Methods for Psychology[END_REF] were performed (normality was satisfied according to Kolmogorov-Smirnoff and Jarque-Béra tests). The Mauchly test was employed to test the sphericity [START_REF] Mauchly | Significance test for sphericity of a normal n-variate distribution[END_REF] . The Greenhouse-Geisser correction was employed when the sphericity was not satisfied. The significance threshold was set to p = 0.05.

Photometric description of the visual stimuli

This section describes the photometric measurements needed to describe the stimuli and implement the glare models. Table 4 summarizes the photometric and geometric characteristics of each stimulus. All measurements and calculations were made considering an observer with eye height at 1.50m.

Vertical illuminance

For each stimulus, the vertical illuminance was measured at 1.50 m height with a LMT B520 illuminance meter aimed towards the respective target, and is reported in Table 4. In addition, Figure 2 shows the profile of vertical illuminance along the walk for the four lanterns A -D when only Lum1 is switched on. Based on previous work (see Section 1.3.1), we have considered two ways of computing the background luminance from luminance maps (see Figure 3(a)). The first method uses the average luminance in the Road Zone (L RZ ); the second one uses the mean luminance in a Disc Zone 30° in diameter (L DZ ) centred at the target which the observers were looking at (see Figure 3(a)). Thirty degree corresponds to the central visual field as defined by Bardy et al. [START_REF] Bardy | The role of central and peripheral vision in postural control during walking[END_REF] when studying central and peripheral vision in postural control while walking.

A Konica Minolta CA2000A imaging photometer with a wide lens (8 mm, 1:1.4, FOV:46°x46°, 980x980) captured luminance maps of the scenes (see Figure 3(a)). The average background luminance was extracted from these maps, using either L RZ or L DZ .

Background illuminance values E RZ and E DZ were computed from L RZ and L DZ respectively, assuming the road and the targets were Lambertian surfaces (see Section 1.3.4).

A luminance map was also captured with all the luminaires switched off to characterize an average ambient luminance L black . The illuminance E black was deduced from this map (E black =πL black ).

Source luminance and illuminance

The source luminance was measured with a calibrated Canon EOS 70D camera (Sigma 4.5mm, 1:2.8; FOV: 180°, 3648x2432) with fish-eye lens, connected to the Photolux software. This device makes it possible to capture a 180° luminance map of the visual scene.

Source areas were manually selected to compute the solid angle and mean luminance of each source. Two methods were considered for selecting the source areas: the selection encompassed either the LED module alone (L LED in the following) or the whole lantern (L Lantern in the following), see Figure 3(b).

The illuminance due to any area in the luminance map can be computed from the luminance, solid angle and eccentricity from the centre of the image (which corresponds to the gaze direction) of the pixels in the area. Vertical illuminance due to the source was thus computed, leading to two illuminance values, respectively E LED and E Lantern .

Psychovisual results

Preliminary analyses

A cluster analysis was first carried out to look for potential groups of observers who share an opinion which differs from that of other groups, as well as potential outliers. Neither was found with hierarchical ascendant clustering (conducted with the percent disagreement distance and average linkage). Therefore, all data were considered in further statistical analyses.

Because of weather conditions at the time of the experiment, the road surface was wet for 20 participants and dry for 13 participants. A preliminary analysis was conducted to check if road surface condition had an effect on discomfort glare, in which case the data would

Static protocol

Discomfort glare ratings were collected for each type of lantern, with one or two luminaires switched on, from participants in four different positions with two gaze directions.

A repeated measures ANOVA was run on the data (after Greenhouse-Geisser correction [START_REF] Howell | Statistical Methods for Psychology[END_REF] ). Table 5 shows the mean and standard deviation values for each factor. The higher the rating, the lower the discomfort glare. Post-hoc Tukey tests [START_REF] Howell | Statistical Methods for Psychology[END_REF] were conducted in order to compare the lantern performance and showed no significant difference between Lanterns A and B, which produced significantly less glare than lantern D, which in turn produced significantly less glare than Lantern C. Lanterns A and B, with opalescent and frosted glass, produced significantly less glare than the two others, with an "acceptable" average rating across positions (see Table 5). Discomfort under Lantern D was judged on average "acceptable" 8.5 m from Lum1, but "just admissible" nearer (4-6 m). Finally, Lantern C which produces the highest luminance (see Table 4) was the most glaring.

According to the post-hoc Tukey tests, participants felt less comfortable when looking along the road than when looking away from the luminaires. More discomfort was experienced at 6.5 m and 4.5 m from Lum1 than at 8.5 m or 2.5 m. In addition, lighting installations were rated as significantly less disturbing when two luminaires were switched on. The situations with the most glare were at 6.5 m and 4.5 m from Lum1 looking straight ahead, with a single luminaire (M=5.95 [1S, 6.5 m, 0°]; M=5.92[1S, 4.5 m, 0°]).

Dynamic protocol

A repeated measures ANOVA (after Greenhouse-Geisser correction) and post hoc

Tukey tests were conducted. An effect of the Lantern was found (F(2.51,80.21) = 12.07, p < 0.0001, η² = 0.274). There was no effect of the number of luminaires (F(1,32) = 1.30, p = 0.2633), however, an interaction was found (F(2.60,83.34) = 3.97, p = 0.0103<0.05, η²=0.110).

According to the post-hoc Tukey tests, there is no significant difference between Lanterns A and B. Lantern A produces significantly less glare than Lanterns C and D.

Lanterns B and D produce significantly less glare than Lantern C. The effect of the Lantern is consistent with the results from the static protocol (see Section 3.2). However, as shown in Table 5, the de Boer rating after a walk is higher (+0.4 in average), suggesting that pedestrians feel less discomfort after walking than when standing in front of a static scene.

The same levels of discomfort glare were found whatever the number of luminaires, except for the lantern C, which produced more glare with two luminaires.

Photometry and discomfort glare

The vertical illuminance at the eye-height is negatively correlated to the mean ratings on the de Boer scale (R² = 0.711). The correlation is even stronger when the data is restricted to conditions 1S (R² = 0.776) or 2S (R² = 0.796). Direct vertical illuminance from the source, computed from the whole lantern, is also correlated with glare (condition 1S: R² = 0.717).

