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AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH
© 2010, Science Huβ, http://www.scihub.org/AJSIR
ISSN: 2153-649X doi:10.5251/ajsir.2010.1.2.350.358
Some of the atmospheric influences on microwave propagation through
atmosphere
P.K.Karmakar*, Lahari Sengupta, M. Maiti and Carlos Frederico
Ange
li
s
1
Centre for Research and Training in Microwaves and M
illime
t
erwaves
Institute of Radiophysics and Electronics, University of
Calcu
tt
a,
92 A.P.C Road. Kolkata 700 009, I
ndia
1Instituto Nacional de Pesquisas Espaciais (INPE), Centro de Previsão de Tempo e
Es
t
udos
Climáticos (CPTEC), National Institute for Space
Research
Center for Weather Forecast and Climate
S
t
udies
Rodovia Pres. Dutra, km 40, Cachoeira Paulista /SP - 12630-000
Brazil
ABSTRACT
Amongst the suspended particles in the atmosphere, water vapor and fog are the most
influencing parameters when microwave propagates through the atmosphere. Attenuation due to
these along with rain are considered in detail, over Kolkata (220 N), India and Cachoeira
Paulista (220S), Brazil
.
Rain,
perhaps is considered to be the worst offender in microwave
propagation. The
rain
patterns
over Kolkata, Brazil and U.K are compared and hence the
attenuation also.
Keywords: Microwaves, water vapor, fog, rain attenuations.
INTRODUCTION
The pressing need for developing the variety of
communication system pushes the scientists and
engineers to explore for the potential use of the
microwave and millimeter wave band of the
electromagnetic spectrum. The most important
advantages of implementing miniaturized
microwave systems are the availability of more
directive antenna gain and large bandwidth. At such
high frequencies, for example, 1% bandwidth at 600
MHz is 6 MHz (the band width of single television
channel) and at 60 GHz, 1% bandwidth is 600
MHz (100 television channel). But, on the other
hand, at frequencies above about 10 GHz,
electromagnetic radiation starts interacting with the
neutral atmosphere and also with the various
meteorological parameters, in particular,
precipitation, producing absorption of energy, and
thus attenuation of signal levels. Implicit in these
predictions of losses is a detailed knowledge of the
physical mechanism of the various meteorological
parameters, and their interactions with
electromagnetic radiation.
The adverse weather causes microwave signal
degradations mostly due to rain and suspended
particles like fog and water vapor. Atmospheric
gases cause signal attenuation through molecular
absorption in certain characteristic frequency
bands.
A very large number of gases exhibit resonant
absorption features. But, only a few have a major
impact on signal propagation through the earth’s
atmosphere in the wavelength range of interest.
Molecular oxygen and water vapor at millimeter
& sub millimeter wavelengths are the most
important constituents.
The purpose of the present work initially is to find
out the different types of losses to be incurred at
the conventional window frequencies i.e., 30 and 94
GHz along with the losses at the first and weak
water vapor resonance line i.e., around 22 GHz in
the microwave/millimeter wave band. For this
purpose, taking the advantages of latitudinal
occupancy, we have used the radiosonde data
available over Kolkata (220 N), India and Rio-de-
Janeiro (
22
0
S),
Brazil, from British Atmospheric
Data Center (BADC), U.K.
Water vapor attenuation: In addition to absorption
by molecular oxygen, molecules of water vapor also
interact with electromagnetic radiation in the
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
351
microwave and millimeter wave regions. The water
vapor molecule being a permanent electric dipole
produces rotational transitions of the order of 104
times stronger than that of the magnetic transitions of
the oxygen molecule. So, even though the
abundance of water vapor in the atmosphere is
considerably less than that of oxygen, it can produce
significant (and intense) level of attenuation near the
resonant frequencies.
Surface values on 1st July ‘09 morning.
10 km height above surface on 1st July ’09 morning.
Fig 1: Comparison of attenuation at microwave
frequencies over Kolkata and Rio-de-Janeiro. where (a)
is for Kolkata (220 N) and (b) is for Rio-de-Janeiro (220
S)
Water vapor attenuation is found to depend
quadratically on water vapor density, particularly at
high densities, above about 12 g/m3.
