117
1 INTRODUCTION
1.1 Humidityoftheatmosphere
Water is the only substance that can be found
naturallyinallthreestates(gas,liquid,solid) inthe
atmosphere. Humidity is the general term to show
the existence of the “water” in the atmosphere.
Parameters related to atmospheric humidity levels
include water
vapor pressure (e), saturation vapor
pressure(e
s),relativehumidity(H),drytemperature
(θ), precipitation height (h), precipitation time
interval(t),pressure(P),watervapordensity(ρ).
Water in any state affects the transmission of
electromagnetic waves. When the wave passes
through a humid atmospheric layer, part of its
energyis reflectedor scattered, another is
absorbed
andtherestispassingwithoutanychange.Therefore
the electromagnetic wave is attenuated. The
attenuation is caused by the scattering and
absorption of electromagnetic waves by drops of
liquid water.The scattering diffuses the signal,
whileabsorptioninvolvestheresonanceofthewaves
with individual molecules of water.
Absorption
increases the molecular energy, corresponding to a
slight increase in temperature, and results in an
equivalentlossofsignalenergy.
Precipitation phenomena result in signal
attenuation,aswellascorrespondingincreaseofthe
system noise temperature. Further on, rain causes
cross‐polarization interference in dual polarization
systems.Thesethreeeffects
causedegradationinthe
received signal quality, particularly for frequencies
above 10 GHz, resulting in increase of the system
outage time. Hence, prediction of their influence is
very important in microwave telecommunications
systemsdesign.
Maximum Rain-Rate Evaluations in Aegean
Archipelagos Hellas for Rain Attenuation Modeling at
Microwave Frequencies
E.Α.Karagianni,C.N.Vazouras&E.H.Papageorgiou
HellenicNavalAcademy,Piraeus,Greece
A.D.Sarantopoulos
HellenicNationalMeteorologicalService,Eliniko,Greece
H.E.Nistazakis
NationalandKapodistrianUniversityofAthens,Athens,Greece
ABSTRACT:By utilizingmeteorologicaldatasuchasrelativehumidity,temperature,pressure, rainrateand
precipitationdurationateight(8)stationsinAegeanArchipelagosfromsixrecentyears(2007–2012),theeffect
of the weather on Electromagnetic wave propagation is studied. The EM
wave propagation characteristics
dependonatmosphericrefractivityandconsequentlyonRain‐Ratewhichvaryintimeandspacerandomly.
Thereforethestatisticsofradiorefractivity,Rain‐Rateandrelatedpropagationeffectsareofmaininterest.This
workinvestigatesthemaximumvalueofrainrateinmonthlyrainfallrecords,fora
5minintervalcomparingit
withdifferentvaluesofintegrationtimeaswellasdifferentpercentagesoftime.Themaingoalistodetermine
the attenuation level for microwave links based on local rainfall data for various sites in Greece (L‐zone),
namelyAegeanArchipelagos,withaviewonimproved accuracy
ascomparedwithmoregenericzonedata
available. A measurement of rain attenuation for a link in the S‐band has been carried out and the data
comparedwithpredictionbasedonthestandardITU‐R method.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 1
March 2016
DOI:10.12716/1001.10.01.13
118
1.2 Theraindrop
The raindrop size distribution and the drop shape
relationhavegreatvariationindifferentprecipitation
conditions. In heavy precipitation phenomena the
raindrop size is composed of lots of median and
small raindrops rather than giant raindrops [1], [7].
Both shape and size are depending from the
dynamics
principles where a raindrop is deforming
asitfallsinair,breakingintosmallerfragments.The
topological change from a big drop into smaller
stablefragmentsisaccomplishedwithinatimescale
muchshorterthanthetypicalcollisiontimebetween
thedrops[2],[3],[8].Regardingstrongprecipitation
phenomena,the
sizeofatypicalraindrop,isabout3
millimeters, although the typical diameter of a rain
droplet is 1mm as emerged from the radar
reflectivityfactorZmeasuredinmm
6
/m
3
.
1.3 Therelativerefractiveindex
Whenthepropagationmediumisamaterialdifferent
than air, the speed of an electromagnetic wave
dependsontherelativedielectricconstantknownas
relative permittivityε
r and to the relative
permeabilityμ
r,withthefollowingformula:
rr
1c
v
(2)
whereε=ε
0
.
εr andμ=μ0
.
μr, are the permittivity and
permeabilityinF/mandH/mrespectively,andεᵣand
μᵣ are the relative permittivity and permeability of
themedium[6],[11].