Various luminance indices can be computed to describe non-uniform sources: mean luminance values L LED and L Lantern (see Section 2.5.3 and Figure 3) as well as maximum luminance L max (this index does not depend on the measurement area). Correlations between these luminance indices and the mean glare ratings have been computed: in Condition 1S, the correlation is stronger with L LED (R² = 0.741) than with L Lantern (R² = 0.457); the strongest correlation is found with L max (R² = 0.771).

We also investigated the influence of photometric variations during the walk in the dynamic protocol. The differences ΔE between the maximum and minimum illuminances, as well as the mean illuminance along the path (up to the first pole in condition 1S, up to the second pole in condition 2S) were computed. Because the source luminance was only available at the four positions of the static protocol, ΔL and the mean luminance were estimated from those four values. Mean ratings in the dynamic protocol were negatively correlated to ΔL max (1S: R² = 0.584) and to ΔL LED (1S: R² = 0.512) and more weakly to ΔL Lantern (1S: R² = 0.359) and to ΔE (R² = 0.427). The mean of the vertical illuminance E tot (R² = 0.773, 1S: R² = 0.900, 2S: R² = 0.976), the mean of L LED (R² = 0.549), the mean of the maximum illuminance (R² = 0.677, 1S: R² = 0.876, 2S: R² = 0.946) and the mean of the maximum luminance (R² = 0.612) on the pathway, were all negatively correlated with the mean global ratings collected from the dynamic protocol. The strongest correlation was found with the mean of the vertical illuminance.

Comparisons of discomfort glare models

This section explores the relevance of the models developed in previous work to predict glare ratings on the de Boer scale, for pedestrian applications. It also investigates the sensitivity of these models when implemented in complex scenes (heterogeneous light source and heterogeneous background). Predictions from the models presented in Section 1.2 (Sch74, Lin14, Lin15, Bul11) are compared to mean ratings obtained from our psychovisual experiment in the static protocol (considered as the reference).

Model implementation

The four models have been evaluated with several variations in their input parameters.

The background was taken as the road zone or as a 30° circular visual field (see Section 2.5.2). Lin14 predictions were computed with the source taken as the whole lantern or as the LED Module inside the lantern. When the source vertical illuminance was needed (Sch74, Lin15, Bul11), it was computed from the whole lantern area.

In Bullough's models [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF][START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] , the ambient illuminance E a is the vertical illuminance when all the luminaires are switched off (E a =E black in Table 4). Our understanding is that the surrounding illuminance E s quantifies the indirect illuminance due to the lighting installation.

For implementation, E s was either computed following the subtracting method described in the original paper [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] (E s =E tot -(E l +E a )), or defined as E RZ or E DZ , computed from the background luminance maps. Because the angular size of the nearest light source was always found higher than 0.3°, whatever the lantern, the source luminance was taken into account in model Bul11 [START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF] (Equation 3). According to preliminary tests, Bul11 performs better when L s is set to L Lantern than L max , and that's why L s is set to L Lantern in the following.

Lin et al. [START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF] proposed to correct their model predictions by offset based on the correlated colour temperature of the source (but the model formulation does not take this variable into account, see Equation 4). An offset of -1.5 could apply with 4000K LEDs.

However, with such an offset, the predictions were outside the de Boer scale range, and that's why we did not take it into account.

Relevance of the glare models for pedestrian applications

Predictions from the glare models are compared with the experimental data collected under a single luminaire in Section 4.2.1. The sensitivity of the results to the model implementation is discussed in Section 4.2.2. Finally, the number of sources is considered in Section 4.2.3.

Relevance with a single source

The GCM model cannot be implemented in our experiment because the luminous intensity at 88° of the lanterns tested in the study is nil. I 88 was deduced from road lighting, with higher poles than in urban lighting, for the point of view of the drivers. 88° corresponds to a viewing distance of 115m from a 4m-height luminaire, which is far beyond where pedestrians look [START_REF] Foulsham | The where, what and when of gaze allocation in the lab and the natural environment[END_REF][START_REF] Fotios | Using eye-tracking to identify pedestrians' critical visual tasks, Part 1. Dual task approach[END_REF] . Therefore, this model seems not to be relevant for pedestrian lighting.

L DZ L RZ L DZ , L LED L DZ , L Lantern L RZ , L LED L RZ , L Lantern E DZ E RZ E s =E tot -E l -E a E s =E DZ E s =E RZ
Lin15 is the only model to overestimate the de Boer score. It is also the best one in terms of RMSE, with a RMSE as low as 0.60 when the background illuminance is computed from the disc zone (Table 6).

Bul11 underestimates the glare ratings, but the model performs quite well, with a RMSE of [1.1-1.3]. The lowest RMSE is obtained when E s is taken as the mean illuminance in the road zone.

As illustrated in Figure 4(a), predictions from Sch74 strongly overestimate the discomfort glare (i.e. underestimate the rating) with RMSE > 4, on a scale range of 1 to 9.

This model was developed for automotive lighting applications and was based on experimental data were the source eccentricity was small (between 0.16° and 1.5°), which is far from the range considered in our study (9° to 62°). Also, the illuminances were between 10 -3 and 10 1 lx in Schmidt-Clausen and Bindels' experiment [START_REF] Schmidt-Clausen | Assessment of discomfort glare in motor vehicle lighting[END_REF] . Therefore, the illuminances experienced by the pedestrians were from one to three orders of magnitude higher than those which fitted the Sch74 model. Our results suggest that Sch74 model shouldn't be generalized outside the photometric range of the original model. While the absolute level is much underestimated, Sch74 predictions are more relevant for ranking (see Table 6, R² = 0.75).

Similarly, Lin14 predictions strongly underestimate the ratings (see Figure 4(b), RMSE > 3.75). Again, it may be due to the fact that the background luminance is outside the range of the data used for model fitting (see Table 1). Moreover, correlations are low with this model (down to R² = 0.385).

As shown in Figure 4, for the most uncomfortable stimuli, the mean ratings vary between 4 and 6 on the de Boer scale whereas the predictions, whatever the model, are nearly constant. This is discussed in Section 5.

Sensitivity of model predictions to the implementation choices

Whatever the model (Sch74, Lin14, Lin15 or Bul11), the predictions are always higher in the de Boer scale with the RZ background than with the DZ background (+0.2/0.3), because L RZ > L DZ. Therefore, the RMSE is lower with L RZ (or E RZ ) for models which underestimate the de Boer ratings, and higher for Lin15 which overestimates the ratings. The RMSE between model predictions computed with RZ and DZ backgrounds was calculated and leads to errors of less than the 0.3 level on the de Boer scale (Sch74: 0.18, Lin14: 0.30, Lin15: 0.30, Bul11: 0.18).

