Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–7

Contents lists available at ScienceDirect

Journal of Atmospheric and Solar-Terrestrial Physics

http://d1364-68

n CorrE-m

animesh

journal homepage: www.elsevier.com/locate/jastp

Rain attenuation prediction during rain events in different climaticregions

Dalia Das a,n, Animesh Maitra b

a Department of Electronics and Telecommunication Engineering, Meghnad Saha Institute of Technology, Techno Complex, Madurdaha, Kolkata 700 150, Indiab S K Mitra Centre for Research in Space Environment, Institute of Radio Physics and Electronics, University of Calcutta, Kolkata 700 009, India

a r t i c l e i n f o

Article history:Received 30 July 2014Received in revised form4 March 2015Accepted 5 March 2015Available online 7 March 2015

Keywords:Rain attenuationTime series predictionPropagation channelEarth-space path

x.doi.org/10.1016/j.jastp.2015.03.00326/& 2015 Elsevier Ltd. All rights reserved.

esponding author.ail addresses: dalia_das311@yahoo.co.uk,.maitra@gmail.com (D. Das).

a b s t r a c t

A rain attenuation prediction method has been applied to different climatic regions to test the validity ofthe model. The significant difference in rain rate and attenuation statistics for the tropical and temperateregion needs to be considered in developing channel model to predict time series of rain attenuation forearth space communication links. Model parameters obtained for a tropical location has been success-fully applied to predict time series of rain attenuation at other tropical locations. Separate model para-meters are derived from the experimental data obtained at a temperate location and these are used topredict rain attenuation during rain events for other temperate locations showing the effectiveness of thetechnique.

& 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the congestion at the lower frequency bands, the sa-tellite communication systems are now operating at the higherfrequency Ku or Ka bands (Ku or Ka). However in these bands,mainly above 10 GHz, rain events cause severe attenuation to thepropagating signal along earth space communication link. If timeseries prediction of rain attenuation during rain events is possible,fade countermeasure techniques such as adaptive control of signalpower, coding and data rate can be effectively implemented tomitigate this attenuation effect. Channel models in the form oftime series generators of rain rate and attenuation have been de-veloped previously (Alassur et al., 2004; Fontan et al., 2007; Hederand Bito, 2008; Carrie et al., 2011; Lemorton et al., 2007). So far,they have not been used to predict rain attenuation or rain rateduring rain events at different points of time. There exist variousshort term rain attenuation prediction methods (Castanet, 2001;Gremont, 1997; Van de Kamp, 2002; Montera et al., 2008; Bolea-Alamanac et al., 2003), all of which predict a single attenuationvalue a short time before the actual occurrence, but not the timeseries of attenuation values for the entire rain event. The abovementioned models are validated on long term basis and not onevent by event basis. In the present study, a channel model hasbeen developed to predict time series of rain attenuation during

the entire rain event.This model is not only tested on long term basis but also event

wise. In our earlier paper (Das and Maitra, 2012a, 2012b), the samemethod has been discussed for rain attenuation and rain rateprediction for experimental data obtained at Kolkata, a tropicallocation. However, the effectiveness of the methodology needs tobe tested for any locations in the globe. In this paper, rain rate andattenuation statistics obtained at tropical and temperate regionsare compared. From the measured data set, model parameters aredeveloped separately for tropical and temperate regions which arebeing used to predict the time series of rain attenuation for boththe regions.

2. Comparision between tropical and temperate region

Data sets from different sites in tropical region as well as intemperate region are taken to check the validity of our model. Thedetails of the measurement links are given in (Maitra et al., 2007;Chakravarty and Mitra, 2010; Adhikari et al., 2011; Riva, 2004;Propagation data and prediction methods required for the designof Earth-space telecommunication systems, 2009; Sánchez-Lagoet al., 2007) and also in Table 1 in a short form. To get propercomparison of attenuation statistics, for Spino d’ Adda and Kolkatameasurements are taken at the frequency 11.6 GHz and 11.172 GHzrespectively. But to test the validity of the model in temperateregion, at Spino d’ adda, attenuation measurements are also takenat 18.7 GHz as the other station data are at frequencies very near

Table 1Parameters of the measurement links.