Therelativerefractiveindex,nisdefinedas
rr
n εμ (3)
Values for the relative refractive index, are
presentedinFigure3 forfouryears observationsin
SkyrosIslandatNorthwestAegeanSea(Figure2).
2 RAINMODELSFORWAVEATTENUATION
2.1 Rainattenuation
The electromagnetic wave attenuation due to rain
(the rain attenuation) is one of the most noticeable
componentsofexcesslosses,especiallyatfrequencies
of10GHzandabove.Considerableresearchhasbeen
carriedouttomodelrainattenuationmathematically
andtocharacterizerainfallthroughouttheworld.A
host of methods for estimating rain attenuation is
based on the power law for specific attenuation
combined with the notion
of effective path length
[10],[14],[15].
r
LkRL
α
(4)
whereL
ristherainattenuation(indB),R istherain
rate(inmm/h),Listheeffectivepathlength(inkm),
and k andαare empirical coefficients, functions of
theoperatingfrequency(f),polarization(k
horαh‐h
for horizontal polarized waves and k
v or kv‐v for
verticalpolarizedwaves)andtemperature(T).
For horizontally polarized waves, k
H andαH
parametersaregiveninTable1forselectedSandX
bandfrequencies[12],[16].
Table1.Parametersforhorizontallypolarizedwaves(h)in
SandX‐band.
_______________________________________________
Frequency(GHz)kH(x10
‐3
)αH
_______________________________________________
2,50,13211,1209
50,21621,6969
1012,171,2571
_______________________________________________
Theequivalentpathlengthdependsontheangle
ofelevationofthecommunicationlink,theheightof
therainlayer(h),andthelatitudeoftheearthstation.
(Figure1)
Figure1.Pathlengththroughrain
Therainrateentersintoequation4becauseitisa
measureoftheaveragesize oftheraindrops.When
therainrateincreasesthatmeansitrainsharder,the
rain drops are larger and thus there is more
attenuation. Also, the conversion of the radar
reflectivity factor to rain rate
is a crucial step in
weather radar measurements. It has been common
practice for over 60 years now to take for this
conversionasimplepowerlawrelationshipbetween
them, using the classical exponential raindrop size
distribution[17],[18].
2.2 RainModels
Rain models differ principally in the way the
effective path length L is calculated.Two rain
models are widely used, the Crane model and the
ITU‐R model (International Telecommunication
Union’s Radio‐communication sector). The two‐
componentCranemodeltakesintoaccountboththe
dense center and the fringe area of a rain cell [11],
[19]. In the design
of a telecommunications’ link a
margin is included to compensate for the effects of
rain at a given level of availability. The statistical
characterizationofrainbeginsbydividingtheworld
into rain climate zones.Within each zone, the
maximum rain rate for a given probability is
determined from actual
meteorological data
accumulatedovermanyyears.
Themethodsofpredictionoftherainattenuation
can be categorized into two groups: the physical
models and the empirical models. The physical
models attempt to reproduce the physical behavior
involved in the attenuation processes while the
119
empiricalmethodologiesarebasedon measurement
databases from stations in different climatic zones
within a given region. The empirical methods are
usedwidely.
Thefactorγ
r=Lr/L(indB/Km),whereLrandLare
defined in equation 4, is called the specific rain
attenuation. One of the most widely used rain
attenuation prediction methods is the empirical
relationshipbetweenthisspecificrainattenuationγ
r
(indB/km)andtherainrateR(inmm/h)[12],[13]
α
r
γkR
(5)
3 RAINRATE
For the determination of the rain attenuation, the
main parameter used is the rain rate R, which is
expressedinmm/h.Therainratecanbedescribedas
thethicknessoftheprecipitationlayer,whichfelled
down over the time period of one hour in the
case
whentheprecipitationisnotevaporated,notsoaked
intothesoil,andisnotblownawaybythewind. The
evaluationofR‐valueisofcrucialimportanceinthe
rain attenuation prediction. The rain attenuation
depends on the meteorological conditions in the
consideredplace.
3.1 IntegrationTime
TheR
‐valuesareexpressedinmm/h.Timeintervals
between the readings of rainfall amount in many
casesareunrealistic.Theperiodoftimebetweenthe
readings of the rainfall amount values is called
integration timeτand it is a very important
parameter,becauseitcansignificantlychangetheR‐
value.High
R‐valuesarehiddenwhenτislong.