Lin14 makes different predictions depending on the source definition (photometry and geometry). This impacts both the source luminance (L LED > L Lantern ) and the source solid angle (W LED < W Lantern ) but in opposite ways, so that the result is not predictable. When comparing the Lin14 predictions computed with L LED and L Lantern , the RMSE is 0.21 on the de Boer scale.

Considering all these implementation issues and Figure 4, it is clear that the glare predictions are more dependent on the models than on their implementation.

Relevance of the glare models for two sources

The Sch74 model is the only one which provides a way to compute discomfort glare with several sources in the visual field. There is no consensus in previous work about the effect of multiple sources on discomfort glare (see Section 1.1). Moreover, published models do not address the number of sources in the same way. De Boer and Schreuder 8 found an improvement of +0.5 on the de Boer scale when the number of visible light sources is halved, which account for the number of luminaires per km in the GCM model. Schmidt-Clausen and Bindels [START_REF] Behar-Cohen | Light-emitting diodes (LED) for domestic lighting: Any risks for the eye?[END_REF] , who developed an automotive lighting model with up to five sources at low eccentricity, assume additivity in the logarithm (see Equation 6): each source illuminance and eccentricity is considered separately with the same background. Additivity is also assumed in discomfort glare models for indoor lighting, such as UGR and DGI [START_REF] Clear | Discomfort glare: What do actually know?[END_REF] . For outdoor lighting, the Bullough et al.'s model predicts the discomfort glare from one source. The authors also show that a second source doesn't impact the glare if it is at least 9° away from the line of sight; it only impacts the surrounding illuminance. Lin et al. [START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF][START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] did not address the multisource issue at all.

In the following, we have considered two computational methods to estimate the discomfort glare ratings in the presence of two glare sources:

 Additive method: the discomfort glare from the two sources Lum1 and Lum2 is taken into account, with the background of condition 2S. As proposed by Schmidt Clausen and Bindels 7 , the contributions of both sources were added. To that purpose, we have adapted Bul08 b , Lin14 and Lin15 as presented in Equation 6. These formulas can easily be generalized to N sources. The predictions of the additive method and of the simplified method were compared. The difference always ranges between -0.1 and 0 (from -0.085 to -0.015 for Sch74, from -0.02 to -0.003 for Bul08, from -0.006 to 0 for Lin15, and from -0.002 to 0 for Lin14). Thus, the contribution of Lum2 as a glare source in our experimental setting is negligible: the second luminaire is "far enough away" [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] . The contribution of Lum2 is to increase the adaptation level and therefore to decrease the discomfort glare. Such findings agree with Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] for urban lighting. Equation 6 allows quantifying the cumulative effect of additional glare source with the models, to see whether the additional sources have a significant effect on glare or if they are "far enough away" to be neglected.

Taking into account Lum1 alone as a glare source while increasing the background luminance due to Lum2 results in higher glare rating predictions, which is consistent with the experimental findings (see Section 3.2). The RMSE and R² between model predictions and mean glare ratings were also computed, see Table 7. They have the same order of magnitude as those obtained in condition 1S (Table 6), and thus the models have similar performances with one and two poles.

Discussion

Findings on pedestrian discomfort glare

A psychovisual experiment was conducted to collect judgements on pedestrian discomfort glare under various urban lighting installations in static and dynamic conditions.

Lanterns with opalescent (Lantern A) and frosted glass (Lantern B) optics obtained the highest scores (i.e. produced the less glare) in our experiment. Moreover, with only one luminaire switched on, the vertical illuminance (R² = 0.776) and the maximum source luminance (R² = 0.771) were the photometric characteristics which showed the strongest correlation with the subjective data in the static protocol. Together, these results confirm previous findings [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF][START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] which recommend frosted or opalescent optics for LED luminaires to limit maximum luminance and thereby reduce pedestrian discomfort glare.

Discomfort glare was rated as lower when assessed globally after a walk, compared to static ratings. In this case, the strongest correlation of the global ratings is obtained with the mean vertical illuminance along the path (R² = 0.773; 1S:R² = 0.900; 2S:R² = 0.980). A possible interpretation would be that the discomfort glare reported after a walk is based on an average feeling.

In urban lighting, a second luminaire may produce glare, but also contributes to an increase of the adaptation level. With the static protocol, we found that glare was significantly lower with two luminaires than with a single luminaire. With the dynamic protocol, however, we found that global ratings did not significantly differ between one or two luminaires; the second part of the walk may have affected the overall judgment more than the first part. In terms of visual adaptation, the second part of the walk with two luminaires was close to condition 1S in the static protocol. The second luminaire was found to impact the background, but did not contribute much to the direct glare. This result is consistent with Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] and with previous pedestrian studies [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF][START_REF] Viliunas | Subjective evaluation of luminance distribution for intelligent outdoor lighting[END_REF] , which found that pedestrians feel the glare from one luminaire at a time [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] , the closest one [START_REF] Viliunas | Subjective evaluation of luminance distribution for intelligent outdoor lighting[END_REF] . However, de Boer and Schreuder 8 found less discomfort glare when halving the number of luminaires, so that further investigations are needed with a larger number of light sources.

As a conclusion about the protocol, the assessment of discomfort glare due to urban lighting with a static protocol (which is usually employed) and one luminaire tends to overestimate the discomfort glare for a pedestrian walking in the street. It is some kind of a "worst case" as far as discomfort glare is concerned.

Predictions of pedestrian discomfort glare

Performance of the models

Existing discomfort glare models have been investigated, and their predictions were compared with mean ratings considered as a reference. The main goal was to check whether these models could be applied in a real-world situation. Three models were found to overestimate the discomfort from glare, while the Lin15 model underestimates it. With RMSE higher than 3.7 on a scale with 9 levels, Sch74 and Lin14 models are not able to predict the mean glare ratings of our experiment, which suggests that these models should not be generalized too far away from their original data range. The illuminances employed to fit the Sch74 7 model were between 10 -3 and 10 -1 lx, much lower than the levels expected in pedestrian lighting; the background luminance of the case study is one order of magnitude lower than the range employed to develop the model Lin14 [START_REF] Lin | Model predicting discomfort glare caused by LED road lights[END_REF] . Bul11 and Lin15 perform better with RMSEs lower than 1.4 and 0.9, respectively, and could be reasonably employed to predict pedestrian glare ratings. Thus, the two models based on illuminance only performed better than the two others. This is consistent with the strong correlation between the mean ratings and the mean vertical illuminance (R² = 0.711).