Site location Country Lattitude (°N) Longitude(°E)

Elevation(deg)

Frequency (GHz) Data used

Kolkata India 22.57 88.48 63° 11.172 2007Douala Cameroon 4.05 9.7 47° 11.6 1987Hongkong China 22.2 114.2 20° 11.6 1981Singapore Singapore 1.3 103.9 41° 11.6 1980Spino d’ Adda Italy 45.4 9.5 37.7° 11.6, 18.7 1994Oberpfaffenhofen Germany 48.08 11.28 27.6° 18.99 1994Blacksburg Virginia 37.2 279.5 45° 19 1979Ottawa California 45.34 284.1 21.185° 19 1997Waltham Massachusetts 42.4 288.78 38° 19 1979

0 1 2 3 4 5 6 7 8 9 1010

10

10

10

10

Rain Attenuation (dB)

Exc

eede

nce

Pro

babi

lity

Spino d' AddaKolkata

0 20 40 60 80 100 12010

10

10

10

Rain Rate (mm/hr)

Exc

eede

nce

Pro

babi

lity

Spino d' AddaKolkata

Fig. 1. Comparison between the cumulative distributions of measured (a) rain rate and (b) rain attenuation data at Spino d' Adda (1994) and Kolkata (2007).

Table 2Coefficients of polynomial expressions for mean and standard deviation of condi-tional distributions of rain attenuation at 11.172 GHz for Kolkata.

Region Segment a0/b0 a1/b1 a2/b2

Tropical (Kolkata) C 0.061/ .22 0.98/ .031 0.00073/� .0026D 0.032/ .27 0.97/ .043 0.0017/� .0036U 0.23/ .3 0.98/ .032 0.00066/� .0033No segmentation 0.12/ .18 0.96/ .12 0.0021/� .0093

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–72

to 18.7 GHz. This frequency (18.7 GHz) is also chosen to show theefficacy of our model at the high frequency range. All the recordedrain rate and attenuation data are passed through a raised squarecosine filter with cutoff frequency 0.025 Hz to eliminate thescintillation effects and other fast fluctuations.

Fig. 1 gives the comparison of the yearly cumulative distribu-tions of measured rain rate (a) and attenuation (b) data for Kolkata

Determine type of signal segment

Determine μ & σ

GeGaussia

va

A

Measurement ((n-1) Ts)

Measurement ((n-2) Ts)

Predicted attenuation series y(nTs)

Fig. 2. Block diagram representation of ti

(2007) and Spino d’ Adda (1994).The distributions for tropicalregion show higher occurrences of rain rate and attenuation valuescompared to temperate region. As the rain climatology is differentin the two regions, separate model parameters are required for thetemperate and tropical regions.

3. Rain attenuation predictor

The measured attenuation values are divided into three seg-ments namely, constant (C), down (D) and up (U) segment ac-cording to the following criteria

(kT )

C(constant) if a(kT ) a((k 1)T ) 1dB

D(down) if a(kT ) a((k 1)T ) 1dB

U(up) if a(kT ) a((k 1)T ) 1dB (1)

s

s s

s s

s s

Δ =– − ≤

– − < −– − >

nerate n random

riableComparison

Correction term

Stored & Delayed by one cycleddition

Measurement (nTs)

me series rain attenuation predictor.

0 500 1000 1500 2000 2500 3000 35000

5

10

15

20

Time (sec)

Atte

nuat

ion

(dB

)MeasurementPrediction

1 2 3 4 5 6 7 8 90

20

40

60

80

Attenuation (dB)

Err

or (%

)

DataMean

Fig. 3. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 25 June 2007at Kolkata. (b) Percentage errors in the predictedvalues against the attenuation during the same rain event.

Fig. 4. Comparison between the predicted and the measured attenuation statistics for (a) Douala , 1987. (b) Hongkong, 1981. (c) Singapore, 1980.

Fig. 5. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 23 April 1994 at Spino d’ Adda. (b) Percentage errors in thepredicted values against the attenuation during the same rain event. The models developed for tropical region is used for μ and s computation.

