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Time series prediction of rain attenuation from rain rate measurement using synthetic storm technique for a tropical location
Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Time series prediction of rain attenuation from rain rate measurement using synthetic storm technique for a tropical location Dalia Das a , Animesh Maitra b,∗ a Department of Electronics and Telecommunication Engineering, Meghnad Saha Institute of Technology, Techno Complex, Madurdaha, Kolkata 700 150, India b 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 16 December 2012 Accepted 15 July 2013 Keywords: Rain attenuation Synthetic storm technique Time series prediction Tropical location
a b s t r a c t A comparison of measured attenuation series with the attenuation series obtained from rain rate measurement by using synthetic storm technique is made for Ku band signal at a tropical location. Validity of the model is tested for the long-term statistics in terms of the cumulative distribution of attenuation occurrence and fade duration. Applicability of the model is also shown to be valid event-wise. It has been demonstrated that the long term statistics of predicted rain attenuation are insensitive to storm translation speed. No significant differences are found when cumulative distributions of predicted attenuation values are compared for different data sampling intervals. It has been observed that there exists a good correlation between the predicted and measured values of attenuation for at least 80% of the events. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Frequencies above 10 GHz are of primary interest in satellite communication systems, since they provide larger transmission bandwidth and higher data rate. However, the use of these frequency bands is limited by different propagation effect mainly due to rain attenuation. If time series prediction of rain attenuation is possible, fade countermeasure techniques such as adaptive control of signal power, coding and data rate can be effectively implemented. The method of time series prediction for rain attenuation has been presented in [1]. Experimental data for rain attenuation to develop channel model are not always available and often they exist only for specific sites, frequencies and elevation. But a large set of rain rate data is available worldwide. As rain attenuation is strongly correlated with rain rate intensity, time series predictor of rain rate can be easily converted into rain attenuation predictor by using so-called synthetic storm technique (SST). SST has been proposed in [2] to convert instantaneous rain rate into attenuation under some assumption. So far, validity of the SST model is presented in terms of yearly cumulative distribution [2–5]. In [6,7] validation results are presented on an event by event basis, but only event duration and peak attenuation are compared for V band signals for temperate region. In this paper, measured rain rate series during a rain event is converted into attenuation series for the Ku band signal for a tropi-
∗ Corresponding author. Tel.: +91 9433733756; fax: +91 3323515828. E-mail address: [email protected] (A. Maitra). 1434-8411/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2013.07.008
cal region. Time series prediction of attenuation is done during rain events using the method described in [1]. However, in the present case, SST converted attenuation values are considered as inputs instead of actual attenuation measurements. Validity of the synthetic storm technique is not only tested event-wise but also with long term statistics. Resemblance between measured and predicted event is also shown by calculating cross correlation coefficient. Storm translation speed suitable for our region is also selected from experimental results.
2. Experimental data Propagation measurements over an earth-space path have been carried out at Kolkata, India (22◦ 34 N, 88◦ 29 E), a tropical location by receiving a Ku band signal at frequency 11.172 GHz transmitted with horizontal polarization from satellite NSS-6 (geostationary at 95◦ E) at an elevation of 63◦ , since June 2004 [8]. The received signal is down converted to an L-band frequency by the low noise block converter (LNBC) and fed to the spectrum analyzer that is used as the receiver for monitoring the satellite signal level. The signal level measurements are recorded with a data logger and stored in a PC. Further, the rain fall rates at the satellite receiver site have been measured simultaneously by an optical rain gauge (ORG). The dynamic ranges for rain rate and attenuation measurements are 500 mm/h and 20 dB respectively. The minimum detectable change in rainfall rate is 0.2 mm/h and rain attenuation is 0.1 dB. The recorded rain rate and attenuation data are passed through a raised square cosine filter with cutoff frequency 0.025 Hz to eliminate the scintillation effects and other fast fluctuations. In the present study,
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D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
Fig. 1. (a) Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007. The storm speed is taken as v = 8 m/s and (b) comparison between the measured attenuation values with the predicted values obtained by time series predictor for the rain event of 17th June, 2007. Measurement needed by the predictor is taken as the attenuation values obtained by SST.
