Progress In Electromagnetics Research B, Vol. 25, 211–224, 2010
RAIN ATTENUATION MODELING IN THE 10–100 GHz
FREQUENCY USING DROP SIZE DISTRIBUTIONS FOR
DIFFERENT CLIMATIC ZONES IN TROPICAL INDIA
S. Das and A. Maitra
Institute of Radio Physics and Electronics
University of Calcutta
Kolkata, India
A. K. Shukla
Space Applications Centre, Indian Space Research Organization
Ahmedabad, India
Abstract—Rain drop size distributions (DSD) are measured with
disdrometers at five different climatic locations in the Indian tropical
region. The distribution of drop size is assumed to be lognormal to
model the rain attenuation in the frequency range of 10–100 GHz. The
rain attenuation is estimated assuming single scattering of spherical
rain drops. Different attenuation characteristics are observed for
different regions due to the dependency of DSD on climatic conditions.
A comparison shows that significant differences between ITU-R model
and DSD derived values occur at high frequency and at high rain rates
for different regions. At frequencies below 30 GHz, the ITU-R model
matches well with the DSD generated values up to 30 mm/h rain rate
but differ above that. The results will be helpful in understanding
the pattern of rain attenuation variation and designing the systems at
EHF bands in the tropical region.
1. INTRODUCTION
Rain attenuation is a major limiting factor above 10 GHz frequency
bands to be used in radio communications. It is also a relevant issue
for space-borne radars for cloud and precipitation characterization.
Although, other forms of hydrometeors (snow, hail etc) also affect
the performance of the system, the attenuation due to rain is most
Received 27 July 2010, Accepted 2 September 2010, Scheduled 9 September 2010
Corresponding author: A. Maitra (animesh.maitra@gmail.com).
212 Das, Maitra, and Shukla
severe [1, 2]. Rain attenuation modeling is usually done in terms of
drop size distribution (DSD) [1–3]. But, the variability of DSD for
different climatic regions is a major concern, especially for the tropical
region [4], which has a huge diversity in climatic conditions. A few
attempts have been made to characterize the rain attenuation over
this region [4–8]. In the absence of measured attenuation data, DSD
measurements can provide useful information on the variation of the
rain attenuation [4, 9, 10].
Rain DSD varies with rain rate as well with the location. Thus
the same rain rate can correspond to different DSDs. Raindrop
size distributions depend on several factors such as rainfall intensity,
circulation system, type of precipitation, wind share, cloud type, etc.
It is thus very difficult to formulate a single DSD model to describe
the actual raindrop size distribution for all location and rain type.
However, it is essential to have a DSD model so that we can model the
attenuation. For attenuation calculation, DSD is normally modeled
with distributions like exponential, gamma [11, 12] and lognormal [13].
The suitability of these DSD models has been studied by many
researchers extensively. However, it is found that the 3-parameters
models like lognormal or modified gamma are better suited than the
exponential model. Further, the lognormal distribution is more suited
for the lower end of drop spectrum due to its steeper gradient than
the gamma distribution. From the various studies over tropical region,
it is found that three-parameter lognormal model is suitable for this
region [4, 13]. Therefore, in the present study, lognormal model is
considered to be the representative distribution for DSD.
Currently, Indian space Research Organization (ISRO), as a part
of earth-space propagation experiment over India region conducting
ground based measurements at five different geographical locations,
namely, Ahmedabad, Shillong, Trivandrum, Kharagpur and Hassan.
These locations fall in different climatic zones of India with different
rain characteristics. The rain DSD is one of such parameters
being measured. In the absence of actual earth-space propagation
measurements, the attenuation modeling using DSD is attempted.
This study will be helpful for understanding the rain attenuation
characteristics over the Indian tropical region.
2. DATA COLLECTION
2.1. Site Selection
In Table 1, the details of the experimental sites are given. The site
selection has been done keeping in mind the variability of climatic
conditions as stated in Section 1.
Progress In Electromagnetics Research B, Vol. 25, 2010 213
Table 1. Site locations and characteristics.
Station Name
Annual
Total
Rain
(mm)
No. of
Rainy
days
Lat
N
Long.
