Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 82
~89
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.8
746
82
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
A An
alysis of Raindrop Diam
et
ers for Rainfall Attenuation in
Southern Africa
O. Ade
t
an
*
, O
.
O.
Obiye
m
i
**
*Departm
ent of Ele
c
tri
cal
and
E
l
ectron
i
c Engin
e
e
r
ing, Ekit
i
St
ate
Universit
y
Ado Ekiti
,
Nig
e
ri
a
**Department of
Electr
i
cal
and
Electronic Eng
i
ne
ering, Osun State University
, Osogbo, Niger
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Aug 6, 2015
Rev
i
sed
O
c
t 12
, 20
15
Accepte
d Nov 6, 2015
The inf
l
uen
ce
of crit
ic
al ra
in
drop diam
ete
r
s on the spe
c
i
f
ic ra
infa
ll
attenuation in D
u
rban (29
o
52
'
S
, 30
o
58'
E)
, South
Africa using v
a
r
i
ous rainf
a
ll
regim
e
s is anal
yz
ed in
this pa
per. Di
ff
erent
r
a
in ra
te v
a
lues
repres
ent
i
ng
drizzle, wid
e
spread, shower and
thunders
torm are selected for th
e purpose of
anal
ys
is
over
th
e m
eas
ured r
a
in
drop s
i
ze d
i
s
t
rib
u
tion.
The
thre
e
-
param
e
te
r
lognormal and g
a
mma DSD mo
dels with
shape
parameter of 2
are used to
estimate the par
a
meters requ
ired
to
inv
e
stigate th
e drop sizes which produce
a m
a
jor contr
i
bu
tion to th
e tot
a
l
specifi
c rainf
a
ll
att
e
nuat
i
on for t
h
e sele
cted
rain r
a
te
valu
es. Th
e com
pute
d
tota
l spe
c
ifi
c
att
e
nua
tion
inc
r
eases wit
h
incre
a
s
i
ng frequ
enci
es
and rain r
a
tes
.
The high
est and prevailing contributio
n
to
the
spec
ific
a
ttenu
ation
oc
cur
s
at
~
2
m
m
for
th
e stratiform (drizzle o
r
widespread)
an
d convectiv
e (s
hower or thund
erstorm) rain
types for th
e
m
odels
cons
ider
ed. Th
e tot
a
l p
e
rcen
ta
g
e
fraction formed b
y
d
r
ops in the
diameter
range 0
.
5 mm
≤
D
≤
2.5 mm and 1.0 mm
≤
D
≤
3.0mmare found
to
be m
o
st crit
ica
l
f
o
r the spe
c
ifi
c
r
a
in at
tenua
tion fo
r the str
a
tiform
(
d
rizz
le
and
widespread) an
d convective (
s
hower
and thunderstorm) rainfall ty
p
e
s
es
peci
all
y
a
t
hig
h
er fr
equenc
ies
.
Keyword:
Dr
op
si
ze
di
st
r
i
but
i
o
n
G
a
mma m
o
d
e
l
Lo
gn
orm
a
l
m
odel
Raindrop c
r
itical diam
eters
Sp
ecific rainfall
atten
u
a
tion
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
O. Adetan,
Depa
rtm
e
nt of
Electrical an
d Electronic
Engineering,
Ek
iti State Un
iv
ersity,
Ado
Ek
iti, Nigeria.
Em
a
il: o
a
d
e
tan@g
m
ail.co
m
1.
INTRODUCTION
Rain
h
a
s b
e
en
id
en
tified
as on
e o
f
th
e m
a
j
o
r an
d
im
p
o
r
tant p
a
ram
e
ters af
fectin
g
th
e prop
ag
ation
of
sig
n
a
ls
in
t
h
e micr
o
w
av
e (
3
-3
0
GH
z)
an
d mil
l
i
m
e
t
er
(
30-
300
G
H
z
)
w
a
v
e
b
a
n
d
s
. O
t
her
r
a
in
f
actor
s su
ch
as
the
canti
ng angle, drop
size and
rai
n
dr
op
sh
ap
es also h
a
ve pr
of
oun
d effects on
w
a
v
e
s
p
r
op
ag
ating
i
n
th
ese
ban
d
s at
e
x
t
r
e
m
el
y
hi
gh f
r
e
que
nci
e
s
[1]
.
The s
p
eci
fi
c
r
a
i
n
fal
l
at
t
e
nua
t
i
on i
s
oft
e
n
pre
d
i
c
t
e
d
fr
o
m
t
h
ree
param
e
t
e
rs, w
h
i
c
h a
r
e;
t
h
e
f
r
eq
ue
ncy
,
rai
n
rat
e
an
d
pol
a
r
i
zat
i
on,
w
h
er
e t
h
e p
o
pul
at
i
on
o
f
t
h
e
rai
n
dr
o
p
s i
s
rep
r
ese
n
ted by
the single par
a
m
e
ter, rainfal
l
rate [2]
.