In his review of Bullough et al's paper 9 , Boyce highlights that the Bul11 model is restricted to zero eccentricity, and suggests that the relevance of such a model for street lighting applications, where drivers/pedestrians do not usually look straight at the sources, remains unknown. On the other hand, Bullough et al [START_REF] Bullough | Discomfort glare from headlamps: Interactions among spectrum, control of gaze and background light level[END_REF] found that discomfort glare assessments collected in a fixed gaze experiment were highly correlated with those collected in a free gaze experiment. The low RMSE (less than 1.4) found on the de Boer scale suggests that Bul11 could be generalized to other eccentricities.

However, none of the models succeeded in predicting the discomfort glare variations among those conditions which produced the strongest glare. As these conditions (Lantern C: from 8.5m to 4.5m; Lantern D: from 6.5m to 2.5m) also provided the highest source luminance values (see Table 4), the poor performance may result from the underestimation of the source luminance due to measurement limitations. Therefore, efforts should be made to improve the measurement of high luminances and contrast before criticizing the models.

Direct and indirect lighting

Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] made a distinction between surrounding illuminance and ambient illuminance, which are both indirect as opposed to direct illuminance from a glare source. The amount of light at the observer's eye can be split into two components: the direct one is due to the light sources and the indirect one to reflections on the surfaces in the scene. Glare happens when the direct component is much higher than the indirect component. We have investigated the same model formulation (Equation 3) with only two terms: the direct component E direct =E l , and the indirect component E indirect =E s =E a defined as the illuminance of the background when the luminaires are switched on, which is supposed to describe the background adaptation level (Dir/Ind in the following). Table 8 shows the RMSE and Spearman correlations of those predictions and the mean glare ratings. This model performs slightly better than Bull11 (see Tables 5 and6) although the Spearman correlation R² is lower.

Implementation of the models

The models using the source luminance as input require arbitrary assumptions about the spatial definition of the sources, which is a current issue for LED lighting because of their strong non-uniformity [START_REF] Ayama | Discomfort glare of white led sources of different spatial arrangements[END_REF][START_REF] Higashi | The development of evaluation for discomfort glare in led lighting of indoor work place: the effect of the luminance distribution of luminous parts on subjective evaluation[END_REF][START_REF] Tashiro | Discomfort glare for white LED light sources with different spatial arrangements[END_REF][START_REF] Kasahara | Discomfort glare caused by white LED light sources[END_REF] . We have considered average luminance over the whole lantern and over the LED module only, which led to a small difference (RMSE = 0.21 on de Boer scale) with Lin14 predictions. But for pedestrian applications, according to Section 3.4 and previous work [START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF][START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] , one of the best correlated photometric descriptions of the source is the maximum luminance. One may wonder whether the average luminance is the most suitable variable to characterize discomfort glare from of a non-uniform luminaire. Kohko et al. [START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] compute an "efficient luminance", first proposed by Tashiro et al. [START_REF] Tashiro | Discomfort glare for white LED light sources with different spatial arrangements[END_REF] , which is a weighted sum of the spatial distribution of the source luminance, and to use it as input for the source luminance in the relevant glare models. Future work is needed in order to investigate the relevance of this index for glare prediction.

Two background zones were tested in the models' implementation. The RMSEs between model predictions obtained with either method were lower than 0.30 on the ninepoint de Boer scale. Therefore, the adaptation zone does not need to be precisely defined if the luminances have the same order of magnitude over the whole background. However, our road zone was large compared to the one tested in other work [START_REF] Uchida | Adaptation luminance simulation for CIE mesopic photometry system implementation[END_REF] and the influence of the adaptation region definition deserves a complete paper itself, as seen in Section 1.3.1, especially as the region definition is difficult because of the free pedestrian gaze [START_REF] Foulsham | The where, what and when of gaze allocation in the lab and the natural environment[END_REF] .

In the design stage, surrounding light elements and surfaces are generally not known and hypotheses are required (e.g. about the material, pavement etc). Glare models can be employed in a worst-case design based on road surface luminance or illuminances recommended by the standard. However, in urban areas, additional ambient lighting provided by billboards and shop windows may increase the background luminance (they may also be additional glare sources) and therefore impact the discomfort glare level predicted in the design stage.

The models based on illuminance perform better and seem easier to implement. But in urban lighting applications, both the source (direct illuminance) and the adaptation (indirect illuminance) terms need to be measured when the source is switched on. From a practical point of view, it is difficult to split the illuminance into a source component and an ambient component. This is, however, possible with complementary luminance measurements, or the use of a baffle at the illuminance meter [START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] .

Measurement issues

As highlighted above, one of the main issues in using discomfort glare models is related to measurement limitations. Whatever the measurement method, some bias appears.

An ILMD may be employed (as was done in this paper) to generate luminance maps and compute the average luminance over various regions (adaptation regions, light sources) as well as direct and indirect illuminances. But, the main problem with ILMDs is the underestimation of the maximum luminance. This limit may explain why, in our data, the model's predictions were nearly constant for those stimuli with the highest glare level. We agree with Slominski 49 that it is "very difficult if not impossible" with current ILMD devices to "precisely define the maximum luminance measured from a long distance (20-90m)".

Measurement errors increase with the distance because the LED chip is included in too few photosensors, even sub-pixel; thus, the pixel luminance averages the luminance of the LED chip and of its surroundings. Measurements also depend on the lens, sensor size and number of pixels. Slominski [START_REF] Slominski | Identifying problems with luminaire luminance measurements for discomfort glare analysis[END_REF] recommends "increasing the focal length value or decreasing the physical size of the area recorded by a single pixel". According to him, "the best solution is to design an HDR device with lens whose field of view of a single pixel of the B/W structure is precisely connected to the resolution of the human eye". A luminance meter may have a wider luminance range, but the measurement process faces the same problems for choosing the relevant measurement area; moreover, the viewfinder towards the source is manually set and the angular aperture needs to be adjusted depending on the distance to the source. Therefore, the measurement region is not fully controlled. On the other hand, illuminance measurement does not meet these problems. However, it is difficult to split the illuminance into a source component and an ambient component. Bullough et al. [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF] and Brons et al. [START_REF] Brons | Outdoor site-lighting performance: a comprehensive and quantitative framework for assessing light pollution[END_REF] proposed using a baffle in the illuminance meter to hide the source from the sensor. With such a trick, it seems difficult however to collect reproducible data.

