Rain Attenuation 
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EM wave interaction with atmosphere
Worldwide rain intensity statistics
Rain
unavailability prediction
©
20012016, Apus Cloud Project e Luigi Moreno
_______________________________________________________________
In this
Session we first discuss the interaction of an EM wave with molecules
encountered
throughout
the propagation path in the atmosphere. This leads to an estimate of rain
specific attenuation, as a function of rain intensity, signal frequency and
polarization. Statistical data on rain intensity are considered, as required by
the ITUR rain attenuation model, which is presented as the basic tool to
predict rain unavailability in any region in the world, at frequencies up to
about 40 GHz.
Even if
this Session is mainly devoted to rain effects, we first consider, in more
general terms, the interaction of EM waves with molecules and particles
encountered throughout the propagation path in the atmosphere.
Two
effects are most significant :
·
absorption: EM energy transferred to
the impacted molecules and converted into heat;
·
scattering: EM energy
reirradiated away from the propagation direction it had before impact.
Both
effects are mainly affected by :
·
Molecule / particle dimensions,
relative to the wavelength of the EM radiation;
·
Electrical properties of the
involved molecules.
We
consider the effect of the atmosphere in the absence of rain and the
attenuation due to raincells.
Phenomena
related to other hydrometeors (snow, ice, fog, hail) and even to dust storms
will not be discussed here (ITUR Rec. P840 gives some indication about the
effect of thick clouds and fog).
Water
vapour and Oxygen attenuation in clear air
In the
frequency range up to about 40 GHz, the atmospheric molecules which interacts
with EM waves are water (in the form of water vapour) and, more marginally,
oxygen.
A water
vapour absorption peak is observed at 22.2 GHz, while the first oxygen
absorption peak is at about 60 GHz.
Other absorption peaks, for both water vapour and oxygen, are at higher
frequencies.
The maximum attenuation due to water vapour (g_{
WV
}
), at 22.2 GHz, is given by (according to
ITUR Rec. P676) :
_{
}
where r
is the vapour density in g/m^{3},
the atmospheric pressure is 1013 hPa and the temperature is 15°C.
This
gives a 0.30 dB/km attenuation at the water vapour saturation level (about 12
g/m^{3} at 15 °C) and 0.18 dB/km at a lower vapour density of 7.5 g/m^{3}.
On the other
hand, the specific attenuation due to oxygen exceeds 1 dB/km in the frequency
range 52 to 68 GHz; the maximum attenuation, at 60 GHz, is about 16 dB/km,
while at 40 GHz it is below 0.1 dB/km.
For
radio hops up to about 40 GHz, the conclusion is that the power loss caused by
atmospheric absorption is usually not significant.In most cases it can be neglected in the Link Budget, also
considering that the hop length is anyway limited by rain attenuation.
An EM
wave, traveling in a given direction through a raincell, loses part of its
power in that direction, as a result of absorption and scattering effects.
In the
impact with a raindrop, the total power lost depends on the "drop cross
section", which is given by the sum of a scattering cross section and an
absorption cross section.
The
drop cross section is a function of the drop radius and of the signal
wavelength.
By
integrating the power lost in the impact with a single raindrop to all the
raindrops in a given volume (raincell), the total loss produced within that
raincell can be estimated.
To do
this, suitable statistical models are needed to relate the number of raindrops
in a raincell and their size distribution to the rain intensity.Such models have been tuned on the basis of
a large amount of experimental data, coming from different regions in the
world.
As a result, the specific rain attenuationg
(dB/km) can be expressed, as a
function of the rain rate R (in mm/h), by the following exponential formula:
_{
}
where
the parameters k and
a
are functions of the signal wavelength and polarization.
ITUR
Rec. P838 gives a table with the k and
a
values, for Vertical and Horizontal
polarizations, in the frequency range 1 to 400 GHz.Formulas are given for the case of any linear or circular
polarization.
Examples
of specific rain attenuation as a function of rain rate, are given in the
figure below; note that the increase in
specific attenuation is about 100 times, when passing from 3 to 12 GHz.Moreover, the Vertical polarization is
significantly less attenuated than Horizontal polarization, at the same
frequency.
Attenuation vs. rain intensity, for different signal
frequencies,
vertical
(red) and horizontal (black) polarizations
Other
rain impairments
EM wave depolarization