Amongst all the well-documented attributes of
millimeter waves is their decisive advantage over
infrared and optical waves when obscuration effects
due to suspended atmospheric particles impose
serious restriction on system performance. For the
potential benefits of operating in the region 10-100
GHz, the system designers have to rely on the
realistic atmospheric propagation models capable of
predicting attenuation by water vapor, fog, haze and
rainy as well.
The propagation effects other than rain can be
evaluated by specifying four input parameters:
frequency in GHz, total pressure in kPa, temperature
in C°and relative humidity in % by using MPM
model (Liebe, 1989). Fig 1 represents the total
attenuation (excluding rain effect) versus frequency
plots over Kolkata (220 N), India and the other one for
Rio-de-Janeiro (220 S) , Brazil, on 1st July 2009 during
morning hours. It is noted that at Kolkata and Rio-de-
Janeiro, the weak resonant line is present at 22.234
GHz at surface. The corresponding peak attenuation
at Kolkata is 0.6 dB/km but at Rio-de-Janeiro it is 0.3
dB/km. The next maxima are at 60 GHz for both the
places and each of them suffers an attenuation of 10
dB/km. But in case of 10 km height from surface, at
Kolkata, a resonant line at 22.234 GHz with
0.005dB/km attenuation is prominent. But on the
other hand, the absence of this line is prominent at
Rio-de-Janeiro. The reason behind the absence of
the 22.234 GHz resonant line at Rio-de-Janeiro,
Brazil at 10km height may be due to the fact that no
or very little transportation of water vapour from the
surface takes place at that height over Rio-de-Janeiro
although the present authors in separate
communications have shown that the integrated
water vapor content over Brazil, during morning
hours is about 40 kg m-2 (Karmakar et al 2010 ) and
that over Kolkata this value goes upto 60 kg m-2 (
Karmakar et al 1994). In another paper one of the
present authors (Sen et al 1989) concluded that any
transportation of water vapour from the surface to the
higher altitudes have been negligible effect within
12-24 hours time scale. If the time scale is increased
to 48 hrs, the integrated water vapour content is
poorly correlated with that around 2 km height which
happens to be the scale height over Brazil (Karmakar
et al 2010). The difference in behavior in this type of
variation for a short (12-24 hours) and a long time of
48 hrs scale suggests that the transportation of water
vapour to high altitudes occurred within a time scale
greater than 24 hours. In other words, we can say
that most of the water vapor over Brazil remain within
the troposphere. The Clausius–Clapeyron relation
establishes that air can hold more water when it
warms. This and other basic principles indicate that
warming associated with increased concentrations of
the other green house gases also will increases the
concentration of water vapour. This suggests that in
the morning spell the place of choice at Brazil is
cooler than that at Kolkata.
Since water vapor is a green house gas and because
warm air can hold more water vapour than cooler air,
this amplifies the original warming due to water
vapour.
Another important consideration is that the water
vapour being the only green house gas whose
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
352
concentration is highly variable in space and time in
the atmosphere, its real time measurement is highly
emerging topic of research interest to be persuaded
in different locations all over the globe. The IPCC
fourth assessment report (Cracknell et al 2007) says
that a further warming of about 0.10 C per decade
would be expected even if the concentration of all
green house gases and aerosols had been kept
constant. This report also says that in order to reduce
the level of existing uncertainties, the modeling of
nature society interaction is urgently required on a
long term basis taking into account non linear
changes in climate systems.
Attenuation due to fog: Fog can be formed in
variety of ways depending mostly on the
condensation mechanism. Generally, we encounter
the type of fog, which is formed by the cooling of land
after sunset by thermal radiation in calm and clear
sky. The cool ground produces condensation in the
nearby area by conduction of heat. This type of fog
mostly prevails at night and does not last long after
sunrise. It generally occurs in autumn and winter.
Fog attenuation is comparatively smaller at millimeter
wavelength. Fog is composed of suspended
spherical water droplets with radii small enough to
keep them suspended in air by micro turbulence
(Liebe et. al., 1989). Attenuation due to fog in the
millimeter wave band is mainly caused by absorption
and scattering which in turn depends on the extent of
the fog density (in other words visibility) and its index
of refraction. According to Gibbins (1988), the fog
density is given in terms of visibility V (km) by
54.1
024.0 ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=V
Mgm-3 (1)
Fig. (2) shows the variation of extent of the fog in
terms of density. However, it is to be remembered
here, that, we are concerned with the radiation fog for
which the fog density approaches nearly 1gm/m3. But
over U.K.(non-tropical zone), Gibbins (1988) pointed
out that fog occurs typically of the order of 1-2% of
the time over a period of one year. The density of this
type of fog is 0.02 gm/m3 for which the visibility is 300
m and is termed as moderate fog.