One may speculate that computations based on the background luminance and the overall illuminance may lead to the lowest measurement uncertainty: it would first need to measure the overall illuminance, then to capture a luminance map with an ILMD. The background photometry would then be computed from the luminance map (luminance and then illuminance, based on a Lambertian reflection hypothesis). Finally, the source-related illuminance (and the source luminance) would be computed by subtracting the background illuminance from the overall illuminance. However, this is very speculative and would deserve a complete study.

Conclusions on our model investigations

Even though our results depend on the measurement and calculation choices and uncertainties, our findings do not. Two of the tested models (Bul11 and Lin15) give fair results to predict the discomfort glare on the de Boer scale in urban pedestrian settings. A simplified model based on Bul11 also leads to good results (Dir/Ind). The main issue to predict pedestrian discomfort glare is the choice of the model; predictions are not very sensitive to implementation choices.

Limits and future work

Our experiment was designed in an outdoor but controlled luminous environment, which would obviously be different in real-world situations (because of vehicles' headlamps, shop windows, etc.). Pilot studies would be needed to investigate the potential bias between glare ratings in controlled and field environments. Our "walking condition" is a step in this direction.

According to Miller et al. [START_REF] Miller | Pedestrian Friendly Outdoor Lighting[END_REF][START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF] , the pedestrian could feel "overhead glare" [START_REF] Boyce | Overhead glare and visual discomfort[END_REF] , i.e.

discomfort glare under the luminaires. Eccentricities above 62° were not assessed in this work in the static protocol and it would be interesting in future work to quantify this overhead glare and study if the glare models are able to take it into account.

This paper focused on discomfort glare models using the de Boer scale, but other models could be tested, either developed for outdoor [START_REF] Bennett | Characterizing discomfort glare from roadway lighting[END_REF] or indoor [START_REF] Clear | Discomfort glare: What do actually know?[END_REF][START_REF] Luckiesh | Brightnesses in visual field at borderline between comfort and discomfort (BCD)[END_REF] applications. Especially, Kohko et al. [START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] investigated the pedestrian glare under seven light sources focusing on the luminance uniformity issue. They compared the subjective data collected on the de Boer scale with indoor glare models (e.g. DGI, UGR) and recommended to use the mDGI index (DGI index where the source luminance is replaced by the efficient luminance) for both uniform and non-uniform light sources.

Finally, the dynamic protocol was a first step to include temporal variations in discomfort glare assessment. All current models were fitted to ratings in static experimental conditions. In future work, we plan to test static models in scenarios where temporal changes occur, due to body and gaze motion. underestimation of the source luminance) may impact the accuracy of the models, especially for high glare levels (i.e. low ratings). Such limitations deserve to be investigated in future work to ensure an accurate implementation of discomfort glare models in urban environments. In addition, current models do not take into account the temporal changes in the pedestrian's glare experience. Therefore, in future work, we plan to investigate the glare rating during a walk. Table 1. Range of values for variables used for modelling discomfort glare in previous work 7- 9,12-14 . The last column shows the experimental data used in this paper.

General conclusion

Figure 1 .

 1 Figure 1. Experimental setup with both luminaires switched on (left) and illustration of the

Figure 2 .

 2 Figure 2. Vertical illuminance along the walk in condition 1S, for lanterns A, B, C and D.

Figure 3 .

 3 Figure 3. (a) Areas for the background luminance estimation. DZ (Disc Zone): Disc 30° in diameter. RZ (Road Zone), rectangle including the road surface and the targets. (b) Areas for the source luminance estimation: LED Module area and Lantern area.

  possibly be split according to the road surface condition. Repeated measures ANOVA was run on the data from each protocol (Static or Dynamic), with the "Stimulus" as an intrasubject factor (64 modalities in the Static protocol, 8 modalities in the Dynamic protocol) and the "Road surface condition" as an inter-subject factor (2 modalities: dry or wet road surface). No significant effect of the road surface condition was found either in the Static protocol (Road surface condition: F(1,31) = 1.20, p = 0.28, Road surface condition*Stimuli: F(63,1953) = 0.44, p = 1.00) or in the Dynamic protocol (Road surface condition: F(1,31) = 1.35, p = 0.25, Road surface condition*Stimuli: F(7,217) = 0.64, p = 0.72). Therefore, road surface condition was not considered in further analyses. Only the luminance maps captured in dry conditions were considered in further computations.

  The lantern (F(2.45,78.39) = 19.02, p < 0.0001, η² = 0.373), the gaze direction (F(1,32) = 7.79, p < 0.05, η² = 0.196), the number of luminaires (F(1,32) = 5.62, p < 0.05, η² = 0.149) and the position (F(2.24,71.57) = 5.19 p < 0.05, η² = 0.139), all had statistically significant main effects on discomfort glare. The variation of discomfort glare with the positions is significantly different depending on the lantern ("Lantern*Position": F(3.99,127.68) = 16.09, p < 0.0001, η² = 0.335). No other significant interaction was found ("Lantern*Direction": F(2.92,93.37) = 1.037, p = 0.3796; "Position*Direction": F(2.27,72.76) = 0.229, p = 0.876; "Lantern*Number of luminaires": F(2.50,80.04) = 0.87, p = 0.460); "Number of luminaires*Position": F(2.28,73.00) = 1.731, p = 0.166; "Number of luminaires*Direction": F(1,32) = 0.134, p = 0.717).

Figure 4 .Figure 4

 44 Figure 4. Model predictions versus mean glare ratings in condition 1S: (a) Sch74, (b) Lin14, (c) Lin15, (d) Bul11. For each model, the predictions vary depending on the implementation choices (e.g. L DZ vs. L RZ in Sch74)

b 6 )

 6 Bul08 instead of Bul11 was computed for Bullough's model to avoid adding bias with the additional luminance term (Simplified method: discomfort glare from the closest luminaire (Lum1) alone is taken into account, under the background of condition 2S. Lum2 only contributes to the background.

