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Content uploaded by Roland Brémond
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All content in this area was uploaded by Roland Brémond
Content may be subject to copyright.
Review of the Mechanisms of Visibility Reduction by
Rain and Wet Road
Nicolas Hautière, Eric Dumont, Roland Brémond, Vincent Ledoux
Keywords: rain, wet road, visibility, windshield
1 Introduction
Rain drastically modifies the visual environment of road users, particularly at
night. It changes visibility through its effects on headlights, windshield, pavement
and markings. Rain lessens the performance of headlamps and other light
sources by filtering part of their luminous power, thus reducing the illuminance on
the roadway ahead of the vehicle. Rain affects the capacity of the driver to see
through the windshield. Rain also affects visibility by changing the amount of
headlight retro-reflected by the road surface toward the driver. The film of water
on the pavement makes delineation and pedestrian crossing markings almost
invisible by cancelling the retroreflective properties of the beads in the painting
materials. The same physical phenomenon makes the pavement appear darker
than in dry conditions.
This is a brief list of commonplace facts on the visual effects of rain [10]. In the
following, we seek to explicit the physical and psychophysical ground of these
facts, based on scientific references when available.
The outline of the paper is as follows: in the first section, we study the visual
effects of the falling rain; in the second section, we tackle the visual effects of
sprayed water; in the third section, we list the properties of wet materials,
specially pavement markings; finally, we propose synthetic diagrams describing
the effects of rain on roadway visibility.
2 Visual effects of the falling rain
2.1 The nature and microstructure of rain
Rain is a population of water droplets falling, interacting with each other and with
the environment. While falling, a rain drop undergoes rapid shape distortions.
This shape is size-dependent. Small drops are usually spherical, but as their size
grows, they tend to a spherical oblate shape. The shape of a rain drop is
described in [2] as the cosine distortion of a sphere at the tenth order:
( )
θ θ
=
= +
∑
10
1
( ) 1 cos
n
n
r a c n (1)
where a is the radius of the undistorted sphere, c
1,…,10
are coefficients which
depend on the radius of the drop, and θ is the elevation polar angle. θ=0
corresponds to the direction of the rain. Shapes of various sized drops are
presented in Figure 1a. Rain drops come in a wide range of sizes. Their size
distribution is often modeled using Marshall-Palmer distribution [16]:
−Λ
=
0
( )
a
N a N e
(2)
where a is the radius of a drop, N(a) the number of drops per volume unit with
sizes between a and a+da, N
0
=0.08 cm
-4
, Λ=82R
-0.21
and R is the rain density in
mm.h
-1
. This distribution is plotted in Figure 1b.
(a) (b)
Figure 1: (a) shapes of rain drops. (b) Marshall-Palmer rain drop size distribution.
Rain drops fall at a constant speed called the terminal velocity. An empirical
study is presented in [11] on the terminal velocity of rain drops for different drop
sizes. This data are approximated in [27] with the following function:
(
)
− ×
= − 3 1,15
1,57 10
9,4 1
a
term
V e (3)
2.2 Light scattering in rain
Some experiments were conducted in an attempt to relate optical extinction on a
long distance to rain density. [26] reports the results from five other
investigations, and concludes that the optical depth τ obtained from the
measurements corresponds within 25% to the value computed on the basis of
different rain drop distributions. The optical depth is computed by integrating the
extinction coefficient k
s
along the optical path L as follows:
τ
=
∫
0
L
s
k dz
(4)
The general relation found between the extinction coefficient k
s
(m
-1
) and rain
intensity R (mm.h
-1
) is the following:
γ
=
s
k aR
(5)
where
a
and
γ
differ with respect to the location and the optical devices used in
the experiments. Experimental curves are plotted in Figure 2.
Finally, [21] measured the back-scattering of a light source in rain. Based on
these measurements, they proposed an empirical model. However, the relevance
of this model was not tested since.
Figure 2: Different experimental curves relating the atmospheric extinction coefficient and the
intensity of the rain.
2.3 Consequences on roadway visibility
Light scattering in rain is rather limited. Using an analogy with the visual effects
of fog, the effects of scattering in rain can be a problem for driving when the
meteorological visibility (V
met
=3/k
s
) falls below 400 m, which is equivalent to a
300 mm.h
-1
rain according to Eq. (5). Such levels of precipitation are seldom
observed.
3 Visual effects of sprayed water
3.1 Visual effects of rain on the windshield
To the best of our knowledge, there is no analytic model for the overall reduction
of visibility induced by rain on the windshield. [9] focus on the appearance of rain
drops. They show that the field of view refracted by a spherical drop is about
165°, and assimilate the drop with a fish-eye lens. The corresponding optical
diagram is presented in Figure 3a.
(a) (b)
Figure 3: Optical diagram illustrating the fish-eye lens effect created by a rain drop.
One can assume rain drops on the windshield to have a similar effect, save for
the deformation of the spherical drops on the windshield. The drops on the
windshield roughly reflect the road environment, which is illustrated in Figure 3b.
On the other hand, several experimental studies on wiper usage focused on
object visibility and seeing distance. Some driver visibility studies were restricted
to stationary vehicles in artificial rain [13][18]. Other studies were conducted in
actual rain. They showed that wipers do not interfere with the perception of the
road scene with respect to saccadic eye movements [6]. Moreover, seeing
distances are significantly reduced when rain intensity increases [3][12][17]. In
particular, [3] investigated the visibility distance of target vehicles under natural
downpours. The observers were onboard a vehicle, and notified when they
detected a target car while their wipers were engaged or recently stopped. These
experiments showed that detection distances decrease significantly with ambient
lighting and that visibility distance decreases as rain intensity increases. Visibility
distance was found to be lower for observers onboard a moving vehicle (vs.
stationary) because of the higher concentration of water on the windshield.