Asanexample,weassumethatitwasrainingfor
5minutesandthetotalamountoftheprecipitation
atthistimewas20mm.Fortheremaining55minutes
wasnotrainingandduringtheremainingminutesof
3 hours as well. Thereby,
the average R‐value is 20
mm/h.Ontheotherhand,ifwecounttheaverageR
forameasuringdurationof15minutes,itwillbe80
mm/h,for10minutes120mm/handfor5minutesit
willbe240mm/h. Similarly,if wecount R‐value for
every
rainy minute, we will find that R=240 mm/h,
sinceineveryofthose5minutestheamountofthe
precipitationwas4mm/min.Thedifferentoutcomes
fortheR‐valuesmakethiswayofcountedunreliable)
3.2 The“one‐minute”rainrate
Almost all rain attenuation prediction methods
requireone–minuteintegration
timerainratevalues.
Table2.RainHeightinmmduring5min,10min,15min,
1h,3hand12h
HellasIslandRainHeightinmm
5min 10min 15min 1h 3h 12h
_______________________________________________
Mykonos 7,213,4 17,6 47,4 66,9 108,8
Naxos ‐ 0,80 7,10 18,6 38,4 38,8
Thyra12,0 23,8 31,8 48,9 51,5 51,5
Rodos 12,1 19,6 26,4 51,3 72,1 73,2
Samos 10,0 15,1 20,0 43,7 53,7 78,3
Chios15,3 16,2 25,9 42,0 56,0 159,0
Mytilini 8,612,2 16,1 31,6 40,1 67,6
Skyros 0,01 2,40
3,00 74,0 74.0 74,0
_______________________________________________
However,inourcase,5‐min,10‐min,15‐min,1‐h
and 12‐hourly instances data are used. There are
variousmodelsforconversionof(τ‐min)into(1‐min)
rainfallstatistics (see e.g. [5], [9], [10], [14]), usually
based on either equal rainfall rate or equal
probabilityapproach;an
exampleofthelatter(asin
[9])resultsinarelationshipoftheform
R
1min=a(Rτmin)
b
(6)
where R
τ min is rain rate value measured inτ
minutesτ≥1min)andR
1minthe“one‐minute“rainrate
value, while a and b are appropriate regression
coefficients. The difficulty with such techniques is
that they usually require 1‐min measured data to
estimate the regression coefficients, which
consequently are location‐specific. An alternative
approach(forτbetween5and60minutes)is given
by
thesyntheticmodelbasedonsoftwaresimulation
suggestedinAnnex3of[23].
Figure2.MeteorologicalStations inAegean’sIslands
On the other hand, the main advantage of the
“Worst‐month”modelwhichwasproposedbyITU‐
R[12]isthatonlytheworst‐monthstatisticsmustbe
collected,althoughitisappropriateincaseswhenthe
requiredreliabilityoftheradiosystemisotherthan
99.99%. This month is not
necessarily the same
month in different year. The fraction of time when
the threshold value of rain rate (so, and rain
attenuation value) was exceeded is identical to
probability that the threshold value of rain rate
wouldbeexceeded[15],[19].
Mytilini
Skyros
Chios
Samos
M
y
konos
120
Table3.RainRateat0,001%and0,01%inmm/h
_______________________________________________
HellasProvince RainRateat0,001%RainRateat0,01%
Island(Lat/Log) inmm/hinmm/h
_______________________________________________
Mykonos86,447,4
Naxos‐11.0
Thyra144,048,9
Rodos145,251,3
Samos120,043,7
Chios183,642,0
Mytilini103,231,6
Skyros80,748,0
_______________________________________________
4 DATAANALYSIS
Our survey is focused on those measurements
referredasAegeanArchipelagos,namely,Mykonos,
Naxos,Santorini,Rodos,Samos,Chios,Mytiliniand
Skyrosislandswhichcoverthewholenorthwestand
northeastregionofAegeanSea.
(a)
(b)
(c)
(d)
Figure3. Rain rate and relative refractive indexes for the
periodJanuary2010–December2013forSkyrosIsland.
The precipitation amount as a meteorological
indexonSkyroshasamaximumvalueof74mmfor
the period January 2010 to December 2013. This
valueappearedinMay2012for55minutes,givinga
R‐valueof81mm/h.Thedayfollowingthisstorm,an
R‐value of 43 mm/h
(36 mm for 50 minutes) was
observed.Thenextmaximumvaluesforprecipitation
heightappearedinJune2011(64mm)for1hourand
20minutesandinFebruary2012(53mm)for6hours,
giving R‐values at 48 mm/h and 8,8 mm/h
respectively.
