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Variability of Rain Attenuation in the 100-200 GHz Band Calculated from Experimental Drop Size Distributions

Authors:
Variability of Rain Attenuation in the 100-200 GHz
Band Calculated from Experimental Drop Size
Distributions
Santiago Pérez-Pena1, José Manuel Riera1, Ana Benarroch1, Domingo Pimienta-del-Valle1, Pedro Garcia-del-Pino1
1 Information Processing and Telecommunications Center (IPTC), Universidad Politécnica de Madrid (UPM), Madrid, Spain,
jm.riera@upm.es
Abstract The attenuation produced by rain can be
derived from experimental Drop Size Distributions (DSD)
using physical models of scattering in particles (Mie and its
Rayleigh approximation). As the frequency increases within
the mm-wave bands, the specific attenuation becomes more
dependent on the DSD, whereas attenuation is mainly
determined by the rain rate R in lower frequency bands. As is
well-known, Mie scattering becomes dominant in the mm-wave
band instead of Rayleigh scattering, which is the main
extinction mechanism in cm-wave frequencies. In this
document, long-term DSD measurements from an optical
Laser disdrometer available in Madrid, Spain, were used to
estimate the specific attenuation produced by rain. A very long
period of twelve years has been used for the analysis of rain
attenuation in the 100-200 GHz band. The results compare well
on average with the ITU-R specific attenuation model of Rec.
P.838-3, but they show a significant variability.
Index Terms—atmosphere, rain attenuation, attenuation
measurement, D-band.
I. INTRODUCTION
The projected migration of future mobile-access
networks to the 30-100 GHz range is going to move the
wireless backhaul/fronthaul links towards higher frequencies
along the mm-wave band, beyond 100 GHz [1].
The specific attenuation produced by rain γ (dB/km)
significantly affects mm-waves. γ is mainly caused by liquid
particles since the attenuation generated by ice crystals and
snowflakes is lower in this band. As the frequency increases
within the mm-wave band, the specific attenuation becomes
more dependent on the DSD, whereas attenuation is mainly
determined by the rain rate R(mm/h) in lower frequency
bands. As is well-known, Mie scattering [2]-[3] becomes
dominant in the mm-wave band instead of Rayleigh
scattering [4], which is the main extinction mechanism in
cm-wave frequencies.
The use of the Mie theory to calculate rain attenuation in
these frequencies has been applied in other studies, as in [5]
and some of its references, using different DSD models.
Instead of using any model, this study makes use of the
experimental DSD measured for twelve years (2008-2019)
using an optical Laser disdrometer, the Thies Laser
disdrometer [6], located at Escuela Técnica Superior de
Ingenieros de Telecomunicación (ETSIT) of Universidad
Politécnica de Madrid (UPM), Madrid, Spain, to evaluate
rain specific attenuation in the 100-200 GHz band and
compare with existing models. The assessment of the quality
and features of the DSD was carried out previously [7].
The DSD measured by the Laser disdrometer are
available in discrete bins, organized by diameter classes, Di
(mm). N(Di) (m-3mm-1) is the number of particles per volume
(m3) and per diameter units and quantifies the DSD.
In this document, Section II presents the Laser
disdrometer. Section III describes how γ is computed
through the combination of the Mie theory [2]-[3] with the
Liebe parametrization of the complex refractivity index of
water [8]-[9]. Section IV presents the results of γ in the 100-
200 GHz band and compare them with the ITU-R model.
These results include the γ plotted versus R and the relative
probability distribution of the error between the measured γ
against fitting curves. Section V explains some particular
cases found. Section VI outlines the conclusions.
II. THIES LASER DISDROMETER
The Thies Laser disdrometer [6] generates a horizontal
beam of infrared light (780 nm) from an optical laser. The
beam surface is S = 45.6 cm2. A photo diode measures the
optical intensity and transforms it into an electrical signal.
When a precipitation particle falls across the light beam, its
diameter and speed are calculated from the amplitude and
duration of the reduction in the received signal.