An additional effect must be considered when a linearly polarized EM
wave travels through a raincell: a rotation of the polarization plane, so that
an orthogonally polarized component can be observed at the output of the cell.
The depolarization effect
is related to the raindrop shape and to the dropping angle (in most cases, not
perfectly vertical).
It is possible to establish
a statistical relation between rain attenuation and depolarization effect. For
a given probability P, we define the "equiprobable" levels in
copolar attenuation (CPA_{P}) and crosspolar discrimination (XPD_{P})
as:
_{
}
XPD_{P} can be
predicted from CPA_{P} (that is when the CPA cumulative distribution is
known) as:
_{
}
where :_{
}
_{
}
_{
}
Interference due to wave
scattering
A raincell may become a potential source of
interference to other radio systems, since part of the EM energy which impacts
the cell is scattered in multiple directions. The propagation model to be
applied in such conditions is described by ITUR Rec. P.45210.
It is rather unlikely that a
PP link may produce a significant interference effect to another PP link,
through raincell scattering. The TX
power level is usually at (or below) 1 W and the cell scattering works almost like
an omnidirectional radiator, so a low power density is associated with the
scattered signal.
On the other hand, high
power radio transmitters, in particular large earth stations for satellite
communications, have the potential for producing a not negligible interference
through raincell scattering. Detailed
procedures are recommended by ITUR documents to take account of this, when the
satellite system operates in frequency bands shared with terrestrial systems.
An
important input to any rain attenuation model is the expected rain activity in
the region where the radio hop will operate, as derived from longterm
statistics.
More
specifically, it was found useful to refer to the lowprobability tails of rain
statistics, since we are mainly interested in rare events with very heavy
rainfall.
The
rain rate exceeded for 0.01% of the time is
the significant parameter, useful to characterize the rainfall activity in a
given region.
If possible, this rain rate should be derived from reliable
statistical data about the local rain events. When local data are not
available, the procedure recommended by ITUR can be used.
In the last
release of Rec. P837 a new approach is reported to estimate the rain rate
exceeded for any percentage of time, in any part of the world. This is based on
data files (available from the ITU website), derived from 15 years of data of
the European Centre of Mediumrange Weather Forecast (ECMWF). They cover all
the world, with latitude and longitude grids in 1.5° steps.A suitable interpolation procedure is
recommended.
To give
an approximate information about the rain rates used in rain attenuation predictions,
the previous ITUR approach is reported, which was based on world maps with
"rain regions".
Each region was labeled with a letter; in the table below, each letter
is associated with the corresponding rain rate (in mm/h) exceeded for 0.01% of
the time :
A 
8 