0.05 0.10 0.15 0.20 0.25 0.30 0.35
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Visibility in km
Fog density in gm/m^3
Fig 2: Fog density versus visibility characteristics.
Comparing the size of the suspended water droplets
(fog) and the wavelength in the millimeter wave band,
the Rayleigh approximation may be adopted for
defining the refractivity model. Using the Rayleigh
absorption approximation (Van de Hulst, 1957),
refractivity is written as
(
)
(
)
(
)
2/12/3 +
−
=
ε
ε
w
mMN ppm (2)
Where, w
m= specific weight for water = 1.0
and M is defined as given in equation (1) and is the
complex permittivity.
According to Liebe et al (1989) we define the power
loss of the radio wave while propagating through fog
as
(
)
fNf
′
′
=
182.0
α
dB/km 3)
where
(
)
fN
′
′
is complex refractivity.
An attempt has been made to describe the fog
attenuation at 30 and 94 GHz considering
temperatures as the parameters ranging from 284 K
to 303 K. This is pictorially present in Fig. (3). It is
clear from the figure that within the said temperature
range, the 30 GHz attenuation never exceeds 0.35
dB/km. But on the other hand, the 94 GHz
attenuation shows, for the same range of
temperatures and for fog densities 0.5 gm/m3, its
value ranges from 2.1029 to 1.6283 dB/km. For the
sake of clarity, it is also observed that for 0.5 gm/m3
and for temperature 284.7 K the 94 GHz attenuation
is more or less 7 times larger than that at 30 GHz.
This ratio becomes very much pertinent to our study
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
353
because we are concerned with the radiation fog
whose density mostly approaches towards 0.3-0.7
gm/m3. But, in case of the advection fog; its density is
less (nearly equal to 0.2 gm/m3) and hence this
attenuation ratio is not that much prominent to be
noticed in microwave propagation.
Fig 3: Fog density versus attenuation curve.
To exemplify the dependence of temperature on fog
attenuation at 30 and 94 GHz, Fig 4 has been
presented keeping fog density equals to 0.5 gm/m3.
280 285 290 295 300 305
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Fog density=0.5gm/m^3
Attenuation in dB/km
Tem perature in kelvin
Fo g atte nua tion a t 9 4 G Hz
Fo g atte nua tion a t 3 0 G Hz
Fig 4: Temperature versus attenuation curve.
4. ESTIMATION OF RAIN
The rain rate profiles during 1985-86 were recorded
at the Institute of Radio Physics and Electronics,
University of Calcuttta, using a ‘Dynabab’ fast
response rain gauge having response time 10 s. A
statistics of the peak rain rate during the said period
is shown in Fig (5). (Karmakar, 1990) This is
comparable to a similar histogram for longer period of
four years obtained from the measured rain rates at
U.K. (Norbury and white, 1975) as shown in Fig (5).
The distribution of duration of the rain events at
Kolkata and U.K. are shown in Fig (6). This shows a
similar trend in the order of the values except few
cases of very high rain rates occurring in Kolkata (a
tropical zone).
The total number of rain events with rain rates
exceeding 25mm/hr is 85 measured at Kolkata in
1986, while in U.K. the total number is only 77 for rain
rates exceeding 20 mm/hr measured over four years
(1970-73). This exhibits only the great abundances of
large rain events in the tropical station like Kolkata,
relative to that at U.K.
The rainfall intensity data and the corresponding rain
attenuation data for the year 2009 over Cachoeira
Paulista (22 deg South), Brazil, is also provided by
the precipitation monitor.
Fig 5: statistics of peak rain rate over Kolkata (1985)
and that over U.K. (1970-73). Similarly of these two
histograms exhibited.
The rain monitor has the capability of measuring
maximum rain rate upto 250 mm/hr and a minimum
upto 0.0005 mm/hr with a resolution time 10 secs.
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
354
Fig 6: Histogram of duration of rain events over
Kolkata and that over U.K. Histogram shows the same
nature.