5 REFRACTIVITY
Another parameter to
consider is the relative
refractiveindexoftheatmospheregiveninequation
3,whichaffectsthecurvatureoftheelectromagnetic
wave path and graces the fading phenomenon. For
example, the anomalous electromagnetic wave
propagation can cause disturbances to radar work,
because variation of the refractive index of the
atmosphere can induce
loss of radar coverage.
Accuratepredictionoflossesduetothesefactorscan
ensureareliabilityofthetelecommunicationsystem,
decreasetheequipmentcostandprotectpeople.
5.1 RefractiveIndex
Therelativerefractiveindex,n,forthetroposphere,is
computedby[20]
6
n1N10
(7)
whereNistheradiorefractivityexpressedby:
5
dry wet
2
Pe
N N N 77,6 3, 732 10
TT
(8)
withPbeingtheatmosphericpressure(inmbars),e
the water vapor pressure (in mbars), and T the
absolutetemperature(in
0
K).
This expression may be used for all radio
frequencies. The relationship between water vapor
pressureeandrelativehumidityisgivenby:
s
He
e
100
(9)
where
s
t
b
t
d
eEFaexp
tc
(10)
wherea=6.1121mbisthevapourpressureatthetriple
pointandithasthesameuniteswithe
sand
121
472
EF 1 10 7, 2 P 0,0032 5,9 10 t
(11)
wheretisthetemperature(in
°
C),Pis thepressure
(inmbars),Histherelativehumidity(in%)e
sisthe
saturation vapor pressure (in mbars) at the
temperaturet(in
°
C)and the coefficientsb, candd
forwaterforthemeasuredtemperature,are:
b=18.678,c=257.14,d=234.5.
Vapor pressure e in mbars is obtained from the
watervapourdensity(ing/m
3
)usingtheequation:
ρΤ
e
216,7
(12)
whereisgivening/m
3
.
Skyrosannualaveragesfortheperiod2010to2013
are N
dry=272, EFwater=1,001, es=20,3, e=13,02,
N
wet=57,07, N=328,95, n=1,0003 andρ=9,67 while
Naxosaverageswhich is locatedsouth fromSkyros
for the same period, areθ=18,8
0
C dry temperature,
P=1013,77 mbars,Η=68,44% relative humidity,
N=336.18andρ=11,3.
Itisnoticeablethatourstatisticsbasedat12‐hour
measurements 6:00 and 18:00, and this for the
followingreason:Duringthe12‐hourmeasurements,
the station, recorded summed with the last 3 hour
andallmeasurementswereprecededduring
that12
hour and were given separately in each 3‐hour
observation.
Note that the maximum value R, appeared in
Naxos, on 5th of November 2013 at 06:00 UTC and
this value is 55,8 mm/h, much smaller than this
appearedinSkyros(81mm/h).
Table2. Observed parameters values at a specific
parameteratitsminimumvalue(inbold).
_______________________________________________
τH PθH N R
minutes mm mbars
0
C %mm/h
_______________________________________________
803,4981,6 11,4 81 318 3
00 1021,8 ‐0,6 65 310 0
100 1006,9 32,4 19 293 0
00 1006 27,4 19 288 0
_______________________________________________
Table3. Observed parameters values at a specific
parameteratitsmaximumvalue(inbold).
_______________________________________________
τH PθH N R
minutes mm mbars
0
C %mm/h
_______________________________________________
720 20,8 1016,9 20,8 88 336 2
00 1035 2,458 212 0
00 1000,9 35,2 31 321 0
00 1020,7 22 100 380 0
00 1013,3 29 78 388 0
5574 1009,9 15,4 88 341 81
_______________________________________________
Intables2and3,observedparametersvaluesare
presented, for precipitation time interval (τ),
precipitation height (h), pressure (P), dry
temperature (θ), relative humidity (H), refractivity
(N) and Rain‐Rate (R) at a specific parameter at its
minimum (Table 2) and maximum value (Table 3)
respectively.
Instrongprecipitationphenomena,asit
isshowninfigure4,thetemperaturedecreasesand
the relative humidity increases. The relative
refractiveindexwillbeincreasedasitisproportional
to the water vapor pressure (which in turn is
proportionaltotherelative humidity)andinversely
proportionaltotemperature.Thesame
phenomenon
is observed when the precipitation has very small
rain‐ratesalthoughthetemperature,pressurerelative
humiditychanges‐andconsequentlyrefractivityand
relativerefractiveindexchanges‐occuracoupleof
hourslaterasitispresentedinthediagramoffigure
5.