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–7 3

where a(kTs) is the attenuation sample measured at the instantkTs, k¼1,2,3, …., Ts is the time interval between two consecutivesamples.

The distributions of conditional occurrence that if at an instantthe attenuation is x dB then the attenuation will be y dB after Tssecond, are derived from the experimental data set for Kolkata foreach segment type (C, D, U). Ts is taken to be 10 s. The measured

distributions are well described by Gaussian distribution. Themean (μ) and standard deviation (s) of measured distributions forthe complete data set are obtained at different values of attenua-tion (x) and are plotted against attenuation. A second order poly-nomial is fitted for each curve and μ and s are expressed in termsof attenuation, as follows:

Table 3Coefficients of polynomial expressions for mean and standard deviation of conditional distributions of rain attenuation at 11.6 GHz for Spino d’Adda.

Region Segment a0/b0 a1/b1 a2/b2

Temperate (Spino d’ Adda) C 0.017/0.181 0.45/0.0018 �0.00014/0.00012D �0.0284/0.013 0.52/0.014 �0.00011/�0.00012U 0.05/0.04 0.42/0.020 0.00009/�0.00017No segment 0.06/0.09 0.41/0.018 0.00016/�0.00008

Fig. 6. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 23 April 1994 at Spino d’ Adda. (b) Percentage errors in thepredicted values against the attenuation during the same rain event. The models developed for temperate region is used for μ and s computation.

Fig. 7. Comparison between the predicted attenuation values obtained from tem-perate and tropical region models along with the measurement during the rainevent of 23 April 1994 at Spino d’ Adda.

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

Prediction Error (%)

Exc

eede

nce

Pro

babi

lity

Using Tropical Model

Using Temperate Model

Fig. 8. Comparison of the cumulative distributions of prediction error obtainedfrom temperate and tropical region models for all the rain events of the year 1994at Spino d’ Adda.

Table 4Coefficients of polynomial expressions for mean and standard deviation of condi-tional distributions of rain attenuation at 18.7 GHz for Spino d’ Adda.

Region Segment a0/b0 a1/b1 a2/b2

Temperate (Spi-no d’ Adda )

C 0.052/ .49 1/0.0022 �0.00042/�0.00035

D �0.0851/.037

1/0.028 �0.00017/�0.00024

U 0.14/ .12 .98/ .027 0.00017/�0.00022

No segmentation 0.07/ .18 1/0.028 0.00044/� .00025

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–74

x a a x a x( ) (2)0 1 22μ = + +

x b b x b x( ) (3)0 1 22σ = + +

The values of the polynomial coefficients for m(x) and s(x) arecomputed from the measured data set at frequency 11.172 GHz forthe tropical location (Kolkata) and given in Table 2.

Once the fading channel model is characterized with the meanand standard deviation of the measured distributions of condi-tional occurrences of rain attenuation values, this can be used topredict the time series of rain attenuation, using the measure-ments at prior instants, during a rain event. The predictor output isy (nTs), where n¼1,2,3,…., and Ts is the time interval at whichpredictions are made. The predictor is started as soon as a rainevent starts and stops to predict rain attenuation values, when therain event stops.

The procedure described below is used to obtain the predictedattenuation values y(nTs).

i.

The signal segment type Δ(nTs) is determined from the twolastly measured samples using relation (1).

ii.

The values of μ and s are computed from relations (2) and (3)and using Table 2 for the attenuation value x, measured at theinstant (n-1)Ts.

iii.

The Gaussian random variable is generated with computedvalues of μ ands. For a given μ and s, if the generated Gaussianrandom variable lies within μ72s, then the variable is taken topredict rain attenuation. Otherwise random variable is gener-ated again with the same μ and s which is the predicted valueof attenuation at the instant nTs.

iv.