Altho
ugh
th
e rainfall rate re
m
a
in
s v
e
ry u
s
efu
l
an
d
h
a
s
been
b
r
oadl
y
use
d
f
o
r
rai
n
at
t
e
nuat
i
o
n pr
edi
c
t
i
on [
3
]
,
[
4
]
an
d [5]
,
a
go
o
d
kn
o
w
l
e
d
g
e of
t
h
e dr
o
p
si
ze
d
i
stribu
tio
n
(DSD) is v
e
ry essen
tial in
th
e est
i
m
at
io
n
of
t
h
e rai
n
fal
l
at
t
e
nua
t
i
on at
t
h
ese ra
di
o f
r
eq
ue
ncy
ban
d
s
because it governs all the microwa
v
e
and rainfall integral
relations. T
h
e
m
odeling
of t
h
e DSD va
ries
from
one cl
i
m
at
e t
o
anot
her
.
D
r
o
p
si
ze di
st
ri
bu
t
i
on m
odel
i
n
g
i
n
t
e
m
p
erat
e regi
on;
c
h
arac
t
e
ri
zed by
m
odera
t
e
rain
fall is well su
itab
l
e with
m
o
d
e
ls su
ch
as p
r
o
p
o
s
ed
by
M
a
rshal
l
an
d P
a
lm
er [6]
,
Law
s
and
Pars
o
n
s [
7
]
a
n
d
t
h
e ne
gat
i
v
e
ex
po
ne
nt
i
a
l
m
odel
of
gam
m
a [8
]
.
The m
odeling
of
DSD i
n
the
tropical re
gion is
m
o
st suitable with the gl
obally accepte
d Ajayi and
O
l
sen
[
9
] logno
r
m
al
m
o
d
e
l. In
Dur
b
an
,
Sou
t
h
Af
r
i
ca, a r
e
aso
n
ab
le
n
u
m
b
e
r
of
wor
k
s
h
a
ve b
een carr
i
ed
o
u
t
o
n
rain
fall attenu
atio
n
and
D
S
D
[10
]
,
[11
]
,
[12
]
, [13
]
, [14
]
an
d [1
5
]
estab
lish
i
n
g
th
e su
itab
ility o
f
th
e l
o
gnorm
a
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 6
,
N
o
. 1
,
Febru
a
ry
2
016
: 8
2
–
89
83
and
gam
m
a
model
s
fo
r
DS
D
m
odel
i
n
g i
n
t
h
e re
gi
o
n
.
Si
m
i
l
a
rl
y
,
vari
o
u
s
app
r
oaches
an
d m
odel
s
ha
ve
been
adopted by
some researc
h
ers
across t
h
e
gl
o
b
e t
o
i
n
vest
i
g
a
t
e t
h
e pa
rt
i
c
ul
a
r
c
ont
ri
but
i
ons
o
f
cert
a
i
n
rai
n
d
r
o
p
di
am
et
ers t
o
the speci
fi
c rai
n
at
t
e
nuat
i
o
n [
16]
, [
1
7]
, [1
8]
, [1
9]
and [
20]
. The i
n
fl
uenc
e of cri
t
i
cal
rai
n
d
r
o
p
di
am
et
ers on t
h
e speci
fi
c rai
n
fal
l
at
t
e
nuat
i
on i
n
D
u
r
b
a
n
,
So
ut
h A
fri
ca
usi
n
g va
ri
o
u
s
rai
n
fal
l
re
gi
m
e
s i
s
an
alyzed
in
this work. Differen
t rai
n
rate
v
a
lu
es
represe
n
ting drizzle
(below
5m
m
/
h), wi
des
p
read
(
5
-
2
0
m
m
/
h) sho
w
e
r
(2
0
-
5
0
m
m
/
h
) an
d t
h
u
nde
rst
o
rm
(ab
ove
5
0
m
m
/
h) as cl
assi
fi
ed acc
or
di
n
g
t
o
[
9
]
an
d
[2
1]
are
selected for t
h
e
purpos
e
of analysis
ove
r the m
easur
e
d
rai
n
d
r
o
p
si
ze
di
st
ri
but
i
o
n.
The t
h
ree
-
pa
ra
m
e
t
e
r
l
o
g
n
o
r
m
a
l
and gam
m
a
DSD
m
odel
s
wi
t
h
sha
p
e pa
ram
e
ter of
2 as det
e
rm
i
n
ed i
n
[1
5]
fo
r D
u
r
b
a
n
,
Sout
h
Africa are
use
d
to
represe
n
t the m
easured
DSD,
N(D).
2.
