Weather Effects Impact on the Optical Pulse Propagation in Free Space

Abstract

Optical wireless links offer gigabit per second data rates and low system complexity. For ground-space and or terrestrial communication scenarios, these links suffer from atmospheric loss mainly due to fog, scintillation and precipitation. We investigate here the impact of fog, rain and snow effects and evaluate their performance on the basis of attenuation data collected for the optical pulse propagated through the troposphere.

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Weather Effects Impact on the Optical Pulse Propagation in Free Space

M. S. Awan*, Marzuki*, E. Leitgeb*, F. Nadeem*, M. S. Khan*, C. Capsoni**
* Graz University of Technology, Institute for Broadband Communication, Graz, Austria
** Poltecnico Di Milano, Milan, Italy

Abstract- Optical wireless links offer gigabit per second data
rates and low system complexity. For ground-space and or
terrestrial communication scenarios, these links suffer from
atmospheric loss mainly due to fog, scintillation and
precipitation. We investigate here the impact of fog, rain and
snow effects and evaluate their performance on the basis of
attenuation data collected for the optical pulse propagated
through the troposphere.

Keywords: Free-Space Optics (FSO), specific attenuation,
visibility, empirical model.
I. FSO INTRODUCTION
Optics (FSO) Free-Space
communication is the concept of transmitting very high
bandwidth digital data using laser beam directly through the
atmosphere. Recently FSO –links are identified as an
attractive alternative to the existing radio links for
applications involving ground-to-ground (short and long
distance terrestrial links), satellite uplink/downlink, inter-
satellite, satellite or deep space probes to ground, ground-to-
air/air-to-ground terminal (UAV, HAP etc.). Moreover,
growing demands for higher data rates and wider bandwidths
from the end user to manipulate multimedia information in
the recent years allegorises a challenge for the future Next
Generation Networks (NGN). The prime advantages of FSO
usage are: a wider bandwidth with data rates exceeding
easily 100 Gbit/s using WDM techniques, low power
consumption, better security against eavesdropping, better
protection against interference, and no frequency regulation
issues [1].
However, a well known disadvantage of FSO links in the
troposphere is their sensitivity to weather conditions –
primarily to fog and precipitation, causing substantial loss of
the optical power over the channel path [2]. Even though, if
fog, snow and rain concerns only a small fraction of the time
and or affects only a small portion of the overall propagation
path yet it severely impairs the optical link performance and
limits the communication link availability primarily due to
the Mie scattering phenomena [3]. The main cause for such
significant losses is the sensitivity of the transmitted optical
signal to the drop size distribution of the atmospheric
particles of fog, snow and rain. Recent investigations showed
that optical signal losses under dense maritime fog and
moderate continental fog conditions reached up to 480
dB/km and 120 dB/km respectively [4, 5]. Similarly, the
optical power loss under intense shower conditions can be as
large as 30 dB/km [6], and for a heavy snow event the
attenuations can be more than 55 dB/km [7]. To counteract
these losses with enough excess power by FSO technology,
or optical wireless
we require first, based on theoretical models as well case
studies, to study, analyse and evaluate in detail the impact of
such weather effects on the transmitted optical pulse in free
space that jeopardize the performance of FSO links in terms
of availability, reliability and quality of service.
In this work, we investigate the impact of fog, rain and
snow effects on the transmitted optical signal by evaluating
their attenuation behaviour based on measurement data
collected at Graz, Milan, Nice and Prague. The data used in
the analysis for Graz, Milan, Nice and Prague consists of six
months (September 2005-February 2006), two months
(January 2005 – February 2005), eight days (24 June 2004 –
01 July 2004) and two months (September 2007 & December
2007), respectively.
II. THEORETICAL BACKGROUND
Transmitted optical pulses in free space are mainly
influenced by two main mechanisms of signal power loss –
absorption and scattering. Absorption is mainly due to water
vapours and carbon dioxide, and depends on the water
vapour content that is dependent on the altitude and
humidity. By appropriate selection of optical wavelengths for
transmission the losses due to absorption can be minimised.
It was found that scattering (especially Mie scattering) is the
main mechanism of optical power loss as the optical beam
looses intensity and distance due to scattering. The beam loss
due to scattering can be calculated from the following
empirical, visibility range dependent, formula:
0.195
17 0.55
scat
V
λ
⎝⎠
where V is visibility range in km, λ is transmission
wavelength in nm. Visibility range is typically defined as the
distance at which the transmitted optical intensity is
attenuated to 5% of its original value [5]. The visibility range
V can be calculated from transmittance (τ) according to the
formula mentioned in the following equation [8]:

ln( ). 3.27
( )
ln() ln()
MM
ττ
where dL is the link distance, τth and τM are the threshold of
transmission (5%) and the measured percentage of
transmission at a minute scale. To calculate the total received
power and the link budget, following link equation:
2
()
recT atm TR
T
L
Θ
where dR is the transmitter aperture diameter,
transmitter beam divergent angle, L is the link distance,
V
⎛
⎜
⎞
⎟
α=
(1)
thL
dm
V m
τ−
=≅
(2)
22
R
d
PP
=τ τ τ
(3)
T
Θ is the
978-1-4244-2517-4/09/$20.00 ©2009 IEEE

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atm
τ
the transmitter and receiver optics efficiency, respectively.
To determine the probability of attenuation that it is equal
to or exceeds a certain threshold value x dB during an
arbitrary time interval t0 such that the optical link is
unavailable, is PAtot(x) given by the following relationship
[13]:

( ){( )} ( )
tottottot
A
PAxP A txEx
=≥=

where x is the normalized link margin such that x=x*/L
(dB/km) and its value also represents the highest value of the
atmospheric attenuation, and x* is the link margin whose
upper bound is determined by the dynamical range of the
receiver having a typical value of about 30-40 dB.
the cumulative distribution of the total attenuation and
( )
tot
A
E
x is the cumulative exceedance probability of the
atmospheric attenuation. The percent availability of the FSO
links such that it fulfils the quality of service (QoS)
requirements can be expressed by the following equation:


(1 ( ))*100%
tot
Availability PAx
=−

In order to determine the reliability and the quality of the free
space link, the attenuation coefficient
stochastic process whose distribution is empirically defined
about a lognormal distribution. It is important to mention
here that the availability and quality of service (QoS) of FSO
links is strongly dependent upon and is influenced by various
weather effects especially fog, rain and snow besides the
wavelength used for transmission purpose [4, 5].
is the atmospheric transmission factor, and
Tτ &
R τ are
0
(4)
( )
x is
tot
PA
(5)
scat
α
is considered a
III. EMPIRICAL AND THEORETICAL ATTENUATION MODELS
In FSO systems, modulating the instantaneous intensity
of a laser source data are transmitted and the received
intensity is detected with a photodiode. During propagation
of optical pulses in free space, photons are absorbed and
scattered by the atmospheric particles, such as fog, rain and
snow droplets. Generally, these droplets have radii in a range
between 1 µm to 5000 µm, with drop-size concentration
decreasing sharply with increasing drop sizes [9] and cause
varying attenuation depending on their distribution.
However, the droplets
The Beers-Lambert law defines the optical power loss
through the atmosphere that varies on the order of hours [10].
The appropriate model for the attenuation coefficient (α)
varies depending on the presence of precipitation. Normally,
the optical links in free space measure visibility data with the
attenuation coefficient. In order to calculate the attenuations
caused by fog, rain and snow usually we rely on two
approaches –empirical approach and the theoretical approach
(microphysical models). The empirical approach is very easy
and quick to implement whereas, the theoretical approach is
somewhat difficult and time consuming. The one very
commonly adopted empirical approach concerns computing
signal attenuations based on the visibility range estimate. In
the case of clear or foggy weather with no rain, hail or snow,
Kim’s model is employed to compute the attenuation due to
fog (
Fog
α
), that is very accurate for the narrow wavelength
range between 785 – 1550 nm [10],
3.91(
V
)
550
q
Fog
−
λ
α=