Rain fall rate at Cachoeira Paulista (220 S), Brazil
were measured during Dec, 2008 till July, 2009. It is
noted that heavy rainfall is largely restricted to late
afternoon or in the evening hours. Although there are
no dry spells as such, the rainy season over Brazil is
normally considered to be the period between
December and May. However April is the wettest
month. The dominant rain forming mechanism in this
region is due to convective activity. It is interesting to
note that rain rate rarely goes beyond 100 mm/hr
during our study. There were few events occurred
when rain rates attain a maximum value of 107
mm/hr. A statistical analysis of the number of rain
events over Cachoeira Paulista(CP, 220S), Brazil
during the year 2009, reveals that the number of
occurrence goes beyond 200 for rain rate upto 15
mm/hr but quite interestingly it is observed that the
number of events goes well below75 for the rain rates
ranging from 15 to 25 mm/hr. And subsequently the
number of events for the higher rain rates takes a
sequential step down reaching ultimately to highest
rain rates 107 mm/hr. Eventually, this distribution
represents a log-normal distribution over CP, Brazil.
But on the other hand the rain rate distribution over
Kolkata (220N), India, strikingly revealed that the
normal distribution is well fitted with the measured
data. In case of log-normal distribution, it was found
by Chi-square test that probability lies between 0.30
to 0.50, whereas in case of normal fitting it was
observed that the probability lies between 0.85 and
0.75 and it was also found that only 12% is the
probability of the raining beyond 50 mm/hr. The same
procedure has been adopted to find out the
probability of raining at around 50 mm/hr over CP,
Brazil and is found to be about 20%. However, the
occurrence of the rain events at Brazil is presented in
Fig (7).
20 40 60 80 100 120
0
10
20
30
40
50
60
No. of events
Rain rate in mm/hr
Fig 7: Histogram of rain rate over Cachoeira Paulista
(220 S), Brazil
A cumulative distribution of the rain rate has been
presented in Fig (8) from the data obtained by the
fast response rain gauge located at the Institute of
Radio Physics and Electronics, Kolkata, India. It is
shown by the continuous line curve as shown in Fig
(8). Two other curves have also been included for
comparison. The broken line curve is an average
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
355
curve of 5 minute rain rate averaged over a period of
1979-83 (Sinha et. al., 1987) based on data obtained
at kolkata using ordinary tipping bucket rain gauges.
The dashed curve in Fig (8) shows a clock minute
surface rainfall rates for CCIR rain climate region 1,
which actually include India (CCIR 1974).
The curves are in close agreement except the curve
for the year 1985, extends up to about 240 mm/hr
which again shows a large abundance of rain fall in
Kolkata, while the other two show higher occurrence
of rain fall rate above about 80 mm/hr.
Fig 8: Percent of time rainfall rate exceeded ordinate.
5. RAIN ATTENUATION
At frequencies above 10 GHz electromagnetic
radiation starts interacting with the neutral
atmosphere and with various meteorological
parameters, in particular, with the precipitation.
Moreover, water droplets present in the radio path act
as an imperfect conductor. Hence millimeter waves
after interfacing with them cause a displacement
current which is directly proportional to the frequency
of the wave. Therefore, the attenuation due to the
presence of water droplets in the propagation path
varies as wave frequency. However rain attenuation
and scattering by rain primarily depends on shape,
size and the complex dielectric constants of the
drops, and on the wavelength and polarization of the
incident electromagnetic wave. For spherical
droplets, the theory of absorption and scattering was
formulated by Mie’s theory (1908) and afterwards for
the non-spherical droplets, it was formulated by
Oguchi and Hosoya (1974). In fact, rain attenuation is
characterized by non-uniformity of rain fall intensity,
rain drop number density, rain drop temperature in
addition to its intrinsic variability in time and space.
The most commonly used raindrop sizes
were given by Laws and Parsons (1943), Marshall
and Pamer (1948), Joss et. al. (1968). For practical
applications, however the relation between the rain
rate and specific attenuation for a number of rain
drop size distributions is approximated to simple
power law (Fedi, 1979) in the form of
b
aR=
α
dB/km. (4)
However, to deduce the rain attenuation statistics
from the rain rate data, as a first step equation (4)
has been used. Assuming Laws and Parsons
Distribution of raindrop Hardens et. al. (1978)
estimated theoretically the values of a and b from
which the values of the parameters for 10, 12, 18, 22,
30, 35, 40, 53, 94 and 100 GHz were obtained by
interpolation, (refer to table 2). Now, the rain
attenuations have been calculated for different rain
rates, considering Laws and Parsons drop size
distribution and shown in Fig (9).