the four year measurement period (2005–2008) has been considered during which total 694 rain events are observed. In this paper, when cumulative distribution is calculated, the entire time span of measurement is considered. 3. Model testing with experimental data The synthetic storm technique (SST) converts a rain rate time series recorded at a given location into a signal attenuation time series. This conversion requires the knowledge about the length of the signal path through the rain cell, the velocity (v) of the rain cell and the rain rate (R) at the location under investigation. The physical and mathematical fundamentals of the method are described in [2]. The vertical structure of the precipitation medium is modelled with two layers [2], layer A with raindrops at 20 ◦ C and layer B with melting hydrometeors at 0 ◦ C. The input parameters needed by the SST model for our region are considered as follows. The altitude above sea level of the earth station is HS = 0.025 km. According to [9] the height of the precipitation (rain and melting layer) above sea level used in the simulation is calculated as HB = 5 km. Also, the depth of the melting layer (h) is considered to be 0.4 km regardless of the latitude. According to [2] the height above sea level, HA , of the upper limit of layer A is given by: HA = HB − h = 4.6 km The radio path lengths are given by LA =
HA − HS = 5.5836 km sin()
LB =
HB − HS = 5.135 km sin()
The parameters k and ˛ necessary to relate rainfall rate to the specific rain attenuation (dB/km) are calculated from [10]. We have
Fig. 2. Comparison between the cumulative distributions of prediction errors (%) due to SST prediction as shown in Fig. 1(a), and time series prediction with SST values as input as shown in Fig. 1(b).
used different storm speeds v = 1–12 m/s to show the sensitivity of this parameter to the SST model. The measured rain rate values for the rain event on 17 June 2007 are converted to attenuation values using SST and compared with the actual measurements in Fig. 1(a). Good matching has been observed between measurement and prediction. These SST predicted values are now used as measurements for the method described in [1] to predict the time series of rain attenuation for the rain event on 17 June 2007. The time series predicted values are compared with the actual attenuation measurements in Fig. 1(b). Fig. 2 gives the comparison between the cumulative distributions of the prediction errors (%) occurred in Fig. 1(a) and (b). For the first case, shown in Fig. 1(a), the error occurred only due to SST prediction. Whereas in the second case, shown in Fig. 1(b), the error is due to both SST prediction and time series prediction, resulting in a small increase in the total error. However, the overall error is still small indicating that the SST predicted values can be considered as the input to the time series predictor in the absence of actual attenuation measurements.
Fig. 3. Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007 with (a) 10 s sampling interval and (b) 60 s sampling interval.
D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
If we use different time resolution for rain rate measurements, a significant difference is found for higher attenuation values in a single rain event as is evident from Fig. 3. Although overall accuracy of attenuation prediction is better for smaller sampling interval as expected with SST, for higher interval better matching is observed for higher attenuation values. This is because of the fact that for smaller sampling interval high rain rate values at the receiving site are recorded more frequently giving high SST estimates of attenuation values which do not match with measured attenuations as high rain rates may not occur over the entire signal path. So the matching between prediction and measurement for higher attenuation values is shown to be apparently poorer for smaller sampling interval. The cumulative distributions of total signal attenuation for both the measured and the synthesized events for the complete period (averaged over the whole four year measurement period) are shown in Fig. 4. The agreement between both the distributions is quite good. In this paper, when cumulative distribution is calculated, the entire time span of measurement is considered. Fade duration statistics can also be predicted by the SST. Comparisons between the predicted and measured cumulative distributions of fade durations for different thresholds are shown in Fig. 5. A good matching has been observed between the measured and predicted statistics. Although for single rain event time series is different for different sampling interval (Fig. 3), when cumulative
35
Fig. 4. Comparison between the measured and predicted rain occurrence statistics for the period 2005–2008.
distributions of rain attenuation resulting from SST simulation for sampling interval namely 10, 30 and 60 s are compared, no significant differences are found as indicated in Fig. 6(a). In Fig. 6(b), cumulative distributions of predicted rain attenuation values are plotted for different storm translation speed along with the measurement. From Fig. 6(b) it is clear that long term statistics derived from the SST model is almost insensitive to storm
Fig. 5. Comparison between the measured and predicted fade duration ‘statistics for the period 2005–2008 for different threshold.
Fig. 6. Cumulative distributions of predicted signal attenuation values for (a) different sampling time interval and (b) different storm speed.