Precipitation particles are measured every one-minute and
are grouped in a diameter-speed grid known as a spectrum.
Each bin of the grid is a combination of diameter (Di) and
speed (vj) classes, which are categorized in 22 (i = 1…,22)
and 20 (j = 1,…,20) non-uniform classes, between 0.125-8
mm and 0-10 m/s, respectively. Figs. 1 to 3 show three
different examples of Laser disdrometer spectra,
corresponding to rain, snow, and drizzle, respectively. In
these figures, the color of each bin reveals the number of
particles detected in that minute. Besides, the figures show
the Gunn-Kinzer (GK) curve [10], which models vj(D)
(m/s), as a function of Di (mm). The GK curve was modified
for the Madrid altitude h (m) via δv(h) (h = 680 m, then δv(h)
= 1.025), according to [11]. The GK curve and its correction
are presented in (1)-(2). Equation (1) is strictly valid only
for 0.109 ≤ Di ≤ 6 mm.



(1)

!
"
#
$
%
(2)
The DSD are calculated from the Laser disdrometer
spectrum using (3), where n(Di,vj) is the number of particles
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such as IEEE Xplore under the license granted by the "Agreement Granting EurAAP Rights Related to
Publication of Scholarly Work."
with D
i
(mm) and v
j
(m/s), Δt = 60 s is the integration time
and dD
i
(mm) is the D
i
width.
&
'
(
)
'
+
+
$
+
,
-
.
/
0
1
'
(3)
Fig. 1. Rain spectrum provided by the Laser distrometer.
Fig. 2. Snow spectrum provided by the Laser distrometer.
Fig. 3. Drizzle spectrum provided by the Laser distrometer.
DSD were obtained for the D
i
used by the Laser
disdrometer, with dD
i
of 0.125 mm (D
i
< 0.5 mm), 0.25 mm
(0.5 ≤ D
i
< 2 mm) and 0.5 mm (D
i
≥ 2 mm).
Only rain is considered in this study. As commented in
the introduction, attenuation produced by hail and snow is
lower in the frequency band under investigation.
A two-step preprocessing procedure has been applied to
the disdrometer data before calculating the DSD. This
procedure, whose objective is to eliminate errors, to
maintain data integrity and to remove particles different
from liquid rain, was investigated and assessed in a previous
work [12] and was included in [13]. The first step is a
preliminary data quality control applied to each individual
spectrum for the detection of noise and the identification of
drizzle and the second step consists of a set of filters applied
to particles in each spectrum.
By means of the data quality control, a spectrum is
removed if it is identified as noise. When R < 0.1 mm/h, a
spectrum is considered as noise if it contains less than 10
particles. Spectra are also inspected to determine if they
contain mostly drizzle particles [12, 13]. A one-minute
spectrum is identified as drizzle if at least 95% of the
particles in the spectrum have a diameter ≤ 0.5 mm and
more than 99% have a diameter ≤ 1 mm [12]. An example is
shown in Fig. 3.
In the second step various filters are applied [12, 13].
Particles with large diameters and low speeds are removed
since they can be spurious particles or snowflakes, as seen
in Fig. 2. This is achieved using the Locatelli-Hobbs
empirical diameter–fall speed relationship [14]. Likewise,
isolated particles located at least at 4 empty bins away from
the main cluster of bins containing particles are also
removed [15]. Moreover, very small particles (diameter < 1
mm) with fall speeds higher than 6.6 m/s are removed [12].
It is important to notice that individual particles are
removed but not the one-minute spectrum containing them.
III. A
BSORPTION AND
S
CATTERING OF
E
LECTROMAGNETIC
W
AVES IN
W
ATER
D
ROPS
The extinction cross section (σ
ext
(D
i
) (m
2
)) models the
absorption and scattering effects that attenuate the radio
waves due to interaction with raindrops. γ can be obtained by
the integration of the extinction produced by all the drops
with different sizes [16]. Therefore, γ must be calculated
over all the D
i
:
2
=
1
34

(
5
678
'
9
&
'
9
1
'
'
(4)
σ
ext
(D
i
) has been calculated applying the Mie theory [2]-
[3], representing the raindrops as small spheres of discretized
radius with a refractive index different from that of the air.