DIS
D
R
O
ME
TER D
A
TA
A
NAL
YSI
S
The Jos
s
-
W
al
d
v
o
g
el
(J-
W) R
D
-
80
[2
2]
di
sd
rom
e
t
e
r i
n
st
al
led i
n
20
0
8
at
the ro
o
f
t
o
p of t
h
e Sch
o
o
l
of
El
ect
ri
cal
, El
ect
ro
ni
c and C
o
m
put
er Engi
ne
eri
n
g, U
n
i
v
e
r
si
t
y
of Kw
aZul
u
-
Nat
a
l
was
use
d
t
o
o
b
t
a
i
n
ov
er 8
0
,
000 data sam
p
les for this work. The dis
d
rom
e
ter c
onve
rts
the
m
o
m
e
ntum
of each falling
drop im
pacting on
the sens
or’s s
u
rface int
o
an el
ectric pulse
of
commensur
ate voltage
.
T
h
e
detectable
diameter range is di
vide
d
in
to
20
in
terv
als. Th
e sam
p
li
n
g
tim
e,
T
o
f
th
e d
i
sdro
m
e
ter
is 6
0
s
with
th
e sa
m
p
lin
g
area,
S
of 5
0
cm
2
(0
.0
05
m
2
).
T
h
e data was
gat
h
ere
d
over
a peri
od of
three
(3)
year
s
.
The
data was
sorte
d
and cla
ssified int
o
differe
n
t
typ
e
s o
f
rain
b
a
sed
on
rain
fall rates
R
(
mm
/h
) as classified in [6] and [18]
nam
e
l
y
: dri
zzl
e,
wi
de
sprea
d
,
sho
w
e
r
an
d t
h
un
de
rst
o
rm
. The m
i
nim
u
m
and m
a
xim
u
m
rai
n
fal
l
rat
e
s
were
0.
00
3
mm
/h
and
11
7.15
mm/
h
resp
ectiv
ely.
Rain
fall ev
en
ts with
o
v
e
rall su
m
o
f
drop
s
less th
an
10
were ig
no
red
fro
m
th
e d
i
sd
ro
m
e
t
e
r d
a
ta
to
co
m
p
en
sate fo
r t
h
e
d
e
ad
-t
i
m
e errors. Th
e instru
m
e
n
t
is lo
cated
at an
altitu
d
e
of
14
0 m
e
ters ab
ov
e sea
l
e
vel
.
The l
o
c
a
t
i
on si
t
e
i
s
free o
f
n
o
i
s
e a
nd
pr
ot
ect
ed
f
r
om
very
st
ro
ng
wi
n
d
s.
Eq
ui
pm
ent
out
ag
e was
obs
er
ved
b
u
t
v
e
ry
m
i
nim
a
l
.
From
t
h
e di
s
d
r
o
m
e
t
e
r
m
easure
m
ent
, N
(
D
i
) is
calculated as
[22]:
∗
∗
∗
(1
)
whe
r
e
is the num
b
er of
drops m
eas
ured in
the dropsize cl
ass,
n
i
i
s
t
h
e
n
u
m
b
er o
f
dr
op
s pe
r c
h
an
nel
,
v(D
) is th
e
Gu
n-Ki
n
zer [2
3
]
termin
al v
e
locity o
f
water
d
r
op
lets and
dD
i
is the c
h
a
n
ge in
diam
eter
of t
h
e
(cha
n
n
el) i
n
mm
.
3.
DR
OP S
S
IZ
E DIST
RIB
U
TI
ON
MO
DELS
Rain
d
r
op
size d
i
stribu
tio
ns were u
s
ed
to
estimate
th
e sp
ecific rain
fall atten
u
a
tio
n. Two
DSD m
o
d
e
ls
are co
n
s
i
d
ered
in
th
is
wo
rk
; the lo
gno
rm
al an
d
th
e g
a
mm
a DSD m
o
d
e
ls.
3.
1. L
o
gn
orm
a
l
D
S
D
M
o
del
The l
o
g
n
o
rm
al di
st
ri
b
u
t
i
o
n m
odel
i
s
ex
pre
s
s
e
d
by
[
9
]
an
d
[
21]
:
√
2
1
2
ln
(2
)
whe
r
e
(co
n
c
entratio
n of
rainfall d
r
op
s) is a fu
nctio
n
o
f
clim
ate, geogra
phical location
of m
easurem
e
n
ts
an
d rai
n
fall ty
p
e
, µ is t
h
e m
ean
o
f
ln
an
d
σ
is
th
e stand
a
rd dev
i
atio
n wh
ich d
e
term
in
es the wi
d
t
h
of th
e
d
i
stribu
tio
n.
Th
e three
p
a
rameters in
(2
) abov
e are related
t
o
th
e rai
n
fall rate
R
by
[9]
:
(3
)
ln
(4
)
ln
(5
)
whe
r
e
,
,
,
,
and
are coe
fficie
n
ts of m
o
m
e
nt regres
si
on
d
e
term
in
ed
u
s
ing
t
h
e least squ
a
res
m
e
t
hod
of
reg
r
essi
on t
e
c
hni
q
u
e. T
h
e t
h
ree-
param
e
t
e
r l
o
g
n
o
rm
al
DSD m
odel
as
det
e
rm
i
n
ed i
n
[
15]
i
s
gi
ve
n
as:
0.3104
0
.1331
l
n
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Ana
l
ysis
o
f
Ra
ind
r
o
p
Di
a
m
eters fo
r Ra
in
f
a
ll Atten
u
a
tio
n in
S
o
u
t
h
e
rn Africa
(O
.