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D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
Fig. 7. Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007 with storm speed (a) 8 m/s and (b) 12 m/s.
but also on an event by event basis. The cumulative distribution of signal attenuation and fade duration statistics from predicted values matched well with that obtained from measured values. SST does not significantly depend on the sampling rate at which rain recordings are taken. Long-term statistics of SST simulated result is insensitive to storm speed. But for individual events, 8 m/s storm speed gives best result for Indian region. It can be concluded that the SST model can be used for predicting time series of signal attenuation at a tropical region to implement fade mitigation technique. Acknowledgments
Fig. 8. Cumulative distributions of cross correlation coefficients between measured and predicted attenuation values for all the rain events of the four year period, 2005–2008.
speed. For both Fig. 6(a) and (b) good matching has been observed between the statistics of measured attenuation values and all the predicted values. Fig. 7 shows how the value of the storm speed, used in the predictions, affects the time series. For higher values of the storm speed, the peak attenuation becomes larger at a given rain rate. The zero lag cross correlation coefficient of the individual events for the four year period 2005–2008 has been calculated for different wind speed v = 1–12 m/s. Fig. 8 shows the cumulative distributions of the computed with different storm speed. From Fig. 8 it is clear that if we choose v = 8 m/s, cumulative distributions for show higher values indicating that matching between prediction and measurement is good. But if we increase v above 8 m/s or decrease below 8 m/s, cumulative distributions for show lower values. This indicates that for our region, suitable storm translation speed is 8 m/s. 4. Conclusion Development of channel model to predict time series of rain attenuation is not always possible in different climatic areas and at different frequency bands due to lack of attenuation measurements. However, rain recordings are easier to obtain. These can be converted directly into rain attenuation series by using synthetic storm technique. In this paper, validity of the SST model has been presented for Ku-band signal for a tropical location, India. The model is validated not only on a cumulative distribution basis,
This work has been supported by the grants under the project entitled “Integrated studies on water vapour, liquid water content and rain of tropical atmosphere and their effects on radio environment”, funded by Indian Space Research Organization (ISRO), Bangalore, India, being implemented at S.K. Mitra Centre for Research in Space Environment, University of Calcutta. References [1] Das D, Maitra A. Time series predictor of Ku – band rain attenuation over an earth – space path at a tropical location. Int J Satell Commun Netw 2012;30(January/February):19–28. [2] Matricciani E. Physical–mathematical model of the dynamics of rain attenuation based on rain rate time series and a two-layer vertical structure of precipitation. Radio Sci 1996;31(March–April (2)):281–95. [3] Matricciani E. Prediction of fade durations due to rain in satellite communication systems. Radio Sci 1997;32(March–April (3)):935–41. [4] Matricciani E, Riva C. The search for the most reliable long term rain attenuation CDF of a slant path and the impact on prediction models. IEEE Trans Antennas Propag 2005;53(September (9)):3075–9. [5] Kanellopoulos SA, Panagopoulos AD, Matricciani E, Kanellopoulos JD. Annual and diurnal slant path rain attenuation statistics in Athens obtained with the synthetic storm technique. IEEE Trans Antennas Propag 2006;54(August (8)):2357–63. [6] Fontan FP, Nunez A, Valcarce A, Fiebig UC. Converting simulated rain-rate series into attenution series using the synthetic storm technique. In: COST 280 PM9104 3rd international workshop. 2005. ˜ P, Fiebig UC. Validation of the synthetic storm [7] Sánchez-Lago I, Fontán FP, Marino technique as part of a time-series generator for satellite links. IEEE Antennas Wireless Propag Lett 2007;6:372–5. [8] Maitra A, Chakravarty K, Bhattacharya S, Bagchi S. Propagation studies at Ku-band over an earth-space path at Kolkata. Ind J Radio Space Phys 2007;36:363–8. [9] Rain height model for prediction methods, ITU-R Recommendations, Propagation in Nonionized Media, Rec. 839, Geneva; 1992. [10] Maggiori DD. Computed transmission through rain in the 1–400 GHz frequency range for spherical and elliptical drops and any polarization. Alta Freq 1981;50:262–73.