6 DISCUSSION
The main models for calculation of
electromagnetic
wave attenuation due to atmospherichumidity and
heavy precipitation phenomena, were revised. In
AegeanSea,Hellas,whenthereliabilityoftheradio
system of 99,99% is required, R‐value equals to
approximately 50 mm/h. The attenuation of
horizontally polarized electromagnetic waves is
greater than the attenuation of vertically polarized
electromagnetic
waves. The dependency of the
average specific electromagnetic wave attenuation
due to rain on the operating frequency was
determined.
Figure4. Hourly paremeters presentation on a rainy day
withstormsinMay2012atSkyrosisland
Figure5.Hourlyparemeterspresentationonadrizzleday
attheendofJanuary2011atSkyrosisland.
The variations of the atmospheric humidity,
temperature and pressure cause the fluctuations of
122
the atmospheric refractive index. The atmosphere
refractivityfluctuatesbetween288and388fornights.
Thisintervalisshorteningby14%fordayperiods.In
heavy precipitation phenomena (R>10mm/h)
refractivity values are between 317 and 363 with
N=340atthemaximumR‐value.
Figure8. Measurements in moderate precipitation
phenomenashowedapowerlossofabout10to12dBmat
2,4GHz
Measurements performed in a rainy day, for 40
minutes, with a wireless system at 2,4 GHz with
minimumconnectionrequirementsapproximatelyat
‐80 dBm. The first measurement was performed
without rain, at free space and the signal’s power
was varied from‐60to‐53 dBm. With the use of a
directionalantennathereceivingpowerwasbetween
‐37to‐29dBm.InthecaseofrainwithR‐valueat12
mm/hthesignal’spowervariedinbetween‐71to‐64
dBm. This 10 to 12 dBm attenuation was expected
due to the path loss equation (4), [21] and
measurements
are in accordance with theoretical
results.
7 CONCLUSION
Despitethefactthatmanyfiberopticcablelinkshave
been installed in Greece, terrestrial or satellite
microwavelinksplayanimportantroleinproviding
communicationaccesstoislandsandruralorremote
areas. The fast growth in telecommunications,
increased demand for bandwidth,
congestion in
lower frequency bands and miniaturization of
communicationequipmenthaveforcedthedesigners
toemployhigherfrequencybandssuchastheC(4to
8GHz),Ka(26.5to40GHz),Ku(12to18GHz)andV
(40 to 75 GHz) bands. Rain is the most important
factor
for signal propagation deterioration in these
frequencies. The contribution of rain attenuation to
the quality of signal in these bands, needs to be
studied. The aims of this paper are to estimate the
magnitude of rain attenuation using the ITU‐R
model,carryoutlinkperformanceanalysis,andthen
proposereasonable,
adequatefademarginsthatneed
tobeappliedforallprovincesinGreece.
TheEMwavepropagationcharacteristicsdepend
on atmospheric refractivity. Nevertheless,
atmospheric refractivity varies in time and space
randomly. Therefore the statistics of atmospheric
refractivity and related propagation effects are of
main interest. This work investigated the major
differences between radio refractivity changes for
Northwest Aegean Archipelagos. Radio refractivity
values were calculated from measured
meteorological parameters (relative humidity,
temperatureandpressure)duringarecentperiodof
4 years. The results showed that radio refractivity
fluctuates between 288 and 388 but in strong
precipitation phenomena where R≥24mm/h it
fluctuates
inbetween326to363(N‐units).
The rainfall rate exceeded for a probability of
0,01%oftheaverageyearandthelocation(24,32◦E,
38,50◦N) is 48 mm/h and it is in accordance with
previous published studies and ITU
recommendations[22],[23].Rainfalleventswithrain
ratesof
81,48,25mm/hwereobservedinSkyros.The
durationsoftheseprecipitationswere55minutes,80
minutes and 109 minutes respectively. The
percentagesofthetimewere0.01%,0.015%and0,02
%respectively.
Incorporatingdataonextremeweathereventslike
heavyprecipitationimpacts,intoGISmapswouldbe
of tactical advantage for military operations [24].
More measurements have to be performed for
various conditions of precipitation. Moreover, the
analysis of rainfall data of the longer period (of
severaldecades)and several pointsmust becarried
out to determine the parameters involved in rain
attenuationprediction.
ACKNOWLEGMENTS
Authorswould
liketoacknowledgethecontribution
ofHellenicNationalMeteorologicalService,Division
of Climatology‐Applications for providing
meteorologicaldatausedinthisstudy.
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