D 
19 

G 
30 

K 
42 

N 
95 
B 
12 

E 
22 

H 
32 

L 
60 

P 
145 
C 
15 

F 
28 

J 
35 

M 
63 

Q 
115 
The
world maps are shown below.
ITUR Rain regions, North America
(from ITUR Rec. P8371 Fig.1, by ITU permission)
ITUR Rain regions, Centre and South America
(from ITUR Rec. P8371 Fig.1, by ITU permission)
ITUR Rain regions, Europe, Africa and Middle East
(from ITUR Rec. P8371 Fig.2, by ITU permission)
ITUR Rain regions, Asia and Oceania
(from ITUR Rec. P8371 Fig.3, by ITU permission)
Rain
intensity model
In
order to apply raincell models
to the estimate of rain attenuation in a radio hop, it is necessary to consider
how the raincell size compare to the hop length.
While in
very short hops (below some 2  3 km) the whole length may be affected by
rainfall, in longer hops a raincell occupies only a portion of the whole
distance.
ITUR Rec. P530 defines an "effective
hop length" D_{EFF}, in order to take account ofraincell size :
_{
}
_{
}
Note
that the effective length is a function of the local rain rate R (in
mm/h). As shown in the diagram below,
the effective length is more compressed with high rain rates (a raincell with
high rain rate is expected to occupy a smaller area).On the other hand, the effective length is close to the real
length as far as the latter is approximately below 4 km.
Conversion from real path length to effective length
D_{EFF},
for various rain rate values
ITUR
Rec. P530 gives a stepbystep procedure to estimate the time percentage that
rain attenuation exceeds a given threshold on a radio hop.
Input
parameters are the hop length, the signal frequency and polarization, and the
operating region. The recommended
procedure is as follows :
·
Estimate of the local rain rate R
for 0.01% of time. This should derive from longterm statistical data collected
in the specific zone; otherwise, ITUR data can be used, as indicated
in the previous section.
·
Application of the
specific loss (g)
formula
, given the rain rate R, the signal frequency F and polarization (H
or V).
·
Reduction of the hop length to the
Effective Length D_{EFF} (km), according to the above formula.
·
Computation of Rain Attenuation
exceeded for 0.01% of time :
_{
}
·
Extrapolation to other time percentages p, in the range from 1% to
0.001% :
_{
}
for
temperate climate (latitude greater then 30°, North or South), while for
tropical / equatorial climate (latitude below 30°) :
_{
}
An example is given below, where A_{0.01}
has been assumed to be 30 dB. Note that
the abscissa gives the attenuation exceeded for the corresponding time
percentage.
Percentage of time vs. Rain attenuation,
assuming A_{0.01} = 30 dB, in different
climates
The
ITUR prediction method is considered to be valid for frequencies up to 40 GHz
and hop lengths up to 60 km.
Frequency
/ polarization scaling model
An alternative model
proposed by ITUR (Rec. P.530) can be applied when experimental results are
available about rain attenuation on the same hop, measured at a different
frequency and/or polarization.
In that case, we need to
scale the measured result to the frequency and/or polarization used in the
project of interest.
The following empirical
formula can be used to estimate rain attenuation A_{2} at frequency F_{2},
for a given time percentage, when longterm experimental statistics at
frequency F_{1} predict attenuation A_{1} for the same time
percentage (frequency in GHz, attenuation in dB):
_{
}
where_{
}
_{
}
Similarly, when longterm
experimental statistics on a given polarization at frequency F predict
attenuation A for a given time percentage, then the attenuation on the
orthogonal polarization, at the same frequency and for the same time percentage
can be estimated as :
_{
}_{
}
For a
given radio hop, the attenuation due to rain for 0.01% of the time can be
estimated, according to the ITUR procedure, as a function of the local rain
rate, of the hop length, and of the signal frequency and polarization.
To
predict the hop unavailability caused by rain, it is convenient to reverse the formulas given above, in order to
get the time percentage p as a function of the attenuation A exceeded for p%
(note anyway the 0.001% to 1% application range) :
_{
}
where :
_{
}
for
temperate climate and :
_{
}
for tropical / equatorial climate.
Then, the
rain unavailability is predicted as the probability that the rain attenuation
exceeds the Fade Margin FM :
_{
}
The
same result can be graphically derived from the Time % vs. Rain Attenuation curve.
The hop
Fade Margin is computed as a result of Link Budget. In
presence of heavy rainstorms, the thin water layer on the antenna radome (if
used) produces an additional loss; the Fade Margin is reduced to take account
of the "wet radome loss", a
conservative figure being about 1 dB.
Quite
often the rain unavailability prediction is transformed from a percentage
probability to "minutes in one year".As a reference, the 0.01% probability is equivalent to about 50
min/year.
However,
since the prediction method is based on longterm rain intensity statistics,
also the estimated unavailability must be considered as an average, to be
expected during a period of several years.
Effect
of crosspolarized interference
Signal depolarization caused
by rain contributes to rain unavailability by reducing the discrimination to a
crosspolar interfering signal. Typically,
the problem arises in radio systems using a cochannel frequency plan, with the same radio channel used
on both polarizations.
The stepbystep procedure
reported by ITUR Rec. P.530 is as follows :
Computation of the "reference attenuation" A_{P}::
_{
}
where
U and V have been
previously defined
.
Computation of the normalized parameter m
(if m>40, then m=40)
:
_{
}
where A_{0.01}
is the
attenuation exceeded for 0.01% of
the time
.
Estimate of probability P_{XPR} (unavailability due to
crosspolar interference):
_{
}
Reliable estimates of P_{XPR}
are in the range 10^{2} to 10^{5}.
Finally, the overall rain
unavailability can be estimated as the larger of P_{XPR} (see above)
and P_{RAIN} (
probability of
unavailability due to rain attenuation only
).
Further Readings
Crane R.K., "Prediction of attenuation by rain", IEEE Tr. Communications, vol. 28, n. 9, 1980, pp.171733.
Fedi F., "Prediction of attenuation due to rainfall on Terrestrial Links", Radio Sci., vol. 16, n.5, 1981, pp. 731743.
Olsen R.L., "Cross polarization during precipitation on a terrestrial link. A review", Radio Sci., vol. 16, n. 5, 1981, pp. 761779.
Holt A.R. et al., "Frequency scaling propagation parameters using dualpolarization radar results", Radio Sci., vol. 19, n. 2, 1984, pp. 222230.
Segal B., "Spatial correlation of intense precipitation with reference to the design of terrestrial microwave networks", IEE Int. Conf. on Antennas and Propagation (ICAP), Norwich 1983.
End of
Session #6
_______________________________________________________________
©
20012016, Apus Cloud Project e Luigi Moreno