Contents lists available at ScienceDirect
International Journal of Electronics and Communications (AEÜ) journal homepage: www.elsevier.com/locate/aeue
Time series prediction of rain attenuation from rain rate measurement using synthetic storm technique for a tropical location Dalia Das a , Animesh Maitra b,∗ a Department of Electronics and Telecommunication Engineering, Meghnad Saha Institute of Technology, Techno Complex, Madurdaha, Kolkata 700 150, India b 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 16 December 2012 Accepted 15 July 2013 Keywords: Rain attenuation Synthetic storm technique Time series prediction Tropical location
a b s t r a c t A comparison of measured attenuation series with the attenuation series obtained from rain rate measurement by using synthetic storm technique is made for Ku band signal at a tropical location. Validity of the model is tested for the long-term statistics in terms of the cumulative distribution of attenuation occurrence and fade duration. Applicability of the model is also shown to be valid event-wise. It has been demonstrated that the long term statistics of predicted rain attenuation are insensitive to storm translation speed. No significant differences are found when cumulative distributions of predicted attenuation values are compared for different data sampling intervals. It has been observed that there exists a good correlation between the predicted and measured values of attenuation for at least 80% of the events. © 2013 Elsevier GmbH. All rights reserved.
1. Introduction Frequencies above 10 GHz are of primary interest in satellite communication systems, since they provide larger transmission bandwidth and higher data rate. However, the use of these frequency bands is limited by different propagation effect mainly due to rain attenuation. If time series prediction of rain attenuation is possible, fade countermeasure techniques such as adaptive control of signal power, coding and data rate can be effectively implemented. The method of time series prediction for rain attenuation has been presented in [1]. Experimental data for rain attenuation to develop channel model are not always available and often they exist only for specific sites, frequencies and elevation. But a large set of rain rate data is available worldwide. As rain attenuation is strongly correlated with rain rate intensity, time series predictor of rain rate can be easily converted into rain attenuation predictor by using so-called synthetic storm technique (SST). SST has been proposed in [2] to convert instantaneous rain rate into attenuation under some assumption. So far, validity of the SST model is presented in terms of yearly cumulative distribution [2–5]. In [6,7] validation results are presented on an event by event basis, but only event duration and peak attenuation are compared for V band signals for temperate region. In this paper, measured rain rate series during a rain event is converted into attenuation series for the Ku band signal for a tropi-
∗ Corresponding author. Tel.: +91 9433733756; fax: +91 3323515828. E-mail address: [email protected] (A. Maitra). 1434-8411/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.aeue.2013.07.008
cal region. Time series prediction of attenuation is done during rain events using the method described in [1]. However, in the present case, SST converted attenuation values are considered as inputs instead of actual attenuation measurements. Validity of the synthetic storm technique is not only tested event-wise but also with long term statistics. Resemblance between measured and predicted event is also shown by calculating cross correlation coefficient. Storm translation speed suitable for our region is also selected from experimental results.
2. Experimental data Propagation measurements over an earth-space path have been carried out at Kolkata, India (22◦ 34 N, 88◦ 29 E), a tropical location by receiving a Ku band signal at frequency 11.172 GHz transmitted with horizontal polarization from satellite NSS-6 (geostationary at 95◦ E) at an elevation of 63◦ , since June 2004 [8]. The received signal is down converted to an L-band frequency by the low noise block converter (LNBC) and fed to the spectrum analyzer that is used as the receiver for monitoring the satellite signal level. The signal level measurements are recorded with a data logger and stored in a PC. Further, the rain fall rates at the satellite receiver site have been measured simultaneously by an optical rain gauge (ORG). The dynamic ranges for rain rate and attenuation measurements are 500 mm/h and 20 dB respectively. The minimum detectable change in rainfall rate is 0.2 mm/h and rain attenuation is 0.1 dB. The recorded rain rate and attenuation data are passed through a raised square cosine filter with cutoff frequency 0.025 Hz to eliminate the scintillation effects and other fast fluctuations. In the present study,
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D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
Fig. 1. (a) Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007. The storm speed is taken as v = 8 m/s and (b) comparison between the measured attenuation values with the predicted values obtained by time series predictor for the rain event of 17th June, 2007. Measurement needed by the predictor is taken as the attenuation values obtained by SST.