The difference between the predicted and measured value of

0 1 2 3 4 5 60

20

40

60

80

100

Attenuation (dB)

Err

or (%

)

DataMean

0 500 1000 1500 2000 25000

1

2

3

4

5

6

Time (sec)

Atte

nuat

ion

(dB

)

MeasurementPrediction

Fig. 9. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 23 April 1994 at Spino d’ Adda , (b) Percentage errors in thepredicted values against the attenuation during the same rain event. The models developed for temperate region (18.7 GHz) is used for μ and s computation.

Fig. 10. Comparison between the predicted and the measured statistics at Spino d’ Adda for the year 1994 for (a) rain occurrence, (b) fade slope at an attenuation level of3 dB.

Fig. 11. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 2nd August 1994 at Obepfaffenhofen. (b) Percentage errors inthe predicted values against the attenuation during the same rain event. The models developed for tropical region is used for μ and s computation.

Fig. 12. (a) Comparison between the predicted and the measured attenuation during a rain event occurred on 2nd August 1994 at Obepfaffenhofen. (b) Percentage errors inthe predicted values against the attenuation during the same rain event. The models developed for temperate region is used for μ and s computation.

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–7 5

attenuation is taken as correction term and added to the nextpredicted value to make it closer to the measured value.

v.

The above steps (i–iv), are repeated to predict time series ofrain attenuation for the entire rain event. The block diagram

representation of the rain attenuation predictor is shown inFig. 2.

The validity of the model is now tested for the rain events at

Fig. 13. Comparison between the predicted and the measured attenuation statistics for (a) Blacksburg , 1979 (b) Ottawa, 1997 and (c) Waltham, 1979.

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–76

Kolkata. Fig. 3(a) gives the result of the comparison of predictedattenuation values with the measured values for a rain event oc-curring on 25 June 2007. A good matching has been observedbetween the experimental and predicted data. Fig. 3(b) gives theplots of percentage errors against attenuation. The above figureshows that mean error is less than 20% which confirms the suit-ability of the predictor.

The models of μ and s developed for Kolkata are now used topredict time series of rain attenuation for Douala, Hongkong andSingapore, other locations in the tropical region. Fig. 4(a) gives acomparison between the predicted and measured attenuationstatistics for the year 1987 at Douala. A reasonably good matchinghas been observed between measurement and prediction. Thesimilar matching is obtained for Hongkong (1981) and Singapur(1980) as is evident from the Fig. 4(b and c) respectively. This nowconfirms that the channel model developed for Kolkata can also beused successfully for other locations in the tropical region.

The models of μ and s obtained for Kolkata are now applied topredict the time series of rain attenuation during the rain event of23 April, 1994 at Spino d’ Adda. From Fig. 5(a) we observe that theagreement between prediction and measurement is not good andfrom Fig. 5(b) it is clear that mean prediction error is also veryhigh. It reveals that models of μ and s for tropical region will notbe valid for the temperate region and a different set of models isrequired for temperate region.

The data from Spino d’ Adda are now used to obtain the modelsof μ and s for the temperate region. The data of the year 1994 forSpino d’ Adda taken at the frequency 11.6 GHz are used to developthe model parameters for the temperate region and the computedvalues of the polynomial coefficients for μ and s are given in Ta-ble 3. These are now used to predict the time series of rain at-tenuation during the same rain event and comparison with theactual measurement is shown in Fig. 6(a). A good matching hasbeen observed between the prediction and measurement withmean error being below 20%.

Fig. 7 gives the comparison between the predicted attenuationvalues obtained from tropical and temperate region models for thesame rain event as shown in Figs. 5 and 6 but with fewer data. Weobserve from the figure that tropical model gives larger values of

over and under prediction compared to the temperate modelwhich confirms the fact that in tropical region, more intense rainwith larger variations occurs. Fig. 8 gives a comparison of thecumulative distributions of prediction errors obtained by tropicaland temperate model parameters for all the rain events of the year1994 at Spino d’ Adda. From the figure it is clear that when long-term statistics are considered, prediction error becomes muchsmaller if temperate models are used for the prediction of at-tenuation instead of tropical models at a temperate location.