Table 2
Frequency Vertical
polarization (a) Vertical
polarization (b)
11 0.012 1.23
18 0.053 1.07
24 0.10 1.03
30 0.17 0.98
40 0.31 0.91
60 0.63 0.81
80 0.86 0.76
100 1.06 0.73
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
356
0 50 100 150 200
0
5
10
15
20
25
30
35
40
45
50
55 100 GHz
80 GHz
60 GHz
40 GHz
30 GHz
24 GHz
18 GHz
11 GHz
Attenuation in dB/km
Rain rate in mm/hr
Fig 9: Predicted rain attenuation assuming Laws and
Parsons Distribution.
From this curves it was noticed that all curves
increase linearly irrespective of frequencies. But the
radiometric measurements show that rain attenuation
curves become saturated after a certain rain rate.
This was also observed that as we move towards the
higher frequency, the saturation evolves at a lesser
rain rate. To clarify the situation we have initially
started measuring rain attenuation by multi-channel
microwave radiometer installed at Cachoeira Paulista
,Brazil ( S).
Rain attenuations have been measured from the
brightness temperature available from the multi
channel zenith looking microwave radiometer. The
rain attenuation were calculated by using the relation
= (5)
Where is the mean atmospheric temperature in
Kelvin = 290K
is the cosmic background noise temperature in
Kelvin= 3K
is the measured brightness temperature in Kelvin
For tropical locations like Kolkata, India ( N), &
Cachoeira Paulista ,Brazil ( S), the value of
will be higher than those in temperate latitudes due to
higher temperatures and large water vapour content.
The cumulative distributions for the signal attenuation
at different frequencies over CP, Brazil have been
studied.
Figure 10 shows the cumulative distribution of
measured rain rate for the year 2009 over Cachoeira
Paulista (220 S), Brazil, when compared with ITU-R
(2003) recommendation, the experimental results
show approximately good agreement at lower rain
rates. This prediction model was reported to agree
well for temperate regions where the rain structure is
considered to be stratiform in nature. But the two
distributions show a monotonous decrease in rain
rate. The difference between measured and standard
prediction model is the existence of “break point” in
the exceedence curve. The presence of such break
point in the exceedance curve was reported by
several authors (Pan et al., 1994; Ramchandran and
Kumar, 2007; Mandeep and Allnutt, 2007). The break
point here refers to the point at which the trend gets
reversed (Kumar et al., 2006; Bryant et al., 2001).
The break point of rain rate observed approximately
at 8 and 76 mm/hr. over CP. When the rain structure
is stratiform, the rainfall is widespread, with low rain
rates (Mandeep and Allnutt, 2007). But at 76 mm/hr
there occurs another break point. This usually occurs
in the tropics. When the cloud builds up, the water
droplets are trapped in updrafts inside the cloud and
are vertically transported. This enhances the
coalescence of water particles resulting in convective
heavy rain (Flavin, 1982). Hence, there lies the
probability that at the breakpoint either the rain
structure changes or it happens due to the changes
in cloud morphology.
The rain attenuation (dB) exceedence also show the
breakpoints for some frequencies around the water
vapour band. (Fig.11). There exists a good similarity
in nature between rain rate and attenuation
breakpoint. The measured attenuation exceedance at
Am. J. Sci. Ind. Res., 2010, 1(2): 350-358
357
different frequencies around the said band have been
compared with the world standard prediction models
ITU-R P.618-8 (ITU-R P.618-8, 2003.) and
Ramchandran & Kumar model (Ramchandran &
Kumar, 2007).
It has been observed that measured result is very
close to ITU-R model except the existence of
breakpoint. The reason behind this may be due to the
fact that these models are applicable for temperate
region where rain rate is low and rain height is
considered to be more or less constant. The ITU-R
model includes a few rain zones which is not
accommodating the wide range of rain conditions in
the tropical zone. Hence, a detailed and large data
bank has to be formed over a tropical region to make
the idea of existence of breakpoint clear.
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