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Testing Rainfall Rate Models for Rain Attenuation Prediction Purposes in Tropical
Climate
E. O. Olurotimi*1 and J. S. Ojo
2
1Department of Physics, The Federal University of Technology,
P. M. B. 704, Akure, Ondo State, Nigeria [email protected]
Abstract
One minute rainfall rates are a key tool for rain attenuation modeling. Availability of this data are still very
scarce worldwide especially in the tropics with insufficient propagation measurement. The scenario at the tropical and
the equatorial locations is of concern due to the nature of the climate which is characterized by high rainfall intensity,
enhanced frequencies of rain occurrence and the increase presence of large raindrops when compare with the temperate
climates. In this work, four different rainfall rate distribution models were compared to find the best fit over the tropical
stations using data from our propagation measurement - Nigeria Environmental Climatic Observatory Program for radio
wave propagation purposes.
1. Introduction
The dynamics of rainfall in the tropical regions are quite distinct from those of the temperate and high latitude.
Rainfall, cloud and atmospheric turbulence could cause a serious impairment to communication signals both for
terrestrial and Earth-space systems at the frequencies above 10 GHz [1]. Also, at these frequencies, the use of terrestrial
and earth to satellite radio links operation is well established due to congestion of lower frequency spectrum; most
serious problems in system design come from attenuation, depolarization and scattering interference by precipitation
particles along the radio path at those frequencies [2, 3]. The best possible estimates given by the available information
can be provided by the use of prediction models due to sparse measured data. Hence, the need to choose the right model
for tropical region of ours is very important.
In this work, convectional models were compared with the 2-year of continuous measurement of point of
rainfall. Rainfall data of 1-minute integration time to find the best rainfall cumulative model over the tropical stations
observed. The convectional models used are: Rice and Holmberg; Kitami; Moupfouma and ITU-R model. Also, for
existing attenuation prediction: Moupfouma, ITU-R and Crane Global model were employed.
2. Data and Methodology
2-year rainfall rate used in this work was obtained from Nigeria Environmental Climatic Observatory Program
pro weather station using tipping bucket rain gauge at 146 mm high with resolution and effectiveness of 0.2 mm per tip
and aperture size of 400 cm2. The Rain gauge is one of the instruments available for data compilation in the NECOP
equipment located at the Federal University of Technology, Akure, Ondo State and University of Lagos, Lagos State.
Detailed propagation methodology and equipment set up can be found in our previous work [4]. Table 1 presents the
characteristics of the experimental site. Rain rate prediction models were tested using the recommended method by
ITU-R (2009), where for certain percentage of time ranging between 0.001% and 1% of the year for which data is
available, the percentage of relative error between the predicted value and measured value are obtained with expression:
% 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑒𝑟𝑟𝑜𝑟 = 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑝% − 𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑝%)
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑝%) (1)
The mean error, μ and standard deviation, σ are used to calculate the root mean square (rms). The parameters are
defined as follows:
978-1-4673-5225-3/14/$31.00 ©2014 IEEE
𝑟𝑚𝑠 = μ2 − σ2 (2)
Table 1: Site Characteristics of the Study Locations
3 Results and Discussion
3.1 Rainfall rate distribution for the surface rainfall data
Fig. 1 presents the bar chart which shows the utmost rainfall per day of the year on the period which signifies
worsening of signal level could be observed. The two locations comprise of two main seasons which are dry and wet
season; dry season starts from November to February in the following year while the wet-season is between March and
October. Thus, the average accumulated rainfall over the two stations where peak and worst month was observed over
Akure was September while it was June for Lagos with average rainfall of about 198 mm and 239 mm respectively. The
minimum rainfall amount of about 1.5 mm and 5.6 mm occurred in December and January over Akure and Lagos
respectively due to Intertropical Discontinuity movement. In addition, the average monthly rainfall of a location
depends on the effects of movement of the Intertropical Discontinuity. Also, Nigeria has two seasons which are: wet
season between March and October and dry season between November and February of the following year. Heavy
rainfall usually falls during the wet season in the two locations of this research and during this period the ITD moves
across the country.
3.2 Comparison of measured rainfall rate and ITU prediction
Figs. 2 (a and b) present the cumulative distribution of rainfall rate which shows the comparison of averaged 2-
year rainfall rate measured with the recent ITU-P. 837-6 [5] model for each of the stations. It could be noticed that the
slope is steepest for lower rainfall rate, which means that the lower rainfall rate contributes most to the total rainfall; and
the higher the rainfall rate the lower the corresponding percentage of time recorded even as the lower the rainfall rate
the higher the percentage of time. It could be further observed that the recent ITU-R P.837-6 model overestimated the
rainfall rate value at 0.01% exceedance of time by about 21% for Akure and underestimated by about 31% for Lagos.