Ad
etan
)
84
0.0738
0
.0099
l
n
(7
)
268
.07
.
(8
)
3.
2. Ga
mma
DS
D Mo
del
The t
h
ree
-
pa
ra
m
e
t
e
r gam
m
a
di
st
ri
b
u
t
i
o
n
m
odel
i
n
D
u
rba
n
as ex
pre
ssed
by
To
ka
y
and
Sh
ort
[2
4]
in
th
e fo
r
m
o
f
(2
) w
a
s stud
ied
by
Adetan
and
Afu
llo
[
15]
wi
t
h
N
o
(m
-3
mm
-1-
µ
)
i
ndi
cat
i
ng t
h
e scal
i
ng
para
m
e
t
e
r,
µ
(un
itless) is th
e sh
ap
e p
a
rameter, and
Ʌ
is th
e slo
p
e
p
a
rameter in
mm
-1
. Wh
ile th
e shap
e p
a
ram
e
ter
d
o
e
s
i
n
fl
ue
nce t
h
e
s
l
ope
of t
h
e
di
st
ri
b
u
t
i
on at
l
a
r
g
er di
am
et
er bo
un
d, i
t
c
ont
ri
b
u
t
e
s l
a
r
g
el
y
on
t
h
e cu
rvat
ure
of t
h
e
d
i
stribu
tio
n at sm
a
ll d
i
a
m
e
t
ers. Th
e g
a
mm
a
d
i
stribu
tion
is
p
a
rticu
l
arly usefu
l
in
trop
ical reg
i
on
s
wh
ere th
e
ex
pon
en
tial d
i
strib
u
tion
was fo
und
to
b
e
in
ad
equ
a
te [9
]
and
[24
]
.
∗
ex
p
(9
)
whe
r
e
78259
.
,
6
.3209
.
and
μ2
4.
THE SPECIFIC
RAINFAL
L
ATTENUATION
AND THE E
X
TI
NCTION CROSS
SECTION
Gen
e
rally,
th
e sp
ecific rainfall
atten
u
a
tion
γ
(
dB/
k
m
)
i
s
gi
ve
n
by
t
h
e
rel
a
t
i
o
n
[2
5]
:
4.
343
1
0
.
/
(1
0)
whe
r
e
is th
e to
tal ex
tin
ctio
n
cro
s
s-sect
io
n
,
wh
ich
is a fun
c
tio
n
o
f
th
e
d
r
op
d
i
am
e
t
er,
D
, the
wavel
e
ngt
h,
and
t
h
e co
m
p
lex
refractiv
ity ind
e
x
o
f
water
drop
,
m
(
whi
c
h
de
pe
nds
on
t
h
e f
r
eq
ue
ncy
,
f
and
the tem
p
erature,
T
).
The
ex
t
i
n
ct
i
on c
r
os
s
sect
i
on,
i
s
ev
al
uat
e
d
usi
n
g
(
1
1
)
as
p
r
o
v
i
d
e
d
by
Od
ed
ina
and
Afu
llo
[13
]
in
a p
o
wer law relatio
n
,
wh
ere
κ
and
α
are the coefficients that depe
nd
on
rain
rate, te
m
p
eratu
r
e,
pol
a
r
i
zat
i
on a
n
d ca
nt
i
n
g
an
gl
e
o
f
dr
opl
et
s.
2
(1
1)
The classical s
cattering the
o
ry of Mie [26],
[2
7]
i
s
use
d
t
o
com
put
e t
h
e
val
u
es
o
f
κ
a
nd
α
wh
ile
assum
i
ng that
each spherical
raindrop
illuminated by a
plane
wa
ve is
uni
fo
rm
l
y
distributed i
n
a
ra
in field
medium
. The distance
betwe
e
n each
drop i
s
assum
e
d la
rge enough to
avoi
d collis
ion. Table
1 shows the
val
u
es of
κ
and
α
at
f
= 5-10
0
GH
z
. Th
e to
tal rain
fall atte
n
u
a
tion
th
erefo
r
e,
i
s
eval
uat
e
d by
i
n
t
e
g
r
at
i
ng
ov
e
r
all th
e raindrop sizes.
4.
343
1
0
∗
2
(1
2)
Tabl
e 1. Val
u
e
s
o
f
κ
and
α
at
f
= 5-
100
GHz
at
T
= 20
o
C
Fr
equencies(
GHz
) k
5 0.
0048
3.
3911
10
0.
3857
4.
5272
19.
5
1.
6169
4.
2104
25
2.
4567
4.
0186
40
4.
3106
3.
5077
60
6.
0493
3.
0094
80
7.
0623
2.