Figure 1 .

 1 Figure 1. Experimental setup with both luminaires switched on (left) and illustration of the experimental settings (right). The geometrical shapes (circle, square, triangle, star) correspond to the viewing positions in the "Static" protocol; targets 0° and 10° are used to control the participants' gaze direction.

Figure 2 .

 2 Figure 2. Vertical illuminance along the walk in condition 1S, for lanterns A, B, C and D. The four black symbols (circle, square, triangle & star) correspond to the rating positions in the static protocol (see Section 2.3.1). The sun symbol marks the position of pole Lum1.

Figure 3 .

 3 Figure 3. (a) Areas for the background luminance estimation. DZ (Disc Zone): Disc 30° in diameter. RZ (Road Zone), rectangle including the road surface and the targets. (b) Areas for the source luminance estimation: LED Module area and Lantern area.

Figure 4 .

 4 Figure 4. Model predictions versus mean glare ratings in condition 1S: (a) Sch74, (b) Lin14, (c) Lin15, (d) Bul11. For each model, the predictions vary depending on the implementation choices (e.g. L DZ vs. L RZ in Sch74)

Table 6

 6

	The Sch74 and Lin14 models obtained a RMSE above 3.75. The Bul11 and Lin15
	models performed much better, with a RMSE lower than 1 in some conditions.

presents the Root Mean Square Error (RMSE), which is a global index of the errors with respect to the experimental data. The Spearman correlation (R²) is also reported.

  This work investigates the discomfort glare experienced by pedestrians under various urban lighting installations. Psychovisual tests were conducted on a closed outdoor area with four urban lighting installations to collect discomfort glare judgments. The results confirm previous work[START_REF] Miller | Correspondence: Glare in pedestrian-friendly outdoor lighting[END_REF][START_REF] Kohko | Study on evaluation of LED lighting glare in pedestrian zones[END_REF] which recommended optics to limit maximum luminance and vertical illuminance. Four predictive models have been tested with our data. The models from Lin et al. (2015)[START_REF] Lin | Eye movement and pupil size constriction under discomfort glare[END_REF] andBullough et al. (2008, 2011) [START_REF] Bullough | Predicting discomfort glare from outdoor lighting installations[END_REF][START_REF] Bullough | A method for estimating discomfort glare from exterior lighting system[END_REF] provided the best predictions of the experimental data. Measurement and calculation choices were needed in order to implement these models in complex visual scenes. Little impact of the background and source definition was found on the model predictions. However, measurement uncertainties (e.g.

Table 2 .

 2 Lighting characteristics. Average illuminances were measured on a 13.3 m x 5.5 m grid, according to the NF-EN13201[START_REF]Road Lighting -Part 2: Performance Requirements[END_REF] standard. In condition 2S (two luminaires), Lum1 and Lum2 were located on the left corners of the rectangular grid[START_REF]Road Lighting -Part 2: Performance Requirements[END_REF] . In condition 1S (one luminaire), Lum1 was located in the middle of the left side of the rectangular grid.

	Lantern	A	B	C	D
	Optics	Cover opalescent glass	Cover frosted glass	Cover clear glass	Flat glass
	LED Module	LED High Power 18 LEDs	LED High Power 18 LEDs	LED MidPower 30 LEDs	LED High Power 12 LEDs
	Lantern luminous flux 3000 lm	2500 lm	2500 lm	2000 lm
	Luminous efficiency 70 lm/W	79 lm/W	84 lm/W	85 lm/W
	Average illuminance in condition 1S [min;max]	12 lx [2 lx; 57 lx]	11 lx [2 lx; 28 lx]	11 lx [4 lx; 40 lx]	12 lx [2 lx; 34 lx]
	Average illuminance in condition 2S [min;max]	13 lx [3 lx; 58 lx]	13 lx [3 lx; 29 lx]	14 lx [7 lx; 42 lx]	14 lx [3 lx; 34 lx]

Table 3 .

 3 Characteristics of the panel

	Panel (%)

Table 4 .