To reproduce the raindrops radiative properties, we need
the relative refractive index m = N
1
/N
2
of water
precipitation, where N
1
is the complex refractive index of
the raindrop and N
2
is the refractive index of air. An
empirical model was applied based on the Liebe
parameterizations for water [8]-[9], which describes the
complex refractive index for the frequency range from 1 to
1000 GHz. A temperature value of 290 K was used for the
complex refractive index.
Additionally, R can also be obtained by the integration of
all the drops with different sizes [17] as:
R
=
π
6
:
(
D
i
3
:
N(D
i
)
:
v(D
i
)
:
dD
i
i
(5)
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such as IEEE Xplore under the license granted by the "Agreement Granting EurAAP Rights Related to
Publication of Scholarly Work."
IV. S
PECIFIC
A
TTENUATION
C
ALCULATED FROM
DSD
M
EASURED BY THE
L
ASER
D
ISDROMETER
In this section, γ is calculated from the DSD measured in
Madrid in a period of twelve years (2008-2019).
Specific Attenuation versus Rainfall Rate
Figs. 4 to 6 present the estimations of γ versus R at 100
GHz, 150 GHz, and 200 GHz with the fitting curve
calculated from the regression coefficients k an α derived
from the power law γ = kR
α
. Besides, in these figures the γ
calculated using the ITU-R Rec. P.838-3 prediction [18], for
an elevation angle = 0° and a tilt angle = 45°, is also shown.
Each scatter point corresponds to a one-minute γ value.
Fig. 4. Specific attenuation versus rainfall rate, 100 GHz.
Fig. 5. Specific attenuation versus rainfall rate, 150 GHz.
Through the comparison of Figs. 4 to 6, the dispersion of
the one-minute measured points becomes higher when the
frequency rises from 100 GHz to 200 GHz. The variability
is higher than what is found at lower cm-wave frequencies,
exemplified in Fig. 7 for 19.7 GHz The fitting curves in
Figs. 4 to 6 are coincident with the ITU-R P. 838-3 [18]
curve up to R = 5 mm/h. Beyond R = 5 mm/h, the ITU-R P.
838-3 [18] curve begins to underestimate the γ obtained
from the measured DSD.
Figs. 8 and 9 present the fitting coefficients k and α,
respectively, for each of the twelve years and their average
(solid black line) for the 100-200 GHz frequency band.
Besides, the ITU-R P. 838-3 [18] coefficients k and α are
shown for the same frequencies (dashed black line).
Fig. 6. Specific attenuation versus rainfall rate, 200 GHz.
Fig. 7. Specific attenuaton versus rainfall rate, 19.7 GHz.
Fig. 8. Fitting coefficient, k. DSD (solid), ITU-R P. 838-3 (dashed).
Fig. 9. Fitting coefficient, α. DSD (solid), ITU-R P. 838-3 (dashed).
This paper's copyright is held by the author(s). It is published in these proceedings and included in any archive
such as IEEE Xplore under the license granted by the "Agreement Granting EurAAP Rights Related to
Publication of Scholarly Work."
Both fitting coefficients follow the tendency of the ITU-R
P. 838-3 [18], which means that, as frequency increases, the
fitting coefficient k increases whereas α decreases.
Interannual differences among them become more evident
as the frequency rises.
Despite analyzing a wide frequency range, 100-200 GHz,
it seems that, in terms of γ, the whole band has a similar
behavior. This band behavior is the same as the one
described in the ITU-R P. 838-3 [18] prediction.