6621
100
7.
6874
2.
4156
5.
RESULTS
A
N
D
DI
SC
US
S
I
ON
5.1. Specific Attenuation, Ra
infa
ll Rate a
n
d
Frequencies
Al
t
h
o
u
gh
vari
ous m
e
t
hods
have
been a
d
opt
e
d
by
a n
u
m
b
er of rese
arche
r
s t
o
i
n
v
e
st
i
g
at
e t
h
e
part
i
c
ul
a
r
co
nt
ri
b
u
t
i
ons
of ce
rt
ai
n d
r
o
p
di
a
m
et
ers t
o
t
h
e sp
ecific rain
att
e
n
u
a
tion
,
ou
r ap
pro
ach
is to
esti
m
a
te
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 6
,
N
o
. 1
,
Febru
a
ry
2
016
: 8
2
–
89
85
th
e sp
ecific
rain
attenu
ation
by in
teg
r
ating th
e
raind
r
op
size d
i
stri
b
u
tion
N(D
)
an
d th
e estin
ctio
n
cro
ss
section
Q(
t)
over t
h
e
rai
n
dr
op
di
am
et
er
s as indicated in equa
tion
(10
)
.
For instan
ce,
Lee et
al
. [
1
6]
and
[
17]
, i
n
Si
nga
p
o
re
,
Fis
e
r
[18], i
n
the
Czech Re
publ
ic,
Lam et
al
.
[19
]
in
Malaysia, and
Ma
r
z
uk
i e
t
a
l
.
[20
]
in
th
e
Eq
uat
o
ri
al
In
d
one
si
a co
ncl
u
d
e
d t
h
at
sm
al
l
and m
e
di
um
-si
ze dr
o
p
s c
ont
ri
b
u
t
e
d m
o
re t
o
t
h
e rai
n
fal
l
at
t
e
nuat
i
o
n
as frequ
en
cy i
n
creases. Th
ey also
no
ted
t
h
at th
e p
r
ev
ailing
con
t
ri
b
u
tion
to
th
e sp
ecificatten
u
a
tion
is fo
rm
ed
by
rai
n
dr
o
p
s
o
f
di
am
et
er not
excee
di
n
g
2
mm
e
s
pecially at higher
fre
quencies
.The
attenuation creat
ed by
drops in t
h
e
dia
m
eter interval
s 0.1
≥
D
≥
7.
0
mm
at va
rious
fre
quencies
of transm
i
ssi
on i
s
sh
ow
n i
n
Ta
b
l
es 2
.
The total speci
fic attenuation increases
with in
creasing
freq
u
e
n
c
ies for all
the rainfall re
gim
e
s. The specific
rain
attenu
ation
in
creases wit
h
in
creased
rai
n
rates
with
the th
un
d
e
rstorm h
a
v
i
n
g
t
h
e h
i
gh
est atten
u
a
tion
.
Th
e
hi
g
h
est
an
d
pr
evai
l
i
ng c
o
nt
ri
but
i
o
n t
o
the s
p
ecific attenua
tion
occurs at
~
2
m
m
fo
r the
stratif
orm
(drizzle
or
wi
des
p
read
)
and c
o
nvect
i
v
e (sh
o
w
er
or t
h
un
de
rst
o
rm
) rai
n
t
y
pes sh
o
w
n
i
n
Fi
g
u
res
1 a
nd
2
fo
r t
h
e
ga
m
m
a
and
l
o
gn
orm
a
l
m
odel
s
, res
p
e
c
t
i
v
el
y
(see T
a
bl
es 4
an
d
5)
. The
hi
ghest
and
p
r
evai
l
i
n
g
co
nt
ri
b
u
t
i
o
n t
o
t
h
e
specific attenuation for the drizzle
and wi
d
e
sprea
d
rai
n
fal
l
ty
pes o
ccurs
in the diam
eter
range 0.5
mm
≤
D
≤
2.
5
mm
wh
ile
th
at of sho
w
er and
t
h
und
erst
o
r
m
rain
typ
e
s o
c
cu
rs in th
e
rang
e
1
.
0
mm
≤
D
≤
3.
0
mm
and
1.
5
mm
≤
D
≤
3.5
mm
re
specti
v
ely.
5.
2.
I
n
fl
ue
nce of
R
a
i
ndr
op Di
ame
t
ers on
Speci
fi
c Rai
n
At
tenu
ati
o
n
Th
e
p
e
rcen
tage con
t
ribu
tion
form
ed
b
y
rai
n
d
r
op
d
i
am
eter in
terv
als to
t
h
e
o
v
e
rall rain atten
u
a
tion
fo
r
d
i
fferen
t
rai
n
t
y
p
e
s is illu
strated
in
Tab
l
e 3. Th
e con
t
ri
b
u
t
i
o
n of larg
er
d
i
a
m
eters as
o
b
s
erv
e
d
is in
significan
t
to
th
e t
o
tal atten
u
a
tion
.