(6)
where q is the parameter related to size distribution of the
droplets

In the case of rain, the optical power loss is relatively
wavelength insensitive. For rain, an accepted empirical
model based on the visibility range from [11] is,
2.9
Rain
V
The attenuation in case of snow can be more severe than
the attenuation in case of rain due to the much larger droplet
size. Based on [12], the attenuation for snow based on
visibility range is,
58
Snow
V
The underlying electromagnetic theory behind the
theoretical (microphysical) models is well known. For these
models, we assume that multiple scattering is negligible, and
all the scatterers are acting independently and are distributed
uniformly along the atmospheric transmission path. For fog,
the attenuation of optical pulse is mainly due to Mie
scattering effect and the loss effects due to absorption can be
ignored. Therefore the extinction coefficient is evaluated by,
r
r Qm rn r dr
β=πλ
∫
Where m and r are the refractive index and radius of the
fog droplets, respectively.
ext
Q is the extinction efficiency and
n(r) is the size distribution (i.e., modified gamma) of the fog
droplets. For rain conditions the usual equations are:
r
r n r dr
β=α
∫
Where n(r) and r is the gamma distribution and radius of the
rain drops, respectively. The rain rate can be calculated as,
∞
=
∫
and the terminal velocity ( )v r of rain droplets in stagnant air
is given by,
1.2
( )9.65 10.3v re−
=−

The model dealing with snow attenuations is,
R
C v
where terminal velocity
α=

(7)
α=
(8)
2
1
2
( , / ) ( )
Fogext
r
[dB/km] (9)
2
1
4.34( ) ( )
Rainscat
r
[dB/km] (10)
3
0
4.8( ) ( )r v r n r dr
R
[mm/hr] (11)
r
[m/s] (12)
3
0.3619
w
Snow
t
ρ
β=
[dB/km] (13)
tv of the snowflakes is,
3
0.1155
t
aD
gC
C
ρ
v
=
[m/s] (14)
Here,
mm/hr,
air density in g/cm3,
Although snowflakes have a very complicated shape, yet
they do not exhibit any preferred dimension, hence assuming
the spherical shape of snow droplets seems reasonable.
Additionally, the sizes for rain droplets can be much larger
w
C is the thickness of snowflakes in g/cm2,
C is the drag coefficient for snow.
ρ is the water density in g/cm3, R is snowfall rate in
3
a ρ is the
D

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than 5 mm, but since they are hydro-dynamically unstable so
they tend to break into relatively smaller dimensions.
IV. IMPACT OF WEATHER EFFECTS AND THE ANALYSIS
Fall of the received optical power below the receiver
sensitivity threshold introduces a fade. This fade can be
described as short-term fade or the long-term fade depending
upon the time duration of the optical power interruption. The
type of fade that occur due to rain, fog and snow is the long-
term fade whose duration could be a few minutes or it can
reach up to several hours. In this contribution we would
focus our discussion only on the long-term fades introduced
by fog, rain and snow conditions to the FSO link in free
space. We analyse here one month rain attenuation data from
Prague, one snow event
Fig. 1 shows an empirical simulation of the rain, snow
and fog attenuation effects against visibility range. From this
plot it is evident also that fog, rain and snow cause
significant propagation losses to the optical signals
transmission in free space.
100 200 300400 500600 700800
100
200
300
400
500
600
700
800
Attenuation in (dB/km)Attenuation in (dB/km)
Visibility in metersVisibility in meters
Kim Fog Model at 950 nm Kim Fog Model at 950 nm
Kruse Fog model at 950 nmKruse Fog model at 950 nm
Rain attenuation at 950 nm Rain attenuation at 950 nm
Snow attenuation at 950 nmSnow attenuation at 950 nm

Fig. 1: Simulation of empirical model for fog, rain and snow conditions for
FSO link at 950 nm

We will analyze here first the attenuations caused by rain
to the propagation of optical pulses transmitted in free space.
We take a rain event recorded at Prague for the transmission
of 850nm pulses on 850 m link. From the analysis of this
measured rain event data, it was observed that rain
attenuation occurs for percentages of time smaller than
0.66% and the maximum measured value of 18 dB
corresponds to 0.0005% of time of year. The minimum
measured visibility during rain events is 1000 m. Fig. 2
shows two sample rain events occurred during the
attenuation measurement campaign of year 2006 – 2007 on
18.09.2006 at Prague and at Milan during year 2005-2006
measurement campaign on January 17th 2005. The maximum
rain rate during this particular rain event was recorded to be
about 44 mm/hr and the maximum attenuation reached
during this rain event was 8.5 dB/km at Prague. The
maximum change in specific attenuations during the rain
events recorded were about ± 1.70 dB/km averaged on a
minute scale. While for Milan the maximum attenuation
reached was about 6 dB/km at a rain rate of about 3 mm/hr
with a maximum change in specific attenuation of about ±
0.7 dB/km. It is evident from these sample rain events that
rain events have minimum impact on the optical signal
propagation.
05101520
Rain rateRain rate
2530354045
1
2
3
4
5
6
7
8
9
Specific attenuation (dB/km)Specific attenuation (dB/km)
Prague - Rain attenuations at 850 nm
Milan - Rain attenuations at 785 nm (path)
Milan - Rain attenuations at 785 nm (V)