Specific Attenuation Variability
Figs. 10 to 12 show the relative probability of the error
between γ from measured DSD and γ from the fitting curve
for 100 GHz, 150 GHz, and 200 GHz. The error used is
obtained as log10 from DSD) - log10(γ from fitting curve).
The solid black line represents the outline of the
histograms by a non-parametric kernel-smoothing
distribution. The solid red line is a normal distribution
calculated from the measured values, where µ is the mean
error and σ is the standard deviation error.
Fig. 10. Relative probability distribution of the error, 100 GHz.
The dispersion of rain specific attenuation around its
fitting values, for a given rain rate, is high in all the
considered frequencies, but it increases with frequency from
100 to 200 GHz, as seen in Figs. 10 to 12.
Furthermore, Fig. 13 presents both the σ value along the
100-200 GHz frequency band for each year (2008-2019) and
the average value of those years (solid black line). This
figure confirms the increment in dispersion from 100 GHz to
200 GHz. Moreover, the interannual differences, in terms of
dispersion, become slightly higher as the frequency rises.
V. EFFECT OF NUMEROUS SMALL PARTICLES
As mentioned in Section 2, in a previous publication [12]
the validation of the Laser disdrometer data was carried out
through the elimination of non-liquid precipitation particles.
However, after obtaining γ using the Mie theory [2]-[3],
some outliers have appeared separated from the main cluster
point when plotting γ versus R for the highest frequencies
within the range studied. Examples of these outliers are
presented in green in Fig. 14 for 200 GHz during 2017. The
outliers produced very high attenuation for low R (typically
R < 1 mm/h). The number of such outliers is proportionally
small.
Fig. 11. Relative probability distribution of the error, 150 GHz.
Fig. 12. Relative probability distribution of the error, 200 GHz.
Fig. 13. Standard deviation of the error, σ error.
The Laser disdrometer spectra measured for the outliers
were isolated. One of them is presented in Fig. 15. If we
compare this spectrum with those of Figs. 1 to 3, it is
observed that there is a large concentration of particles in
the area of the spectrum that corresponds to drizzle (other
examples of these spectra are directly classified as drizzle).
Specifically, in Fig. 15 there are grids that contain more
than 100 particles with a small Di. In this case, the high
number of small particles produce γ = 17.45 dB/km at 200
GHz with R = 0.74 mm/h, whereas for a similar value of R,
a typical spectrum with less than 16 particles per grid
produces γ(200 GHz) ~ 1 dB/km.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Error
0
0.03
0.07
0.1
0.13
Relative probability
Nonparametric kernel-smoothing distribution
Normal distribution ( = 0, = 0.119)
100 GHz
Relative probability
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Error
0
0.03
0.07
0.1
0.13
Relative probability
Nonparametric kernel-smoothing distribution
Normal distribution ( = 0, = 0.208)
200 GHz
This paper's copyright is held by the author(s). It is published in these proceedings and included in any archive
such as IEEE Xplore under the license granted by the "Agreement Granting EurAAP Rights Related to
Publication of Scholarly Work."
In (5) it is observed that R is calculated using D
i3
. As the
diameter of these particles is small (less than 1 mm), the
values of R do not rise excessively despite the appearance of
a high number of particles N(D
i
). Meanwhile in (4) the large
numbers of N(D
i
) significantly increase the values of γ. This
is the reason why γ increases while R is kept low.
Furthermore, for these spectra with a large number of
small particles the σ
ext
(D
i
) grows with the frequency [4], so
that the γ corresponding to such spectra increases as the
frequency rises towards 200 GHz.
Fig. 14. Specific attenuation versus rainfall rate, 200 GHz. Year 2017.
Fig. 15. Outlier producing spectrum provided by the Laser distrometer.
Year 2017.
VI. C
ONCLUSIONS
In this paper, the variability of rain attenuation in the
100-200 GHz band has been studied using a large database
of experimental DSD measured with a Laser disdrometer in
Madrid, Spain, during a period of twelve years (2008-2019).
In terms of γ, the fitting coefficients k and α described in
the ITU-R P. 838-3 [18] predict well the average behavior.