Fo
r instan
ce, t
h
e
h
i
gh
est co
n
t
ri
b
u
t
i
o
n in
t
h
e
d
i
ameter ran
g
e
4.0
mm
≤
D
≤
7
.0
mm
is
1.
46
%
an
d 0.0
005
%
at
f =
100
GH
z
res
p
ectively for t
h
e thunde
rstorm
a
nd drizzle
rain types
.
T
h
e largest
cont
ri
b
u
t
i
ons
t
o
t
h
e
s
p
eci
fi
c a
t
t
e
nuat
i
o
n are
due
t
o
d
r
o
p
di
a
m
et
ers not
e
x
c
eedi
n
g
2
mm
fo
r
all rainfall reg
i
m
e
s
at all frequ
en
ci
es and
th
is co
nfirm
s
th
e resu
lts ob
ta
i
n
ed i
n
S
i
nga
po
re,
I
n
d
o
n
esi
a
an
d C
zec
h R
e
p
u
b
l
i
c
. He
nce
,
the diam
eter range
s 0.5
mm
≤
D
≤
2.5
mm
are critical to
atten
u
a
tion
in
Du
rb
an
b
e
in
g a co
astal reg
i
on
characte
r
ized
by drizzle rainfa
ll type.
Tab
l
e
2
.
To
tal
Sp
ecific Rai
n
Atten
u
a
tion Form
ed
b
y
Rain
drop
s i
n
th
e Diameter In
terv
al
0
.
1
mm
≥
D
≥
7.
0
mm
fo
rVari
o
u
s
Rain
fall reg
i
mes at
f
=
5-
10
0
GHz
Rain Ty
pes
f (
GHz
)
γ
(
dB
/km
)
Drizzle
(
1
.
41
mm/h
)
5
10
19.
5
40
60
80
100
0.
0057
21
0.
0432
65
0.
2092
61
0.
7902
70
1.
4569
75
2.
0836
24
2.
6307
04
Widespread
(
14.
21
mm/h
)
5
10
19.
5
40
60
80
100
0.
0239
46
0.
2013
46
0.
9013
62
2.
8815
11
4.
7398
11
6.
2730
28
7.
5191
03
Shower
(
44.
52
mm/h
)
5
10
19.
5
40
60
80
100
0.
0753
75
0.
6899
45
2.
9031
66
8.
1216
19
12.
192
99
15.
166
1
17.
409
3
T
hunder
s
torm
(
77.
70
mm/h
)
5
10
19.
5
40
60
80
100
0.
2049
19
2.
0193
29
8.
0518
79
20.
055
57
27.
805
48
32.
763
83
36.
217
87
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Ana
l
ysis
o
f
Ra
ind
r
o
p
Di
a
m
eters fo
r Ra
in
f
a
ll Atten
u
a
tio
n in
S
o
u
t
h
e
rn Africa
(O
.
Ad
etan
)
86
Tabl
e 3.
Perc
e
n
t
a
ge (
%
) Con
t
ribu
tio
n of the
Sp
ecific
Attenu
atio
n fo
rm
ed
b
y
Drop Diameters
(
mm
)
Rain
Typ
e
s
f(
GHz
) 0.
1
≤
D
≤
2
0.
5
≤
D
≤
2.
5
1.
0
≤
D
≤
3.
0
1.
5
≤
D
≤
3.
5
4.
0
≤
D
≤
7.
0
Drizzle
5
10
19.
5
40
60
80
100
95.
55
94.
21
95.
21
96.
95
97.
83
98.
31
98.
59
99.
25
98.
95
99.
18
99.
51
99.
64
99.
69
99.
71
81.
93
85.
05
82.
82
77.
09
72.
43
68.
90
66.
29
29.
99
34.
59
31.
21
24.
29
19.
94
17.
20
15.
41
0.
004
0.
007
0.
005
0.
002
0.
001
0.
0007
0.
0005
Widespread
5
10
19.
5
40
60
80
100
79.
42
75.
26
78.
33
84.
29
87.
78
75.
16
91.
19
93.
44
91.
49
92.
95
95.
49
96.
79
97.
50
97.
92
92.
77
93.
37
92.
98
91.
14
88.
99
87.
09
85.
53
60.
22
65.
17
61.
60
53.
18
46.
99
42.
69
39.
67
0.
192
0.
296
0.
216
0.
105
0.
061
0.
041
0.
031
Shower
5
10
19.
5
40
60
80
100
58.
01
52.
26
56.
45
65.
44
71.
35
75.
16
77.
70
80.
41
76.
14
79.
29
85.
34
88.
83
90.
88
92.
15
90.
08
88.
19
89.
63
91.
61
92.
00
91.
79
91.
38
76.
64
79.
28
77.
44
71.
89
66.
90
63.
01
60.
09
1.
505
2.
150
1.
662
0.
906
0.
571
0.
408
0.
319
T
hunder
s
torm
5
10
19.
5
40
60
80
100
38.