Based on these experiments, a model was proposed for the visibility distance of
cars through the windshield in rain condition in daytime condition. This model can
be simplified by:
(
)
12
0
b
c
c L
D c rt e
−
= (6)
where c
0
, c
1
, c
2
are strictly positive constant values, rt characterizes the
accumulation of rain water on the windshield, r being the intensity of the rain and
t the time between wiper movements, and L
b
the background luminance.
3.2 Visual effects of water sprayed by other vehicles
The water sprayed by vehicles has undeniable effects on visibility. [8] studied
these effects. Unfortunately, no model came out of it, because of several
experimental difficulties which impeded the identification of prevailing
parameters. Other studies showed that splash and spray is reduced by 95% on
porous asphalt compared to other ordinary pavement surfaces. Figure 4, taken
from [20], shows a heavy vehicle on a road section with and without porous
asphalt. However, such a figure is dubious since it is not backed up with a
measurement protocol. The most rigorous works have been conducted for the
development of heavy vehicle spray reduction devices. Even though these
researches do not directly address driver visibility, the metering systems which
were used to study such devices might be used to investigate this particular
problem. A synthesis of the works conducted before 2000 is proposed in [15].
Figure 4: Water sprayed by a heavy vehicle on ordinary and porous asphalt [20].
4 Light reflections on wet materials
4.1 Water at the surface
The water on a surface (e.g. a puddle on the pavement) makes it specular
because of the smooth air-water interface. Optical interactions on such a surface
are governed by Fresnel equation for dielectric materials:
θ θ
=
1 1 2 2
sin sin
n n (5)
A film of water on a Lambertian surface can also make the surface appear
darker [14]. This is mainly caused by internal reflections at the water-air interface.
Part of the light reflected by the Lambertian surface is reflected back when it hits
the water-air interface. This light is again subject to absorption by the material of
the surface before being reflected again. This leads to a sequence of absorptions
which darkens the surface.
(a) (b)
Figure 5: Illustration of the Fresnel equation: a material with a layer of water on its surface reflects
less light because of internal reflections at the water-air interface.
4.2 Water underneath the surface
The presence of water underneath a surface is another important factor
influencing the appearance of the material. In the case of pulverulent materials,
(sand or limestone), water can penetrate inside holes formerly filled with air. This
modifies the reflection properties of the material, favoring forward scattering [25].
The main reason is that the refraction index of water is higher than the index of
the air, and usually closer to the index of the material. This means that a ray of
light entering the material is less refracted because the refraction index is more
homogeneous when the material is wet. As illustrated in Figure 6, the
consequence is that the ray undergoes more scattering before leaving the
surface. This increases the total amount of absorbed light, and the overall effect
is a material with reduced reflectivity.
Figure 6: Shortest path for a ray of light to enter and exit the material with (left) a 90° mean
scattering angle and (right) a 30° mean scattering angle.
4.3 Consequences on roadway visibility
Rain changes the visual aspect of the road. The road surface appears more
specular or darker, depending on the observation angle. This can be dazzling for
the driver, especially in daytime with the sun at grazing angles, or at night with
opposing headlights. With visual performance impaired by glare, it is more
difficult for the driver to detect hazards. The visibility of retro-reflective road
markings is also particularly impaired. These markings are designed to send
headlight back toward the vehicle. They are usually made of a painting onto
which glass beads with a high refraction index (between 1.5 and 2.5) are
encrusted (Figure 7a). The optical properties of the beads are described in more
details in [29] and [23]. In daytime, on wet roads, retroreflective materials reflect
sunlight, and sometimes appear darker than the pavement. At night, when the
road is slightly wet, the retroreflective efficiency of the beads is reduced, as
illustrated in Figure 7b. When the road is wet and the water layer is higher than
the size of the beads, headlight is mostly reflected at the air-water interface
(Figure 7c), so markings may disappear. This is why all weather markings were
developed. A nice introduction to this particular issue is proposed in [5].
(a) (b) (c)
Figure 7: Optical mechanisms governing retroreflection on pavement markings with encrusted
beads in (a) dry, (b) humid and (c) wet conditions.
5 Conclusion
In this paper, we have provided physical explanations for the effects of rain on
roadway visibility. These explanations are based on either optical or
psychophysical models. We have classified the visual effects of rain into three
main categories. The first category concerns light scattering by rain drops. The
second category concerns splash and spray. It encompasses both rain falling on
the windshield and water splashed by other vehicles. The third category
concerns wet road surfaces, especially road markings, whose appearance is
modified by the water layer.
Figure 8: Visual effects of rain in daytime
In the end, the reduction of visibility caused by rain and sprayed water results
from a combination of these three categories of effects. We can estimate a priori
that the effects of the second and third categories have the highest impact on
visibility, scattering effects being negligible for common intensity downpours. To
give a schematic view of these effects, we propose two diagrams. Figure 8
shows the various effects of rain on daytime visibility: reduced transmission,
atmospheric veil, wet windshield, spray and specular reflections. Figure 9 shows
the nighttime rain situation, with the same effects as in daytime plus specular
reflection overcoming retroreflection on the pavement.
From this review of the literature, we have seen that the mechanisms of visibility
reduction by rain and wet road are numerous. The technical solutions to enhance
the perception of the driver in rainy weather are thus also numerous: adaptive
wipers, adaptive headlights, anti-splash and spray devices, porous pavement,
retroreflective markings… A next step should be to focus on headlights. The
quantitative visibility models should enable to define scenarios and to compute
the necessary power to compensate for the visibility loss, or to find alternative
strategies to compensate for the backscattering of light.
(a)
(b)
Figure 9: Nighttime visibility (a) in clear weather (b) in rainy weather.
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