the four year measurement period (2005–2008) has been considered during which total 694 rain events are observed. In this paper, when cumulative distribution is calculated, the entire time span of measurement is considered. 3. Model testing with experimental data The synthetic storm technique (SST) converts a rain rate time series recorded at a given location into a signal attenuation time series. This conversion requires the knowledge about the length of the signal path through the rain cell, the velocity (v) of the rain cell and the rain rate (R) at the location under investigation. The physical and mathematical fundamentals of the method are described in [2]. The vertical structure of the precipitation medium is modelled with two layers [2], layer A with raindrops at 20 ◦ C and layer B with melting hydrometeors at 0 ◦ C. The input parameters needed by the SST model for our region are considered as follows. The altitude above sea level of the earth station is HS = 0.025 km. According to [9] the height of the precipitation (rain and melting layer) above sea level used in the simulation is calculated as HB = 5 km. Also, the depth of the melting layer (h) is considered to be 0.4 km regardless of the latitude. According to [2] the height above sea level, HA , of the upper limit of layer A is given by: HA = HB − h = 4.6 km The radio path lengths are given by LA =
HA − HS = 5.5836 km sin()
LB =
HB − HS = 5.135 km sin()
The parameters k and ˛ necessary to relate rainfall rate to the specific rain attenuation (dB/km) are calculated from [10]. We have
Fig. 2. Comparison between the cumulative distributions of prediction errors (%) due to SST prediction as shown in Fig. 1(a), and time series prediction with SST values as input as shown in Fig. 1(b).
used different storm speeds v = 1–12 m/s to show the sensitivity of this parameter to the SST model. The measured rain rate values for the rain event on 17 June 2007 are converted to attenuation values using SST and compared with the actual measurements in Fig. 1(a). Good matching has been observed between measurement and prediction. These SST predicted values are now used as measurements for the method described in [1] to predict the time series of rain attenuation for the rain event on 17 June 2007. The time series predicted values are compared with the actual attenuation measurements in Fig. 1(b). Fig. 2 gives the comparison between the cumulative distributions of the prediction errors (%) occurred in Fig. 1(a) and (b). For the first case, shown in Fig. 1(a), the error occurred only due to SST prediction. Whereas in the second case, shown in Fig. 1(b), the error is due to both SST prediction and time series prediction, resulting in a small increase in the total error. However, the overall error is still small indicating that the SST predicted values can be considered as the input to the time series predictor in the absence of actual attenuation measurements.
Fig. 3. Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007 with (a) 10 s sampling interval and (b) 60 s sampling interval.
D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
If we use different time resolution for rain rate measurements, a significant difference is found for higher attenuation values in a single rain event as is evident from Fig. 3. Although overall accuracy of attenuation prediction is better for smaller sampling interval as expected with SST, for higher interval better matching is observed for higher attenuation values. This is because of the fact that for smaller sampling interval high rain rate values at the receiving site are recorded more frequently giving high SST estimates of attenuation values which do not match with measured attenuations as high rain rates may not occur over the entire signal path. So the matching between prediction and measurement for higher attenuation values is shown to be apparently poorer for smaller sampling interval. The cumulative distributions of total signal attenuation for both the measured and the synthesized events for the complete period (averaged over the whole four year measurement period) are shown in Fig. 4. The agreement between both the distributions is quite good. In this paper, when cumulative distribution is calculated, the entire time span of measurement is considered. Fade duration statistics can also be predicted by the SST. Comparisons between the predicted and measured cumulative distributions of fade durations for different thresholds are shown in Fig. 5. A good matching has been observed between the measured and predicted statistics. Although for single rain event time series is different for different sampling interval (Fig. 3), when cumulative
35
Fig. 4. Comparison between the measured and predicted rain occurrence statistics for the period 2005–2008.
distributions of rain attenuation resulting from SST simulation for sampling interval namely 10, 30 and 60 s are compared, no significant differences are found as indicated in Fig. 6(a). In Fig. 6(b), cumulative distributions of predicted rain attenuation values are plotted for different storm translation speed along with the measurement. From Fig. 6(b) it is clear that long term statistics derived from the SST model is almost insensitive to storm
Fig. 5. Comparison between the measured and predicted fade duration ‘statistics for the period 2005–2008 for different threshold.
Fig. 6. Cumulative distributions of predicted signal attenuation values for (a) different sampling time interval and (b) different storm speed.