3.3 Models testing
Figures 3(a and b) present the comparison of cumulative distribution of measured 1-minute rainfall rate and
other models such as: Rice and Holmberg, 1973-RH model; Moupfouma and Martin, 1995-Moupfouma model; ITU-R
model (1997) and Ito and Hosoya, 1999-Kitami model. The cumulative distribution is as usual based on rainfall rates
and percentage of time. The higher the rain intensity the lower the lower the corresponding percentage of time recorded,
while the lower the rain intensity the higher the percentage of time. In figure 3a , at the lowest percentage of time of
99.999% that 0.001% exceedance, rainfall rate is about 200 mm/h, 174.2 mm/h, 158.1 mm/h, 159.6 mm/h, and 184.6
mm/h for RH, Moupfouma, ITU-R, Kitami and the measured data respectfully, while at the higher time percentage of
99.99% the rainfall rates are 120.4 mm/h, 106.8 mm/h, 94.4 mm/h, 95.3 mm/h and 98.5 mm/h for RH, Moupfouma,
ITU-R, Kitami and the measured data respectfully. Also, Figure 3b presented similar trend, where at 99.99% of time
rainfall rate is about 123 mm/h, 105.5 mm/h, 87.9 mm/h, 89.2 mm/h and 100 mm/h for RH, Moupfouma, ITU-R,
Kitami and the measured data respectfully. It is also about 200 mm/h, 172 mm/h, 151.7 mm/h, 152.1 mm/h and 169.1
mm/h at the lower percentage time of 99.999% for RH, Moupfouma, ITU-R, Kitami and the measured data respectfully.
In order to buttress the aforementioned assertion, Table 2 presents the statistical analysis of the cumulative
distribution of the measured rainfall rates with the predefined models. The models were tested using the percentages of
the relative error defined in equation (1), the Root Mean Square error defined in equation (2) to judge the performance
of each of the model. Since the regression models for attenuation prediction often use only rain rate at a single
exceedance probability level, 0.01% of a year, the RMS values for that probability level are separately tabulated while
exceedance probability levels for both 0.01 and 0.001% of the year are presented for the average relative error for
Station Latitude
(o N)
Longitude
(o E)
Altitude
(m)
Average
annual rainfall
(mm/year)
Region
climate
Akure 7.17 5.18 358 1598.5 Rain forest
Lagos 6.35 3.20 129 1861.5 Coastal
multimedia purposes. However, results from Table 2 shows that RH model over estimated the measured data by more
than 25% at exceedance probability levels for both 0.01 and 0.001% of the year in the two locations. The ITU-R agree
with the measured rainfall rates for interval between 99% and 99.9% of time at both locations, underestimated the
measured data at Lagos while the measured date were overestimated at Akure using the average relative error at 99.99%
most needed for rain attenuation prediction. The Kitami model overestimate the measured value at 0.01% of the year at
Akure, while it underestimates the measured data at this percentage of time as well as at 0.001% needed for multimedia
applications. For the two locations considered in this work, the Moupfouma model appears to best fit with measured
data followed by ITU model judging from the lowest % RMS values as well as the average relative error.
3.4 Terrestrial Path Attenuation Exceeded for 0.01% of Time Path Length
Figs 4 (a and b) present the attenuation prediction models for terrestrial line-of-sight links, for 0.01% of time
over the two stations at the frequencies of 12, 20, 30 and 40 GHz. Hence, in all the frequencies considered the three
models increase as the propagation path increases. Fig 4(a) shows that the ITU-R model offers the lowest attenuation
values at all the frequencies while Crane Global model curve tends to provides highest attenuation values at very initial
stages bends more than that of Moupfouma model curve at path length 4, 6 and 8 km. It further intersects with
Moupfouma model at these path lengths except at frequency 40 GHz where the Crane Global model gives the highest
attenuation values throughout the propagation path. Fig 4(b) reveals that Moupfouma model provides the highest
attenuation values at all frequencies while Crane Global model gives the lowest attenuation values in all the frequencies
considered, Crane Global model which tends to provide the lowest attenuation values flattened out and intersects with
ITU-R model at path length greater than 5 km.
Fig. 1: The average monthly rainfall accumulated (mm) during the observed period.