86
32.
99
37.
06
46.
58
53.
48
58.
25
61.
56
63.
28
57.
46
61.
72
70.
61
76.
28
79.
84
82.
17
79.
76
75.
54
78.
67
84.
43
87.
42
88.
95
89.
74
80.
28
79.
81
80.
25
79.
31
77.
08
74.
80
72.
84
5.
46
7.
37
5.
93
3.
57
2.
41
1.
80
1.
46
(a)
(b
)
Fig
u
re
1
.
Rain
fall atten
u
a
tio
n
an
d rai
n
drop
d
i
a
m
eters fo
r
rainfall re
gim
e
s at vari
ous
f
r
eq
u
e
ncies f
o
r (a
)
R=
1.
41
an
d
(
b
) R
=
7
7
.
7
0
mm
/h
usi
n
g gam
m
a
DS
D
m
odel
1E-05
0.0001
0.001
0.01
0.1
1
00
.
511
.
522
.
533
.
5
4
d
γ
(dB/km
)
R
a
i
ndrop di
am
et
er
(m
m
)
10GHz
20GHz
30GHz
40GHz
100GHz
0.001
0.01
0.1
1
10
0
0
.5
1
1
.5
2
2
.5
3
3
.5
4
4
.5
5
d
γ
(dB/km
)
R
a
i
ndrop di
am
et
er
(m
m
)
10GHz
20GHz
30GHz
40GHz
100GHz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
I
J
ECE Vo
l. 6
,
N
o
. 1
,
Febru
a
ry
2
016
: 8
2
–
89
87
(a)
(b
)
Fig
u
re
2
.
Rain
fall atten
u
a
tio
n
an
d rai
n
drop
d
i
a
m
eters
fo
r
rainfall re
gim
e
s at vari
ous
f
r
eq
u
e
ncies f
o
r (a
)
R
=
1.
41
mm
/h
an
d (b
) R=
1
20
mm
/h
usi
n
g
l
o
gn
o
r
m
a
l
DSD
m
odel
.
Tabl
e
4. R
a
i
n
a
t
t
e
nuat
i
o
n crea
t
e
d by
d
r
o
p
s i
n
t
h
e
di
am
et
er range
0
.
1
m
m
≥
D
≥
7.
0
mm
at
va
ri
o
u
s
fre
que
nci
e
s
fo
r t
h
e
gam
m
a m
odel
Fr
equency
(GHz
)
Drizzle
W
i
despr
ead
Shower
T
hunder
s
torm
10
0.
015
0.
199
0.
707
1.
311
20
0.
081
0.
925
3.
079
5.
533
30
0.
186
1.
844
5.
723
9.
943
40
0.
318
2.
781
8.
111
13.
670
100
1.
336
7.
624
18.
032
27.
440
Tabl
e
5. R
a
i
n
a
t
t
e
nuat
i
o
n crea
t
e
d by
d
r
o
p
s i
n
t
h
e
di
am
et
er range
0
.
1
m
m
≥
D
≥
7.
0
mm
at
va
ri
o
u
s
fre
que
nci
e
s
for th
e log
normal
m
o
d
e
l
Fr
equency
(GHz
)
Drizzle
W
i
despr
ead
Shower
T
hunder
s
torm
10
0.
043
0.
201
0.
689
2.
019
19.
5
0.
209
0.
901
2.
903
8.
051
40
0.
790
2.
881
8.
121
20.
055
60
1.
457
4.
739
12.
192
27.
805
80
2.
083
6.
273
15.
166
32.
763
100
2.
630
7.
519
17.
409
36.
217
6.
CO
NCL
USI
O
N
Th
is
p
a
per con
s
id
ered th
e
critical rang
e
o
f
ra
indrop
di
a
m
eters at which t
h
e s
p
eci
fic rai
n
fall
atten
u
a
tion
is
m
o
st in
flu
e
n
c
ed
.
For t
h
e
DSD m
o
d
e
ls consid
ered
, th
e t
o
tal p
e
rcen
tag
e
fractio
n fo
rm
ed
b
y
rai
n
dr
op
s i
n
t
h
e di
am
et
er ran
g
e 0.
5 m
m
≤
D
≤
2.
5
mm
an
d
1.
0
mm
≤
D
≤
3.
0
mm
are re
s
p
ectively found to be
0.0001
0.001
0.01
0.1
1
0
0
.5
1
1
.5
2
2
.5
3
d
γ
(dB/km
)
R
a
i
ndrop di
am
et
ers
(m
m
)
10GHz
19.
5GHz
40GHz
60GHz
80GHz
100GHz
0.001
0.01
0.1
1
10
0
0
.5
1
1
.5
2
2
.5
3
3
.5
4
4
.5
5
d
γ
(dB/km
)
R
a
i
ndrop di
am
et
ers
(m
m
)
10GHz
19.