 4 Photometric characteristics of the stimuli

				Eccentricity	LMT B520		Konica-Minolta CA-2000A				Canon EO
	Lantern Position Direction	θ Lum1 (°)	θ Lum2 (°)	Etot (lx) 1S	Etot (lx) 2S	L RZ (cd/m²) 1S	L DZ (cd/m²) 1S	L RZ (cd/m²) 2S	L DZ (cd/m²) 2S	E black (lx)	L LED (cd/m²) Lum1	L LED (cd/m²) Lum2	L Lantern (cd/m²) Lum1	L Lante (cd/m Lum2
		8.5m	0° 10°	22.6 30.4 17.7 9.2	5.2 4.8	5.6 5.1	0.197 0.096 0.113 0.056	0.349 0.205	0.247 0.12	0.050 0.060	1.49E+04 5.40E+03 3.40E+03 1.79E+
		6.5m	0° 10°	28.5 10.1 36.3 18.6	7.9 7.1	8.4 7.7	0.144 0.055 0.099 0.05	0.32 0.211	0.217 0.122	0.047 0.060	1.29E+04 6.00E+03 4.10E+03 1.98E+
	A	4.5m	0° 10°	38.2 11.2 45.7 19.6	12.3 10.7	13.1 11.5	0.108 0.042 0.085 0.043	0.317 0.226	0.214 0.124	0.047 0.053	1.30E+04 7.70E+03 3.90E+03 2.17E+
			0°	54.7 12.6	15.5	16.2	0.072 0.034	0.308	0.206	0.050
		2.5m	10°	62.1 20.9	11.2	12.7	0.066 0.044	0.226	0.129	0.053	1.10E+04 9.80E+03 4.30E+03 2.97E+
		8.5m	0° 10°	22.6 30.4 17.7 9.2	5.5 5.0	5.7 5.3	0.221 0.117 0.116 0.068	0.341 0.188	0.232 0.12	0.047 0.057	1.39E+04 2.54E+03 4.60E+03 1.08E+
		6.5m	0° 10°	28.5 10.1 36.3 18.6	8.3 7.6	8.7 7.8	0.171 0.071 0.115 0.065	0.315 0.205	0.199 0.124	0.050 0.057	1.36E+04 2.29E+03 4.70E+03 9.50E+
	B	4.5m	0° 10°	38.2 11.2 45.7 19.6	12.5 10.7	13.0 11.3	0.131 0.051 0.104 0.059	0.309 0.216	0.183 0.122	0.047 0.053	1.69E+04 4.10E+03 4.40E+03 1.73E+
			0°	54.7 12.6	13.8	14.4	0.099 0.044	0.297	0.174	0.047
		2.5m	10°	62.1 20.9	10.6	11.6	0.089 0.058	0.214	0.124	0.053	1.22E+04 7.50E+03 4.20E+03 1.81E+
		8.5m	0° 10°	22.6 30.4 17.7 9.2	20.9 19.8	22.3 21.0	0.314 0.237 0.159 0.104	0.637 0.334	0.542 0.205	0.057 0.082	1.29E+05 4.90E+03 1.69E+04 1.27E+
		6.5m	0° 10°	28.5 10.1 36.3 18.6	24.9 22.6	26.5 25.9	0.207 0.148	0.11 0.1	0.577 0.376	0.454 0.22	0.057 0.079	1.26E+05 8.80E+03 1.50E+04 2.71E+
	C	4.5m	0° 10°	38.2 11.2 45.7 19.6	22.5 20.0	25.6 22.7	0.161 0.144 0.098 0.08	0.603 0.436	0.442 0.238	0.060 0.082	9.30E+04 3.70E+04 8.40E+03 5.30E+
			0°	54.7 12.6	15.4	19.6	0.144 0.069	0.604	0.441	0.063
		2.5m	10°	62.1 20.9	12.1	16.7	0.139 0.096	0.443	0.234	0.079	5.50E+04 6.20E+04 5.50E+03 8.80E+
		8.5m	0° 10°	22.6 30.4 17.7 9.2	6.8 6.0	6.6 6.2	0.257 0.145 0.14 0.079	0.383 0.214	0.271 0.129	0.057 0.085	6.40E+04 4.00E+02 1.20E+04 2.38E+
		6.5m	0° 10°	28.5 10.1 36.3 18.6	16.0 14.6	16.1 14.7	0.205 0.083 0.14 0.073	0.367 0.241	0.222 0.127	0.060 0.085	1.16E+05 5.70E+02 2.93E+04 2.87E+
	D	4.5m	0° 10°	38.2 11.2 45.7 19.6	21.8 20.5	22.6 20.2	0.165 0.128 0.067 0.06	0.365 0.258	0.21 0.133	0.060 0.079	1.52E+05 8.10E+02 2.98E+04 4.20E+
			0°	54.7 12.6	21.3	22.4	0.116 0.042	0.346	0.181	0.060
		2.5m	10°	62.1 20.9	18.3	20.0	0.103 0.061	0.252	0.124	0.085	1.13E+05 9.00E+02 1.94E+04 4.80E+

Table 5 .

 5 Mean values of the glare ratings in the different experimental conditions (standard deviation values are in brackets).

	Factor	Lantern	Number of	Gaze	Position
			luminaires	direction
	Static	A: 6.9 [1.6]	1S: 6.2 [2.0]	0°: 6.3 [2.0]	8.5m: 6.5 [2.1]
	Protocol	B: 6.8 [1.7]	2S: 6.5 [1.9]	10°: 6.5 [1.9]	6.5m: 6.2 [2.0]
		C: 5.6 [2.1]			4.5m: 6.2 [1.9]
		D: 6.2 [2.1]			2.5m: 6.5 [1.8]
	Dynamic	A: 7.4 [1.5]	1S: 6.9 [1.8]
	Protocol	B: 7.1 [1.6]	2S: 6.7 [1.8]
		C: 5.9 [1.9]
		D: 6.7 [1.7]

Table 6 .

 6 Prediction comparisons: RMSE and Spearman correlation R² between predicted scores on the de Boer scale and mean ratings in the "Static" experiment, in condition 1S

	Model	Background	Source	RMSE	R²
	Sch74	L RZ		4.40	0.744
	Sch74	L DZ		4.57	0.751
	Lin14	L RZ	L Lantern	3.94	0.384
	Lin14	L DZ	L Lantern	4.23	0.370
	Lin14	L RZ	L LED	3.76	0.375
	Lin14	L DZ	L LED	4.05	0.368
	Lin15	E RZ		0.81	0.781
	Lin15	E DZ		0.60	0.745
	Bul11	E s =E tot -E l -E a		1.27	0.648
	Bul11	E s =E RZ		1.13	0.720
	Bul11	E s =E DZ		1.30	0.725

Table 7 .

 7 RMSE and R² between the predictions computed with the simplified method and the mean glare ratings collected in Condition 2S.

	Model	Background	Source	RMSE	R²
				with mean	Spearman
				ratings	with mean
					ratings
	Sch74	L RZ		4.46	0.812
	Sch74	L DZ		4.61	0.796
	Lin14	L RZ	L Lantern	3.87	0.566
	Lin14	L DZ	L Lantern	4.09	0.512
	Lin14	L RZ	L LED	3.69	0.543
	Lin14	L DZ	L LED	3.90	0.486
	Lin15	E RZ		0.87	0.745
	Lin15	E DZ		0.70	0.733
	Bul11	E s =E tot -E l -E a		1.42	0.740
	Bul11	E s =E RZ		1.22	0.795
	Bul11	E s =E DZ		1.35	0.787

Table 8 .

 8 RMSE and R² between the Dir/Ind predictions and the mean glare ratings collected in Condition 1S and Condition 2S (simplified method).

	Condition	Background RMSE with	Spearman R²
			mean ratings	with mean
				ratings
	Condition 1S E RZ	0.76	0.655
		E DZ	1.05	0.676
	Condition 2S E RZ	0.84	0.655
		E DZ	0.60	0.688

Acknowledgments

The authors would like to thank Manuel Le Pape for his help, Alexandre Taron for his availability, his help and the facilities, Eric Dumont for his contributions and helpful advice, and all the participants who took part in the experiment.

Funding

This work was supported by Thorn Lighting.