Fig. 2: Comparison of measured rainfall rate with ITU prediction (a) Akure and (b) Lagos
Fig. 3: Comparison of cumulative distribution of rainfall rate models with measured data over
0
50
100
150
200
250
300
Jan Feb March April May June July Aug Sept Oct Nov Dec
Acc
um
ula
ted
Rai
nfa
ll (m
m)
Months
Akure Lagos
0
100
200
0.001 0.01 0.1 1 10
Rai
nfa
ll ra
te (
mm
/h)
Percentage of time rain rate exceeded
(a) MeasuredITU-P. 837-6
0
200
400
0.001 0.01 0.1 1 10
Rai
nfa
ll ra
te (
mm
/h)
Percentage of time rain rate exceeded
(b) MeasuredITU-P. 837-6
0
50
100
150
200
250
0.001 0.01 0.1 1 10
Rai
nfa
ll ra
te (
mm
/h)
Percentage of time ordinated exceeded
(a) RH
KITAMI
Moupfouma
ITU-R
Measured
0
100
200
300
0.001 0.01 0.1 1 10
Rai
nfa
ll ra
te (
mm
/h)
Percentage of tiime ordinate exceeded
(b)RHKITAMI
Moupfouma
ITU-R
Meausred
(a) Akure and (b) Lagos.
Table 2: The statistical analysis of the cumulative distribution of the measured rainfall rates with the predefined
models.
Locations Akure Lagos Akure Lagos
Models
% of RMS error
Average relative error
0.01% of
year
0.001% of
year
0.01% of
year
0.001% of
year
RH 10.5 13.2 25.2 35.4 27.5 34.6
Kitami 9.8 10.2 6.2 -14.2 -7.4 -10.7
Moupfouma 4.5 6.5 5.3 3.4 4.5 3.6
ITU-R 7.5 8.4 5.8 -10.5 -7.2 -10.2
Fig. 4: Comparison of Rain-induced attenuation prediction models exceeded 0.01% of time for terrestrial line of
sight (a) Akure and (b) Lagos.
4. Conclusions
In this paper, we have tested the convectional rain rate models with measured 1-min rain rate data to ascertain
the applicable one for tropical climates for radio wave propagation purposes. Based on the lowest RMS value,
Moupfouma model was found to best fit to the measured data for low, medium and high rainfall rates. Hence,
Moupfouma model gives the best prediction and is appropriate for used in tropical and equatorial regions. Also, the
rain-induced attenuation predictions obtained from the three different existing models on terrestrial line of sight for
0.01% of time gives variation in attenuation at different frequencies.
5. Acknowledgements
The authors give sincere thanks to the Centre for Basic Space Science of NASRDA for their support in providing
NECOP equipment for this research.
6. References
1. J. S. Ojo, M. O. Ajewole, and S. K. Sarkar, “Rain rate and rain attenuation prediction for satellite communication in
Ku and Ka bands over Nigeria,” Progress in Electromagnetics Research B, 5, 2008, pp. 207-223.
2. I. A. Adimula, O. A. Falaiye and A. A. Willoughby, “Effects of rain on microwave and satellite communications in
equatorial and tropical regions,” Nigeria Journal of Physics, 17, 2005, pp.66-71.
3. C. Capsoni, F. Fedi, C. Magistroni, A. Paraboni, and A Pawlina, “Data and theory for a new model of the horizontal
structure of rain cells for propagation applications,” Radio Science, Volume 22, Number 3, 1987, pp. 395-404.
4. J. S Ojo, M. O. Ajewole and E. O. Olurotimi, “Characterization of Rainfall Structure and Attenuation over Two
Tropical Stations in Southwestern, Nigeria for the Evaluation of Microwave and Millimeter-wave Communication,”
Journal of Meteorology and Climate Science, Volume 11 (1), 2013, pp. 40-4.
5. ITU-R P.837-6, Characteristics of Precipitation for Propagation Modelling, Recommendation P, ITU-R Ser.,
International Telecommunication Union, Geneva, Switzerland, 2012.
0
50
100
150
200
250
0 5 10 15 20
Pat
h a
tte
nu
atio
n e
xce
ed
ed
0
.01
% o
f ti
me
(d
B)
Path length (km)
(a)ITU-R 12GHz Moup 12GHz Crane 12 GHz
ITU-R 20GHz Moup 20GHz Crane 20 GHzITU-R 30GHz Moup 30GHz Crane 30 GHzITU-R 40 GHz Moupf 40 GHz Crane 40 GHz
0
100
200
300
400
0 5 10 15 20
Pat
h a
tte
nu
atio
n e
xce
ed
ed
0
.01
% o
f ti
me
(d
B)
Path length (km)
(b)ITU-R 12GHz Moup 12GHz Crane 12GHzITU-R 20GHz Moup 20GHz Crane 20 GHzITU-R 30GHz Moup 30GHz Crane 30 GHzITU-R 40GHz Moup 40GHz Crane 40GHz