However, the dispersion around the mean trend is much
higher than at lower frequencies and increases from 100 GHz
to 200 GHz. This higher dispersion is attributed to the fact
that, for a given rainfall rate, rain specific attenuation is
progressively more dependent on the DSD as the frequency
increases.
Some outliers with high γ and small R, corresponding
with spectra with a very high number of small particles, were
separately analyzed.
The study validates the use of DSD for the calculations
of γ for frequencies where Mie scattering [2]-[3] is more
relevant than Rayleigh scattering [4].
A
CKNOWLEDGMENT
This work was supported in part by the Ministry of Science,
Innovation and Universities of Spain through the RTI2018-
098189-B-I00 project and by Horizon 2020, European Union
Framework Program for Research and Innovation, under
Grant Agreement no. 871464 (ARIADNE).
R
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This paper's copyright is held by the author(s). It is published in these proceedings and included in any archive
such as IEEE Xplore under the license granted by the "Agreement Granting EurAAP Rights Related to
Publication of Scholarly Work."
... Several reports on rain attenuation impacts on communication systems are detailed in [22,[29][30][31][32][33][34][35][36]. In particular, the work in [29] presented a predictive analysis of rainfall attenuation and their probable influence on propagated microwaves for Uttarakhand, a tropical region in India. ...
... The authors [33,34] provide detailed rainfall attenuation distribution statistics over the wireless link at a higher microwave frequency in Japan and Korean territories. Specific practical attenuation measurement and modeling-based investigation approaches to rainfall intensity effects conducted in different countries are presented [35][36][37][38][39][40][41][42][43][44]. ...
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Propagation characteristics of the atmosphere are modeled for the frequency range from 1 to 1000 GHz (1 THz) by the modular millimeter-wave propagation model MPM. Refractivity spectra of the main natural absorbers (i.e., oxygen, water-vapor, suspended droplets and ice particles) are computed from known meteorological variables. The primary contributions of dry air come from 44 O2 lines. Results from extensive 60-GHz laboratory measurements of the pressure-broadened O3 spectrum were applied to update the line data base. The water-vapor module considers 34 local H2O lines plus continuum contributions from the H2O spectrum above 1 THz, which are formulated as wing response of a pseudo-line centered at 1.8 THz Cloud/fog effects are treated with the Rayleigh approximation employing revised formulations for the permittivities of water and ice. The influence of the Earth's magnetic field on O2 absorption line becomes noticeable at altitudes between 30 and 120 km. Anisotropic medium properties result, which are computed by the Zeema propagation model ZPM. Here the elements of a complex refractivity tensor are determined in the vicinity (plus or minus 10 MHz) of O2 line centers and their effect on the propagation of plane, polarized radiowaves is evaluated. A spherically stratified (0-130 km) atmosphere provides the input for the codes MPM and ZPM in order to analyze transmission and emission properties of radio paths. Height profiles of air and water vapor densities and of the geocoded magnetic field are specified. ZPM predicts polarization- and direction-dependent propagation through the mesosphere. Emission spectra of the 9+ line (61150 plus or minus 3 MHz) for paths with tangential heights ranging from 30 to 125 km are consistent with data measured by the shuttle-based millimeter-wave limb sounder MAS.
Article
The inadequacy of previous calculations of terminal velocities at other than sea level conditions is discussed. Attention is called to actual measurements of terminal velocities at different air densities, and empirical formulae are presented which fit the data very closely.
Book
The absorption and scattering of light by small particles is discussed in terms of basic theory, optical properties of bulk matter, and optical properties of particles. The subjects addressed include: electromagnetic theory, absorption and scattering by an arbitrary particle and by a sphere, particles small compared with the wavelength, the Rayleigh-Gans theory, geometrical optics, and miscellaneous particles. Also considered are: classical theories of optical constants, measured optical properties, extinction, surface modes in small particles, the angular dependence of scattering, and applications.