Bailly C Gomez

In order to propose new and sustainable methods for cultivated areas managment, the French INRA-IRD-Supagro laboratory for the study of Soil-Agrosystem-Hydrosystem Interactions (LISAH) develops tools for modelling fluxes (water, soils, solutes) based on a fine characterisation and observation of the landscape mosaics and of its dynamic (field limits, networks, structures, vegetation, agricultural practices, topography, etc.). Such observations require to develop innovative acquisition and processing methods. This poster presents somes of these methods concerning different scales and techniques.

Objective:

Mapping of soil properties over the Lebna catchment (250km²), from the surface to the subsurface

Objectives: Attaining a decimeter to centimeter scale description of landscape features at the watershed scale

Results:

Operationnal method of image acquisition and 3D processing which allows to obtain decimetric to centimetric DEM on areas up to several km²

Results: Vis-NIR hyperspectral imaging data and Digital Soil Mapping methods can be used to map key soil properties, used by soil surveyors to describe soil types, related to soil erosion processes…

Approach in 3 steps: 1 st : Vis-NIR hyperspectral imaging data were used to map key topsoil properties over bare soils of Lebna catchment using multivariate models [START_REF] Gomez | Using Vis-NIR hyperspectral data to map topsoil properties over bare soils in the Cap-Bon Region, Tunisia[END_REF].

2 nd : These topsoil properties estimations were used as covariates in geostatistic methods to produce entire topsoil properties maps over Lebna catchment (see illustration).

3 th : Topsoil properties estimations were used in pedotransfert functions to map sub-surface soil properties [START_REF] Lagacherie | Combining Vis-NIR hyperspectral imagery and legacy measured soil profiles to map subsurface soil properties in a Mediterranean area (Cap-Bon, Tunisia)[END_REF].

Advances in remote sensing of cultivated landscapes at

Field observations

III. Gullies detection with THRS imagery

Results:

Visible-NIR and thermal images allow for ETR mapping at the regional scale. ETR maps can be useful for assessing the available water content of soils Validation at the plot scale against eddy covariance ETR measurements (sites 6 and 7) and against ETR outputs of the HYDRUS-1D water transfer model (sites 1-7)

Results

IV. Soil Crust Mapping

  Lightweight image acquisition : light platforms (kite) and consumer grade cameras  High image redundancy and SfM approaches for processing shaded DEM houses, orchards Reference : Feurer, D.; El Maaoui, M. A.; Planchon, O.; Boussema, M. R. & Pierrot-Deseilligny, M. Kite-Borne photogrammetry for decimetric 3D mapping of several square kilometres areas Proceedings of IEEE 2015 International Geoscience and Remote Sensing Symposium (IGARSS'15), 2015 II. Landscape structures mapping Objective: Mapping landscapes structures which have an impact on hydrological fluxes Approach :  LiDAR DEM analysis to detect topographic discontinuities  DEM-driven stochastic modelling to interpolate the detected lines and remove false detections a. 12 LiDAR profiles with ground truth and aerial views b. principle of Haar wavelet decomposition and classification c. result Stochastic modelling of ditches network a. network correction approaches : reconstruction and cut b. application of the reconstruction c. five equiprobable reconstructed networks ² References : Bailly, J.; Lagacherie, P.; Millier, C.; Puech, C. & Kosuth, P. (2008), 'Agrarian landscapes linear features detection from LiDAR: application to artificial drainage networks', International Journal of Remote Sensing 29(12), 3489-3508. Bailly, J.; Levavasseur, F. & Lagacherie, P. (2011), 'A stochastic algorithm to reconstruct artificial drainage networks from incomplete remote sensing delineations', International Journal of Applied Earth Observation and Geoinformation 13, 853--862.

  Exhaustive mapping of gullies for hydrological modelling Decision rules using : ancillary data (DEM, field borders…) lines characteristiscs (direction, shape...) Desprats J.F., Raclot D., Rousseau M., Cerdan O., Garcin M., Le Bissonnais Y., Ben Slimane A.,Fouche J., Monfort-Climent D. (2013). Mapping linear erosion features using high and very high resolution satellite imagery. Land Degradation & Development, 24: 22-32. doi: 10.1002/ldr.1094. Simulation and computing Potential accessibility at ground in the case of (a) 1 satellite at 561 km or (b) 2 at 720 km Surface temperature and evapotranspiration retrieved from airborne hyperspectral scanner Reference : Lagouarde, J.-P.; Bach, M.; Sobrino, J. A.; Boulet, G.; Briottet, X.; Cherchali, S.; Coudert, B.; Dadou, I.; Dedieu, G.; Gamet, P.; Hagolle, O.; Jacob, F.; Nerry, F.; Olioso, A.; Ottlé, C.; louis Roujean, J. & Fargant, G. The MISTIGRI thermal infrared project: scientific objectives and mission specifications. International Journal of Remote Sensing, 2013, 34, 3437-3466 Objective: Design of a high spatial and temporal resolution thermal satellite Having worked on the spectral sampling (bands, bands resolutions) the LISAH team proposed a spectral configuration allowing for a 1K accuracy in temperature estimation Impact of the revisit time (1, 2, 5 days) on the availability of data (a:Rennes, b: Avignon). Impact of acquisition time (10, 12, and 14 h UTC) for Rennes (c) and Avignon (d) Simulation of different spectral configurations with 4 or 3 bands and different positions in the thermal infrared spectrum Objective: Mapping of vineyard daily evapotranspiration (ETR) over the Peyne catchment (65 km2)

Approach : 12

 12 ETR maps produced from visible-NIR and thermal IR images (ASTER instrument, 90 m resolution) using two water stress indices : WDI (Moran et al., 1994) and S-SEBI (Roerink et al., 2000) Reference : Galleguillos, M., Jacob, F., Prévot, L., Lagacherie, P. and French, A., Comparing two simplified models for inferring daily evapotranspiration from ASTER over a Mediterranean vineyard watershed. Remote Sensing of Environment, 2015, 6 (115), 1326-1340

  Lightweight platform (UAV) ; ultra high resolution  Mapping of soil surface characteristics Reference : C. Corbane, D. Raclot, F. Jacob, J. Albergel, P. Andrieux, Remote sensing of soil surface characteristics from a multiscale classification approach, CATENA, Volume 75, Issue 3, 15 November 2008, Pages 308-318, ISSN 0341-8162, http://dx.doi.org/10.1016/j.catena.2008.07.009. Objective: Monitoring of soil crust dynamics at the crop scale  Contour detection from THRS satellite imagery  Filter combination and decision rules with ancillary data Results