E
Measurement
Period
Climatic
Shillong
(SHL)
2415.3 128.1 25
34’ 91 53’ 3 Years
Hilly, SW &
Ahmedabad
(AHM)
803.4 35.8 23
04’ 72 38’ 3 Years
Plane, SW
Trivandrum
(TVM)
1827.7 99.7 08
29’ 76 57’ 3 Years
Coastal, Plane,
monsoon
Kharagpur
(KGP)
1641.4 82.2 22
32’ 88 20’ 2 Years
Coastal Plane,
monsoon
Hassan (HAS) 912.8 65.0 13
00’ 76 09’ 2 Years
Plane, SW
Condition
NE monsoon
monsoon
SW & NE
SW & NE
monsoon
o
o
o
o
o
o
o
o
o
o
o
o
2.2. DSD Measurement
An impact type disdrometer manufactured by Disdromet (RD-80) is
installed at each of the locations. The disdrometer has a sensitive
styrofoam cone connected with a transducer. When a drop strikes the
cone, an electric signal is generated whose amplitude is proportional to
the momentum of the drop. Using the Gunn-Kinzer relation [14], the
drop diameter is estimated from the terminal velocity. It is assumed
that the momentum is entirely due to the terminal fall velocity of the
drops. It is also assumed that the drops are spherical in shape and no
wind motion is present.
It is to be noted that the bigger drops are not spherical in
shape and thus introduce error in the estimation of rain rate and rain
attenuation from the drop size distribution. The discrepancy will be
greater at high rain rates as bigger rain drops are abundant in that
case. However, it was found that the deviation of rain rate calculated
in this way and measured by a collocated raingauge may not be very
severe [15].
The sensitivity of disdrometer surface is very important for proper
measurement. The surface is cleaned regularly and replaced once
in a year. The known sources of error like acoustic noises are kept
minimized by proper installation of the instrument at the roof top of
a building. Another source of error in disdrometer measurement is the
insensitivity for a time period after a bigger drop strikes. This ‘dead
time’ leads to underestimation of the smaller drops that fall within
this period. But, the effects of these smaller drops are less on rain
attenuation and are within 5% error limit [16]. It has much less effect
214 Das, Maitra, and Shukla
on the DSD spectrum except at very low rain rates. So, for the present
study, the dead time correction has not been considered.
The data collected for years 2005–2007 have been used for the
present analysis. An integration time of 30 seconds is used for DSD
measurement. As a precautionary measure, the measurement instances
which have less than 10 drops recorded have been excluded from
the analysis. Cumulative data of all the available years have been
used to model the attenuation. This may be helpful to minimize the
uncertainties in the measurements.
3. ANALYSIS
3.1. DSD Modeling
From the previous studies over tropical regions, it has been observed
that DSD follows the lognormal distribution as mentioned in Section 1.
Therefore, in the present work, the lognormal model is considered to
describe DSD characteristics.
The lognormal distribution function is given as follows [13]
N(D) =
N
T
σD
√
2π
exp
·
−0.5(ln(D) − µ)
2
σ
2
¸
(1)
where, N(D) is the number density (in m
−3
mm
−1
), N
T
is total number
of drops, D is drop diameter (in mm), σ is the standard deviation and
µ is the mean of ln(D). N
T
, σ and µ are rain rate dependent variables.
Various methods are suggested to obtain these parameters [13, 17].
In our approach, we use method of moment technique [4] to estimate
these parameters as they are linearly related to the moments of
measured DSD. It has been reported that 3rd, 4th and 6th moments
are more suitable for estimation of model parameters [13] and are used
here accordingly.
The mathematical relationships of the distribution parameters
with these moments are given as follows:
N
T
= exp
·
1
3
(24L
3
− 27L
4
+ 6L
6
)
¸
(2)
µ =
1
3
(−10L
3
+ 13.5L
4
− 3.5L
6
) (3)
σ
2
=
1
3
(2L
3
− 3L
4
+ L
6
) (4)
Here L
3
, L
4
, and L
6
are the natural logarithms of 3rd, 4th and 6th
moments respectively.
Progress In Electromagnetics Research B, Vol. 25, 2010 215
After calculating the DSD parameters for the whole observation
period they are modeled in following form
N
T
= aR
b
(5)
µ = c + d ln(R) (6)
σ = e + f ln(R) (7)
Here, a, b, c, d, e and f are parameters of the model and evaluated by
the least squares method. These parameters have some dependency on
the rain climatology, as reported in the literature [13, 17]. In estimation
of these parameters, all types of rain have been included at a particular
location. An example of lognormal model for the measured DSD
between 25–26 mm/h rain fall for different region is shown in Fig. 1.
(a) (b)
(c) (d)
(e)
Figure 1. Measured and fitted lognormal mo del at 25–26 mm/h rain
rate for (a) AHM, (b) TVM, (c) KGP, (d) SHL and (e) HAS. The error
bar indicates the ± one standard deviation from the mean drop size
concentrations.