Now for the rain event of 23 April 1994, time-series predictionof attenuation is done with the attenuation measurement taking atfrequency 18.7 GHz for Spino d’ Adda. For this purpose, the valuesof the polynomial coefficients for m(x) and s(x) are further com-puted from the measured data set at frequency 18.7 GHz for Spinod’ Adda. The values of the polynomial coefficients for μ and s forSpino d’ Adda at the frequency 18.7 GHz are given in Table 4.

Fig. 9 gives the comparison between prediction and measure-ment at frequency 18.7 GHz during same rain event with the va-lues of coefficients taken from Table 4. Again a good matching isobserved between prediction and measurement with mean errorwithin 20%. Therefore successful prediction with our method isalso demonstrated at higher frequency 18.7 GHz.

The cumulative distributions of total signal attenuation for boththe measured and the predicted values for the year 1994 for Spinod’ Adda are shown in Fig. 10(a). The agreement between bothdistributions is quite good. Comparisons between the predictedand measured cumulative distributions of fade slope for attenua-tion level 3 dB for Spino d’ Adda is shown in Fig. 10(b). Thematching between the measured and predicted fade slope statis-tics is quite good.

The models of μ and s developed for Spino d’ Adda are nowused to predict the time series of rain attenuation for other loca-tions in the temperate region. We consider the rain event on 2ndAugust, 1994 at Oberpfaffenhofen, another temperate location. Wepredict the time series of rain attenuation for that rain event byusing the tropical model parameters and compare with actualmeasurement in Fig. 11 (a). We see that matching between pre-diction and measurement is not good and prediction error is quitelarge. For the same rain event, when we apply temperate model

D. Das, A. Maitra / Journal of Atmospheric and Solar-Terrestrial Physics 128 (2015) 1–7 7

parameters, good prediction with low prediction error has beenobserved in Fig. 12. A comparison of the statistics obtained frommeasurement and prediction for Blacksburg for the year 1979,Ottawa for 1997 and Waltham for 1979 are shown in Fig. 13(a–c)respectively. All the three comparisons show good matching be-tween prediction and measurement. Therefore, the models of μand s developed for one temperate location can also be success-fully used for other locations in the temperate region. It mayhowever be noted that the rain attenuation occurrence pattern atdifferent locations in the temperate region are more or less similaras is evident from Fig. 13(a–c) as well as for the locations in thetropical region as indicated in Fig. 4(a–c). Event wise rain at-tenuation measurements are available to us for Kolkata, Spinod’Adda and Oberpfaffenhofen for one year period. The experi-mental data of rain attenuation for other six regions (Douala,Hongkong, Singapur, Blacksburg, Ottawa, Waltham) are takenfrom ITU-R data bank, in terms of yearly cumulative distribution.From these data, we have generated time series of rain attenuationvalue by using the time series synthetic method described in Rec.ITU-R Recommendations P.1853-1 (2012). These time series gen-erated data have been used as measurement while applying ourprediction method for these six regions.

4. Conclusion

The comparison of measured rain rate and attenuation statis-tics obtained from tropical and temperate regions indicates thedifference in rain characteristics of the two regions. The method topredict the rain attenuation values during rain events has beenapplied to different regions. Models of μ and s of conditionaldistributions of rain attenuation developed for a tropical location,Kolkata is successfully applied to predict rain attenuation series forother tropical locations. However these models generated with thedata from a tropical location are not suitable for the temperateregion as is evident from a large error observed in predicting thetime series of rain attenuation in this region. Separate models of μand s, obtained from the data of a temperate location, Spino d’Adda provide a good prediction of rain attenuation at differentlocations in the temperate region, indicating the efficacy of theprediction technique. If large set of data are available at differentlocations at different frequencies, a global model for μ and s can bedeveloped which will be applicable to all over the world for timeseries prediction of rain attenuation during rain events.

Acknowledgements

This work has been supported by the grants from the IndianSpace Research Organization ISRO under the project “Integratedstudies of water vapor, liquid water content and rain of the tropical

atmosphere and their effects on radio environment”. We wish toacknowledge Carlo Riva for supplying data of Spino d’ Adda andalso for giving the opportunity to access ITU-R data bank. We alsothank F.P. Fontan for giving attenuation data of Oberpfaffenhofen.

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