Fig. 2: Rain attenuations against a rain rate in mm/hr from rain events at
Prague and Milan for FSO links operating at 850 nm and 785 nm

In order to assess the optical signal loss effects due to
snow, we analyze three snow events that were recorded; one
long snow event at Graz during 25 – 28 November 2005 and
the two in Milan on 18.01.2005 and 28.01.2005. The
maximum attenuation measured for snow at Graz reached to
55 dB/km with a mean attenuation of about 3 dB/km
averaged on a minute scale. While the changes in specific
attenuation occurred around ± 15 dB/km & ± 18 dB/km on a
minute and second scales, respectively. Whereas, for Milan
the maximum attenuations reached to 65 dB/km, a mean
attenuation of about 8 dB/km and with a change in specific
attenuation of about ± 16 dB/km. Figure 3 below, shows the
time series of these particular snow events on a second scale.
It is concluded that the optical signal loss effects due to snow
attenuations are much higher when compared with the rain
attenuations.
01000200030004000
Time in minutesTime in minutes
5000600070008000900010000
-20
-10
0
10
20
30
40
50
60
70
Specific attenuation (dB/km)Specific attenuation (dB/km)
Graz - Snow attenuations at 950 nm (25-28.11.2005)
Milan - Snow attenuations at 785 nm (18.01.2005)
Milan - Snow attenuations at 785 nm (28.01.2005)

Fig. 3: Snow events measured attenuations at Graz and Milan for a FSO
link during 25 -28 November 2005 and January 2005, respectively

From the knowledge of the Mie scattering theory, we
know that fog is the biggest attenuating effect to the
propagation of optical signal transmission especially in the
troposphere. The time series analysis of the measured fog
(radiation and advection) attenuations for Graz (Austria),
Milan (Italy), La Turbie Nice (France) and Prague (Czech
Republic) have been already reported and discussed in details
[4, 6, 13, 14]. From these analyses, it was concluded that the

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fog attenuations are strongly dependent on the local climate
and the fog microphysics as the fog attenuations vary
spatially and temporally with time. It was also observed that
on the average the changes in fog specific attenuation values
occur about ±6 – ±8 dB/km in case of moderate continental
fog conditions like as in Graz, Milan and Prague.
Fog can be classified into many types on the basis of its
formation mechanism, climatic conditions and the drop size
distribution. However, the two most common types of fog
are continental and maritime fog. The fog conditions at Graz,
Milan and Prague are the continental type while at La Turbie
Nice it is the dense maritime fog. The fog microphysics of
these two types of fog is very different, so is their
attenuations to the optical signal transmissions in these fog
environments. The attenuations in continental fogs reach up
to 120 dB/km while in dense maritime fogs the average value
is about 480 dB/km.

Fig. 4: Fog attenuations comparison for Graz and La Turbie (Nice)

Fig. 4 above, shows the time series of these two fog types
attenuations on a minute scale. The time series of these two
fog types changes in specific attenuations shows that the
changes occur much more sharply in dense maritime fog
conditions than in moderate continental fog conditions.
These changes in specific attenuations are normally between
± 6 - ± 8 dB/km under moderate continental fog conditions
with an average temperature change of about 10˚C during the
whole fog event, while these changes for dense maritime fog
environments can reach up to ± 300 dB/km as shown in Fig.
5 in the form of a histogram of changes in specific
attenuations.

Fig. 5: Histogram of changes in specific attenuations for La Turbie
(Nice)
It is evident from the above plot that the changes in
specific attenuation for dense maritime fog events are more
concentrated around 0 dB/km suggesting that most of the
time the fog was stable. We believe that the large changes
observed in the changes were mainly due to the wind
turbulence causing changes or the order of ±300 dB/km. The
Table 1 below summarises some basic statistics of the optical
links installed at the above mentioned four locations.