36
D. Das, A. Maitra / Int. J. Electron. Commun. (AEÜ) 68 (2014) 33–36
Fig. 7. Comparison between the measured attenuation values with the predicted values obtained from SST for the rain event of 17th June, 2007 with storm speed (a) 8 m/s and (b) 12 m/s.
but also on an event by event basis. The cumulative distribution of signal attenuation and fade duration statistics from predicted values matched well with that obtained from measured values. SST does not significantly depend on the sampling rate at which rain recordings are taken. Long-term statistics of SST simulated result is insensitive to storm speed. But for individual events, 8 m/s storm speed gives best result for Indian region. It can be concluded that the SST model can be used for predicting time series of signal attenuation at a tropical region to implement fade mitigation technique. Acknowledgments
Fig. 8. Cumulative distributions of cross correlation coefficients between measured and predicted attenuation values for all the rain events of the four year period, 2005–2008.
speed. For both Fig. 6(a) and (b) good matching has been observed between the statistics of measured attenuation values and all the predicted values. Fig. 7 shows how the value of the storm speed, used in the predictions, affects the time series. For higher values of the storm speed, the peak attenuation becomes larger at a given rain rate. The zero lag cross correlation coefficient of the individual events for the four year period 2005–2008 has been calculated for different wind speed v = 1–12 m/s. Fig. 8 shows the cumulative distributions of the computed with different storm speed. From Fig. 8 it is clear that if we choose v = 8 m/s, cumulative distributions for show higher values indicating that matching between prediction and measurement is good. But if we increase v above 8 m/s or decrease below 8 m/s, cumulative distributions for show lower values. This indicates that for our region, suitable storm translation speed is 8 m/s. 4. Conclusion Development of channel model to predict time series of rain attenuation is not always possible in different climatic areas and at different frequency bands due to lack of attenuation measurements. However, rain recordings are easier to obtain. These can be converted directly into rain attenuation series by using synthetic storm technique. In this paper, validity of the SST model has been presented for Ku-band signal for a tropical location, India. The model is validated not only on a cumulative distribution basis,
This work has been supported by the grants under the project entitled “Integrated studies on water vapour, liquid water content and rain of tropical atmosphere and their effects on radio environment”, funded by Indian Space Research Organization (ISRO), Bangalore, India, being implemented at S.K. Mitra Centre for Research in Space Environment, University of Calcutta. References [1] Das D, Maitra A. Time series predictor of Ku – band rain attenuation over an earth – space path at a tropical location. Int J Satell Commun Netw 2012;30(January/February):19–28. [2] Matricciani E. Physical–mathematical model of the dynamics of rain attenuation based on rain rate time series and a two-layer vertical structure of precipitation. Radio Sci 1996;31(March–April (2)):281–95. [3] Matricciani E. Prediction of fade durations due to rain in satellite communication systems. Radio Sci 1997;32(March–April (3)):935–41. [4] Matricciani E, Riva C. The search for the most reliable long term rain attenuation CDF of a slant path and the impact on prediction models. IEEE Trans Antennas Propag 2005;53(September (9)):3075–9. [5] Kanellopoulos SA, Panagopoulos AD, Matricciani E, Kanellopoulos JD. Annual and diurnal slant path rain attenuation statistics in Athens obtained with the synthetic storm technique. IEEE Trans Antennas Propag 2006;54(August (8)):2357–63. [6] Fontan FP, Nunez A, Valcarce A, Fiebig UC. Converting simulated rain-rate series into attenution series using the synthetic storm technique. In: COST 280 PM9104 3rd international workshop. 2005. ˜ P, Fiebig UC. Validation of the synthetic storm [7] Sánchez-Lago I, Fontán FP, Marino technique as part of a time-series generator for satellite links. IEEE Antennas Wireless Propag Lett 2007;6:372–5. [8] Maitra A, Chakravarty K, Bhattacharya S, Bagchi S. Propagation studies at Ku-band over an earth-space path at Kolkata. Ind J Radio Space Phys 2007;36:363–8. [9] Rain height model for prediction methods, ITU-R Recommendations, Propagation in Nonionized Media, Rec. 839, Geneva; 1992. [10] Maggiori DD. Computed transmission through rain in the 1–400 GHz frequency range for spherical and elliptical drops and any polarization. Alta Freq 1981;50:262–73.