5GHz
40GHz
60GHz
80GHz
100GHz
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Ana
l
ysis
o
f
Ra
ind
r
o
p
Di
a
m
eters fo
r Ra
in
f
a
ll Atten
u
a
tio
n in
S
o
u
t
h
e
rn Africa
(O
.
Ad
etan
)
88
m
o
st crit
ical f
o
r th
e sp
ecific rain
atten
u
a
ti
o
n
for th
e stra
tiform
(drizzle and wi
des
p
re
ad) and convective
(sh
o
w
er
an
d t
h
un
de
rsto
rm
) in D
u
r
b
a
n
, S
o
uth
Af
rica.
Th
e con
t
ri
b
u
t
i
o
n
o
f
larg
er
dia
m
eters to
th
e to
tal atten
u
a
tio
n
is v
e
ry low and
in
sign
ifican
t wh
en
com
p
ared to medium
and sm
a
ller dia
m
eters. The critical
diameters are the range of
diam
e
t
ers that contri
bute
sig
n
i
fican
tly to
th
e
rain
atten
u
a
tion
.
The
h
i
gh
est con
t
ri
b
u
tion
o
f
raind
r
op
s d
i
am
ete
r
s to
t
h
e sp
ecific rai
n
attenuation wa
s created
by dr
op diam
eter
s not e
x
ceedi
ng
2
mm
, es
p
eci
al
l
y
at
hi
gher
fre
que
nci
e
s. Thi
s
confirm
s
the results obtaine
d by [16],
[17] in Singa
pore;
[18] in Czech Republic; [19]
in Malaysia and [20] in
Eq
uat
o
ri
al
In
d
one
si
a.
At
f
r
e
que
ncy
a
b
o
v
e
40
GH
z
, the
drop size
diam
e
t
er that
gives
the largest c
o
ntri
bution
to
th
e to
tal att
e
n
u
a
tion
fo
r al
l th
e rain
rates co
n
s
i
d
ered
does n
o
t
ex
ceed
3
mm
(9
0
%
).
Th
is is si
m
ilar
to
th
e
r
e
su
lts ob
tain
ed
b
y
[
2
0
]
. A
go
od
und
er
stand
i
ng
o
f
th
is
rain
fall atten
u
a
tio
n
ch
aracterist
i
c will
b
e
h
e
lpfu
l to
p
r
op
erly d
e
sig
n
adequ
a
te fad
e
m
a
rg
in
lev
e
ls,
ac
h
i
eve th
e exp
ected
q
u
a
lity of serv
ice in a rad
i
o
com
m
uni
cat
i
on sy
st
em
oper
a
t
i
ng i
n
t
h
i
s
regi
o
n
an
d fo
r t
h
e p
u
r
p
o
s
e of
l
i
nk b
u
d
g
et
de
si
gn by
t
h
e en
gi
nee
r
s
an
d serv
ice
p
r
ov
id
ers in th
is
particu
l
ar
reg
i
o
n
.
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BIOGRAP
HI
ES OF
AUTH
ORS
ADETAN Oluwumi holds B.En
g. de
gr
ee in
El
e
c
tri
cal
and E
l
e
c
t
r
onic Eng
i
nee
r
in
g from
the then
Ondo State University
, Ado Ekiti, Niger
i
a in 19
99; M.Eng. degr
ee in Electr
i
cal and Electronic
Engineering (C
ommunications Option) from the
Feder
a
l University
of
Tech
nolog
y
,
Akure,
Nigeria in 201
0 and Ph.D. degree in 2014 from
the School of Electr
i
cal,
Electronic and
Com
puter Engineering
,
Univers
i
t
y
of Kwazulu-N
at
al, South Africa. He joined th
e Department of
Electrical and Electron
i
c Engin
e
er
ing, Ekiti State University
, Nige
ria in 2000. He is a registered
m
e
m
b
er the Institute of E
l
e
c
tr
ica
l
and El
ectr
onics Engine
ers (IEEE) and C
ouncil for th
e
Regulation of Engineer
ing in Nige
ria (COREN).
His
res
earch in
t
e
res
t
is
to s
t
ud
y the eff
ects
of
rain on microwave propagation and wireless communi
cations
s
y
s
t
em
s
.
He is
curre
ntl
y
the A
c
tin
g
Head of
Department of Computer Eng
i
ne
ering,
Ekiti
Sta
t
e Univ
ersit
y
,
Niger
i
a
.
OBIYEMI Obisey
eob
t
ained B
.
Eng. and
M.Eng.
Degre
e
in
Ele
c
tr
ica
l
En
gineer
ing from
University
of Ilorin, Nigeria in
2006 and 201
0
respectiv
ely
.
He joined the
Department of
Electrical
and Electronic Engineering
,
Osun
St
ate University in 2010 and
He is currently
workingtowards the PhD degree from the Departme
nt of Electr
i
cal and El
ectronic Engineering
,
Universit
y
of
Ilo
r
in, Nig
e
ri
a.
Evaluation Warning : The document was created with Spire.PDF for Python.