Table 1: Basic statistics of free space optical links at four locations
* The range for atmospheric link losses attenuation for Milan is 21 dB

The apparent changes in the average and the maximum
values of specific attenuations measured and mentioned
under Table 1 (for Graz, Milan and Prague) for continental
fog conditions are strongly dependent upon the fog
microphysics and also due to the local weather conditions.
However, despite Milan, Prague and Graz are located in the
same temperate area, we feel that there are two major
differences which are expected to affect to some extent the
fog attenuation measurements: a) the climate during winter is
colder in Graz than Prague and Milan, where daily
temperature minima are often below 0°C, while in Milan
temperature rarely falls below 0°C but average temperature
in Prague during winter remains -0.4°C , and b) Milan and
Prague are large cities the microclimate is that of a dense
urban area. On the other side, Graz is a midsize town, with
the optical link being located in a suburban environment with
no tall buildings and many wide open areas around.
Therefore it is reasonable that fog episodes are heavier in
Graz than in Milan and Prague. We present in Table 2, some
statistics of all the fog events measured during the September
2005 to February 2006 measurement campaign at Graz since
the fog attenuations measured at Graz shows the worst case
fog events as compared with the Milan and Prague fog
attenuation events.


Table 2: Fog episodes detected at Graz from September 2005 to February
2006. The last two columns show laser attenuation values measured during
fog: alongside with the 50% and 99% percentiles of the attenuation
distribution

For Nice, the fog conditions are dense maritime type
that are not dependent on any particular season but are more

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dependent on the marine environment. Fig. 6 as shown
below, presents the scatter of the fog attenuation data during
a fog event measured on 28th July 2004 with 950 nm
wavelength as fog attenuations for Nice shows a worse fog
attenuation scenario. The measured data points are compared
with the four commonly used empirical models to measure
the fog attenuations. It is apparent that the dependence of
specific attenuation on visibility for dense maritime fog does
not converge to a particular model.

Fig. 6: Measured attenuation comparison with different empirical models

Since the fog attenuations at Graz shows a worse
scenario of fog attenuations under the moderate continental
fog conditions, we draw a contour plot of the measured
attenuations of six months duration in order to visualize their
diurnal behaviour. This knowledge can be handful to identify
the time intervals that can have the highest & lowest
attenuation values for such type free space optical links. This
information would consequently be useful in the link budget
designs for locations having such fog environments.


Fig. 7: Contour plot of fog attenuations for Graz at 950 nm

We plotted the collected six months fog attenuations data
for Graz in Fig. 7. From this contour plot we can see, that
there are few individual high attenuation events scattered in
the plot. However, it is difficult to conclude from this plot
any particular time slots when the fog attenuations are
particularly high. From this plot, it is clear that especially in
October to end of January the overall attenuations are high
most of the time in the range of 120 dB/km - 180 dB/km on a
second scale. Also in the start of September and the end of
February the attenuations are comparatively lesser as
compared the other months. The reason could be that in these
months winter starts to come and finish, respectively. So
there is a very high likelihood of the less severe or a kind of
very light fog conditions. Additionally, the very high
attenuation individual events are mostly occurring during the
evening and especially very late night hours (i.e., during the
18-24 time interval), while the attenuations are generally
lesser in the 00-06 time interval. From this data set, however
it is very difficult to clearly identify the regions and time
events of very high attenuation levels.
V. CONCLUSIONS
This contribution explains the impact of rain, snow and fog
effects on the propagation of optical wireless links in free
space. It was found out that for optical wireless links in the
troposphere, fog is the most limiting factor as compared with
the losses incurred by rain and snow.
This paper provides some useful statistics of the fog
attenuations from the measured attenuations of terrestrial
optical wireless links. We also tried to evaluate the atmospheric
environments of Graz, Milan, Nice and Prague on the basis of
three weather conditions i.e., rain, snow and fog and studied
their effect on the optical signal propagation. Obviously, more
attenuation data is required to make an in depth analysis of
these links under fog, rain and snow conditions. Additionally,
we tried to figure out the time intervals of fog evolution, its
dissipation and its occurrence based on the fog attenuation
trends. This information can prove very useful when to apply a
certain fade margin, that can have a significant impact on the
optical wireless links availability and improving the quality of
service (QoS) demands for applications requiring high data
rates communication.
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