Modelling the Probability of Discomfort Due to Glare at All Levels: The Case of Outdoor Lighting

ABSTRACT

To limit glare, lighting engineers need to estimate the level of discomfort produced by a lighting installation. Outdoor, most discomfort glare models predict a mean level of discomfort on a judgment scale, which corresponds to a “mean road user.” However, in real life, the inter-individual variability of the sensitivity to glare is large; predicting the mean discomfort does not describe the full pattern of responses in a population. We propose a methodology to model the Discomfort Level, computing the probabilities that an observer reports any of the levels of a discomfort scale. This methodology is demonstrated for outdoor lighting, where no probabilistic model is available. Using a dedicated psychophysical experiment, we extend the results of a previous study where a formula was proposed to compute the Glare Excitation due to a multi-source stimulus, at the Borderline between Comfort and Discomfort (BCD), with a background luminance consistent with outdoor lighting. This formula is first extended to other discomfort levels and background luminance levels, and strengthened thanks to a different experimental protocol and to the use of up to 10 glare sources simultaneously. From this experiment, a formula of the Glare Excitation is proposed in the range of outdoor lighting. Then, a probabilistic model of the Discomfort Level is proposed, allowing computing the probability of ratings at each level of an ordinal scale from the Glare Excitation computed with our formula. It is hoped that the proposed model avoids most of the modeling methodological caveats of previous discomfort glare models.

KEYWORDS:

• Discomfort glare
• psychophysics
• probability distribution
• outdoor lighting

Aknowledgments

We are grateful to Lancelot Valverde for his help in the experimental part of the study, and to all the participants.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. According to Stevens (1957) however, the sensation is a power function of the stimulus (see also Luce (1959)).

2. Adrian (1991) shows the GCM model could be converted to be expressed with the same factors and structure as Eq. 2(2) $G=\frac{1}{L_b^{\gamma }}\sum _{i=1}^{N_S}\frac{L_i^{\alpha }{\omega }_i^{\beta }}{p_i^{\delta }}$(2) .

3. The DGP model proposed by Wienold and Christoffersen (2006) can be included in both classes, as it uses a 4-points scale in the experimental protocol, and uses the collected data to predict a proportion of people above a discomfort threshold.

Additional information

Funding

The authors have no funding to report.